JP5034326B2 - Membrane filtration prediction method and membrane filtration prediction program - Google Patents

Description

The present invention, time changes in membrane filtration resistance generated when the filtration by membrane to be filtered liquid, time changes in membrane filtration flow rate, a method of predicting the time variation of the transmembrane pressure difference relates及 beauty prediction program.

  The method of filtering a liquid through a separation membrane is a method of obtaining a filtrate by bringing the liquid that is the liquid to be filtered into contact with the separation membrane and applying pressure from the liquid to be filtered side or a negative pressure on the permeate side. At this time, the non-membrane permeable substance contained in the liquid to be filtered adheres to the membrane surface, and the adhered substance causes an increase in membrane filtration resistance. When membrane filtration resistance is increased, when membrane filtration is performed by applying a constant membrane filtration pressure, the membrane filtration flow rate decreases, and when membrane filtration is performed at a constant membrane filtration flow rate, the transmembrane pressure difference is reduced. Increase. In the former case, the planned flow rate cannot be secured, and in the latter case, energy for increasing the pressure is required and at the same time the burden on the separation membrane increases. Such an increase in membrane filtration resistance is greatly influenced by membrane filtration conditions and is an important factor for continuing membrane filtration. That is, if it is possible to accurately predict changes in membrane filtration resistance, membrane filtration flow rate, and transmembrane pressure difference over time, it becomes possible to find membrane filtration conditions for efficient and stable filtration.

  In addition, as a method of suppressing such an increase in membrane filtration resistance, the liquid to be filtered flows in a direction parallel to the membrane surface using a pump that aerates the membrane surface with an air diffuser installed at the lower part of the membrane. There is a method of performing membrane filtration while washing the membrane surface, for example, allowing the separation membrane to move or vibrate. In such a membrane filtration method, it is possible to suppress an increase in membrane filtration resistance by sufficiently washing the membrane, but such membrane surface cleaning requires energy and is more than necessary. Performing membrane cleaning increases operating costs. In other words, it is important for proper operation of the membrane filtration apparatus to perform necessary and sufficient membrane cleaning.

In addition, the membrane surface may be washed with a chemical solution by temporarily interrupting the filtration. In this case, the filtration operation efficiency is reduced due to the temporary interruption of the operation, and the cost of the chemical solution is increased. Therefore, it is important at which timing the membrane cleaning is performed.
Therefore, if the time change of the membrane filtration resistance during filtration can be accurately predicted, quantitative membrane filtration conditions can be determined, which is very effective. For example, it becomes possible to determine the minimum amount of aeration air necessary for suppressing an increase in membrane filtration resistance.

Non-Patent Document 1 discloses a mathematical model for predicting membrane filtration resistance. According to Non-Patent Document 1, it is proposed to express the increase and decrease of the amount of extracellular polymer substance (hereinafter referred to as EPS) adhering to the filtration membrane as a mathematical model and predict the membrane filtration resistance based on EPS. .
H. Nagaoka, “MODELING OF BIOFOULING BY EXTRACELLULAR POLYMERS IN A MEMBRANE SEPARATION ACTIVATED SLUDGE SYSTEM”, Wat. Sci. Tech. Vol.38, No.4-5, pp497-504,1998.

  However, the membrane filtration resistance prediction based on Non-Patent Document 1 has the following problems.

  First, the measurement of EPS requires specialized knowledge, equipment, labor, and time, and EPS cannot be easily measured in an actual membrane filtration operation. For this reason, even if the EPS is measured and predicted, the data will be insufficient and the prediction accuracy will decrease, and it will take time to collect enough data. It is easy to miss the timing for modifying and changing the conditions.

  Secondly, since the solid component in the liquid to be filtered is not taken into account, the membrane filtration resistance prediction accuracy is not sufficient. If the solid component in the liquid to be filtered adheres to the membrane, it contributes to an increase in membrane filtration resistance, and easily peels off from the membrane. Therefore, accurate prediction is difficult with the method of Non-Patent Document 1 that does not consider the influence of the solid component in the liquid to be filtered.

Therefore, the purpose of the present invention, to provide a method, a 及 beauty prediction program for predicting membrane filtration resistance generated when the filtration by membrane to be filtered liquid, membrane filtration flow rate, the time variation of the transmembrane pressure difference accurately It is in.

In order to solve the above problems, the membrane filtration prediction method in the membrane filtration device of the present invention has any of the following configurations.
(1) In a membrane filtration method in which a filtrate is filtered through a separation membrane using a pressure difference between the filtrate side and permeate side of the separation membrane (hereinafter referred to as transmembrane pressure difference) as a driving force, A membrane filtration prediction method for predicting a change in membrane filtration resistance over time and / or a change in transmembrane pressure difference over time when membrane filtration is continued while controlling the bundle) to a set value,
As numerical values for the membrane filtration prediction calculation, at least the setting value of the membrane filtration flow rate (flux), the initial value of the membrane filtration resistance, the supernatant component substance amount value and / or the solid component substance amount value of the liquid to be filtered Using
Obtaining a membrane filtration resistance value and / or a transmembrane pressure value at an arbitrary time by performing at least the following calculation step 1 and calculation step 2 and / or calculation step 3;
(Calculation step 1) Calculate the supernatant component substance amount value and / or the solid component substance amount value of the liquid to be filtered adhering to the separation membrane at an arbitrary time,
(Calculation step 2) At least the membrane filtration resistance value at any time using the supernatant component substance amount value and / or solid component substance amount value of the liquid to be filtered adhering to the separation membrane obtained in calculation step 1 To calculate,
(Calculation step 3) At least using the supernatant component substance amount value and / or the solid component substance amount value of the liquid to be filtered adhering to the separation membrane obtained in calculation step 1 or obtained in calculation step 2 Using the membrane filtration resistance value, calculate the transmembrane pressure difference value at any time,
Furthermore, by repeatedly performing the calculation step while updating the time, to determine the change over time of the membrane filtration resistance and / or the change over time of the transmembrane pressure difference,
The calculation step 1 is a calculation step based on an amount of change in a supernatant component substance amount and / or a solid component substance amount of a liquid to be filtered adhering to a separation membrane within a predetermined time,
The calculation formula in calculation step 1 includes a term of a rate at which the supernatant component and / or solid component of the filtrate to be attached to the separation membrane, and a supernatant component of the filtrate to be filtered attached to the separation membrane and / or Or a term of the rate at which the solid component peels from the separation membrane,
The rate of adhering to the separation membrane is calculated using the transmembrane pressure difference value or the membrane filtration flow rate (flux) value, the supernatant component substance amount value and / or the solid component substance amount value of the liquid to be filtered, And,
The separation rate from the separation membrane includes the transmembrane pressure value or the membrane filtration flow rate (flux) value, the supernatant component substance amount value and / or the solid component substance amount value of the liquid to be filtered attached to the separation membrane. membrane filtration prediction method characterized in that it is calculated using a secondary function number.

(2) In a membrane filtration method in which the filtrate is filtered through a separation membrane using the pressure difference between the filtrate to be filtered and the permeate side (hereinafter referred to as transmembrane pressure difference) as a driving force, A membrane filtration prediction method for predicting a change over time in membrane filtration resistance and / or a change over time in membrane filtration flow rate (flux) when membrane filtration is continued while controlling to a set value,
Use at least the setting value of the transmembrane pressure difference, the initial value of the membrane filtration resistance, and the supernatant component substance amount value and / or the solid component substance amount value of the liquid to be filtered as numerical values for the membrane filtration prediction calculation. ,
At least calculating the membrane filtration resistance value and / or the membrane filtration flow rate (flux) at an arbitrary time by performing the following calculation step 1 and calculation step 2 and / or calculation step 4;
(Calculation step 1) Calculate the supernatant component substance amount value and / or the solid component substance amount value of the liquid to be filtered adhering to the separation membrane at an arbitrary time,
(Calculation step 2) At least the membrane filtration resistance value at any time using the supernatant component substance amount value and / or solid component substance amount value of the liquid to be filtered adhering to the separation membrane obtained in calculation step 1 To calculate,
(Calculation step 4) At least using the supernatant component substance amount value and / or solid component substance amount value membrane of the liquid to be filtered adhering to the separation membrane obtained in calculation step 1 or obtaining in calculation step 2 The membrane filtration flow rate (flux) value at an arbitrary time is calculated using the membrane filtration resistance value.
Furthermore, by repeatedly performing the calculation step while updating the time, obtain the change over time of the membrane filtration resistance and / or change over time of the membrane filtration flow rate (flux),
The calculation step 1 is a calculation step based on an amount of change in a supernatant component substance amount and / or a solid component substance amount of a liquid to be filtered adhering to a separation membrane within a predetermined time,
The calculation formula in calculation step 1 includes a term of a rate at which the supernatant component and / or solid component of the filtrate to be attached to the separation membrane, and a supernatant component of the filtrate to be filtered attached to the separation membrane and / or Or a term of the rate at which the solid component peels from the separation membrane,
The rate of adhering to the separation membrane is calculated using the transmembrane pressure difference value or the membrane filtration flow rate (flux) value, the supernatant component substance amount value and / or the solid component substance amount value of the liquid to be filtered, And,
The separation rate from the separation membrane includes the transmembrane pressure value or the membrane filtration flow rate (flux) value, the supernatant component substance amount value and / or the solid component substance amount value of the liquid to be filtered attached to the separation membrane. membrane filtration prediction method characterized in that it is calculated using a secondary function number.

(3) The calculation formula in the calculation step 1 is
The rate at which the supernatant component substance in the filtrate to be filtered is calculated based on the transmembrane pressure difference or the membrane filtration flow rate (flux) and the amount of the supernatant component substance in the filtrate, and the membrane The difference between the differential pressure value or the membrane filtration flow rate (flux) and the rate of separation of the supernatant component material from the separation membrane calculated based on the amount of the supernatant component material and the solid component material adhering to the separation membrane Including a calculation formula for calculating the amount of the supernatant component substance of the liquid to be filtered adhering to the separation membrane after a predetermined time, and
The rate at which the solid components in the filtered liquid adhere to the separation membrane calculated based on the transmembrane differential pressure value or membrane filtration flow rate (flux) and the amount of solid component substances in the filtered liquid, and the transmembrane differential pressure Based on the difference between the value or the membrane filtration flow rate (flux) and the rate of separation of the solid component from the separation membrane calculated based on the amount of the supernatant component substance and the amount of the solid component substance adhering to the separation membrane The method for predicting membrane filtration according to (1) or (2), comprising a calculation formula for calculating the amount of solid component substances in the liquid to be filtered adhering to the separation membrane after time.

(4) The formula for obtaining the rate at which the supernatant component and / or solid component of the liquid to be filtered adhering to the separation membrane peels from the separation membrane includes a term based on the membrane detergency value. The membrane filtration prediction method according to any one of (1) to (3) .
(5) The membrane filtration prediction method according to any one of (1) to (4), wherein the liquid to be filtered is a mixed liquid containing microorganisms .

The film resistance prediction program of the present invention has the following configuration in order to achieve the above object.
(6) When the filtration of the liquid to be filtered by the separation membrane is continued while controlling the transmembrane pressure difference to the set value, the time change of the membrane filtration resistance value that changes with time and / or the membrane filtration flow rate (flux) ) A computer program for predicting the time change of a value,
Time-series value of transmembrane pressure difference, time-series value of supernatant component substance amount and / or solid-component substance amount of filtrate to be filtered, time-series value of membrane detergency, membrane adherence attached to separation membrane Data input means for inputting the initial value of the amount of supernatant component substance and / or the amount of solid component substance of the filtrate and the initial value of membrane filtration resistance,
Time-series value of transmembrane pressure input by the data input means, time-series value of supernatant component substance amount and / or solid-component substance amount of filtered liquid, time-series value of membrane detergency, Data recording means for recording the initial value of the amount of supernatant component substance and / or the amount of solid component substance of the liquid to be filtered adhering to the separation membrane, and the initial value of membrane filtration resistance;
The transmembrane pressure difference value at an arbitrary time t _i (where i = 0 to n, t _{i + 1} = t _i + Δt _i , t ₀ = 0, n is a natural number representing the number of steps) from the data recording means. , supernatant component substance quantity value and / or solid components substance quantity value of the filtrate, membrane washing force value, and the supernatant component substances of the liquid to-be-filtrated attaching on the separation membrane in the case of the time t ₀ and / or reads the initial value of the solid component amount of substance, furthermore, in the case other than the time t ₀ attaching on the separation membrane at the time t _i recorded in the data recording means by component amount calculating value recording unit described later The supernatant component substance amount value and / or the solid component substance amount value of the filtrate to be filtered is read out, and the filtrate to be filtered attached to the separation membrane at time t _{i + 1} is recorded using a pre-recorded adhesion component quantity calculation formula. Calculate supernatant component substance amount value and / or solid component substance amount value Component amount calculating means,
Component amount calculation value recording means for recording the supernatant component substance amount value and / or the solid component substance amount value of the liquid to be filtered adhering to the separation membrane at time t _{i + 1} calculated by the component amount calculation means,
Next membrane filtration resistance calculation means and / or membrane filtration flow rate (flux) calculation means (membrane filtration resistance calculation means) Read the membrane filtration resistance initial value from the data recording means, and read the membrane filtration resistance initial value and components Based on the non-membrane permeable substance amount value and / or the solid component substance amount value in the supernatant component of the liquid to be filtered adhering to the separation membrane at time t _{i + 1} calculated by the amount calculating means, the membrane filtration recorded in advance Membrane filtration resistance calculating means for calculating the predicted value of the membrane filtration resistance at time t _{i + 1} using the resistance predicted value calculation formula,
(Membrane filtration flow rate (flux) calculation means) The membrane filtration resistance initial value and the transmembrane differential pressure value at time ti _{+ 1} are read from the data recording means, and the read membrane filtration resistance initial value and the membrane at time ti _{+ 1} . Based on the differential pressure value and the supernatant component substance amount value and / or solid component substance amount value of the liquid to be filtered adhering to the separation membrane at time t _{i + 1} calculated by the component amount calculation means, recorded in advance Membrane filtration flow rate (flux) calculation means I for calculating a predicted value of membrane filtration flow rate (flux) at time t _{i + 1} using a membrane filtration flow rate (flux) predicted value calculation formula I, or the data recording means The transmembrane pressure difference value at time t _{i + 1} is read out from time t _{i + 1} , based on the read transmembrane pressure difference value at time t _{i + 1 and} the membrane filtration resistance prediction value at time t _{i + 1} calculated by the membrane filtration resistance calculation means. Record in advance Membrane using a filtration flow rate (flux) predicted value calculation formula II, the time t membranous filtration flowrate (flux) for calculating a predicted value of the _{i + 1} membrane filtration in flow rate (flux) calculation means II,
The predicted value of the membrane filtration resistance at time t _{i + 1} calculated by the membrane filtration resistance calculation means and / or the membrane filtration flow rate (flux) at time t _{i + 1} calculated by the membrane filtration flow rate (flux) calculation means. Membrane filtration predicted value recording means for recording the predicted value of
Time-series value recording means for recording the predicted value of the membrane filtration resistance and / or the predicted value of the membrane filtration flow rate (flux) at the times t _{0 to} t _n recorded by the membrane filtration predicted value recording means as time-series values; And
Output means for outputting the time series value of the membrane filtration resistance prediction value and / or the time series value of the membrane filtration flow rate (flux) prediction value recorded by the time series value recording means;
With the features of
The pre-recorded formula for calculating the amount of adhering component is the value of the amount of the supernatant component substance and / or the amount of the solid component substance adhering to the separation membrane at time _i and the adhering amount from time t _i. based on the amount of change and that change in increase and decrease by time t _{i + 1,} there at time t _{i + 1} at attachment component value calculation formula for obtaining the supernatant component material amount and / or solid components substance amount of the filtrated liquid adhering to the separation membrane And
The amount of change from the time t _i to the time t _{i + 1} in said adhesion component value calculation formula is, the speed supernatant components thereof and / or the solid components of the filtrate are adhered to the separation membrane, attached to the separation membrane Calculated based on the difference from the rate at which the supernatant component and / or solid component of the liquid to be filtered peels from the separation membrane,
The rate at which adhere to the separation membrane, transmembrane pressure value or membrane filtration flow rate (flux) value at time t _i and the supernatant component substance quantity value of the filtrate at the time t _i and / or solid components substance amount Calculated with the value, and
The rate at which detaches from the separation membrane, transmembrane pressure value or membrane filtration flow rate (flux) value at time t _i and the supernatant component substance quantity value of the filtrated liquid adhering to the separation membrane at time t _i and / or membrane filtration prediction program characterized by being calculated by using the solid component substance quantity value secondary function.

(7) When the filtration of the liquid to be filtered by the separation membrane is continued while controlling the membrane filtration flow rate (flux) to the set value, the time change and / or the intermembrane difference of the membrane filtration resistance value that changes with time A computer program for predicting a temporal change in pressure value,
The time series value of membrane filtration flow rate (flux), the time series value of the amount of supernatant component substance and / or the amount of solid component substance in the liquid to be filtered, the time series value of membrane detergency, attached to the separation membrane Data input means for inputting the initial value of the amount of the supernatant component and / or the amount of the solid component of the liquid to be filtered and the initial value of the membrane filtration resistance,
Time-series value of membrane filtration flow rate (flux) input by the data input means, time-series value of supernatant component substance amount and / or solid-component substance amount of filtered liquid, and membrane cleaning power Data recording means for recording the series value, the initial value of the amount of the supernatant component substance and / or the amount of the solid component substance of the filtered liquid adhering to the separation membrane, and the initial value of the membrane filtration resistance,
Membrane filtration flow rate (flow) from the data recording means at an arbitrary time t _i (where i = 0 to n, t _{i + 1} = t _i + Δt _i , t ₀ = 0, n is a natural number representing the number of steps). flux) value, the supernatant component substance quantity value and / or solid components substance quantity value of the filtrate, membrane washing force value, and, in the case of time t ₀ is of the filtrate adhering to the separation membrane supernatant reads the initial value of the component substance amount and / or solid components substance amount, further, in the case other than the time t ₀ on the separation membrane at the time t _i recorded in the data recording means by component amount calculating value recording unit described later The supernatant component substance amount value and / or the solid component substance amount value of the attached liquid to be filtered is read, and the attached substance adhering to the separation membrane at time t _{i + 1} is calculated using a pre-recorded attached component amount calculation formula. The amount of the supernatant component in the filtrate and / or the amount of the solid component Component amount calculating means for calculating a value;
Component amount calculation value recording means for recording the supernatant component substance amount value and / or the solid component substance amount value of the liquid to be filtered adhering to the separation membrane at time t _{i + 1} calculated by the component amount calculation means;
Next membrane filtration resistance calculation means and / or transmembrane differential pressure calculation means (membrane filtration resistance calculation means) Read the membrane filtration resistance initial value from the data recording means, and read the membrane filtration resistance initial value and component amount calculation means Based on the non-membrane permeable substance amount value and / or the solid component substance amount value in the supernatant component of the filtrate to be filtered adhering to the separation membrane calculated at time t _{i + 1,} the membrane filtration resistance prediction value recorded in advance Membrane filtration resistance calculation means for calculating the predicted value of the membrane filtration resistance at time t _{i + 1} using the calculation formula,
(Transmembrane differential pressure calculation means) The membrane filtration resistance initial value and the membrane filtration flow rate (flux) value at time t _{i + 1} are read from the data recording means, and the read membrane filtration resistance initial value and membrane filtration at time t _{i + 1} . Based on the flow rate (flux) value and the supernatant component substance amount value and / or solid component substance amount value of the liquid to be filtered adhering to the separation membrane at time t _{i + 1} calculated by the component amount calculation means, in advance Using the recorded transmembrane differential pressure predicted value calculation formula I, the transmembrane differential pressure calculating means I for calculating the predicted value of the transmembrane differential pressure at time t _{i + 1} , or the membrane at time t _{i + 1} from the data recording means reads the filtration flow rate (flux) value, the basis of the membrane filtration flow rate (flux) value at time t _{i + 1} read, and membrane filtration resistance prediction value at time t _{i + 1} calculated by the membrane filtration resistance calculation means Record in advance The using transmembrane pressure predicted value calculation formula II, the time t _{i +} transmembrane difference to calculate the predicted value of the transmembrane pressure in the _one pressure calculating means II,
The predicted value of the membrane filtration resistance at the time t _{i + 1} calculated by the membrane filtration resistance calculation unit and / or the predicted value of the transmembrane pressure difference at the time t _{i + 1} calculated by the transmembrane pressure difference calculation unit is recorded. Membrane filtration predicted value recording means,
A time series value recording means for recording the predicted value of the membrane filtration resistance and / or the predicted value of the transmembrane pressure difference at the time t _{0 to} t _n recorded by the membrane filtration predicted value recording means, as a time series value, and
Output means for outputting the time series value of the membrane filtration resistance prediction value and / or the time series value of the transmembrane pressure difference prediction value recorded by the time series value recording means;
With the features of
The pre-recorded formula for calculating the amount of adhering component is the value of the amount of the supernatant component substance and / or the amount of the solid component substance adhering to the separation membrane at time _i and the adhering amount from time t _i. based on the amount of change and that change in increase and decrease by time t _{i + 1,} there at time t _{i + 1} at attachment component value calculation formula for obtaining the supernatant component material amount and / or solid components substance amount of the filtrated liquid adhering to the separation membrane And
The amount of change from the time t _i to the time t _{i + 1} in said adhesion component value calculation formula is, the speed supernatant components thereof and / or the solid components of the filtrate are adhered to the separation membrane, attached to the separation membrane Calculated based on the difference from the rate at which the supernatant component and / or solid component of the liquid to be filtered peels from the separation membrane,
The rate at which adhere to the separation membrane, transmembrane pressure value or membrane filtration flow rate (flux) value at time t _i and the supernatant component substance quantity value of the filtrate at the time t _i and / or solid components substance amount Calculated with the value, and
The rate at which detaches from the separation membrane, transmembrane pressure value or membrane filtration flow rate (flux) value at time t _i and the supernatant component substance quantity value of the filtrated liquid adhering to the separation membrane at time t _i and / or membrane filtration prediction program characterized by being calculated by using the solid component substance quantity value secondary function.

  According to the present invention, as will be described below, the time change of the membrane filtration resistance generated when the liquid to be filtered is filtered through the membrane, the time change of the transmembrane pressure difference, or the time change of the membrane filtration flux. Alternatively, the time change of the membrane filtration flow rate can be accurately predicted. As a result, for example, the operating conditions can be determined efficiently by preliminarily examining operating conditions such as transmembrane pressure difference and filtration flow rate that suppress the rapid increase in membrane filtration resistance due to clogging of the membrane seen at the end of operation. It becomes possible.

  The membrane filtration prediction method of the present invention uses a pressure difference between the filtrate side and the permeate side of the separation membrane (hereinafter referred to as a transmembrane differential pressure) as a driving force, and membrane filtration when filtering the filtrate through the separation membrane. It is related with the method of predicting.

  Here, the liquid to be filtered is a liquid containing a suspended substance and is used for membrane filtration, and is not particularly limited. For example, in the case of a liquid containing microorganisms, since the microorganisms and microbial metabolites as substances are generally present in the liquid to be filtered at a relatively high concentration, the resistance when the liquid to be filtered is subjected to membrane filtration. It is difficult to predict fluctuations such as, but according to the present invention, it becomes possible to predict fluctuations such as resistance when the filtrate to be filtered through a membrane, and a membrane filtration device for membrane filtration of the filtrate to be filtered Therefore, the present invention is particularly effective when a liquid containing a microorganism such as a microorganism culture solution or activated sludge is used as a liquid to be filtered. is there. Further, the present invention is preferably applied to the case of a liquid to be filtered having a suspended substance concentration of 100 mg / L or more. The membrane filtration method may be a whole-volume filtration method in which membrane filtration is performed while concentrating the filtrate, or a cross-flow method in which membrane filtration is performed while generating a flow of the filtrate on the membrane surface.

  Further, the separation membrane has a function of capturing a substance having a certain particle diameter or more contained in the filtrate by applying pressure to the filtrate or sucking from the permeate side. Depending on the particle size, there are dynamic filtration membranes, microfiltration membranes, ultrafiltration membranes, nanofiltration membranes, reverse osmosis membranes and the like. The separation membrane used in the present invention is preferably a dynamic filtration membrane, a microfiltration membrane, or an ultrafiltration membrane. In addition, examples of the shape of the separation membrane include a flat membrane and a hollow fiber membrane, but the shape is not particularly limited.

  In the membrane filtration prediction method of the present invention, a change in the membrane filtration resistance with time and / or a change with time in the transmembrane pressure difference when the membrane filtration is continued while controlling the membrane filtration flow rate as a set value is predicted. Alternatively, a time-dependent change in membrane filtration resistance and / or a time-dependent change in membrane filtration flow rate (flux) when membrane filtration is continued while controlling the transmembrane pressure difference as a set value is predicted.

  Here, the transmembrane pressure difference is the pressure difference between the filtrate side and the permeate side of the separation membrane. As a means for generating this, for example, a method of pressurizing the filtrate side with a pump, a pump The method of sucking from the permeate side and the method of utilizing the water head difference between the liquid to be filtered side and the permeate side. The transmembrane pressure difference can also be measured as a difference between the pressure measurement value on the filtrate side of the separation membrane and the pressure measurement value on the permeate side, and is generated by a hydraulic flow at this time. It is preferable to measure or calculate the pressure loss, and calculate by subtracting the pressure loss from the difference between the pressure measurement value on the filtrate side of the separation membrane and the pressure measurement value on the permeate side.

  The membrane filtration flow rate is the flow rate of the membrane filtrate, and the membrane filtration flux is the membrane filtration flow rate per unit area of the separation membrane.

  To continue membrane filtration while controlling the membrane filtration flow rate as a set value, or to continue membrane filtration while controlling the transmembrane pressure difference as a set value, the membrane filtration flow rate or the transmembrane pressure difference is set in advance. In addition to the method of controlling the membrane filtration flow rate and the transmembrane differential pressure to be constant values, the method of periodically or intermittently stopping filtration, the membrane filtration flow rate and the transmembrane difference This includes a case where the set value is changed with time, such as a method of continuously or intermittently changing the pressure. As a method of continuing membrane filtration while controlling the membrane filtration flow rate as a set value, install a suction pump on the membrane permeate side of the separation membrane to obtain the membrane filtrate, and control the suction pump with a flow rate inverter The method etc. are mentioned. In addition, as a method of continuing the membrane filtration while controlling the transmembrane pressure as a set value, the pressure required for the membrane filtration is increased by a method of pressurizing the liquid to be filtered side of the separation membrane or a method using a water head difference. In addition, a method for controlling the pressure may be used.

  The membrane filtration resistance is resistance generated when the liquid to be filtered is filtered through a membrane, and is generally defined by the equation (1).

Here, ΔP is the transmembrane pressure difference [Pa], μ is the viscosity of the membrane filtrate [Pa · s], R is the membrane filtration resistance [1 / m], and J is the membrane filtration flux [m / s]. . Here, μ may directly measure the viscosity of the membrane filtrate, but when the membrane filtrate is water or an aqueous liquid containing some solute, it is converted from the temperature according to the equation (2). Also good.

  Here, F = 0.01257187, B = −0.005806436, C = 0.001130911, D = −0.000005723952, and T is the absolute temperature [K]. That is, when the Celsius temperature is σ [° C.], it is expressed as T = σ + 273.15.

  Prediction is a numerical value that serves as an input (time series value of membrane filtration flow rate or time series value of transmembrane pressure difference, etc.). Change).

  In the membrane filtration prediction method of the present invention, when membrane filtration is continued while controlling the membrane filtration flow rate (flux) to a set value, at least the membrane filtration flow rate ( (Flux) set value, initial value of membrane filtration resistance, and supernatant component substance amount value and / or solid component substance amount value of the filtrate to be filtered while controlling the transmembrane pressure difference to the set value As a numerical value for the membrane filtration prediction calculation, at least the setting value of the transmembrane pressure difference, the initial value of the membrane filtration resistance, and the amount of supernatant component substance and / or solids of the liquid to be filtered The component substance amount value is used.

  Here, the initial value of the membrane filtration resistance is the membrane filtration resistance value at the start of membrane filtration, such as the membrane filtration resistance value when permeating pure water to the separation membrane, the membrane filtration resistance value after washing the separation membrane, etc. May be a measured value or a virtual value based on the type of separation membrane.

  In addition, the supernatant component of the liquid to be filtered is the supernatant when the liquid to be filtered is centrifuged or gravity-precipitated, or when the liquid to be filtered is filtered through a separation membrane having a larger pore diameter than the separation membrane of the membrane filtration device. This is the filtrate. The solid component of the liquid to be filtered is a precipitate when the liquid to be filtered is centrifuged or gravity-precipitated, or when the liquid to be filtered is filtered through a separation membrane having a pore size larger than the separation membrane of the membrane filtration device. A non-membrane permeable substance.

  Further, the substance amount is a substance amount such as a dissolved substance or a suspended substance contained in the supernatant component or the solid component. For example, the total amount of organic carbon (TOC), chemical oxygen demand ( COD), biochemical oxygen demand (BOD), suspended solids concentration (MLSS), dry weight, suspended solids loss on ignition (MLVSS), etc.

  Here, the supernatant component substance amount value is the value of the substance amount in the supernatant component, but in the present invention, the substance amount value of the non-membrane permeate contained in the supernatant component, that is, the supernatant The substance amount value obtained by subtracting the substance amount value contained in the membrane permeate when the filtrate or supernatant component is filtered through the separation membrane from the substance amount value in the component is defined as the supernatant component substance amount value. Is preferred. Here, in view of ease of measurement, accuracy, and automation, the amount of supernatant component substance in the liquid to be filtered is preferably defined by the amount of substance measured based on the TOC, and the solid component substance in the liquid to be filtered The amount is preferably defined by the amount of substance measured based on TOC, MLSS, or MLVSS. The supernatant component substance amount value and the solid component substance amount value of the liquid to be filtered may be measured values or virtual values.

  In the membrane filtration prediction method of the present invention, the supernatant component substance amount value and / or the solid component substance amount value of the liquid to be filtered are used. Here, by using the supernatant component substance amount value or the solid component substance amount value, a value necessary for membrane filtration prediction can be obtained quickly and easily. In addition, by using the data of the supernatant component substance amount value and the solid component substance amount value, if the solid component of the liquid to be filtered adheres to the separation membrane, it contributes to membrane filtration resistance, and easily peels from the separation membrane. The effect of entraining and peeling off the supernatant component adhering to the separation membrane can be accurately reproduced.

  In addition, the set value of the membrane filtration flow rate (flux) is the set value of the membrane filtration flow rate or the membrane filtration flux, and may be an actual measurement value or a virtual value, and a value that changes continuously or intermittently even at a constant value. It is good. The set value of the transmembrane pressure is a set value of the transmembrane pressure, and may be an actual measurement value, a virtual value, a constant value, or a value that changes continuously or intermittently.

  In the membrane filtration prediction method of the present invention, when membrane filtration is continued while controlling the membrane filtration flow rate to a set value, at least calculation step 1 and calculation step 2 and / or calculation step 3 described later are performed. To obtain the membrane filtration resistance value and / or the transmembrane differential pressure value at an arbitrary time, and to continue the membrane filtration while controlling the transmembrane differential pressure to the set value, at least calculation step 1 and calculation described later By performing Step 2 and / or Calculation Step 4, a membrane filtration resistance value and / or a membrane filtration flow rate (flux) value at an arbitrary time is obtained.

That is, it means that there are the following three types of calculation steps for membrane filtration prediction when membrane filtration is continued while controlling the membrane filtration flow rate to a set value.
(A) Calculation step 1, calculation step 2, and calculation step 3 described later
(B) Calculation step 1 and calculation step 2 described later
(C) Calculation step 1 and calculation step 3 described later

  Here, in the case of (a) (see FIG. 1), the membrane filtration resistance value and the transmembrane pressure difference value at an arbitrary time, and in the case of (b), the membrane filtration resistance value at an arbitrary time, In the case of (c), the transmembrane pressure difference value at an arbitrary time can be obtained.

Similarly, it means that there are the following three types of calculation steps for membrane filtration prediction when membrane filtration is continued while controlling the transmembrane pressure difference to a set value.
(D) Calculation step 1, calculation step 2, and calculation step 4 described later
(E) Calculation step 1 and calculation step 2 described later
(F) Calculation step 1 and calculation step 4 described later

  Here, in the case of (d) (see FIG. 2), the membrane filtration resistance value and the membrane filtration flow rate (flux) value at an arbitrary time, and in the case of (e), the membrane filtration resistance at an arbitrary time. In the case of (f), the membrane filtration flow rate (flux) value at an arbitrary time can be obtained.

  Here, in the calculation step 1, the supernatant component substance amount value and / or the solid component substance amount value of the liquid to be filtered adhering to the separation membrane at an arbitrary time is calculated.

  Here, the calculation step 1 is a calculation step based on the amount of change in the amount of the supernatant component substance and / or the amount of the solid component substance of the liquid to be filtered adhering to the separation membrane within a predetermined time. The calculation formula in (1) is the term of the rate at which the supernatant component and / or solid component of the filtrate is attached to the separation membrane, and the supernatant component and / or solid component of the filtrate to be attached to the separation membrane Including the term of the rate at which the substance peels from the separation membrane, and the rate of attachment to the separation membrane includes the transmembrane differential pressure value or the membrane filtration flow rate (flux) value, the supernatant component substance amount value of the liquid to be filtered, and The rate of separation from the separation membrane is calculated using the solid component substance amount value, and the rate of separation from the separation membrane or the membrane filtration flow rate (flux) value and the filtration target attached to the separation membrane Calculated using the supernatant component substance amount value and / or the solid component substance amount value of the liquid Rukoto is preferable. Thereby, calculation of the supernatant component substance amount value and / or solid component substance amount value of the liquid to be filtered adhering to the separation membrane at an arbitrary time can be accurately predicted.

  In addition, the calculation formula in the calculation step 1 is calculated based on the transmembrane pressure difference value or the membrane filtration flow rate (flux) and the amount of the supernatant component substance in the filtrate. From the separation membrane calculated based on the rate at which the substance adheres to the separation membrane, the transmembrane differential pressure value or membrane filtration flow rate (flux), the amount of the supernatant component substance and the amount of the solid component substance adhering to the separation membrane Includes a calculation formula for calculating the amount of supernatant component substance of the liquid to be filtered adhering to the separation membrane after a predetermined time based on the difference from the rate at which the supernatant component substance peels, and the transmembrane pressure difference value Alternatively, the rate at which the solid components in the filtrate to be filtered are calculated based on the membrane filtration flow rate (flux) and the amount of solid component substances in the filtrate, the transmembrane pressure difference value or the membrane filtration flow rate. Calculated based on (flux) and the amount of supernatant and solid components adhering to the separation membrane That the solid component from the separation membrane based on a difference between the speed of peeling, to include a formula for calculating the solids substance content of the filtered liquid adhering to the separation membrane after a predetermined time, further preferred. As a result, if the solid component of the liquid to be filtered adheres to the membrane, it contributes to the membrane filtration resistance and easily peels off from the membrane. Can be reproduced.

  In addition, the formula for determining the rate at which the supernatant component and / or solid component of the filtrate attached to the separation membrane peels from the separation membrane is the supernatant component substance of the filtrate to be attached to the separation membrane. It is more preferable to include a second-order or higher-order function term of the quantity value and / or the solid component substance quantity value. If it is less than the secondary, the rate at which the supernatant component and / or solid component of the liquid to be filtered adhering to the separation membrane peels off from the surface of the separation membrane is often smaller than the actual, but it should be secondary or higher. Thus, the degree of peeling can be increased and reproduced with higher accuracy.

  Moreover, it is more preferable that the formula for obtaining the rate at which the supernatant component and / or the solid component of the liquid to be filtered attached to the separation membrane peel from the membrane includes a term based on the membrane detergency value. Here, the membrane detergency is the stress for peeling off the substance adhering to the separation membrane surface, and the value of the membrane detergency is the value of the shear force generated on the membrane surface, the membrane surface to be filtered The value of the flow rate of the liquid, the value calculated based on the shearing force and the flow rate, or the power value of the cleaning means (the power value of the cleaning means is, for example, aeration of cleaning of the separation membrane from the lower part of the separation membrane The flow rate of the aeration and the output value of the aeration blower correspond to each other, and when cleaning the separation membrane by flowing the liquid to be filtered, the power for generating the flow (for example, filtered by a liquid pump) When the liquid is made to flow, the output value of the liquid pump is equivalent, and when the separation membrane is washed by moving the separation membrane, the moving speed and the power value for that (for example, in the case of a rotary filtration membrane) The times When the cleaning of the separation membrane is performed by vibration, the degree of vibration (for example, frequency) and the power value (for example, motor) It is preferable to use a value calculated on the basis of the actual results of the membrane filtration test. . As a result, factors that do not depend on the performance of the separation membrane, such as aeration, are determined as factors that determine the rate at which the supernatant components and / or solid components of the liquid to be filtered adhering to the separation membrane peel from the separation membrane. Can be added, which makes it easier to reflect the operating conditions of the membrane filtration device.

  As mathematical formulas satisfying such conditions, for example, there are the following formulas (3) and (4). In the present invention, it is recommended to follow the formulas (3) and (4). However, the scope of the present invention is not limited to the equations (3) and (4).

  However, (τ−λx · ΔP) ≧ 0 and (τ−λp · ΔP) ≧ 0.

Here, substance amount value X is included in the solid component [gC / m 3], substance amount value of the non-membrane permeable substance ^P is contained in the supernatant component [gC / m 3], ^Xm is per unit membrane area The amount of substance contained in the solid component adhering to the separation membrane [gC / m ² ], Pm is the amount of the non-membrane permeable substance contained in the supernatant component adhering to the separation membrane per unit membrane area [gC / M ² ], t is the time [s], τ is the membrane cleaning power value [Pa], γx is the peel coefficient [1 / m / s] of the substance contained in the solid component, and γp is the non-component contained in the supernatant component. The peel coefficient [1 / m / s] of the membrane permeable substance, λx is the friction coefficient [1 / Pa] of the substance contained in the solid component, and λp is the friction coefficient [1 of the non-membrane permeable substance contained in the supernatant component. / Pa], ηx is the reciprocal of the density of the substance contained in the solid component [m 3 ^/ gC], ηp is the non-membrane permeable substance contained in the supernatant component Time is the inverse ^[m 3 / gC] of. Here, the first term on the right side of the expression (3) indicates the rate at which the solid component material adheres to the separation membrane, and the second term indicates the rate at which the solid component material peels from the separation membrane. The first term on the right side of the equation () represents the rate at which the supernatant component material adheres to the separation membrane, and the second term represents the rate at which the supernatant component material peels from the separation membrane. Further, by multiplying both sides of the formulas (3) and (4) by the membrane area A, the left side of the formula (3) is the amount of change in the amount of substance contained in the solid component attached to the separation membrane, and the formula (4) It is possible to convert the membrane filtration flux J on the right side into the membrane filtration flow rate Q to the amount of change in the amount of the non-membrane permeable substance contained in the supernatant component attached to the separation membrane on the left side. As will be described later, when the membrane cleaning power value τ is expressed as a function of the power value of the cleaning means, the formula (3) and (4) are replaced by τ by substituting the function into τ. It is possible to convert to a calculation formula relating to the power value of the cleaning means instead of the force value.

  Further, as described above, the amount of change in the supernatant component substance and / or solid component substance adhering to the separation membrane is determined, and the supernatant component substance and / or solid component substance of the liquid to be filtered adheres to the separation membrane. When based on the calculation formula expressed as the difference between the speed and the peeling speed, it can be expressed as a differential equation regarding the amount of the supernatant component substance and / or the amount of the solid component substance of the liquid to be filtered attached to the separation membrane. At this time, as an integration method for solving the differential equation, there are an Euler method, a Runge-Kutta method, a Runge-Kutta-Gill (RKG) method, and the like.

  Further, in the calculation step 2, at least the membrane filtration at an arbitrary time using the supernatant component substance amount value and / or the solid component substance amount value of the liquid to be filtered adhering to the separation membrane obtained in the calculation step 1 Calculate the resistance value.

  Here, the calculation of the membrane filtration resistance at an arbitrary time in the calculation step 2 can calculate the value of the membrane filtration resistance at an arbitrary time by, for example, following equation (5).

  Here, Rm is the initial value [1 / m] of membrane filtration resistance, αx is the amount of membrane filtration resistance generated per unit amount of Xm [m / gC], and αp is the amount of membrane filtration resistance generated per unit amount of Pm. Amount [m / gC].

  In calculation step 3, at least using the supernatant component substance amount value and / or solid component substance amount value of the liquid to be filtered adhering to the separation membrane obtained in calculation step 1, or in calculation step 2 The transmembrane pressure difference value at an arbitrary time is calculated using the obtained membrane filtration resistance value.

  Here, when the membrane filtration prediction is configured in (c) (that is, calculation step 1 and calculation step 3), the amount of the supernatant component substance of the liquid to be filtered attached to the separation membrane obtained in calculation step 1 The transmembrane pressure difference value at an arbitrary time is calculated using the value and / or the solid component substance amount value. As such a method, for example, a mathematical formula obtained by substituting the formula (5) into the formula (1) may be used. Further, when the membrane filtration prediction is configured by (a) (that is, calculation step 1, calculation step 2, and calculation step 3), the membrane filtration resistance value obtained in calculation step 2 is used to determine the membrane at an arbitrary time. The differential pressure value is calculated. As the method, it is preferable to calculate using the formula (1) or a mathematical formula based on the formula (1).

  In calculation step 4, at least using the supernatant component substance amount value and / or solid component substance amount value of the liquid to be filtered adhering to the separation membrane obtained in calculation step 1, or in calculation step 2 The membrane filtration flow rate (flux) value at an arbitrary time is calculated using the obtained membrane filtration resistance value.

  Here, when the membrane filtration prediction is configured by (f) (that is, calculation step 1 and calculation step 4), the amount of the supernatant component substance of the liquid to be filtered attached to the separation membrane obtained in calculation step 1 The membrane filtration flow rate (flux) value at an arbitrary time is calculated using the value and / or the solid component substance amount value. As such a method, for example, a mathematical formula obtained by substituting the formula (5) into the formula (1) may be used. Further, when the membrane filtration prediction is configured by (d) (that is, calculation step 1, calculation step 2, and calculation step 4), the membrane filtration resistance value obtained in calculation step 2 is used to determine the membrane at an arbitrary time. Calculate the filtration flow rate (flux) value. As the method, it is preferable to calculate using the formula (1) or a mathematical formula based on the formula (1).

  In the present invention, when the membrane filtration is predicted when the membrane filtration is continued while the membrane filtration flow rate is controlled to a set value by repeatedly performing the calculation step while updating the time, the membrane filtration resistance is changed over time. Change and / or change in transmembrane pressure differential over time, and when performing membrane filtration prediction while continuing the membrane filtration while controlling the transmembrane differential pressure to the set value, Change and / or change with time of membrane filtration flow rate (flux) is obtained.

  In the calculation step 1, the calculation step 2, the calculation step 3, and the calculation step 4, calculation is performed according to a predetermined calculation formula, which is described in the description of each calculation step in the calculation formula. May include parameters other than measured values, data, and substance amounts. In such a case, it is necessary to determine a parameter value in performing the calculation in each calculation step. In the present invention, the method for determining the parameter value is not particularly limited, but the filtrate or the supernatant of the filtrate is actually filtered using a separation membrane having the same material and shape as the separation membrane of the membrane filtration device. It is preferable to actually measure or calculate changes in the transmembrane pressure difference, the membrane filtration flux or membrane filtration flow rate, and the membrane filtration resistance, and estimate or determine the parameters based on the results. This includes many parameters determined by the properties of the liquid to be filtered and the separation membrane used, and by following the parameter estimation / determination method described above, This is because prediction can be performed with high accuracy.

Next, the membrane filtration prediction program of the present invention will be described.
Hereinafter, an example of the best embodiment of the membrane filtration prediction program of the present invention will be described with reference to the drawings.

  FIG. 3 is a processing flow executed by the membrane filtration prediction program of the present invention, and FIG. 4 is an example of the configuration of a membrane filtration prediction device that implements the membrane filtration prediction program of the present invention. This membrane filtration predicting device is composed of a computer 1 to which an auxiliary storage device 2, an input device 3 and a display device 4 are connected, and a control program is stored on the main memory of this computer.

  First, when continuing while controlling the transmembrane pressure difference to a set value, when predicting the time change of the membrane filtration resistance value and / or the time value of the membrane filtration flow rate (flux) value that change over time , Time series value of transmembrane pressure difference, time series value of supernatant component amount and / or solid component substance amount of filtrate, time series value of membrane detergency, of filtrate to be filtered attached to separation membrane The initial value of the supernatant component substance amount and / or the solid component substance amount and the initial value of the membrane filtration resistance are input from the input device 3 (data input means: step S100) (wherein the supernatant component substance amount and / or the solid content) When entering the time series value of the amount of the component substance, if the time series value of the amount of the supernatant component substance is input, the initial value of the amount of the supernatant component substance of the liquid to be filtered attached to the separation membrane is When time-series values of component substances are input, solid formation of the liquid to be filtered attached to the separation membrane When the initial value of the substance amount is input as the time-series value of the amount of the supernatant component substance and the amount of the solid component substance, the amount of the supernatant component substance and the amount of the solid component substance of the liquid to be filtered attached to the separation membrane Are stored in the main memory on the computer 1 (data recording means: step S200). In addition, when the amount of supernatant components and / or the amount of solid components of the filtrate to be filtered changes over time, such as when performing a membrane filtration of the total volume filtration type, the filtrate to be filtered at any time calculated separately. It is preferable to record the amount of the supernatant component substance and / or the amount of the solid component in the main memory as needed. When predicting the time change of the membrane filtration resistance value and / or the time difference of the transmembrane differential pressure value that changes over time when continuing while controlling the membrane filtration flow rate (flux) to the set value, The value input in S100 and the value stored in step S200 can be predicted by replacing the time series value of the transmembrane pressure difference with the time series value of the membrane filtration flow rate (flux).

The values may be individually input by an input device such as a keyboard, or may be input as a data file prepared in advance. Here, the time series value means a data set in which a certain time and data at that time are paired. For example, assuming that t _i (1 ≦ i ≦ n, n: number of data) is time and d _i is data at t _i , (t ₁ , d ₁ ), (t ₂ , d ₂ ),. _Let t _n , d _n ) be a set of data. Here, if t _{i + 1} −t _i = Δt _i , Δt _i is not necessarily constant, but it is time to make Δt _i constant by supplementing data appropriately by extrapolation or interpolation. Series values can be generated. Here, i = 0 to n, t _{i + 1} = t _i + Δt _i , t ₀ = 0, n is a natural number representing the number of steps, and Δt _{i is} obtained by appropriately extrapolating or interpolating data. Is constant, Δt _i = t _n / n.

  In the membrane filtration prediction program of the present invention, in the case of prediction when continuing the membrane filtration while controlling the transmembrane pressure difference to the set value, at least a component amount calculating means and a membrane filtration resistance calculating means described below and / Alternatively, the membrane filtration flow rate (flux) is calculated by performing the membrane filtration flow rate (flux) calculation means to obtain the membrane filtration resistance value and / or membrane filtration flow rate (flux) value at an arbitrary time. When membrane filtration is continued while controlling to a value, at least a later-described component amount calculation means, a membrane filtration resistance calculation means, and / or a transmembrane pressure difference calculation means are performed, so that the membrane filtration resistance value at an arbitrary time And / or determining a transmembrane pressure value.

That is, it means that the following three types are included as the configuration of the membrane filtration prediction program when membrane filtration is continued while controlling the transmembrane pressure difference to a set value.
(G) Component amount calculation means, membrane filtration resistance calculation means, and membrane filtration flow rate (flux) calculation means described later (h) Component amount calculation means, membrane filtration resistance calculation means described later (i) Component amount calculation means, described later Membrane filtration flow rate (flux) calculation means

  Here, in the case of (g) (see FIG. 5), the membrane filtration resistance value and the membrane filtration flow rate (flux) value at an arbitrary time, and in the case of (h), the membrane filtration resistance at an arbitrary time. In the case of (i), the membrane filtration flow rate (flux) value at an arbitrary time can be output.

Similarly, it means that the following three types are included as the configuration of the membrane filtration prediction program when membrane filtration is continued while controlling the membrane filtration flow rate to the set value.
(J) Component amount calculating means and membrane filtration resistance calculating means and transmembrane differential pressure calculating means described later (k) Component amount calculating means and membrane filtration resistance calculating means described later (m) Component amount calculating means and transmembrane difference described later Pressure calculation means

  Here, in the case of (j) (see FIG. 6), the membrane filtration resistance value and the transmembrane pressure difference value at an arbitrary time, and in the case of (k), the membrane filtration resistance value at an arbitrary time, In the case of (m), the transmembrane pressure difference value at an arbitrary time can be obtained.

Next, in the component amount calculation means in step S300, the liquid to be filtered attached to the separation membrane at time t _{i + 1} using the data at time t _i according to the attached component amount calculation formula recorded in advance in the auxiliary storage device 2. The supernatant component substance amount value and / or the solid component substance amount value are calculated. That is, inter-membrane differential at time t _i from the time series values stored in the main memory pressure value or membrane filtration flow rate (flux) value or of the filtrated supernatant component substance quantity value and / or the solid component materials The volume value and membrane detergency value are read out, and the initial value of membrane filtration resistance, and in the case of time t ₀ , the amount of the supernatant component substance and / or the amount of solid component substance of the liquid to be filtered adhering to the separation membrane In cases other than the initial value, t ₀ , the supernatant component substance amount value and / or the solid component substance amount value of the liquid to be filtered adhering to the separation membrane at time t _i is read out. Supernatants component substance quantity value and / or solid components substance amount value pre-recorded attached component quantity of the filtration liquid adhering to the separation membrane at the time t _{i + 1} by using the read-out values at the time t _i Calculated according to the calculation formula. However, when the time series value of the amount of supernatant component substance and the initial value of the amount of supernatant component substance of the liquid to be filtered adhering to the separation membrane are recorded in step S200, the separation at time t _{i + 1} is performed. The supernatant component substance amount value of the liquid to be filtered adhering to the membrane, the time series value of the solid component substance amount, and the initial value of the solid component substance amount of the liquid to be filtered adhering to the separation membrane are recorded. In this case, the solid component substance amount value of the liquid to be filtered adhering to the separation membrane at time t _{i + 1} is obtained by calculating the supernatant component amount substance amount, the time series value of the solid component substance amount, and the subject matter adhering to the separation membrane. When the initial values of the amount of the supernatant component of the filtrate and the amount of the solid component are recorded, the amount of the supernatant component of the filtrate and the solid component of the filtrate attached to the separation membrane at time ti _{+ 1} The substance amount value is calculated. These operations are processed by the central processing unit in accordance with the instructions of the control program in the main memory.

  The pre-recorded adhesion component amount calculation formula is determined based on the transmembrane differential pressure value or the membrane filtration flow rate (flux) value, the supernatant component amount value, and the solid component amount value of the filtrate. The supernatant of the liquid to be filtered adhering to the separation membrane determined based on the rate at which the supernatant and solid components adhere to the separation membrane and the transmembrane pressure difference value or the membrane filtration flow rate (flux) value It is determined based on the difference between the component amount and the solid component amount from the separation rate from the separation membrane, the transmembrane differential pressure value or the membrane filtration flow rate (flux) value, and the supernatant component amount value of the liquid to be filtered. The supernatant of the filtrate attached to the separation membrane determined based on the rate at which the supernatant components of the filtrate are attached to the separation membrane and the transmembrane differential pressure value or the membrane filtration flow rate (flux) value The amount of the component is based on the difference from the separation rate from the separation membrane, the transmembrane pressure difference value or the membrane filtration flow rate (flux) value, and solid formation of the filtrate The solid component of the liquid to be filtered, which is determined based on the quantity value, adheres to the separation membrane, which is determined based on the transmembrane differential pressure value or the membrane filtration flow rate (flux) value. It is preferable that the solid component amount of the liquid to be filtered is based on a difference from the rate of separation from the separation membrane.

  More preferably, the supernatant component substance in the filtrate to be calculated, which is calculated based on the transmembrane pressure difference value or the membrane filtration flow rate (flux) and the amount of the supernatant component substance in the filtrate, is supplied to the separation membrane. The supernatant component material is calculated from the separation membrane calculated based on the adhesion speed, the transmembrane differential pressure value or the membrane filtration flow rate (flux), the amount of the supernatant component substance adhering to the separation membrane, and the amount of the solid component substance. It includes a calculation formula for calculating the amount of the supernatant component substance of the liquid to be filtered adhering to the separation membrane after a predetermined time based on the difference from the peeling speed, and the transmembrane pressure difference value or the membrane filtration flow rate ( Flux) and the rate at which the solid component in the filtrate is attached to the separation membrane calculated based on the amount of the solid component substance in the filtrate, the transmembrane pressure difference value or the membrane filtration flow rate (flux) Solid formation from the separation membrane calculated based on the amount of supernatant component substance and solid component substance adhering to the separation membrane There based on a difference between the speed of peeling is to include a formula for calculating the solids substance content of the filtered liquid adhering to the separation membrane after a predetermined time.

  Moreover, it is preferable that the formula which calculates | requires the speed | rate which peels the supernatant component and / or solid component of the to-be-filtered liquid adhering to a separation membrane include the term based on a membrane cleaning power value.

  Furthermore, it is preferable that the adhesion component amount calculation formula recorded in advance is expressed by a mathematical formula based on the formula (3) and / or the formula (4). However, the scope of the present invention is not limited to the equations (3) and (4). Here, the above equations (3) and (4) are expressed as differential equations. If this is calculated using the Euler method, for example, they are expressed as equations (6) and (7). Can do.

  However, (τ−λx · ΔP) ≧ 0 and (τ−λp · ΔP) ≧ 0, which satisfies the condition of equation (8).

Here, the first term on the right side of the equation (7) indicates the rate at which the solid component material adheres to the separation membrane, and the second term indicates the rate at which the solid component material peels from the separation membrane. The first term on the right side of the equation () represents the rate at which the supernatant component material adheres to the separation membrane, and the second term represents the rate at which the supernatant component material peels from the separation membrane. Therefore, when calculating the solid component amount of material adhering to the separation membrane at the time t _{i + 1,} at the time of calculating the supernatant component substance amount adhering to (7), the separation membrane at the time t _{i + 1} For calculating the amount of solid component substances and the amount of supernatant component substances adhering to the separation membrane at time t _{i + 1,} the expressions (6) and (7) are used. . Further, by multiplying both sides of the formulas (6) and (7) by the membrane area A, the amount of change in the amount of the substance contained in the solid component attached to the separation membrane on the left side of the formula (7), It is possible to convert the membrane filtration flux J on the right side into the membrane filtration flow rate Q to the amount of change in the amount of the non-membrane permeable substance contained in the supernatant component attached to the separation membrane on the left side. Further, when the membrane cleaning power value τ is expressed as a function of the power value of the cleaning means, the function is substituted into τ, so that the expressions (7) and (6) are not the film cleaning power value but the cleaning power value. It can be converted into a calculation formula relating to the power value of the means.

  Further, as described above, the amount of change in the supernatant component substance and / or solid component substance adhering to the separation membrane is determined, and the supernatant component substance and / or solid component substance of the liquid to be filtered adheres to the separation membrane. When based on the calculation formula expressed as the difference between the speed and the peeling speed, it can be expressed as a differential equation regarding the amount of the supernatant component substance and / or the amount of the solid component substance of the liquid to be filtered attached to the separation membrane. At this time, as an integration method for solving the differential equation, there are an Euler method, a Runge-Kutta method, a Runge-Kutta-Gill (RKG) method, and the like.

The symbols appearing in the above formula are as shown in Table 1. In step S400, the solid component substance amount value and / or supernatant component substance amount value of the liquid to be filtered adhering to the separation membrane at time t _{i + 1} calculated in step S300 is recorded in the main memory on the computer 1. .

In the membrane filtration resistance calculation means, the central processing unit follows the instruction of the control program in the main memory, and the membrane filtration resistance initial value stored in the main memory by the data recording means (step S200) and the component amount calculation means (step Using the solid component substance amount value and / or the supernatant component substance amount value of the liquid to be filtered adhering to the separation membrane at time t _{i + 1} calculated in S300), the membrane filtration recorded in advance in the auxiliary storage device 2 The predicted membrane filtration resistance value at time t _{i + 1} is calculated using the predicted resistance value calculation formula. This pre-recorded calculation formula is the sum of the membrane filtration resistance determined by the solid component substance amount value and / or the supernatant component substance amount value of the liquid to be filtered adhering to the separation membrane and the initial value of the membrane filtration resistance. Is more preferably calculated based on the equation (5). For this purpose, for example, the following equation (9) is used.

Here, symbols appearing in the equation (9) are as shown in Table 1.

Further, the membrane filtration flow rate (flux) calculation means reads the membrane filtration resistance initial value and the transmembrane pressure difference value at time t _{i + 1} from the data recording means, and the read membrane filtration resistance initial value and time t _{i + 1} . Pre-recorded based on the transmembrane differential pressure value and the supernatant component substance amount value and / or solid component substance amount value of the liquid to be filtered adhering to the separation membrane at time ti _{+ 1} calculated by the component amount calculating means The predicted value of the membrane filtration flow rate (flux) at time t _{i + 1} is calculated using the calculated membrane filtration flow rate (flux) predicted value calculation formula I, or the transmembrane pressure difference at time t _{i + 1} from the data recording means The membrane filtration flow rate recorded in advance based on the transmembrane pressure difference value at time ti _{+ 1} read out and the membrane filtration resistance prediction value at time ti _{+ 1} calculated by the membrane filtration resistance calculation means (Flux) Pre A predicted value of the membrane filtration flow rate (flux) at time t _{i + 1} is calculated using the measured value calculation formula II.

Here, when the membrane filtration prediction program includes (i) (that is, the component amount calculation means and the membrane filtration flow rate (flux) calculation means), the membrane filtration prediction program adheres to the separation membrane at the time t _{i + 1} obtained by the component amount calculation means. The membrane filtration flow rate (flux) value at time t _{i + 1} is calculated using the supernatant component substance amount value and / or the solid component substance amount value of the liquid to be filtered. As such a method, for example, a mathematical formula obtained by substituting the formula (5) into the formula (1) may be used. Further, when the membrane filtration prediction includes (g) (that is, the component amount calculating means, the membrane filtration resistance calculating means, and the membrane filtration flow rate (flux) calculating means), at the time t _{i + 1} obtained by the membrane filtration resistance calculating means. The membrane filtration flow rate (flux) value at an arbitrary time is calculated using the membrane filtration resistance value. As the method, it is preferable to calculate using the formula (1) or a mathematical formula based on the formula (1). For this purpose, for example, Expression (10) or Expression (11) is used.

Here, symbols appearing in the expressions (10) and (11) are as shown in Table 1.

Further, the transmembrane pressure calculating means reads the membrane filtration resistance initial value and the membrane filtration flow rate (flux) value at time t _{i + 1} from the data recording means, and the read membrane filtration resistance initial value and time t _{i + 1} . Based on the membrane filtration flow rate (flux) value and the supernatant component substance amount value and / or the solid component substance amount value of the liquid to be filtered adhering to the separation membrane at time t _{i + 1} calculated by the component amount calculation means. Then, using the pre-recorded transmembrane pressure difference predicted value calculation formula I, the predicted value of the transmembrane pressure difference at time t _{i + 1} is calculated, or the membrane filtration flow rate (flux) at time t _{i + 1} from the data recording means reads the value, the membrane filtration flow rate (flux) value at time t _{i + 1} that is read, the based on the membrane filtration resistance prediction value at time t _{i + 1} calculated by the membrane filtration resistance calculation means, prerecorded Transmembrane pressure difference A predicted value of the transmembrane pressure difference at time t _{i + 1} is calculated using the measured value calculation formula II.

Here, when the membrane filtration prediction program includes the above (m) (that is, the component amount calculating means and the transmembrane pressure calculating means), the coating attached to the separation membrane at the time t _{i + 1} obtained by the component amount calculating means. The transmembrane pressure difference value at time t _{i + 1} is calculated using the supernatant component substance amount value and / or the solid component substance amount value of the filtrate. As such a method, for example, a mathematical formula obtained by substituting the formula (5) into the formula (1) may be used. Further, when the membrane filtration prediction includes the above (j) (that is, the component amount calculation means, the membrane filtration resistance calculation means, and the transmembrane pressure difference calculation means), the membrane filtration resistance at the time t _{i + 1} obtained by the membrane filtration resistance calculation means The transmembrane pressure difference value at an arbitrary time is calculated using the value. As the method, it is preferable to calculate using the formula (1) or a mathematical formula based on the formula (1). For this purpose, for example, Expression (12) or Expression (13) is used.

Here, symbols appearing in the expressions (12) and (13) are as shown in Table 1.

Further, in the membrane filtration predicted value recording means (step S600), the membrane filtration resistance prediction value at time t _{i + 1} calculated by the membrane filtration resistance calculation means and / or the membrane filtration flow rate (flux) calculation means. The calculated predicted value of the membrane filtration flow rate (flux) at the time t _{i + 1} is recorded in the main memory on the computer 1.

When predicting the time change of the membrane filtration resistance value and / or the membrane filtration flow rate (flux) value that change over time when continuing while controlling the transmembrane pressure difference to the set value, When continuing the amount calculation means, the component amount calculation value recording means, the membrane filtration resistance calculation means and / or the membrane filtration flow rate (flux) calculation means, the membrane filtration predicted value recording means while controlling the membrane filtration flow rate to the set value In addition, when predicting the temporal change of the membrane filtration resistance value and / or the temporal change of the transmembrane pressure difference value that change with time, the component amount calculation means, the component amount calculation value recording means, the membrane filtration resistance calculation means, By repeating the transmembrane pressure difference calculating means and the membrane filtration predicted value recording means while updating the time by Δt _i , time series data of predicted values for each Δt _i on the memory (corresponding to times t _{0 to} t _n) Time-series data of predicted values to be generated). Here, the end of the prediction may be the final time t _n of the time-series data stored in the memory in step S200 or a time set in advance.

  Finally, in the output means (step S700), the time series data of predicted values is displayed on the display device 4 in accordance with the instruction of the control program in the main memory. The display is preferably performed in a table in which the time and the predicted value are paired, a graph in which the vertical axis indicates the predicted value, and the horizontal axis indicates the time. Alternatively, two different predicted values (for example, a membrane filtration flow rate value and a membrane filtration resistance value) at an arbitrary time may be displayed as a pair, one as a vertical axis and the other as a horizontal axis. Further, this table or graph may be output by a printer or the like.

  The program is distributed through a tangible storage medium represented by a flexible disk, a CD-ROM, and the like, and a transmission path (including automatic public transmission) such as a wired or wireless network.

  Hereinafter, the present invention will be described in detail, but the present invention is not limited to only these examples.

Example 1
First, a membrane filtration test was conducted using activated sludge as a liquid to be filtered and using the membrane filtration test apparatus 400 shown in FIG. The membrane filtration test apparatus 400 pressurizes a pure water chamber 410 containing pure water or a stirring cell 401 (Amicon 8050 manufactured by Millipore Corporation) with nitrogen gas 405 (the pressure is measured by a pressure gauge). ), The activated sludge as the liquid to be filtered by the separation membrane 402 installed in the membrane fixing holder 406. In membrane filtration, the liquid to be filtered can be stirred by rotating a stirring bar 404 immersed in the liquid to be filtered by a magnetic stirrer 403. The membrane permeate was received by a beaker 407 mounted on an electronic balance 408, the amount of the membrane permeate was measured by the electronic balance 408, and the measured value was taken into the personal computer 409. Moreover, the presence or absence of pressurization of each part of the membrane filtration test apparatus was adjusted by opening and closing the valve 412, the valve 413, and the valve 414.

  First, a membrane filtration test using pure water was performed to measure the initial value of membrane filtration resistance. Here, the membrane filtration pressure was 20 kPa, and the stirring speed by the magnetic stirrer 403 was 600 rpm. Moreover, the measured value in the electronic balance 408 was taken into the personal computer 409 at intervals of 2 seconds. The membrane filtration test using pure water was conducted until an amount of 80 ml of membrane permeate was obtained.

  Next, a membrane filterability evaluation test using activated sludge was performed. First, the pure water chamber 310 was removed, and the dotted line 415 in FIG. 7 was connected. 12 ml of activated sludge was put into the stirring type cell 401, the membrane filtration test was conducted at a membrane filtration pressure of 20 kPa and a stirring speed by the magnetic stirrer 403 of 600 rpm. The measured value in the electronic balance 408 was taken into the personal computer 409 at intervals of 2 seconds, and the membrane filtration test for 700 seconds was performed.

  The membrane filtration test was also performed using a centrifugal supernatant obtained by centrifugation (3500 rpm, 10 minutes).

  In each membrane filtration test described above, data indicating the relationship between the filtration time taken into the personal computer 409 and the amount of filtrate was processed as follows. First, the membrane filtration flux at any filtration time was calculated using the differential coefficient of the filtrate amount at any filtration time. Next, from the membrane filtration flux at the arbitrary filtration time, the membrane filtration resistance at the arbitrary filtration time was calculated according to the formula (1) using the membrane filtration pressure. From the results calculated as described above, a relationship between the total filtrate amount per unit membrane area and the membrane filtration resistance was created.

  From the relationship between the total filtrate volume per unit membrane area and the membrane filtration resistance created from the results of the membrane filtration test using pure water, the average value of the membrane filtration resistance in the section where the filtrate volume is 70 to 80 mL is calculated. The initial value was membrane filtration resistance.

  Here, a membrane filtration prediction program for predicting the results of the membrane filtration test as described above was created using numerical calculation software MATLAB (made by Mathworks, USA).

First, the time-series value of the transmembrane pressure difference ΔP [Pa], the time-series value of the supernatant component amount P [gC / m ³ ] and the solid component amount X [gC / m ³ ] of the liquid to be filtered, and the membrane The time series value of the detergency is entered as a data file prepared in advance, the initial value of membrane filtration resistance, the initial value of the amount of the supernatant component substance and the solid component of the filtered liquid adhering to the separation membrane, and the membrane area The value and the permeated water viscosity value were configured to be input directly from the keyboard. The input data and values are recorded in the memory.

  Moreover, as said adhesion component amount calculation formula, said Formula (3) and said Formula (4) are used as a membrane filtration resistance prediction value calculation formula, and said Formula (5) is used as a membrane filtration flow rate (flux) prediction value calculation formula. A mathematical formula in which J = Q / A is substituted into the formula (1) is recorded in advance.

As component amount calculating means, the inter-membrane differential at the time t _i which is recorded in the memory pressure value, the upper Kiyonari component values and solid component quantity value of the filtrate at the time t _i, membrane washing force value at time t _i, and, the supernatant component substances of the filtrate adhering to the separation membrane at the time t _i recorded in the initial value or the memory of the supernatant component material amount and the solid component amount of the liquid to-be-filtrated attaching on the separation membrane A structure for reading a quantity value and a solid component quantity value, and calculating a supernatant component substance quantity value and a solid component quantity value of the liquid to be filtered adhering to the separation membrane at time t _{i + 1} using the attached component calculation formula; did. At this time, the Runge-Kutta method was used as the integration method.

The supernatant component substance amount value and the solid component substance amount value of the liquid to be filtered adhering to the separation membrane at time t _{i + 1} calculated by the component amount calculating means have a structure recorded in a memory (component amount calculation). Value recording means).

As the membrane filtration resistance predicted value calculation means, the membrane filtration resistance initial value recorded in the memory is read out, and the read membrane filtration resistance initial value and the separation membrane at the time t _{i + 1} calculated by the component amount calculation means Using the supernatant component substance amount value and the solid component amount value of the attached filtrate to be filtrated, the membrane filtration resistance value at time ti _{+ 1 was} calculated according to the membrane filtration resistance prediction value calculation formula. Here, the formula (5) was used as a formula for calculating the membrane filtration resistance prediction value.

As the membrane filtration flow rate (flux) predicted value calculation means, the transmembrane differential pressure value and the membrane area value recorded at the time t _{i + 1} recorded in the memory are read, and the read transmembrane differential pressure value and membrane at the time t _{i + 1} are read. Using the area value and the membrane filtration resistance value at time t _{i + 1} calculated by the membrane filtration resistance predicted value calculation means, the membrane filtration flow rate at time t _{i + 1} according to the membrane filtration flow rate (flux) predicted value calculation formula II It was set as the structure which calculates a value. Here, the above formula (1) was used as the membrane filtration flow rate (flux) predicted value calculation formula II.

The membrane filtration resistance value at time t _{i + 1} calculated by the membrane filtration resistance predicted value calculation means and the membrane filtration flow value at time t _{i + 1} calculated by the membrane filtration flow rate (flux) prediction value calculation means are stored in memory. It was set as the structure to record (membrane filtration predicted value recording means).

Moreover, in the membrane filtration test of the activated sludge and the centrifugal supernatant thereof using the membrane filtration test apparatus, the volume of the liquid to be filtered decreases as the filtration continues. Therefore, calculation of the material balance regarding water, a solid component substance, and a supernatant component substance is needed. Therefore, calculating the following equation (14), (15), in accordance with (16), respectively, the filtered liquid volume at time _{t i + 1,} the solid component amount of substance at time _{t i + 1,} the supernatant component material amount at the time _{t i + 1} (Matebara correction value calculation means).

Here, V (t) is the filtrate volume [m ³ ] at time t.

It was also recorded the filtrate volume at time t _{i + 1} to the calculated solid component amount of substance at time t _{i + 1,} the supernatant component material amount at the time t _{i + 1} in the memory.

The component amount calculating means, the materialized correction value calculating means, the membrane filtration resistance predicted value calculating means, and the membrane filtration flow rate (flux) predicted value calculating means are t until the time t _n recorded in advance is reached. _The structure is such that the time is updated according to _{i + 1} = t _i + Δt (where Δt = t _n / n).

The membrane filtration resistance value and the membrane filtration flow rate value recorded at the time t _{0 to} t _n recorded in the membrane filtration predicted value recording means were recorded in the memory as time series values (time series value recording means). Further, using the membrane filtration flow rate value at times t _{0 to} t _n recorded in the memory, the total filtrate amount value per unit membrane area at times t _{0 to} t _n is expressed by the following equation (17) (time t _i the total filtrate volume value per unit membrane area in a unit membrane area at time t ₀ ~t _i the integral membrane filtration flux in the range of) calculated using the calculated time t ₀ ~t _n Data obtained by pairing the total filtrate amount value and the membrane filtration resistance value was recorded in the memory. A structure in which the horizontal axis represents time, the vertical axis represents the membrane filtration flow rate value or the membrane filtration resistance value, or the horizontal axis represents the total filtrate volume value per unit membrane area, and the vertical axis represents the membrane filtration resistance value. It was.

Here, v (t) is the total filtrate amount value [m] per unit membrane area at time t.

In order to reproduce the results of the membrane filtration test using the membrane filtration prediction program, first, the MLSS concentration of activated sludge, the TOC concentration of the centrifugal supernatant, and the TOC concentration of the membrane permeate were measured. Here, the solid component substance amount X was calculated by multiplying the MLSS measurement value by 60/113, assuming that the characteristic formula is C ₅ H ₇ O ₂ N. Further, the amount P of the supernatant component substance was calculated by subtracting the TOC concentration of the membrane permeate from the TOC concentration of the centrifuged supernatant. as a result,
X = 6.84 × 10 ³ [gC / m ³ ]
P = 289 [gC / m ³ ]
Met.

First, the result of the membrane filtration test using the centrifugal supernatant was predicted.
Here, since the centrifugal supernatant does not contain a solid component, the solid component substance amount value at time zero is X (0) = 0, and the solid component substance amount value adhering to the separation membrane is Xm (0) = 0. It was. As a result, the membrane filtration prediction program can be modified to include only the supernatant component without including the solid component.

Also, the supernatant component substance amount value P (0) = 289 at time zero, the supernatant component substance amount value Pm (0) = 0 attached to the separation membrane, and the membrane filtration resistance initial value Rm = 8.5 × 10 ¹⁰ , membrane cleaning power value τ = 10 (constant value), membrane filtrate viscosity μ = 1.0 × 10 ⁻³ , transmembrane pressure difference value ΔP = 20 × 10 ³ were input. In addition, a resistance coefficient αp, a peeling coefficient γp, and a friction coefficient λp were input as parameters necessary for the membrane filtration program, and a membrane filtration prediction result was output. And the said membrane filtration prediction was repeatedly performed changing resistance coefficient (alpha) p, peeling coefficient (gamma) p, and friction coefficient (lambda) p so that the difference of a measured value and a membrane filtration prediction result might become the minimum. As a result, when the resistance coefficient αp = 940 × 10 ¹⁰ , the peeling coefficient γp = 5.4 × 10 ² , and the friction coefficient λp = 4.2 × 10 ⁻⁵ , the actual measurement value and the membrane filtration prediction result were minimized. . The membrane filtration prediction result and the actual measurement result at this time are shown in FIG. Thus, the membrane filtration prediction result is very similar to the actual measurement result, indicating that the membrane filtration prediction can be realized with high accuracy.

  Next, the results of the membrane filtration test using sludge were predicted.

The supernatant component substance amount value P (0) = 289 at time zero, the solid component substance amount value X (0) = 6.84 × 10 ^{3 at} time zero, and the supernatant component substance amount value Pm attached to the separation membrane (0) = 0, solid component substance amount value Xm (0) = 0 attached to the separation membrane, membrane filtration resistance initial value Rm = 8.5 × 10 ¹⁰ , membrane cleaning power value τ = 10 (constant value) Membrane filtrate viscosity μ = 1.0 × 10 ⁻³ and transmembrane pressure difference ΔP = 20 × 10 ³ were input. As the parameters determined above, the resistance coefficient αp = 940 × 10 ¹⁰ , the peeling coefficient γp = 5.4 × 10 ² , and the friction coefficient λp = 4.2 × 10 ⁻⁵ were input. In addition, a resistance coefficient αx, a peeling coefficient γx, and a friction coefficient λx were input as parameters necessary for the membrane filtration program, and a membrane filtration prediction result was output. And the said membrane filtration prediction was repeatedly performed changing resistance coefficient (alpha) x, peeling coefficient (gamma) x, and friction coefficient (lambda) x so that the difference of a measured value and a membrane filtration prediction result might become the minimum. As a result, when the resistance coefficient αx = 20 × 10 ¹⁰ , the peeling coefficient γx = 3.3 × 10 ³ , and the friction coefficient λx = 1.1 × 10 ⁻⁵ , the actual measurement value and the membrane filtration prediction result were minimized. . The membrane filtration prediction result and the actual measurement result at this time are shown in FIG. Thus, the membrane filtration prediction result is very similar to the actual measurement result, indicating that the membrane filtration prediction can be realized with high accuracy.

(Example 2)
The membrane filtration result in the following membrane separation apparatus 300 was predicted.

A schematic structure of the membrane separation apparatus 300 is shown in FIG. The membrane separator is a submerged membrane separation activated sludge device (MBR), which is a wastewater treatment device for treating factory wastewater mainly composed of acetic acid. Industrial wastewater containing acetic acid as a main component was intermittently charged into a filtrate storage tank 301 having an average flow rate of 2.3 m ³ / d and an effective capacity of 2.3 m ³ . In the filtrate storage tank 301, activated sludge is stored as the filtrate to be filtrated 304, the separation membrane 302 is immersed in the filtrate to be filtered 304, and an aeration pipe is installed below the separation membrane 302, Air is supplied to the air diffuser from an aeration blower 303 which is a membrane surface cleaning means. In other words, in this device, the air bubbles supplied from the air diffuser come into contact with the membrane surface, and the activated sludge flow due to aeration also occurs at the same time. It becomes. The separation membrane 302 is a flat membrane type microfiltration membrane (effective membrane area 7.8 m ² ) made of PVDF (polyvinylidene fluoride), and the membrane filtrate 305 is obtained by suction from the permeation side.

In the membrane separation apparatus 300, a membrane filtration test apparatus 500 as shown in FIG. 11 was installed using one flat membrane element (effective membrane area 1.3 m ² ) in the separation membrane 302. In addition, the activated sludge 504 which is a to-be-filtered liquid is the same activated sludge as Example 1.

In the membrane filtration test apparatus 500, a separation membrane 502 (effective membrane area 1.3 m ² ) is installed in an activated sludge storage tank 501 that contains activated sludge 504 that is a liquid to be filtered, and an aeration blower 503 is provided on the separation membrane. Is caused by a water head difference ΔH while preventing accumulation of sludge cake on the membrane surface of the separation membrane 502 (while giving membrane cleaning power to the membrane surface) by contacting the air valve supplied from the air through the air diffusion pipe 507 Membrane filtration was performed using the transmembrane pressure as the driving force. Here, the valve 516 was used for switching between the stop and start of the membrane filtration, the membrane filtration flow rate was measured by the flow meter 514, and the measured value of the membrane filtration flow rate was recorded on the recorder 515 at intervals of 1 second. Here, the transmembrane pressure difference in the separation membrane 502 was changed as shown in FIG. 12 by periodically changing the water head difference ΔH and opening and closing the valve 516.

In order to predict the results of the membrane filtration test, the following membrane filtration prediction program was created.
This membrane filtration prediction program is the same as the membrane filtration prediction program described in Example 1 except for the following points.

  In the membrane filtration test apparatus, the amount of the filtrate to be filtered is reduced by the membrane filtration, so that the factory waste water is introduced and the volume of the filtrate to be filtrated is kept almost constant. Therefore, it was determined that the amount of the solid component substance and the amount of the supernatant component substance did not change in the process of membrane filtration, and the material correction value calculation unit was deleted from the membrane filtration prediction program described in Example 1.

  Using the membrane filtration prediction program as described above, a change in the membrane filtration flow value in the membrane filtration test apparatus was predicted.

Since the same sludge and separation membrane as in Example 1 are used, the supernatant component substance amount value P = 289 (constant value) and the solid component substance amount value X = 6.84 × 10 ³ (constant value) of the liquid to be filtered , Initial value Pm (0) = 0 of supernatant component substance adhering to the separation membrane, initial value Xm (0) = 0 of solid component substance adhering to the separation membrane, initial value Rm of membrane filtration resistance = 8.5 × 10 ¹⁰ and the viscosity of the membrane filtrate μ = 1.0 × 10 ⁻³ were input. Moreover, the transmembrane differential pressure change shown in FIG. 12 was input as a data file as the time series value of the transmembrane differential pressure. Further, as the parameters determined above, resistance coefficient αp = 940 × 10 ¹⁰ , αx = 20 × 10 ¹⁰ , peeling coefficient γp = 5.4 × 10 ² , γx = 3.3 × 10 ³ , friction coefficient λp = 4.2 × 10 ⁻⁵ and λx = 1.1 × 10 ⁻⁵ were input. However, regarding the membrane cleaning power value τ, since the situation is different from that in Example 1, a value different from that in Example 1 was input, and a membrane filtration prediction result was output. The membrane filtration flow rate prediction was repeated while changing the membrane cleaning power value τ so that the difference between the actual measurement value and the membrane filtration flow rate prediction result was minimized. As a result, when τ = 16, the actual measurement value and the membrane filtration flow rate prediction result were minimized. FIG. 13 shows the membrane filtration flow rate prediction result and the actual measurement result at this time. Thus, the membrane filtration flow rate prediction result is very similar to the actual measurement result, indicating that the membrane filtration flow rate prediction can be realized with high accuracy.

(Example 3)
The membrane filtration results in the membrane separation apparatus 300 described in Example 2 were predicted.

First, in the input means, a data file prepared in advance with time series data of transmembrane pressure difference ΔP [Pa], activated sludge supernatant component amount P [gC / m ³ ] and solid component amount X [gC / m ³ ]. As entered. The time series change of the transmembrane pressure difference inputted at this time is as shown in FIG. The initial membrane filtration resistance Rm is Rm = 8.5 × 10 ¹⁰ [m ⁻¹ ].
As entered directly from the keyboard. The time-series data is a data set every 2 seconds for 2000 seconds.

  In addition, in this example, each specification value used for performing the above calculation is summarized in Table 2.

  These input time series values and initial values of membrane filtration resistance were stored in the memory in the data recording means.

Next, in the component amount calculation means, the transmembrane pressure difference at time t _i : ΔP (t _i ),
Activated sludge supernatant component substance amount: P (t _i ), solid component substance amount: X (t _i ),
The amount of supernatant component adhering to the separation membrane: P _m (t _i ) and the amount of solid component adhering to the separation membrane: X _m (t _i )
To the next time t _{i + 1} from the membrane adhering supernatant component amount of activated sludge: P _m (t _{i + 1} ) [gC / m ² ] and the membrane adhering solid component amount: X _m (t _{i + 1} ) [gC / m ² ]
The above equations (6) and (7) were used to calculate However, it is as the said (8) Formula and the following (18) Formula.

  The symbols used in the above formula are shown in Table 1. The values of various parameters shown here are as shown in Table 2.

Regarding the right side of the equation (6), the second term represents the amount of the supernatant component adhering to the separation membrane during Δt. The third term expresses the amount of the supernatant component peeled from the separation membrane during Δt. Similarly, for the right side of equation (7), the second term represents the amount of solid components adhering to the separation membrane during Δt. The third term expresses the amount that the solid component peels from the separation membrane during Δt. According to the equations (6) and (7), the amount of supernatant component substance P _m (t _{i + 1} ) of the activated sludge adhering to the separation membrane at time t _{i + 1} and the activated sludge adhering to the separation membrane according to the equation (7) The amount of solid component substance X _m (t _{i + 1} ) was calculated.

Subsequently, in the component amount calculation value recording means, the calculated amount of supernatant component substance P _m (t _{i + 1} ) of activated sludge adhering to the separation membrane and the amount of solid component substance X of activated sludge adhering to the separation membrane _m (t _{i + 1} ) was stored in the memory.

Further, in the membrane filtration resistance calculating means, the amount of supernatant component substance P _m (t _{i + 1} ) of activated sludge adhering to the separation membrane stored in the memory and the solid component substance of activated sludge adhering to the separation membrane The CPU calculates the membrane filtration resistance R (t _{i + 1} ) using the amount X _m (t _{i + 1} ) and the membrane filtration resistance initial value R _m stored in the memory. For this calculation, the above equation (9) is used. Using.

In the membrane filtration predicted value recording means, the calculated membrane filtration resistance R (t _{i + 1} ) was recorded on the memory.

In this program, the above components amount calculating means, component amount calculating value recording means, membrane filtration resistance calculation means, time-series data to 2000 seconds of iterations while updating the time t _i the membranous filtration prediction value recording means, membrane filtration Resistance R (t _i ) (i = 1, 2,..., N) was obtained as a time series value. The obtained time series value of the membrane filtration resistance was recorded in the memory (time series value recording means).

  Next, in the output means, the time-series data of the membrane filtration resistance obtained above was displayed as a graph with time on the horizontal axis and membrane filtration resistance on the vertical axis. The results are shown in FIG.

On the other hand, the transmembrane pressure difference ΔP [kPa] is actually changed intermittently as shown in FIG. 14 using the apparatus shown in FIG. 10, and the amount of the supernatant component substance P [gC / m ³ ] of the activated sludge and the solid component substance are shown. The amount X [gC / m ³ ] is respectively
P = 289 [gC / m ³ ]
X = 6.84 × 10 ³ [gC / m ³ ]
The change in membrane filtration resistance of activated sludge was measured. The results are shown in FIG. 16 in comparison with the membrane filtration resistance predicted by this program. The predicted value of the membrane filtration resistance calculated by this program is similar to the actual measurement value, which indicates that the prediction of the membrane filtration resistance can be realized with high accuracy.

Example 4
The following membrane filtration prediction program was created using numerical calculation software Excel VBA (Visual Basic Applications, manufactured by Microsoft).

First, time-series data of membrane filtration flux, time-series data of supernatant component amount P [gC / m ³ ] and solid component amount X [gC / m ³ ] of the filtrate, and time-series of membrane cleaning power The value is input as a data file prepared in advance, the membrane filtration resistance initial value Rm, the supernatant component substance amount and the solid component amount of the liquid to be filtered attached to the separation membrane, the membrane area value, and The permeated water viscosity value was input directly from the keyboard. The input data and values are recorded in the memory.

  Further, as the formula for calculating the amount of adhering component, the above formula (3) and the above formula (4) are used as the membrane filtration resistance prediction value calculation formula, the above formula (5) is used as the membrane filtration pressure prediction value calculation formula, (1 ), A mathematical formula in which J = Q / A is substituted is recorded in advance.

As component amount calculating means, membrane filtration flux value at time t _i recorded in the memory, the upper Kiyonari component values and solid component quantity value of the filtrate at the time t _i, membrane washing force value at time t _i, and, attached to the separation membrane at the time t _i recorded in the memory by the initial value or below described component amount calculating value recording means supernatant component material amount and the solid component amount of the liquid to-be-filtrated attaching on the separation membrane The supernatant component substance amount value and the solid component amount value of the filtrate to be filtered, and the supernatant component substance amount value of the filtrate to be filtered attached to the separation membrane at time t _{i + 1} using the attached component calculation formula and The solid component amount value was calculated. At this time, the Euler method was used as an integration method.

A structure in which the supernatant component substance amount value and the solid component amount value of the liquid to be filtered adhering to the separation membrane at time t _{i + 1} calculated by the component amount calculating means are recorded in the memory by the component amount calculated value recording means. It was.

As the membrane filtration resistance predicted value calculation means, the membrane filtration resistance initial value recorded in the memory is read out, and the read membrane filtration resistance initial value and the separation membrane at the time t _{i + 1} calculated by the component amount calculation means The membrane filtration resistance value at time t _{i + 1} was calculated using the supernatant component substance amount value and the solid component amount value of the attached liquid to be filtered.

As the transmembrane pressure difference predicted value calculation means, the membrane filtration flux value and membrane area value at time t _{i + 1} recorded in the memory are read out, and the membrane filtration flux value and membrane area value at time t _{i + 1} read out are read out The transmembrane differential pressure value at time t _{i + 1} is calculated using the membrane filtration resistance value at time t _{i + 1} calculated by the membrane filtration resistance predicted value calculation means.

The membrane filtration resistance value at the time t _{i + 1} calculated by the membrane filtration resistance predicted value calculation unit and the transmembrane pressure difference value at the time t _{i + 1} calculated by the transmembrane differential pressure prediction value calculation unit are used as the membrane filtration prediction value. The recording means records in the memory.

The component amount calculating means, said membrane filtration resistance predicted value calculating means, and, the transmembrane pressure predicted value calculating means, until a pre-recorded time _{t n, t i + 1 =} t i + Δt ( where, Delta] t = T _n / n).

The membrane filtration resistance value and the transmembrane pressure value recorded at the time t _{0 to} t _n recorded in the membrane filtration predicted value recording means are recorded in the memory as time series values, the time is plotted on the horizontal axis, and the membrane is plotted on the vertical axis. The differential pressure value or the membrane filtration resistance value was graphed and output.

Using the above membrane filtration prediction program, in the membrane separation device 300 (FIG. 10), a change in transmembrane pressure difference was predicted when intermittent operation of 0.8 m / d for 2 minutes and filtration stop for 2 minutes was performed. . FIG. 17 shows the change in transmembrane pressure difference when membrane filtration is performed under the same conditions. In addition, as numerical values necessary for predicting the change in transmembrane pressure difference, the supernatant component substance amount value P = 289 (constant value) of the liquid to be filtered and the solid component substance amount value X = 6.84 × 10 ³ ( Constant value), initial value Pm (0) = 0 of the amount of supernatant component substance adhering to the separation membrane, initial value Xm (0) = 0 of the amount of solid component substance adhering to the separation membrane, membrane filtration resistance Initial value Rm = 8.5 × 10 ¹⁰ , membrane filtrate viscosity μ = 1.0 × 10 ⁻³ , transmembrane pressure difference ΔP = 20 × 10 ³ were input. Further, as the parameters determined above, resistance coefficient αp = 940 × 10 ¹⁰ , αx = 20 × 10 ¹⁰ , peeling coefficient γp = 5.4 × 10 ² , γx = 3.3 × 10 ³ , friction coefficient λp = 4.2 × 10 ⁻⁵ , λx = 1.1 × 10 ⁻⁵ , and membrane cleaning power τ = 16 were input. In FIG. 17, the predicted transmembrane pressure value calculated by this program is similar to the actual measurement value, which indicates that the prediction of transmembrane pressure difference can be realized with high accuracy.

  The present invention can be applied not only to the membrane resistance prediction of a filtration device but also to a membrane clogging alarm device, a filtration flow rate prediction device, and the like, and its application range is not limited to these. The prediction of membrane filtration according to the present invention is suitable when an aqueous liquid in which suspended substances are mixed in water is used as the liquid to be filtered, but suspended substances are mixed in liquid substances other than water. The present invention can also be applied to a case where a mixed liquid is used as a liquid to be filtered.

It is an example of the flowchart of the prediction method of this invention. It is another example of the flowchart of the prediction method of this invention. It is a block diagram which shows the hardware constitutions of the membrane filtration resistance prediction apparatus which consists of embodiment of this invention. It is an example of the flowchart of the membrane filtration prediction program of this invention. It is another example of the flowchart of the membrane filtration prediction program of this invention. It is another example of the flowchart of the membrane filtration prediction program of this invention. It is the schematic of the membrane filtration test apparatus 400 to which the membrane filtration prediction method and program of this invention are applied. It is the predicted value and measured value of membrane filtration resistance at the time of carrying out membrane filtration of the centrifugation supernatant. It is the predicted value and measured value of membrane filtration resistance at the time of membrane filtration of activated sludge. It is the schematic of the membrane separator 300 to which the membrane filtration prediction method and program of this invention are applied. It is the schematic of the membrane filtration test apparatus 500 to which the membrane filtration prediction method and program of this invention are applied. It is a figure showing the time series data of transmembrane differential pressure. It is a figure showing the membrane filtration flow volume predicted value time series data obtained by the membrane filtration prediction program of the present invention. It is a figure showing the time series data of transmembrane differential pressure. It is a figure showing the membrane filtration resistance prediction value time series data obtained by the membrane filtration prediction program of the present invention. It is the figure which compared the membrane filtration resistance prediction value time series data obtained by the membrane filtration prediction program of this invention, and the measured value. It is the figure which compared the transmembrane differential pressure prediction value time series data obtained by the membrane filtration prediction program of this invention, and the measured value.

Explanation of symbols

1: Computer 2: Auxiliary storage device 3: Input device 4: Display device 300: Membrane separation device 301: Filtration liquid storage tank 302: Separation membrane 303: Aeration blower 304: Filtration liquid 305: Membrane filtration solution 400: Membrane filtration Test apparatus 401: Stirring cell 402: Separation membrane 403: Magnetic stirrer 404: Stirring bar 405: Nitrogen gas 406: Membrane fixing holder 407: Beaker 408: Electronic balance 409: Personal computer 410: Pure water chamber 411: Pressure gauge 412: Valve 413: Valve 414: Valve 500: Membrane filtration test device 501: Activated sludge storage tank 502: Separation membrane 503: Aeration blower 504: Activated sludge 506: Factory drainage 507: Aeration pipe 514: Flow meter 515: Recorder 516: Valve

Claims (7)

In a membrane filtration method in which the filtrate is filtered through a separation membrane using the pressure difference between the filtrate side and the permeate side of the separation membrane (hereinafter referred to as the transmembrane pressure difference) as the driving force, the membrane filtration flow rate (flux) is A membrane filtration prediction method for predicting a change over time in membrane filtration resistance and / or a change over time in transmembrane pressure difference when membrane filtration is continued while controlling to a set value,
As numerical values for the membrane filtration prediction calculation, at least the setting value of the membrane filtration flow rate (flux), the initial value of the membrane filtration resistance, the supernatant component substance amount value and / or the solid component substance amount value of the liquid to be filtered Using
Obtaining a membrane filtration resistance value and / or a transmembrane pressure value at an arbitrary time by performing at least the following calculation step 1 and calculation step 2 and / or calculation step 3;
(Calculation step 1) Calculate the supernatant component substance amount value and / or the solid component substance amount value of the liquid to be filtered adhering to the separation membrane at an arbitrary time,
(Calculation step 2) At least the membrane filtration resistance value at any time using the supernatant component substance amount value and / or solid component substance amount value of the liquid to be filtered adhering to the separation membrane obtained in calculation step 1 To calculate,
(Calculation step 3) At least using the supernatant component substance amount value and / or the solid component substance amount value of the liquid to be filtered adhering to the separation membrane obtained in calculation step 1 or obtained in calculation step 2 Using the membrane filtration resistance value, calculate the transmembrane pressure difference value at any time,
Furthermore, by repeatedly performing the calculation step while updating the time, to determine the change over time of the membrane filtration resistance and / or the change over time of the transmembrane pressure difference,
The calculation step 1 is a calculation step based on an amount of change in a supernatant component substance amount and / or a solid component substance amount of a liquid to be filtered adhering to a separation membrane within a predetermined time,
The calculation formula in calculation step 1 includes a term of a rate at which the supernatant component and / or solid component of the filtrate to be attached to the separation membrane, and a supernatant component of the filtrate to be filtered attached to the separation membrane and / or Or a term of the rate at which the solid component peels from the separation membrane,
The rate of adhering to the separation membrane is calculated using the transmembrane pressure difference value or the membrane filtration flow rate (flux) value, the supernatant component substance amount value and / or the solid component substance amount value of the liquid to be filtered, And,
The separation rate from the separation membrane includes the transmembrane pressure value or the membrane filtration flow rate (flux) value, the supernatant component substance amount value and / or the solid component substance amount value of the liquid to be filtered attached to the separation membrane. membrane filtration prediction method characterized in that it is calculated using a secondary function number. In the membrane filtration method of filtering the filtrate to be filtered through the separation membrane using the pressure difference between the filtrate side and the permeate side of the separation membrane (hereinafter referred to as the transmembrane pressure difference) as the driving force, the transmembrane pressure difference is set to the set value. A membrane filtration prediction method for predicting a temporal change in membrane filtration resistance and / or a temporal change in membrane filtration flow rate (flux) when continuing membrane filtration while controlling,
Use at least the setting value of the transmembrane pressure difference, the initial value of the membrane filtration resistance, and the supernatant component substance amount value and / or the solid component substance amount value of the liquid to be filtered as numerical values for the membrane filtration prediction calculation. ,
At least calculating the membrane filtration resistance value and / or the membrane filtration flow rate (flux) at an arbitrary time by performing the following calculation step 1 and calculation step 2 and / or calculation step 4;
(Calculation step 1) Calculate the supernatant component substance amount value and / or the solid component substance amount value of the liquid to be filtered adhering to the separation membrane at an arbitrary time,
(Calculation step 2) At least the membrane filtration resistance value at any time using the supernatant component substance amount value and / or solid component substance amount value of the liquid to be filtered adhering to the separation membrane obtained in calculation step 1 To calculate,
(Calculation step 4) At least using the supernatant component substance amount value and / or solid component substance amount value membrane of the liquid to be filtered adhering to the separation membrane obtained in calculation step 1 or obtaining in calculation step 2 The membrane filtration flow rate (flux) value at an arbitrary time is calculated using the membrane filtration resistance value.
Furthermore, by repeatedly performing the calculation step while updating the time, obtain the change over time of the membrane filtration resistance and / or change over time of the membrane filtration flow rate (flux),
The calculation step 1 is a calculation step based on an amount of change in a supernatant component substance amount and / or a solid component substance amount of a liquid to be filtered adhering to a separation membrane within a predetermined time,
The calculation formula in calculation step 1 includes a term of a rate at which the supernatant component and / or solid component of the filtrate to be attached to the separation membrane, and a supernatant component of the filtrate to be filtered attached to the separation membrane and / or Or a term of the rate at which the solid component peels from the separation membrane,
The rate of adhering to the separation membrane is calculated using the transmembrane pressure difference value or the membrane filtration flow rate (flux) value, the supernatant component substance amount value and / or the solid component substance amount value of the liquid to be filtered, And,
The separation rate from the separation membrane includes the transmembrane pressure value or the membrane filtration flow rate (flux) value, the supernatant component substance amount value and / or the solid component substance amount value of the liquid to be filtered attached to the separation membrane. membrane filtration prediction method characterized in that it is calculated using a secondary function number. The calculation formula in the calculation step 1 is:
The rate at which the supernatant component substance in the filtrate to be filtered is calculated based on the transmembrane pressure difference or the membrane filtration flow rate (flux) and the amount of the supernatant component substance in the filtrate, and the membrane The difference between the differential pressure value or the membrane filtration flow rate (flux) and the rate of separation of the supernatant component material from the separation membrane calculated based on the amount of the supernatant component material and the solid component material adhering to the separation membrane Including a calculation formula for calculating the amount of the supernatant component substance of the liquid to be filtered adhering to the separation membrane after a predetermined time, and
The rate at which the solid components in the filtered liquid adhere to the separation membrane calculated based on the transmembrane differential pressure value or membrane filtration flow rate (flux) and the amount of solid component substances in the filtered liquid, and the transmembrane differential pressure Based on the difference between the value or the membrane filtration flow rate (flux) and the rate of separation of the solid component from the separation membrane calculated based on the amount of the supernatant component substance and the amount of the solid component substance adhering to the separation membrane The method for predicting membrane filtration according to claim 1 or 2, comprising a calculation formula for calculating a solid component substance amount of the liquid to be filtered adhering to the separation membrane after time. 2. The formula for determining the rate at which the supernatant component and / or solid component of the liquid to be filtered adhering to the separation membrane peels from the separation membrane includes a term based on the membrane detergency value. The membrane filtration prediction method according to any one of? The membrane filtration prediction method according to claim 1, wherein the liquid to be filtered is a mixed liquid containing microorganisms. When the filtration of the liquid to be filtered through the separation membrane is continued while controlling the transmembrane pressure difference to the set value, the change in the membrane filtration resistance with time and / or the membrane filtration flow rate (flux) value A computer program for predicting temporal changes,
Time-series value of transmembrane pressure difference, time-series value of supernatant component substance amount and / or solid-component substance amount of filtrate to be filtered, time-series value of membrane detergency, membrane adherence attached to separation membrane Data input means for inputting the initial value of the amount of supernatant component substance and / or the amount of solid component substance of the filtrate and the initial value of membrane filtration resistance,
Time-series value of transmembrane pressure input by the data input means, time-series value of supernatant component substance amount and / or solid-component substance amount of filtered liquid, time-series value of membrane detergency, Data recording means for recording the initial value of the amount of supernatant component substance and / or the amount of solid component substance of the liquid to be filtered adhering to the separation membrane, and the initial value of membrane filtration resistance;
The transmembrane pressure difference value at an arbitrary time t _i (where i = 0 to n, t _{i + 1} = t _i + Δt _i , t ₀ = 0, n is a natural number representing the number of steps) from the data recording means. , supernatant component substance quantity value and / or solid components substance quantity value of the filtrate, membrane washing force value, and the supernatant component substances of the liquid to-be-filtrated attaching on the separation membrane in the case of the time t ₀ and / or reads the initial value of the solid component amount of substance, furthermore, in the case other than the time t ₀ attaching on the separation membrane at the time t _i recorded in the data recording means by component amount calculating value recording unit described later The supernatant component substance amount value and / or the solid component substance amount value of the filtrate to be filtered is read out, and the filtrate to be filtered attached to the separation membrane at time t _{i + 1} is recorded using a pre-recorded adhesion component quantity calculation formula. Calculate supernatant component substance amount value and / or solid component substance amount value Component amount calculating means,
Component amount calculation value recording means for recording the supernatant component substance amount value and / or the solid component substance amount value of the liquid to be filtered adhering to the separation membrane at time t _{i + 1} calculated by the component amount calculation means,
Next membrane filtration resistance calculation means and / or membrane filtration flow rate (flux) calculation means (membrane filtration resistance calculation means) Read the membrane filtration resistance initial value from the data recording means, and read the membrane filtration resistance initial value and components Based on the non-membrane permeable substance amount value and / or the solid component substance amount value in the supernatant component of the liquid to be filtered adhering to the separation membrane at time t _{i + 1} calculated by the amount calculating means, the membrane filtration recorded in advance Membrane filtration resistance calculating means for calculating the predicted value of the membrane filtration resistance at time t _{i + 1} using the resistance predicted value calculation formula,
(Membrane filtration flow rate (flux) calculation means) The membrane filtration resistance initial value and the transmembrane differential pressure value at time ti _{+ 1} are read from the data recording means, and the read membrane filtration resistance initial value and the membrane at time ti _{+ 1} . Based on the differential pressure value and the supernatant component substance amount value and / or solid component substance amount value of the liquid to be filtered adhering to the separation membrane at time t _{i + 1} calculated by the component amount calculation means, recorded in advance Membrane filtration flow rate (flux) calculation means I for calculating a predicted value of membrane filtration flow rate (flux) at time t _{i + 1} using a membrane filtration flow rate (flux) predicted value calculation formula I, or the data recording means The transmembrane pressure difference value at time t _{i + 1} is read out from time t _{i + 1} , based on the read transmembrane pressure difference value at time t _{i + 1 and} the membrane filtration resistance prediction value at time t _{i + 1} calculated by the membrane filtration resistance calculation means. Record in advance Membrane using a filtration flow rate (flux) predicted value calculation formula II, the time t membranous filtration flowrate (flux) for calculating a predicted value of the _{i + 1} membrane filtration in flow rate (flux) calculation means II,
The predicted value of the membrane filtration resistance at time t _{i + 1} calculated by the membrane filtration resistance calculation means and / or the membrane filtration flow rate (flux) at time t _{i + 1} calculated by the membrane filtration flow rate (flux) calculation means. Membrane filtration predicted value recording means for recording the predicted value of
Time-series value recording means for recording the predicted value of the membrane filtration resistance and / or the predicted value of the membrane filtration flow rate (flux) at the times t _{0 to} t _n recorded by the membrane filtration predicted value recording means as time-series values; And
Output means for outputting the time series value of the membrane filtration resistance prediction value and / or the time series value of the membrane filtration flow rate (flux) prediction value recorded by the time series value recording means;
With the features of
The pre-recorded formula for calculating the amount of adhering component is the value of the amount of the supernatant component substance and / or the amount of the solid component substance adhering to the separation membrane at time _i and the adhering amount from time t _i. based on the amount of change and that change in increase and decrease by time t _{i + 1,} there at time t _{i + 1} at attachment component value calculation formula for obtaining the supernatant component material amount and / or solid components substance amount of the filtrated liquid adhering to the separation membrane And
The amount of change from the time t _i to the time t _{i + 1} in said adhesion component value calculation formula is, the speed supernatant components thereof and / or the solid components of the filtrate are adhered to the separation membrane, attached to the separation membrane Calculated based on the difference from the rate at which the supernatant component and / or solid component of the liquid to be filtered peels from the separation membrane,
The rate at which adhere to the separation membrane, transmembrane pressure value or membrane filtration flow rate (flux) value at time t _i and the supernatant component substance quantity value of the filtrate at the time t _i and / or solid components substance amount Calculated with the value, and
The rate at which detaches from the separation membrane, transmembrane pressure value or membrane filtration flow rate (flux) value at time t _i and the supernatant component substance quantity value of the filtrated liquid adhering to the separation membrane at time t _i and / or membrane filtration prediction program characterized by being calculated by using the solid component substance quantity value secondary function. When the filtration of the liquid to be filtered by the separation membrane is continued while controlling the membrane filtration flow rate (flux) to the set value, the change in the membrane filtration resistance value that changes with time and / or the transmembrane pressure difference value A computer program for predicting temporal changes,
The time series value of membrane filtration flow rate (flux), the time series value of the amount of supernatant component substance and / or the amount of solid component substance in the liquid to be filtered, the time series value of membrane detergency, attached to the separation membrane Data input means for inputting the initial value of the amount of the supernatant component and / or the amount of the solid component of the liquid to be filtered and the initial value of the membrane filtration resistance,
Time-series value of membrane filtration flow rate (flux) input by the data input means, time-series value of supernatant component substance amount and / or solid-component substance amount of filtered liquid, and membrane cleaning power Data recording means for recording the series value, the initial value of the amount of the supernatant component substance and / or the amount of the solid component substance of the filtered liquid adhering to the separation membrane, and the initial value of the membrane filtration resistance,
Membrane filtration flow rate (flow) from the data recording means at an arbitrary time t _i (where i = 0 to n, t _{i + 1} = t _i + Δt _i , t ₀ = 0, n is a natural number representing the number of steps). flux) value, the supernatant component substance quantity value and / or solid components substance quantity value of the filtrate, membrane washing force value, and, in the case of time t ₀ is of the filtrate adhering to the separation membrane supernatant reads the initial value of the component substance amount and / or solid components substance amount, further, in the case other than the time t ₀ on the separation membrane at the time t _i recorded in the data recording means by component amount calculating value recording unit described later The supernatant component substance amount value and / or the solid component substance amount value of the attached liquid to be filtered is read, and the attached substance adhering to the separation membrane at time t _{i + 1} is calculated using a pre-recorded attached component amount calculation formula. The amount of the supernatant component in the filtrate and / or the amount of the solid component Component amount calculating means for calculating a value;
Component amount calculation value recording means for recording the supernatant component substance amount value and / or the solid component substance amount value of the liquid to be filtered adhering to the separation membrane at time t _{i + 1} calculated by the component amount calculation means,
Next membrane filtration resistance calculation means and / or transmembrane differential pressure calculation means (membrane filtration resistance calculation means) Read the membrane filtration resistance initial value from the data recording means, and read the membrane filtration resistance initial value and component amount calculation means Based on the non-membrane permeable substance amount value and / or the solid component substance amount value in the supernatant component of the filtrate to be filtered adhering to the separation membrane calculated at time t _{i + 1,} the membrane filtration resistance prediction value recorded in advance Membrane filtration resistance calculation means for calculating the predicted value of the membrane filtration resistance at time t _{i + 1} using the calculation formula,
(Transmembrane differential pressure calculation means) The membrane filtration resistance initial value and the membrane filtration flow rate (flux) value at time t _{i + 1} are read from the data recording means, and the read membrane filtration resistance initial value and membrane filtration at time t _{i + 1} . Based on the flow rate (flux) value and the supernatant component substance amount value and / or solid component substance amount value of the liquid to be filtered adhering to the separation membrane at time t _{i + 1} calculated by the component amount calculation means, in advance Using the recorded transmembrane differential pressure predicted value calculation formula I, the transmembrane differential pressure calculating means I for calculating the predicted value of the transmembrane differential pressure at time t _{i + 1} , or the membrane at time t _{i + 1} from the data recording means reads the filtration flow rate (flux) value, the basis of the membrane filtration flow rate (flux) value at time t _{i + 1} read, and membrane filtration resistance prediction value at time t _{i + 1} calculated by the membrane filtration resistance calculation means Record in advance The using transmembrane pressure predicted value calculation formula II, the time t _{i +} transmembrane difference to calculate the predicted value of the transmembrane pressure in the _one pressure calculating means II,
The predicted value of the membrane filtration resistance at the time t _{i + 1} calculated by the membrane filtration resistance calculation unit and / or the predicted value of the transmembrane pressure difference at the time t _{i + 1} calculated by the transmembrane pressure difference calculation unit is recorded. Membrane filtration predicted value recording means,
A time series value recording means for recording the predicted value of the membrane filtration resistance and / or the predicted value of the transmembrane pressure difference at the time t _{0 to} t _n recorded by the membrane filtration predicted value recording means, as a time series value, and
Output means for outputting the time series value of the membrane filtration resistance prediction value and / or the time series value of the transmembrane pressure difference prediction value recorded by the time series value recording means;
With the features of
The pre-recorded formula for calculating the amount of adhering component is the value of the amount of the supernatant component substance and / or the amount of the solid component substance adhering to the separation membrane at time _i and the adhering amount from time t _i. based on the amount of change and that change in increase and decrease by time t _{i + 1,} there at time t _{i + 1} at attachment component value calculation formula for obtaining the supernatant component material amount and / or solid components substance amount of the filtrated liquid adhering to the separation membrane And
The amount of change from the time t _i to the time t _{i + 1} in said adhesion component value calculation formula is, the speed supernatant components thereof and / or the solid components of the filtrate are adhered to the separation membrane, attached to the separation membrane Calculated based on the difference from the rate at which the supernatant component and / or solid component of the liquid to be filtered peels from the separation membrane,
The rate at which adhere to the separation membrane, transmembrane pressure value or membrane filtration flow rate (flux) value at time t _i and the supernatant component substance quantity value of the filtrate at the time t _i and / or solid components substance amount Calculated with the value, and
The rate at which detaches from the separation membrane, transmembrane pressure value or membrane filtration flow rate (flux) value at time t _i and the supernatant component substance quantity value of the filtrated liquid adhering to the separation membrane at time t _i and / or membrane filtration prediction program characterized by being calculated by using the solid component substance quantity value secondary function.

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