WO2010109265A1

WO2010109265A1 - Method and system for online optimization of a membrane filtration process

Info

Publication number: WO2010109265A1
Application number: PCT/IB2009/007703
Authority: WO
Inventors: Senthilmurugan Subbiah; Srinivas Mekapati
Original assignee: Abb Research Ltd
Priority date: 2009-03-27
Filing date: 2009-12-09
Publication date: 2010-09-30

Abstract

A method and system for online optimization of a membrane filtration process is provided. The method includes receiving fouling parameters of a membrane by a mathematical model and providing an objective function from the mathematical model to an optimizer. Further, the method includes optimizing the objective function by manipulating decision variables by the optimizer. The method includes estimating optimal parameters by the optimizer. Further, the method includes rendering the optimal parameters as set points for one or more control variables by the optimizer. The method also includes controlling the membrane filtration process based on the set points with conditions of the membrane as constraints. The system includes a membrane, a transceiver module, and an optimizer. The optimizer further includes an estimating module and a rendering module.

Description

METHOD AND SYSTEM FOR ONLEVE OPTIMIZATION OF A MEMBRANE FILTRATION

PROCESS

FIELD

The present disclosure relates to the field of membrane filtration processes. More particularly, the present disclosure relates to online optimization of a membrane filtration process.

BACKGROUND

Membrane filtration processes or membrane separation technologies are typically used for purification of a solvent, for example water. Reverse osmosis, nano-fϊltration, and ultra-filtration are a few examples of the membrane filtration processes. These membrane filtration processes are pressure driven membrane separation technologies used in various industries, for example desalination, wastewater treatment, and chemical manufacturing. A major application of the membrane filtration process is in process plants for producing potable water from sea or brackish water.

In a typical membrane filtration process, high pressure is applied on the feed side of a membrane to overcome osmotic pressure of solute and cause transport of the solvent from feed side to permeate or product water side, and solute accumulates near the membrane surface. As a result, the concentration of the solute near the membrane surface increases gradually over a period, adversely affecting the performance of the membrane. This phenomenon is called concentration polarization. The concentration polarization is inversely proportional to the feed velocity across the membrane module.

As recovery of the product water increases, the flow velocity across the membrane decreases, causing increased concentration polarization. Product water recovery also depends on other variables like feed concentration, pressure and temperature. Generally, the concentration is measured in terms of total dissolved salts (TDS) in the plant. In process plants, the membrane fouling rate due to concentration polarization is influenced by multiple factors, for example changes in feed concentration, temperature, pressure, and it is difficult for a plant operator to determine the root cause for changing fouling rate in a process plant. Prediction of the changes in the fouling rate will help the plant operators in taking necessary maintenance actions like cleaning the membrane to restore the performance to desired level.

In the process plants, cleaning of the membrane can be carried out in two ways, one when pressure drop between the feed and reject is more than a threshold value, or at predetermined fixed periodic intervals as per recommendation by the membrane manufacturer. In the first method, the membrane can get damaged due to permanent fouling and in the second approach, the cleaning of the membrane is independent of the fouling taking place in the membrane module. Thus, both these methods of membrane cleaning are not satisfactory since the fouling rate changes with time, and is dependent on the feed flow rate, concentration, pressure and temperature.

The methods used in the current scenario are not based on the actual process plant operating conditions and does not account for the time varying nature of the fouling taking place in the membrane. The fouling can be controlled by maintaining lower concentration gradient near the membrane surface. Thus there is a need to develop an online method that can analyze the available plant data in terms of fouling of the membranes and suggest appropriate membrane cleaning schedule to the plant operators to maintain the performance of the process plant. For example maximizing the product flow rate and extending the life of the membrane while maintaining the product quality.

Further, membrane degrades dynamically during operation of the membrane filtration process in the process plant. Hence there is a need to estimate optimal parameters online and implement the same when subjected to constraints of product water quality and life of the membrane. The estimation of optimal parameters is preferably performed with a mathematical model for the RO plant. The mathematical model is designed to be able to predict the RO plant product water flow rate, product water concentration, concentration polymerization near the membrane surface, reject pressure for a given RO plant feed pressure, feed concentration and feed flow rate.

JP2001062255 describes a model that deals with prediction of transportation parameter of a reverse osmotic membrane, the parameter prediction method to predict the operational status of a reverse osmosis membrane plant. The mathematical model used in this invention is based on the combination of solution diffusion model and film theory model.

Several mathematical models are available in literature, for example "Review of reverse osmosis membranes and transport models", Chemical Engg. Comm., 12 (1981) 279 by M. Soltanieh and W. N. Gill, "Modeling of a spiral wound reverse osmosis module and estimation of model parameters using numerical techniques", Desalination, 173 , 269-286, 2005 by S. Senthilmurugan, Aruj Ahluwalia and Sharad K. Gupta, and "Modeling of a radial flow hollow fiber module and estimation of model parameters using numerical techniques", Journal of Membrane Science, 236, 1-16,2004 by Abhijit Chatterjee, Aruj Ahluwalia, S. Senthilmurugan and Sharad K. Gupta. The foregoing mathematical models describe the solute and solvent transport through the membrane. From literature review, it is concluded that the combination of Spiegler-Kedem and film theory models along with mass and momentum balance equations is preferred. Thus, there is a need to include equations for mass and momentum balance for a membrane in a pressure vessel as this would provide improved prediction. As stated earlier, the models such as that used in JP2001062255 has potential for improvement to include mass and momentum balance equations to help further improvement with prediction of transportation parameter of a reverse osmotic membrane and operational status of a reverse osmosis membrane plant.

hi light of the foregoing discussion there is a need for an efficient approach to estimate the optimal parameters for optimizing the membrane filtration process online. A mathematical model which is a combination of Spiegler-Kedem and film theory models along with mass and momentum balance equations for a membrane in a pressure vessel is made use and customized for optimization.

SUMMARY

Embodiments of the present disclosure provide a method and system to estimate optimal parameters for optimizing a membrane filtration process online.

An example of a method of online optimization of a membrane filtration process includes receiving one or more fouling parameters of a membrane by a mathematical model. The method includes providing an objective function from the mathematical model to an optimizer. The method also includes optimizing the objective function by manipulating a plurality of decision variables by the optimizer. The method includes estimating optimal parameters by the optimizer. Further, the method includes rendering the optimal parameters as set points for one or more control variables by the optimizer. Moreover, the method includes controlling the membrane filtration process based on the set points with conditions of the membrane as constraints.

An example of a system for online optimization of a membrane filtration process includes a membrane for performing filtration in the membrane filtration process. The system includes a transceiver module for receiving one or more fouling parameters and providing an objective function from a mathematical model to an optimizer. The system further includes an optimizer for optimizing the objective function by manipulating a plurality of decision variables. The optimizer includes an estimating module for estimating optimal parameters. The optimizer further includes a rendering module for rendering the optimal parameters as set points for one or more control variables to one or more controllers.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an online optimization system implemented for a membrane filtration process, in accordance with which various embodiments can be implemented; FIG. 2 is a block diagram of an online optimization system implemented for a membrane filtration process, in accordance with one embodiment;

FIG. 3 is a block diagram of a mathematical model used in an optimizer, in accordance with one embodiment;

FIGS. 4A-4B are an exemplary illustration of the trend of fouling parameters; and

FIG. 5 illustrates a method of online optimization of a membrane filtration process.

DETAILED DESCRIPTION

It should be observed that method steps and system components have been represented by conventional symbols in the figures, showing only specific details that are relevant for an understanding of the present disclosure. Further, details that may be readily apparent to person ordinarily skilled in the art may not have been disclosed. In the present disclosure, relational terms, for example, first and second, and the like, may be used to distinguish one entity from another entity, without necessarily implying any actual relationship or order between such entities.

Embodiments of the present disclosure provide a method and system for estimating optimal parameters to optimize a membrane filtration process online.

FIG. 1 is a block diagram of an online optimization system 100 implemented for a membrane filtration process, in accordance with which various embodiments can be implemented. The membrane filtration process is a filtration process used for removal of solute from solvent, for example salt water, and is performed via a membrane. Examples of the membrane filtration process can typically include, but is not limited to reverse osmosis, nano-filtration, and ultra-filtration. Examples of the membrane include, but are not limited to thin film composite membranes. The material of the membrane can be, for example polyimide. The process plant accepts a feed, for example sea water or brackish water that has to be purified to produce product water or permeate, for example pure water. The membrane filtration process further produces waste after filtration, herein referred to as reject.

In some embodiments, the process plant includes a plurality of trains, each train has a plurality of pressure vessels connected in parallel, and each pressure vessel has two or more membranes connected in series. The flow configuration in a train can be either reverse flow or parallel flow. The pressure vessels in the train can be S-type or U-type configuration. Temperature of feed can be determined using a temperature sensor 102 in the process plant. In an embodiment, the process plant can also include a plurality of temperature sensors. Total dissolved solids (TDS) of the feed and product water can be measured by a plurality of TDS sensors, 105A and 105B, present in the process plant. The more minerals dissolved into the water, the higher is the TDS. The TDS sensors, 105A and 105B are also referred to as conductivity meters (CM). The process plant includes a plurality of pressure sensors, HOA and HOB, for evaluating feed pressure and reject pressure. The pressure sensors, HOA and HOB, are denoted as PI. A high pressure pump 115 can be used for pumping the feed to a membrane filtration process module 120 at variable speeds using a variable frequency drive. The membrane filtration process module 120 in the process plant performs the filtration. The membrane filtration process module 120 includes the membrane. The membrane filtration process module 120 can be of different configurations, for example hollow fiber (HF) module, spiral wound (SW) module, plate and frame module, and tubular module.

The process plant also includes a plurality of flow meters, 125A and 125B, for determining product water flow rate 130 and reject water flow rate 135. The flow meters, 125A and 125B, are denoted as FM. The product water flow rate 130 is the flow rate of the product water whereas the reject water flow rate 135 is the flow rate of the reject. The product water flow rate 130 is represented as Q_P and the reject water flow rate 135 is represented as Q_R. The process plant includes an energy recovery device 140 for controlling the reject water flow rate. A reject valve can also be used in place of the energy recovery device 140. The use of the energy recovery device 140 enables recovery of energy from the reject whereas the reject valve only controls the flow of the reject and does not recover any energy. The online optimization system 100 also includes a plurality of first level controllers herein referred to as controllers, 145A and 145B, for controlling one or more control variables. The control variables include feed pressure P_F and the reject water flow rate Q_R. The controllers, 145A and 145B, also provide one or more manipulated variables to the high pressure pump 115 and the energy recovery device 140 or the reject valve.

The online optimization system 100 includes a distributed control system (DCS) for collecting plant data. The plant data includes, but is not limited to data of the TDS sensors 105A and 105B, the pressure sensors, HOA and HOB, the flow meters 125A and 125B, the variable frequency drive of the high pressure pump 115, and the energy recovery device 140 or the reject valve. Further, the online optimization system 100 includes a second level controller herein referred to as an optimizer 155. The online optimization system 100 further includes a mathematical model 160. In an embodiment, the optimizer 155 can include the mathematical model 160. In another embodiment, both the optimizer 155 and the mathematical model 160 can function as either separate unit independent of the DCS or can be included within the DCS. The plant data is transmitted from the DCS to the optimizer 155. The optimizer further sends the plant data to the mathematical model 160.

The optimizer 155 determines optimal parameters for the control variables. The optimal parameters include product water flow rate, product water TDS, feed water flow rate, feed water pressure, reject water flow rate, and membrane life. The optimizer 155 optimizes an objective function by manipulating decision variables subjected to the constraints. The optimal parameters include the objective function, the decision variables and the constraints. For example maximizing the objective function, for example product water flow rate, by manipulating decision variables, for example feed flow rate or reject water flow rate and feed water pressure, subjected to the constraints on product water TDS and membrane life. The optimizer 155 further renders the optimal parameters as set points to the controllers, 145A and 145B. Two way communications occurs between the optimizer 155 and the mathematical model 160 of the membrane filtration process. The optimizer 155 sends the decision variables to the mathematical model 160. The mathematical model 160 sends the objective function values to the optimizer 155. The mathematical model 160 includes model equations or a simple correlation based model along with fouling parameters 165 that change dynamically during the process plant operation. The fouling parameters 165 include, but are not limited to hydrodynamic permeability of the membrane (A), solute permeability (Pm), and reflection coefficient of the membrane (σ).The constraints can also include parameters related to fouling parameters 165.

In some embodiments, the objective function can be a profit function derived from the optimal parameters. For example, the profit function is formulated as given below:

Profit function = (Product water flow rate x cost of product water) - (reject water flow rate x pre- treatment cost) - membrane maintenance cost. The objective function can also include cost function, the product water flow rate and the product water TDS.

In some embodiments, the optimizer 155 determines the optimal parameters by optimizing the objective function value. The optimizer 155 also maintains product water quality and life of the membrane.

In some embodiments, the mathematical model 160 is capable of predicting dynamic degradation of the membrane.

FIG. 2 is a block diagram of an online optimization system 100 implemented for a membrane filtration process, in accordance with one embodiment. The online optimization system 100 includes a membrane 205 for performing filtration in the membrane filtration process. A transceiver module 210 in a mathematical model 160 of the online optimization system 100 receives one or more fouling parameters and provides an objective function from the mathematical model 160 to an optimizer 155. The optimizer 155 optimizes the objective function by manipulating a plurality of decision variables. The online optimization system 100 includes an estimating module 215 in the optimizer 155 for estimating optimal parameters. A rendering module 220 in the optimizer 155 renders the optimal parameters as set points for one or more control variables to one or more controllers, 145A and 145B. The objective function and the decision variables are subsets of the optimal parameters. The controllers, 145A and 145B control the membrane filtration process based on the set points.

In some embodiments, the online optimization system 100 further includes a data acquisition module 225 in a distributed control system (DCS) 150 for collecting plant data of a process plant and a transmission module 230 in the DCS 150 for transmitting the plant data to the optimizer 155.

FIG. 3 is a block diagram of the mathematical model 160 used in an optimizer 155, in accordance with one embodiment. The mathematical model 160 can be based on a first principle model or an empirical model or a combination of both. The mathematical model 160 changes depending upon the configuration of the membrane filtration process module 120 used in the process plant, for example the HF module, the SW module, the plate and frame module, or the tubular module. The mathematical models of the HF module and the SW module are given below.

The product water flow rate and solute concentration obtained from a given HF module can be determined by solving a set of equations that describe mass and momentum transfer processes in the HF module. These equations namely, membrane transport model, concentration polarization model, pressure drop, solvent, and solute mass balances are applicable at any point within the membrane. The coupled differential equations can be solved numerically using finite difference method. The following assumptions have been determined during analysis:

• A bulk stream flows radially outward and there is sufficient axial mixing in the bulk stream. This implies that the bulk flow variables are only dependent on r and it allows us to replace the partial derivative terms that appear in the material balance equations and the pressure drop equation with ordinary derivatives.

• The element chosen for the finite difference method within the membrane is much larger than the fiber dimensions. Hence, for all practical purposes shell side of the membrane can be assumed to be a continuous phase.

• Membrane structure is uniform throughout the module. The fouling parameters within the membrane are constant. There is no variation in bulk flow properties of feed stream. Solution contains only one salt and a solvent (binary solution). Film theory is applicable within the membrane module. Fluid properties and diffusivities remain constant inside the module.

By combining membrane transport equation of Spiegler-Kedem model and film theory based concentration polarization model equation,

Product water flux (m³/m².s): J_x, = —

where A is membrane hydrodynamic permeability (m³/m².s.Pa), σ is reflection coefficient of membrane (-), p is density of sea water, P_b and Pp is pressure of feed side bulk stream and product water stream at membrane local point (Pa) , v is vont-hoff factor of solute (-), R_G is gas constant (J-kmol '/K ¹), T is temperature ('K), M_w is molecular weight of solute (kg/kmol), φ is concentration polarization defined by equation (3), C_b is concentration of bulk feed at membrane local point (kg/m³), and F is an intermediate dummy variable which is defined by equation (3).

Product wat (2)

where, φ = (3)

where, P_n, is solute permeability (m/s).

The mass transfer coefficient (k) used in equation (3) can be expressed as a function of the Reynolds and Schmidt numbers. Sh = a R&^b Sc^m (4)

Equations of the same form are used in for estimating the mass transfer coefficients. The values of 'a' and 'b' for the HF module are constants of mass transfer coefficients correlation. The pressure difference across the membrane which is used in equation (1) for obtaining the product water flux varies throughout the membrane because of friction losses. The pressure drop for the product water and bulk streams can be estimated using Hagen-Poiseuille equation and the modified Ergun's equation respectively. These equations are given below: 32/2

Hagen-Poiseuille equation: — P = - dz 2 P (5) d, where v_p is product water velocity (m/s) at inside the fiber bore, d; is inside diameter of hollow fiber (m), μ is viscosity of water (Pa s), z is axial coordinate

The modified Ergun's equation for pressure drop per length of the packed bed at turbulent condition can be written as:

where, v_r is superficial velocity of feed stream (m/s), c, d, e constants used in equation (6)

The material balance equations for both solute and solvent streams within the module are given below:

Product water stream: — v =J_v V~ such that boundary conditions, v =0, 0 < z < L (7) dz d ²N 4θd_n where θ = - C =

D: -A r>- 2 d_; ² L_m

The length of a hollow fiber is given as, L = ^L_n,² + 4(TIrW)² L_n, is length of module (m).

Bulk stream solute concentration: — (rv_r ) = —θ — - (8) dr L z=L subject to boundary conditions (BC), v, r=D, /2 = VL

V_f is velocity of feed at feed header (m/s)

Likewise for the solute,

subject to BC, C_{b r=D}._n = C_F for D/2 < r < D₀ /2 where C_F is feed concentration (kg/m³), Differentiation of equation (5) and subsequent substitution of equation (7) leads to:

where, I₃ is length of epoxy seal (m), P_atm is atmosphere pressure (Pa), The above equations (1) to (9) are solved numerically by the finite difference method with each of the variables being expressed as a discrete value. Since the product water flow variables vary only along the z-axis while the bulk flow terms vary along the r-axis, the equations are solved sequentially by proceeding from r = D,/2 to DJ2 while solving all the z-axis dependent difference equations at a particular radial grid location. The bulk flow terms at r = D,/2 are known; P_b = P_F, C_b = C_F and v_r = v_F.

The product water flow rate and solute concentration obtained from a given SW module can be determined by solving a set of equations that describe mass transfer processes in the SW module. The following assumptions have been determined during analysis:

• Membrane structure is uniform throughout the module. The fouling parameters within the membrane are constant.

• There is no variation in bulk flow properties.

• Solution contains only one salt and a solvent.

• Film theory is applicable within the membrane module.

• Fluid properties remain constant inside the module.

The mass transport equations of membrane will be same for both the HF module and the SW module. Therefore, the equations (1) to (4) are solved with following pressure drop and mass balance equation given below for SW module.

The pressure drop in both the channels is based on the assumption that Darcy's law is applicable. This leads to the following expression for the pressure drops:

Feed Channel: —± ^ k_Jb.μ.U_b (11) dx dP

Product water Channel: — - - k_f .μ.U (12) dy

Where k^ is the friction parameter in the feed channel {\lπ?),k_fp is the friction parameter in the product water channel (1/m²), U_b, U_p is the velocity of the solution in feed and product water channel (m/s) and μ is the viscosity of solution (Pa.s). Here both friction parameters are experimentally determined for a given module, x and y are directions of feed and product water flow when module unwind condition.

The overall material balance for the feed and the product water sides are given by the following equations:

^ = ^{" 2}V (,3) dx / ⁿb dU p _ 2J. (14) dy /A. where, h_b, h_p are thickness of feed and product water side spacer (m).

Similarly the material balance for the solute on the feed side is represented by the following equation:

Differentiating equation (11) with respect to x and substituting equation (13): d²P_b Ik . μj_^

(16) dx² /K with boundary conditions

P_b = P_F at x = 0 and

'^{• ■}'- (£> at x = L

Similarly differentiating equation (12) with respect to y and substituting equation (14): d% _ - 2k_fDμJ_{v /}

(17) dy^{2 / h}- with boundary conditions:

P_p = P_alm at y = w and at y = 0 ,

P_R is reject pressure (Pa), L is length of spiral wound module (m), w = width of module with respect to number of wounds (m).

The above equations are solved using the method of finite differences. The feed flow path (x direction) is divided into m segments while the product water flow path (y direction) is divided into n segments.

By solving above mathematical model equations of the HF module and the SW module, the product water flux, concentration at local points of the membrane filtration process module 120 can be estimated. The overall product water concentration and flow rate can be estimated by following equation: x=m A=Π

^QP = J J -WN* (18) x=0 y=0 x=m x=n

C_pt = j J J_vS_mC_pdydx (19)

X=O y=Q where S_m is surface area of membrane corresponding finite element.

The lists of model parameters used in the mathematical model 160 are:

• Membrane hydrodynamic permeability (A)

• Reflection coefficient of membrane (σ)

• Solute permeability (P_m)

• The constants of mass transfer coefficients correlation (a and b) • The constants of modified Ergun's equation for the HF module(c, d, e) or Darcy's law constant for feed and product water channel for the spiral wound module (k_β,, k_fp).

The mathematical model 160 is used to describe the physical phenomena occurring in the membrane filtration processes. The mathematical model 160 includes the fouling parameters, for example the hydrodynamic permeability, the solute permeability, and the reflection coefficient to characterize fouling of the membrane. These fouling parameters are time varying in nature and are estimated periodically from the plant data, for example flow rate, temperature, pressure, and quality of feed, reject and product water. Analysis of the fouling parameters will indicate the rate of fouling taking place in a membrane, and cleaning of the membrane is recommended whenever the values of these fouling parameters exceed a pre-defined threshold value. The fouling parameters indicate the dynamic degradation of the membrane. FIG. 4A and FIG. 4B provide an exemplary illustration of the trend of fouling parameters. FIG. 4A illustrates the effect of fouling in terms of the hydrodynamic permeability with respect to time and FIG. 4B illustrates the effect of fouling in terms of the solute permeability with respect to time.

The fouling parameters are estimated by minimizing the error between predictions of the mathematical model 160 and plant measurements. The measurements include feed pressure, feed flow rate, feed concentration, feed temperature, product water flow rate, product water concentration, reject water flow rate and reject pressure.

FIG. 5 illustrates a method of online optimization of a membrane filtration process. At step 505, one or more fouling parameters of a membrane are received by a mathematical model. Plant data of a process plant is collected by a DCS. The collected plant data is transmitted to the optimizer for optimization by the DCS. The fouling parameters received by the mathematical model include, but are not limited to hydrodynamic permeability of the membrane (A), solute permeability (Pm), and reflection coefficient of the membrane (σ). The fouling parameters of the membrane change dynamically and provide information in regard to the fouling of the membrane.

hi a process plant, data is collected by a distributed control system (DCS). The process plant performs the membrane filtration process, for example reverse osmosis. A feed is pumped into a membrane filtration process module via a high pressure pump. A temperature sensor determines the temperature of the feed. A TDS sensor measures the TDS in the feed and a pressure sensor measures pressure exerted by the feed. The membrane filtration process module performs filtration and produces reject water and product water. The pressure of the reject is sensed via another pressure sensor and reject water flow rate is measured via a flow meter. The reject water flow rate is controlled by adjusting an energy recovery device or a reject valve. The TDS in the product water is sensed via another TDS sensor and product water flow rate is measured using the flow meter. The DCS then collects this plant data that includes data from the TDS sensors, the pressure sensors, the flow meters, the high pressure pump, and the energy recovery device or the reject valve. The plant data can also include temperature and conductivity of the feed and conductivity of the product water.

hi some embodiments, the mathematical model can be based on a first principle model, an empirical model, and a combination thereof.

The mathematical model can be one of a dynamic model and a steady state model. The dynamic model takes care of membrane degradation with respect to time and the steady state model considers the membrane degradation at a given time.

At step 510, an objective function is provided from the mathematical model to an optimizer. The mathematical model estimates the objective function value and sends it to the optimizer.

At step 515, the objective function is optimized by the optimizer by manipulating a plurality of decision variables. The optimization can be subjected to constraints. For example, consider product water flow rate to be the objective function and product water TDS and membrane life to be the constraints. Then, feed flow rate, reject water flow rate, feed pressure and product water recovery can be considered as the decision variables that are subjected to the constraints, hi one embodiment, the constraints can be an upper bound limit and a lower bound limit of the feed flow rate, the reject water flow rate and the feed pressure.

At step 520, the optimal parameters are estimated by the optimizer. The optimal parameters are estimated by the optimizer by optimizing the objective function. The optimal parameters include product water flow rate, product water TDS, feed water flow rate, feed water pressure, reject water flow rate, and membrane life. The objective function and the plurality of decision variables are subsets of the optimal parameters. The constraints are inputs to the optimizer to help in the estimation of the optimal parameters.

At step 525, the optimal parameters are rendered as set points for one or more control variables by the optimizer. The optimizer estimates and renders the optimal parameters as the set points for control variables, for example feed pressure P_F and the reject water flow rate Q_R.

At step 530, the membrane filtration process is controlled based on the set points with conditions of the membrane as the constraints. The membrane filtration process is also dynamic. The estimated optimal parameters are rendered as set points for control variables. The set points include one or more set points for feed pressure and for reject water flow rate provided to a variable frequency drive of a high pressure pump and to an energy recovery device or the reject valve respectively.

In some embodiments, only one set point is provided either for the feed pressure or for the reject water flow rate. In such cases, the mathematical model also comprises a model for the high pressure pump (when the set point is provided for the feed pressure) or for the energy recovery device/reject valve (when the set point is provided for the reject flow rate) along with the model for the membrane.

The set points are rendered for the control variables based on the estimating of the optimal parameters. The optimizer estimates the optimal parameters by optimizing an objective function, for example product water flow rate or profit function, at the same time maintaining product water quality. The optimizer also maintains life of the membrane during calculation of the optimal parameters. The optimal parameters thus calculated are sent as inputs to the corresponding controllers of the high pressure pump and the energy recovery device or the reject valve.

In some embodiments, the controllers can provide manipulated variables as input to the high pressure pump and the energy recovery device or the reject valve. The manipulated variables are determined based on the set points received. The controlling of the variable frequency drive of the high pressure pump, the energy recovery device or the reject valve in turn controls the membrane filtration process. Membrane degradation is a dynamic process. However, the online optimization of the membrane filtration process in the present disclosure adapts to the dynamic changes in the membrane by optimizing various parameters subjected to constraints. This ensures that the constraints including product water quality and life of the membrane is optimally maintained. The online optimization of the membrane filtration process enables an increase in life of the membrane and throughput. Further, there are savings in cost of production in the process plant due to a decrease in both plant downtime and maintenance of the membrane.

The foregoing description sets forth numerous specific details to convey a thorough understanding of embodiments of the present disclosure. However, it will be apparent to one skilled in the art that embodiments of the present disclosure may be practiced without these specific details. Some well- known features are not described in detail in order to avoid obscuring the present disclosure. Other variations and embodiments are possible in light of above teachings, and it is thus intended that the scope of present disclosure not be limited by this Detailed Description, but only by the Claims.

Claims

IAVe Claim:

1. A method of online optimization of a membrane filtration process, the method comprising: receiving one or more fouling parameters of a membrane by a mathematical model; providing an objective function from the mathematical model to an optimizer; optimizing the objective function by manipulating a plurality of decision variables by the optimizer; estimating optimal parameters by the optimizer; rendering the optimal parameters as one or more set points for one or more control variables by the optimizer; and controlling the membrane filtration process based on the one or more set points with conditions of the membrane as constraints.

2. A system for online optimization of a membrane filtration process, the system comprising: a membrane for performing filtration in the membrane filtration process; a transceiver module for receiving one or more fouling parameters and providing an objective function from a mathematical model to an optimizer; the optimizer for optimizing the objective function by manipulating a plurality of decision variables, the optimizer comprising: an estimating module for estimating optimal parameters; and a rendering module for rendering the optimal parameters as one or more set points for one or more control variables to one or more controllers.

3. The method and the system as claimed in claim 1 and claim 2 respectively, wherein the objective function includes profit function, cost function, product water flow rate and product water total dissolved solids (TDS); the one or more fouling parameters include hydrodynamic permeability, solute permeability, and reflection coefficient; and the constraints include parameters related to life of the membrane and fouling parameters.

4. The method and the system as claimed in claim 1 and claim 2 respectively, wherein the mathematical model is one of a dynamic model and a steady state model; the mathematical model further comprises of one or more models of elements used in filtration process including elements such as pumps, membrane, energy recovery device and reject valve and is based on one of a first principle model, an empirical model and a combination thereof.

5. The method and the system of claim 1 and claim 2 respectively, wherein the one or more set points comprise a set point for feed pressure and/or for reject water flow rate.

6. The method and the system of claim 1 and claim 2 respectively, wherein the fouling parameters of the membrane change dynamically.

7. The method and the system of claiml and claim 2 respectively, wherein the optimizer determines the optimal parameters using one or more of plant data and model output.

8. The system of claim 2, wherein product water quality and life of the membrane is optimally maintained.

9. A system for performing a method, the method as described herein and in accompanying figures.

10. A method of online optimization of a membrane filtration process in a system, the system as described herein and in accompanying figures.