CN101905906B - New calculation method of head loss of city water supply filtering system - Google Patents

Abstract

The invention discloses a calculation method of head loss of a city water supply filtering system, comprising the following steps of: 1, calculating the head loss of filtering layers with different moments and different thicknesses; 2, calculating specific sedimentation rate of the filtering layers with the different thicknesses; 3, establishing relation functions among the specific sedimentation rate of the filtering layers with the different thicknesses, the filtering time of a filtering pool, the water turbidity to be filtered, the thickness of the filtering layers and the filtering velocity; and commonly establishing a data sample space according to the change data of the water turbidity to be filtered and the filtering speed of the filtering pool, which are actually operated at the corresponding moment; 4, identifying and solving filtering coefficients in the relation functions established in the third step; 5, determining the maximum filtering time determined by the head loss; and 6, obtaining the allowed maximum head loss by the maximum filtering time. By using the maximum head loss determined by using the method of the invention as a triggering condition of stopping filtering, the invention can avoid stopping filtering prematurely, bring the optimal state of the filtering pool into play, optimize the filtering process of a water plant, and improve the automatic level of the water plant.

Description

A kind of computational methods of head loss of city water supply filtering system

Technical field

The present invention relates to a kind of automatic technology and plumbing treatment process, particularly a kind of computational methods of head loss of city water supply filtering system.

Background technology

Filtration is a very important link in the water treatment procedure.Along with the carrying out of filtering, impurity is constantly held back by the filter sand in the filtering layer, and the angle of macroscopic view can cause that then the resistance of filtering layer constantly increases, i.e. it is big that the loss of flood peak constantly becomes; And, then be to cause in the filtering layer than the increase of deposition or perhaps constantly reducing of filtering layer voidage from the angle of microcosmic.The loss of flood peak that is produced when calculating water through filtering layer is in the filtered water mechanics one basic contents, also is the most important content of filtering in practice and the theory.Generally speaking, the definite of filter tank maximum filtering time mainly confirmed by the permission index of the delivery turbidity and the loss of flood peak, is maximum filtering time to reach the time of controlling index earlier.But in the actual filtration process; Two kinds of situation can appear; The one, the loss of flood peak does not reach permissible value when occur leaking turbidity, thereby the remaining loss of flood peak do not obtain utilizing, and is to reach maximum when the loss of flood peak in addition on the one hand; But do not occur leaking turbidity, thereby make filtering layer fail to give full play to its filter capacity.Therefore, the optimum condition of work in filter tank is the maximum filtering time confirmed by turbidity and is equated by the maximum filtering time that the loss of flood peak is confirmed.For this reason, be optimized the rule that research must confirm that the filtrate turbidity and the loss of flood peak increase in time to the filter tank.

But for a long time since lack the filtering layer porosity in filter process in time and the reliable theory of varied in thickness; Turbid matter particle is a difficult problem than the definite of deposition change with time always in the filtering layer; Be merely able at present calculate and filter when just having begun; Filtering layer is in the loss of flood peak of clean conditions, and this has influenced the further research that the loss of flood peak is calculated to a great extent, thereby has influenced the research to filter process modeling, simulation and optimization.

In order to solve than the time dependent rule of deposition, thus set up the loss of flood peak in time, the model of change in depth.There are some scholars to propose some equations at present both at home and abroad, wherein most of based on the experience modeling, or only limit to theoretical research, really do not find application in the practice.Some parameters in the middle of the equation do not propose effective setting or method for solving yet.

Scholars more both domestic and external have proposed the computing formula of section dirty filtering layer filtration resistance, but can only be used for breadboard analog machine basically, are used for real production practices process very less.The equation of common calculated water head loss is as shown in table 1.

Table 1 filtration resistance computing formula

At present, in service in actual production, the condition that finishes filter cycle can have three kinds of situation: the one, and setting-up time cycle rule of thumb; The 2nd, filter back water quality does not reach requirement; The 3rd, the loss of flood peak value of reaching capacity.

For preceding two kinds of situation; Utilize the preceding two kinds of patterns shown in the table 1 to control, the water quality of water is qualified after can guaranteeing to filter, and keeps the quality of filter tank water outlet; But first kind of situation tended to waste the retaining power of filtering layer; Filtering layer is not performed to optimal state, and second kind of situation is unfavorable for the maintenance of filter sand, might causes longly cause deposition corruption or caking in the filtering layer filter cycle.And the third situation can avoid filtering layer to produce negative pressure, under the prerequisite that guarantees effluent quality, to give full play to the retaining power of filtering layer.If can make the detection of filter tank operating mode and backwash control play more reasonably effect triplicity.But all do not develop a kind of feasible, relatively more accurate, practical method of calculated water head loss at present both at home and abroad, make and adopt the loss of flood peak to confirm to have some difficulties filter cycle.

Goal of the invention

The object of the present invention is to provide a kind of computational methods of head loss of city water supply filtering system; Through calculating maximum filtering time; The maximum head loss that obtains allowing to realize the modeling and optimization of filter process, improves the operation level of water factory and reaches purpose of energy saving.Loss of flood peak computational methods disclosed by the invention are a kind ofly to combine present domestic scholars about the loss of flood peak with than the theoretical derivation formula of deposition, and the loss of flood peak data of utilizing water factory's actual production to record are carried out parameters identification method to loss of flood peak equation.Like this, operating personnel just can be according to the maximum head of the permission of calculating loss (can be converted into the congestion degree count value that is installed in below the filter tank) as a condition that stops filter cycle.And this condition also can be programmed as one of trigger condition that filter to finish, thus make filter cycle confirm to obtain reasonably optimizing.

For realizing that the object of the invention adopts following technical scheme: a kind of computational methods of head loss of city water supply filtering system, it is characterized in that, comprise the steps:

The first step: measure the different water pressures of the filtering layer of different-thickness constantly in the filtration system, obtain the pressure differential of water, and calculate the different loss of flood peakes of the filtering layer of each corresponding thickness constantly successively from any filtering layer to another filtering layer:

$H_t={\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HSA00000168007100031.png"\; state="\{\{state\}\}">h</figure-callout>}}_0+\frac{v_1^2-v_2^2}{2g}-\frac{\mathrm{\&Delta;p}}{\mathrm{\&rho;g}}---\left(5\right);$

In the formula, H _tBe meant: the loss of flood peak of water from a certain filtering layer to another filtering layer, unit: rice;

h ₀Be meant: the relative altitude of two filtering layers, unit: rice;

v ₁And v ₂Refer to respectively: the rate of filtration of two filtering layers, unit: meter per second, this parameter is a design parameter, preestablishes;

G: acceleration of gravity, unit: m/s ²

Δ P: the pressure differential of water from a certain filtering layer to another filtering layer, unit: Pa;

ρ: the density of water, unit: kg/m ³

Second step:, calculate the ratio deposition of the filtering layer of each corresponding thickness with the different loss of flood peakes of the filtering layer of different-thickness constantly: $\frac{{\mathrm{<figure-callout\; id="0"\; label="H\; t\; H"\; filenames="HSA00000168007100031.png"\; state="\{\{state\}\}">H</figure-callout>}}_t}{H_{}}={\left(\frac{{\mathrm{\&epsiv;}}_0}{{\mathrm{\&epsiv;}}_0-\mathrm{\&sigma;}}\right)}^2---\left(4\right);$

In the formula, H _t: the loss of flood peak of a certain thickness filtering layer of a certain moment, unit: rice;

H ₀: the loss of flood peak of a certain thickness cleaning filtering layer, unit: rice;

ε ₀: cleaning filtering layer porosity; This parameter is a process design parameter, according to the corresponding filtering layer material of this parameter choosing;

σ: filtering layer compares deposition;

The 3rd the step: set up the filtering layer of different-thickness ratio deposition and filter time, treat the relation function between drainage turbidity, thickness of filter bed and the filtering velocity v:

$t=\frac{{\mathrm{\&lambda;}}_{2}v{\mathrm{\&epsiv;}}_0}{{({\mathrm{\&lambda;}}_1{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HSA00000168007100031.png"\; state="\{\{state\}\}">c</figure-callout>}}_0+{\mathrm{\&lambda;}}_{2}v)}^2}\ln \frac{{\mathrm{\&lambda;}}_1{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HSA00000168007100031.png"\; state="\{\{state\}\}">c</figure-callout>}}_0{\mathrm{\&epsiv;}}_0}{{\mathrm{\&lambda;}}_1{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HSA00000168007100031.png"\; state="\{\{state\}\}">c</figure-callout>}}_0{\mathrm{\&epsiv;}}_0-({\mathrm{\&lambda;}}_1{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HSA00000168007100031.png"\; state="\{\{state\}\}">c</figure-callout>}}_0+{\mathrm{\&lambda;}}_{2}v){\mathrm{\&sigma;e}}^{(\frac{{\mathrm{\&lambda;}}_1}{v}-{\mathrm{\&lambda;}}_2)x}}+\frac{{\mathrm{\&sigma;e}}^{(\frac{{\mathrm{\&lambda;}}_1}{v}-{\mathrm{\&lambda;}}_2)x}}{({\mathrm{\&lambda;}}_1{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HSA00000168007100031.png"\; state="\{\{state\}\}">c</figure-callout>}}_0+{\mathrm{\&lambda;}}_{2}v)}---\left(8\right);$

In the formula, t: the filter time, unit: hour;

V: filter speed, unit: m/h;

c ₀: treat the drainage turbidity, unit: NTU;

ε ₀: the porosity of this filtering layer cleaning filtering layer;

σ: the ratio deposition of the filtering layer of this thickness;

X: the thickness of a certain filtering layer, unit: m;

λ ₁And λ ₂: filtration coefficient;

The delta data of treating drainage turbidity, filter speed according to correspondence water factory's actual production operation is constantly set up data sample space jointly;

The 4th step: to the filtration coefficient λ in the function of said formula (8) ₁And λ ₂Carrying out identification finds the solution;

The 5th step: with the solving result substitution formula (8) in the 4th step, with seasonal σ=95% σ _Max, can know that the maximum filtering time of being confirmed by the loss of flood peak does

$T_{\max }=\frac{0.95{\mathrm{\&lambda;}}_1{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HSA00000168007100031.png"\; state="\{\{state\}\}">c</figure-callout>}}_0+3.0{\mathrm{\&lambda;}}_{2}v}{{\mathrm{\&phi;}}^2}{\mathrm{\&epsiv;}}_0---\left(9\right)$

In the formula, T _Max: maximum filtering time, unit: hour;

c ₀: treat the drainage turbidity, unit: NTU;

V: filter speed, unit: m/h;

ε ₀: cleaning filtering layer porosity;

φ：φ＝λ ₁c ₀+λ ₂v；

λ ₁And λ ₂: filtration coefficient;

The 6th step: with said maximum filtering time substitution formula (8) and (4), the maximum head that obtains allowing loss.

Technical scheme is more specifically, measures the different water pressures of the filtering layer of different-thickness constantly in the filtration system in the said first step, is meant to utilize the different water pressures of the filtering layer of different-thickness constantly in the congestion degree instrumentation amount filtration system.

The loss of flood peak H of a certain thickness cleaning filtering layer in said second step ₀Calculate by formula (1) convolution (2):

$\mathrm{\&Delta;}{H}_i=0.0187\mathrm{\&mu;}{\mathrm{\&alpha;}}^2\frac{v{(1-{\mathrm{\&epsiv;}}_0)}^2}{{\mathrm{<figure-callout\; id="0"\; label="d\; e"\; filenames="HSA00000168007100031.png"\; state="\{\{state\}\}">d</figure-callout>}}_e^0{{\mathrm{\&epsiv;}}_0}^3}\mathrm{\&Delta;}{L}_i---\left(1\right)$

$H_0=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;}{H}_i---\left(2\right)$

In the formula, H ₀: the loss of flood peak of a certain thickness cleaning filtering layer, unit: rice;

Δ H _i: be divided into the n five equilibrium to filtering layer, the corresponding loss of flood peak of every five equilibrium, unit: rice;

V: the rate of filtration in filter tank, unit: m/s;

μ: the dynamic viscosity of water, Ns/m ², water temperature approximates 1.006 * 10 in the time of 20 ℃ ^-3Pas;

d _eThe particle diameter of 0 filtrate, unit: mm;

α: form factor, represent the surface area of aspheric particle and the ratio of equal-volume spheric granules surface area;

ε ₀: cleaning filtering layer porosity;

Δ L _i: be divided into Δ L to whole filtering layer ₁, Δ L ₂Δ L _iDeng filtering layer, unit: rice.

Said the 4th the step in to the coefficient lambda in the function of said formula (8) ₁And λ ₂Carry out identification and find the solution, the method with identified parameters of being meant is to the coefficient lambda in the function of said formula (8) ₁And λ ₂Carrying out identification finds the solution.

The method of said identified parameters is meant differential evolution algorithm or nonlinear regression function algorithm.

Design principle of the present invention is such:

1, model is confirmed

(1) confirm the loss of flood peak with than the deposition relation

In filter process, the solid suspension in the water constantly is trapped within the surface of filtering layer, causes the minimizing of filtering layer voidage on the one hand, causes that on the other hand the filtering material particle particle diameter increases, so the voidage of filtering layer and specific area constantly variation in filter process.Domestic scholars has proposed the loss of flood peak H of a certain thickness cleaning filtering layer ₀For:

${\mathrm{\&Delta;H}}_i={0.0187\mathrm{\&mu;\&alpha;}}^2\frac{{v(1-{\mathrm{\&epsiv;}}_0)}^2}{{\mathrm{<figure-callout\; id="0"\; label="d\; e"\; filenames="HSA00000168007100031.png"\; state="\{\{state\}\}">d</figure-callout>}}_e^0{{\mathrm{\&epsiv;}}_0}^3}{\mathrm{\&Delta;L}}_i---\left(1\right)$

${\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="HSA00000168007100031.png"\; state="\{\{state\}\}">H</figure-callout>}}_0=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&Delta;H}}_i---\left(2\right)$

In the formula, H ₀: the loss of flood peak of a certain thickness cleaning filtering layer, unit: rice;

Δ H _i: be divided into the n five equilibrium to filtering layer, the corresponding loss of flood peak of every five equilibrium, unit: rice;

V: the rate of filtration in filter tank, unit: m/s;

μ: the dynamic viscosity of water, Ns/m ², water temperature approximates 1.006 * 10 in the time of 20 ℃ ^-3Pas;

d _e: the particle diameter of filtrate, unit: mm;

α: form factor, represent the surface area of aspheric particle and the ratio of equal-volume spheric granules surface area;

ε ₀: cleaning filtering layer porosity;

Δ L _i: be divided into Δ L to whole filtering layer ₁, Δ L ₂Δ L _iDeng filtering layer, unit: rice.

Along with filtering layer constantly cuts dirt, the porosity ε of filtering layer reaches the varied in thickness of filtering layer in time, from and will cause d _eVariation.At a certain filtering layer, the t loss of flood peak constantly with the ratio of the loss of flood peak of cleaning filtering layer is:

$\frac{\mathrm{\&Delta;}{H}_t}{\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="HSA00000168007100031.png"\; state="\{\{state\}\}">H</figure-callout>}}_0}={\left(\frac{1-\mathrm{\&epsiv;}}{1-{\mathrm{\&epsiv;}}_0}\right)}^2{\left(\frac{{\mathrm{\&epsiv;}}_0}{\mathrm{\&epsiv;}}\right)}^3{\left(\frac{d_{e0}}{d_{\mathrm{et}}}\right)}^2---\left(3\right)$

Wherein, Δ H _t: the loss of flood peak of a certain a certain filtering layer of the moment, unit: rice;

Δ H ₀: the loss of flood peak of a certain thickness cleaning filtering layer, unit: rice;

ε ₀: cleaning filtering layer porosity;

ε: a certain moment filtering layer porosity, ε=ε ₀-σ;

d _Et: equivalent particle size, mm;

σ: filtering layer compares deposition;

According to the filter bed of forming by bulk material that domestic scholars proposes, can regard as and have or not several capillary groups

The tube bank that becomes, current are exactly the flow process of current in these capillary channels through the filter process of filtering layer so, caliber d capillaceous _mWith particle diameter d _eThere is certain relation,

Along with the carrying out of filtering, the capillary caliber will diminish because of holding back turbid matter gradually, so the d under the clean conditions _M0To be reduced to d _MtThereby, can obtain

$\frac{{\mathrm{<figure-callout\; id="0"\; label="H\; t\; H"\; filenames="HSA00000168007100031.png"\; state="\{\{state\}\}">H</figure-callout>}}_t}{H_{}}={\left(\frac{{\mathrm{\&epsiv;}}_0}{{\mathrm{\&epsiv;}}_0-\mathrm{\&sigma;}}\right)}^2---\left(4\right)$

Wherein, H _t: the loss of flood peak of a certain thickness filtering layer of a certain moment, unit: rice;

H ₀: the loss of flood peak of a certain thickness cleaning filtering layer, unit: rice;

ε ₀: cleaning filtering layer porosity;

σ: filtering layer compares deposition;

The loss of flood peak calculating formula that obtains the filtering layer of different-thickness in conjunction with the Bernoulli equation in the hydraulics is:

$H_t={\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HSA00000168007100031.png"\; state="\{\{state\}\}">h</figure-callout>}}_0+\frac{{\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="HSA00000168007100022.png"\; state="\{\{state\}\}">v</figure-callout>}}_1^2-v_2^2}{2g}-\frac{\mathrm{\&Delta;p}}{\mathrm{\&rho;g}}---\left(5\right)$

In the formula, H _tBe meant: the loss of flood peak of water from a certain filtering layer to another filtering layer, unit: rice;

h ₀Be meant: the relative altitude of two filtering layers, unit: rice;

v ₁And v ₂Refer to respectively: the rate of filtration of two filtering layers, unit: meter per second; This parameter is a design parameter, is pre-set;

G: acceleration of gravity, unit: m/s ²

Δ P: the pressure differential of water from a certain filtering layer to another filtering layer, unit: Pa;

ρ: the density of water, unit: kg/m ³

Wherein the water pressure of the filtering layer of different-thickness can obtain from the reading that water factory is installed in the congestion degree meter the filtering layer of corresponding thickness.

To can determine the different ratio depositions constantly of different-thickness filtering layer by the different loss of flood peak data substitution formulas (4) of the filtering layer of different-thickness constantly that (5) formula calculates.

(2) than the relation of deposition and filtration time

Theory analysis and process according to prior art are derived, and the ratio deposition in the obstruction filtering layer along the regularity of distribution of thickness of filter bed is:

[0101]?σ＝σ _i(t)e ^-θx (6)

Wherein, $\mathrm{\&theta;}=\frac{{\mathrm{\&lambda;}}_1}{v}-{\mathrm{\&lambda;}}_2$

[0103]In the formula, λ ₁And λ ₂: filtration coefficient;

V: filter speed, m/s;

σ: filtering layer compares deposition;

X: the thickness of a certain filtering layer, m;

σ _iFor the ratio deposition on filtering layer top layer, be the function of filtration time t, satisfy following relational expression:

$t=\frac{{\mathrm{\&lambda;}}_{2}v{\mathrm{\&epsiv;}}_0}{{\mathrm{\&phi;}}^2}\ln \frac{{\mathrm{\&lambda;}}_1{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HSA00000168007100031.png"\; state="\{\{state\}\}">c</figure-callout>}}_0{\mathrm{\&epsiv;}}_0}{{\mathrm{\&lambda;}}_1{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HSA00000168007100031.png"\; state="\{\{state\}\}">c</figure-callout>}}_0{\mathrm{\&epsiv;}}_0-{\mathrm{\&phi;\&sigma;}}_i}+\frac{{\mathrm{\&sigma;}}_i}{\mathrm{\&phi;}}---\left(7\right)$

Wherein, φ=λ ₁c ₀+ λ ₂V,

So, σ with time t, the relation between drainage turbidity c0, thickness of filter bed x and the filtering velocity v of treating is:

$t=\frac{{\mathrm{\&lambda;}}_{2}v{\mathrm{\&epsiv;}}_0}{{({\mathrm{\&lambda;}}_1{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HSA00000168007100031.png"\; state="\{\{state\}\}">c</figure-callout>}}_0+{\mathrm{\&lambda;}}_{2}v)}^2}\ln \frac{{\mathrm{\&lambda;}}_1{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HSA00000168007100031.png"\; state="\{\{state\}\}">c</figure-callout>}}_0{\mathrm{\&epsiv;}}_0}{{\mathrm{\&lambda;}}_1{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HSA00000168007100031.png"\; state="\{\{state\}\}">c</figure-callout>}}_0{\mathrm{\&epsiv;}}_0-({\mathrm{\&lambda;}}_1{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HSA00000168007100031.png"\; state="\{\{state\}\}">c</figure-callout>}}_0+{\mathrm{\&lambda;}}_{2}v){\mathrm{\&sigma;e}}^{(\frac{{\mathrm{\&lambda;}}_1}{v}-{\mathrm{\&lambda;}}_2)x}}+\frac{{\mathrm{\&sigma;e}}^{(\frac{{\mathrm{\&lambda;}}_1}{v}-{\mathrm{\&lambda;}}_2)x}}{({\mathrm{\&lambda;}}_1{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HSA00000168007100031.png"\; state="\{\{state\}\}">c</figure-callout>}}_0+{\mathrm{\&lambda;}}_{2}v)}---\left(8\right)$

In the formula, t: the filter time, unit: hour;

V: filter speed, unit: m/h;

c ₀: treat the drainage turbidity, unit: NTU;

ε ₀: cleaning filtering layer porosity;

σ: this thickness filtering layer compares deposition;

X: a certain thickness of filter bed, unit: rice;

λ ₁And λ ₂: filtration coefficient.

2, parameter identification

(1) sets up data sample

According to formula (8), identified parameters λ ₁And λ ₂, need use that t in time changes than deposition σ, treat drainage turbidity c ₀, data such as thickness of filter bed x and filtering velocity v.Try to achieve the loss of flood peak of filtering layer of different filtration time different-thickness according to above-mentioned method after; Can calculate the delta data of the ratio deposition of different-thickness filtering layer, set up sample space jointly with the delta data of treating drainage turbidity, speed etc. of corresponding water factory's actual production operation constantly again.

(2) parameter identification method

For the function of the complex nonlinear as formula (8), can utilize the method for some common identified parameters: for example DE (differential evolution algorithm), nlinfit (nonlinear regression function) scheduling algorithm carry out parameter identification, can find the solution coefficient lambda ₁And λ ₂With finding the solution coefficient substitution (8) formula that obtains, then can obtain corresponding σ _iWith time t, treat drainage turbidity c ₀And the relational expression between the filtering velocity v, and then can obtain σ with t, c ₀, the relation between the v etc.

Differential evolution algorithm (DE) is a kind of employing floating-point vector coding, in continuous space, carries out the optimized Algorithm of Heuristic stochastic search.Effect was obvious when the function of characteristics such as DE is big to some scales, dimension is high, non-linear and non-differentiability was optimized.And the nlinfit function among the MATLAB is to use Gauss-Newton algorithm, can carry out the nonlinear regression function of polynary least square fitting.Also have many evolution algorithms also can be applied to find the solution the parameter problem of complicated function in addition.

3, maximum filtering time

From the angle analysis of microcosmic, when reaching maximum, promptly with initial porosity ε than deposition σ ₀When equating, being considered to filtering layer is to have stopped up fully.But in reality, this situation can not occur, the domestic scholar of having has proposed as σ=95% σ _MaxThe time, think that promptly filtering layer reaches capacity.According to above-mentioned time t and the relation between the σ, can know that the maximum filtering time of being confirmed by the loss of flood peak does

$T_{\max }=\frac{0.95{\mathrm{\&lambda;}}_1{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HSA00000168007100031.png"\; state="\{\{state\}\}">c</figure-callout>}}_0+3.0{\mathrm{\&lambda;}}_{2}v}{{\mathrm{\&phi;}}^2}{\mathrm{\&epsiv;}}_0---\left(9\right)$

Water factory is treated so maximum filtration time then can be estimated according to formula (9) in the frequent interval range substitution formula (9) that keeps of turbidity of drainage.If for different water factories, then maximum filtration time is also also inequality.

Filtration time with maximum; Substitution formula (8) and formula (4) then can be calculated the maximum head loss that allows according to above-mentioned method, can the maximum head loss value that allow be scaled the congestion degree count value so; As one of trigger condition that stops to filter, the cycle of filtering is controlled automatically.

Compared with prior art, the computational methods of head loss of city water supply filtering system provided by the invention have following advantage:

1, the maximum filtering time that calculates is according to the method for the invention confirmed the maximum head loss and as the trigger condition that the filter tank stops to filter, can be avoided stopping prematurely filtration, and filter tank usefulness is performed to optimum state;

2, method of the present invention combines multiple algorithm that model parameter is carried out identification to find the solution; And be applied in the middle of the practice of water supply and drainage knowledge, be unprecedented a kind of innovation, with result's comparison of actual measurement; Reach higher accuracy, had important demonstration effect;

3, owing to receive the restriction of actual production equipment, general filtering layer bottommost can not be installed the congestion degree meter, can utilize along with the approximate σ that time t constantly changes, actual c according to computational methods disclosed by the invention ₀, v substitution formula (8), through estimation methods such as utilization evolution algorithm and dichotomies, the gross head that can obtain being similar to loses, thereby has solved the actual difficulty of bringing;

4, applying of method of the present invention will make the operation of water factory's filter process reach process optimization, and the automatization level of water factory is increased, and also have more important meaning for reducing water producing cost etc.

Description of drawings

Fig. 1 is the FB(flow block) of computational methods of the present invention;

Fig. 2 is that to use thickness that this method obtains be that the filtering layer of 1.09m is than deposition fitting result and comparison diagram as a result through actual measurement;

Fig. 3 uses the loss of flood peak fitting result and comparison diagram as a result through actual measurement that thickness that this method obtains is the filtering layer of 1.09m;

Fig. 4 is the different loss of flood peak figure of the filtering layer of different-thickness constantly that three congestion degree instrumentations of embodiment three get;

Fig. 5 is a ratio deposition of being used the correspondence that this method obtains by the loss of flood peak value of Fig. 4.

The specific embodiment

Below in conjunction with accompanying drawing and embodiment, the present invention is done detailed description further, but embodiment of the present invention is not limited to this.

Embodiment one

The FB(flow block) of computational methods of the present invention is as shown in Figure 1, and the different water pressures of the filtering layer of different-thickness are constantly got by the congestion degree instrumentation that is installed in the filtering layer in the filtration system, the rate of filtration v on pre-set filtering layer surface ₁With rate of filtration v apart from the filtering layer of filtering layer surface 1.09m ₂Be respectively 5.8m/h, 7m/h; The filtering layer surface that the congestion degree instrumentation is got and apart from the water pressure real time data substitution formula (5) of filtering layer surface for the filtering layer of 1.09m:

Obtain the different loss of flood peakes constantly of this thickness of filter bed, with the loss of flood peak substitution formula (4) that obtains:

Obtain different ratio depositions constantly.Wherein, H ₀Calculate by formula (1) convolution (2):

$\mathrm{\&Delta;}{H}_i=0.0187\mathrm{\&mu;}{\mathrm{\&alpha;}}^2\frac{v{(1-{\mathrm{\&epsiv;}}_0)}^2}{{\mathrm{<figure-callout\; id="0"\; label="d\; e"\; filenames="HSA00000168007100031.png"\; state="\{\{state\}\}">d</figure-callout>}}_e^0{{\mathrm{\&epsiv;}}_0}^3}\mathrm{\&Delta;}{L}_i---\left(1\right)$

${\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="HSA00000168007100031.png"\; state="\{\{state\}\}">H</figure-callout>}}_0=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;}{H}_i---\left(2\right).$

Use computational methods of the present invention obtain apart from filtering layer sand face as the filtering layer of 1.09m than deposition fitting result with more as shown in Figure 2, it is thus clear that the ratio deposition that obtains with computational methods of the present invention can reach more accurate degree through the result of actual measurement.

Embodiment two

The FB(flow block) of computational methods of the present invention is as shown in Figure 1, and the different water pressures of the filtering layer of different-thickness are constantly got by the congestion degree instrumentation that is installed in the filtering layer in the filtration system, the rate of filtration v on pre-set filtering layer surface ₁With rate of filtration v apart from filtering layer surface 1.09m ₂Be respectively 5.8m/h, 7m/h; The filtering layer surface that the congestion degree instrumentation is got and apart from the water pressure real time data substitution formula (5) of filtering layer surface for the filtering layer of 1.09m obtains the different loss of flood peakes constantly of this thickness of filter bed, and concrete computational methods are with embodiment one.Use computational methods of the present invention obtain apart from filtering layer surface for for the loss of flood peak fitting result of the filtering layer of 1.09m with as shown in Figure 3, it is thus clear that the loss of flood peak that obtains with computational methods of the present invention can reach more accurate degree through the result of actual measurement.

Embodiment three

Utilize method of the present invention to calculate the maximum head loss of the permission in certain water factory filter tank:

The first step: utilize three congestion degree instrumentation spans in water factory's filtering layer from the filtering layer surface for the drainage of treating that the real-time water pressure data of the filtering layer of 0.55m, 0.80m, 1.09m, water factory set gets into the filtering velocity of above-mentioned three filtering layers and flows out the filtering velocity of above-mentioned three filtering layers, be 7m/h;

Substitution formula (5):

$H_t={\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HSA00000168007100031.png"\; state="\{\{state\}\}">h</figure-callout>}}_0+\frac{{\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="HSA00000168007100022.png"\; state="\{\{state\}\}">v</figure-callout>}}_1^2-v_2^2}{2g}-\frac{\mathrm{\&Delta;p}}{\mathrm{\&rho;g}}---\left(5\right)$

The loss of flood peak of the filtering layer of the different-thickness that obtains changing with filtration time is as shown in Figure 4;

Second step: the filtering layer of the different-thickness that will be calculated by (5) formula is with the loss of flood peak data substitution formula (4) that filtration time changes, and can determine thickness is the different ratios depositions constantly of filtering layer of 0.55m, 0.80m, 1.09m, and its variation tendency is as shown in Figure 5;

$\frac{{\mathrm{<figure-callout\; id="0"\; label="H\; t\; H"\; filenames="HSA00000168007100031.png"\; state="\{\{state\}\}">H</figure-callout>}}_t}{H_{}}={\left(\frac{{\mathrm{\&epsiv;}}_0}{{\mathrm{\&epsiv;}}_0-\mathrm{\&sigma;}}\right)}^2---\left(4\right)$

Wherein, H ₀Calculate by formula (1) convolution (2):

$\mathrm{\&Delta;}{H}_i=0.0187\mathrm{\&mu;}{\mathrm{\&alpha;}}^2\frac{v{(1-{\mathrm{\&epsiv;}}_0)}^2}{{\mathrm{<figure-callout\; id="0"\; label="d\; e"\; filenames="HSA00000168007100031.png"\; state="\{\{state\}\}">d</figure-callout>}}_e^0{{\mathrm{\&epsiv;}}_0}^3}\mathrm{\&Delta;}{L}_i---\left(1\right)$

${\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="HSA00000168007100031.png"\; state="\{\{state\}\}">H</figure-callout>}}_0=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;}{H}_i---\left(2\right).$

The 3rd step: according to above-mentioned steps obtain along with the loss of flood peak of filtration time different-thickness with than the delta data of deposition, according to formula (8):

Set up sample space jointly with the delta data of treating drainage turbidity, the rate of filtration etc. of corresponding water factory's actual production operation constantly again.According to the practical operation situation of Guangdong water factory and the situation of geographical environment water quality of living in, treat general equal can the remaining within certain interval range 2.0-2.6NTU of turbidity of drainage.

The 4th step: the method for using common identified parameters: DE (differential evolution algorithm) carries out match to formula (8), finds the solution coefficient lambda ₁And λ ₂, be respectively λ ₁=1.51 * 10 ^-3, λ ₂=8.62 * 10 ^-5

The 5th step: will find the solution coefficient substitution (8) formula that obtains, and make σ=95% σ _Max,, can know that the maximum filtering time of being confirmed by the loss of flood peak does according to the relation between time t in the above-mentioned formula (8) and the σ

$T_{\max }=\frac{0.95{\mathrm{\&lambda;}}_1{\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HSA00000168007100031.png"\; state="\{\{state\}\}">c</figure-callout>}}_0+3.0{\mathrm{\&lambda;}}_{2}v}{{\mathrm{\&phi;}}^2}{\mathrm{\&epsiv;}}_0---\left(9\right)$

The 6th step: according to the practical operation situation of Guangdong water factory and the situation of geographical environment water quality of living in, treat general equal can the remaining within certain interval range 2.0-2.6NTU of turbidity of drainage, set filtering velocity v=7m/h, ε ₀=0.39, so maximum filtration time estimates that according to formula (9) maximum filtering time can calculate and approximate 110 hours, and the maximum head loss that allow this moment is 2.2m.Filtration time according to maximum; Then can calculate the maximum head loss that allows according to above-mentioned method; Can maximum head loss value be scaled the congestion degree count value so; And in " work of nature " software of the control computer of this factory's central control room, programme, as one of trigger condition that stops to filter.

In the process of using computational methods of the present invention; Because formula (8) is a very complicated non-linear implication; If will calculate than deposition σ according to time t, can not find the solution simply, the solving equation that must seek other obtains the more accurate ground approximation of equattion root.Can utilize numerical methods such as dichotomy, iterative method, can find the solution after the programming.Dichotomy is a kind of of interval iteration method, and it is to repeat to use the zero existence theorem, at every turn with interval compression half the and one of them intervally comprise a root at least, progressively shorten interval, till confirming to satisfy certain required precision.Concrete computational process is following:

At first set between the original area of σ and required required precision, use dichotomy constantly the interval to be shortened then, the approximate σ that last approximation accuracy requires is updated to formula (4) and can tries to achieve the approximate loss of flood peak that changes than deposition σ along with different.

The actual motion of water factory proves that one of trigger condition that the maximum head loss value that employing this method is obtained stops to filter as water factory has reached the effect that saves energy and water resources taxes are used.Concrete energy-conservation data are following, and wherein, economizing on the use of funds contains the water resource expense:

At present, generally be made as the filter cycle in filter tank 48 hours, the recoil with clear water be about 350 tons/inferior, the recoil electricity consumption be about 15 the degree/inferior.If prolonged filtration time N hour, then compare the recoil clear water that per hour can practice thrift in each filter tank of present setting and be: { 350* [N/ (48+N)] }/48 tons; Can using electricity wisely be { 15* [N/ (48+N)] }/48 degree per hour.If lose based on the said method calculated water head all in 36 filter tanks of this water factory, and allow the maximum head loss that allows realize backwash control, then having on the basis annual (calculating) energy-saving and cost-reducing situation such as table 2 now by 365 days as trigger condition:

Table 2

The present filter time cycle (hour)	The filter time cycle after the prolongation (hour)	The time that prolongs (hour)	The annual backwash clear water of practicing thrift (ton)	Annual backwash electricity consumption (degree) of practicing thrift	(unit) economizes on the use of funds
						48	55	7	292663	12543	57296.90
48	60	12	459900	19710	90037.85
						48	65	17	601408	25775	117742.13
48	70	22	722700	30973	141488.15

Claims (1)

1. the computational methods of a head loss of city water supply filtering system is characterized in that, comprise the steps:

The first step: measure the different water pressures of the filtering layer of different-thickness constantly in the filtration system, obtain the pressure differential of water, and calculate the different loss of flood peakes of the filtering layer of each corresponding thickness constantly successively from any filtering layer to another filtering layer:

$H_t=h_0+\frac{v_1^2-v_2^2}{2g}-\frac{\mathrm{\&Delta;p}}{\mathrm{\&rho;g}}---\left(5\right);$

In the formula, H _tBe meant: the loss of flood peak of water from a certain filtering layer to another filtering layer, unit: rice;

h ₀Be meant: the relative altitude of two filtering layers, unit: rice;

v ₁And v ₂Refer to respectively: the rate of filtration of two filtering layers, unit: meter per second, this parameter is a design parameter, preestablishes;

G: acceleration of gravity, unit: m/s ²

Δ P: the pressure differential of water from a certain filtering layer to another filtering layer, unit: Pa;

ρ: the density of water, unit: kg/m ³

Second step:, calculate the ratio deposition of the filtering layer of each corresponding thickness with the different loss of flood peakes of the filtering layer of different-thickness constantly: $\frac{H_t}{H_0}={\left(\frac{{\mathrm{\&epsiv;}}_0}{{\mathrm{\&epsiv;}}_0-\mathrm{\&sigma;}}\right)}^2---\left(4\right);$

In the formula, H _t: the loss of flood peak of a certain thickness filtering layer of a certain moment, unit: rice;

H ₀: the loss of flood peak of a certain thickness cleaning filtering layer, unit: rice;

ε ₀: cleaning filtering layer porosity; This parameter is a process design parameter, according to the corresponding filtering layer material of this parameter choosing;

σ: filtering layer compares deposition;

The 3rd the step: set up the filtering layer of different-thickness ratio deposition and filter time, treat the relation function between drainage turbidity, thickness of filter bed and the filtering velocity v:

$t=\frac{{\mathrm{\&lambda;}}_{2}v{\mathrm{\&epsiv;}}_0}{{({\mathrm{\&lambda;}}_1{c}_0+{\mathrm{\&lambda;}}_{2}v)}^2}\ln \frac{{\mathrm{\&lambda;}}_1{c}_0{\mathrm{\&epsiv;}}_0}{{\mathrm{\&lambda;}}_1{c}_0{\mathrm{\&epsiv;}}_0-({\mathrm{\&lambda;}}_1{c}_0+{\mathrm{\&lambda;}}_{2}v){\mathrm{\&sigma;e}}^{(\frac{{\mathrm{\&lambda;}}_1}{v}-{\mathrm{\&lambda;}}_2)x}}+\frac{{\mathrm{\&sigma;e}}^{(\frac{{\mathrm{\&lambda;}}_1}{v}-{\mathrm{\&lambda;}}_2)x}}{({\mathrm{\&lambda;}}_1{c}_0+{\mathrm{\&lambda;}}_{2}v)}---\left(8\right);$

In the formula, t: the filter time, unit: hour;

V: filter speed, unit: m/h;

c ₀: treat the drainage turbidity, unit: NTU;

ε ₀: the porosity of this filtering layer cleaning filtering layer;

σ: the ratio deposition of the filtering layer of this thickness;

X: the thickness of a certain filtering layer, unit: m;

λ ₁And λ ₂: filtration coefficient;

The delta data of treating drainage turbidity, filter speed according to correspondence water factory's actual production operation is constantly set up data sample space jointly;

The 4th step: to the filtration coefficient λ in the function of said formula (8) ₁And λ ₂Carrying out identification finds the solution;

The 5th step: with the solving result substitution formula (8) in the 4th step, with seasonal σ=95% σ _Max, can know that the maximum filtering time of being confirmed by the loss of flood peak does

$T_{\max }=\frac{0.95{\mathrm{\&lambda;}}_1{c}_0+{3.0\mathrm{\&lambda;}}_{2}v}{{\mathrm{\&phi;}}^2}{\mathrm{\&epsiv;}}_0---\left(9\right)$

In the formula, T _Max: maximum filtering time, unit: hour

c ₀: treat the drainage turbidity, unit: NTU

V: filter speed, unit: m/h

ε ₀: cleaning filtering layer porosity

φ：φ＝λ ₁c ₀+λ ₂v

λ ₁And λ ₂: filtration coefficient

The 6th step: with said maximum filtering time substitution formula (8) and (4), the maximum head that obtains allowing loss;

Wherein, measure the different water pressures of the filtering layer of different-thickness constantly in the filtration system in the said first step, be meant and utilize the different water pressures of the filtering layer of different-thickness constantly in the congestion degree instrumentation amount filtration system;

The loss of flood peak H of a certain thickness cleaning filtering layer in said second step ₀Calculate by formula (1) convolution (2):

${\mathrm{\&Delta;H}}_i=0.0187{\mathrm{\&mu;\&alpha;}}^2\frac{v{(1-{\mathrm{\&epsiv;}}_0)}^2}{d_{e0}^2{{\mathrm{\&epsiv;}}_0}^3}{\mathrm{\&Delta;L}}_i---\left(1\right)$

$H_0=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&Delta;H}}_i---\left(2\right)$

In the formula, H ₀: the loss of flood peak of a certain thickness cleaning filtering layer, unit: rice;

Δ H _i: be divided into the n five equilibrium to filtering layer, the corresponding loss of flood peak of every five equilibrium, unit: rice;

V: the rate of filtration in filter tank, unit: m/s;

μ: the dynamic viscosity of water, Ns/m ², water temperature approximates 1.006 * 10 in the time of 20 ℃ ^-3Pas;

d _E0: the particle diameter of filtrate, unit: mm;

α: form factor, represent the surface area of aspheric particle and the ratio of equal-volume spheric granules surface area;

ε ₀: cleaning filtering layer porosity;

Δ L _i: be divided into Δ L to whole filtering layer ₁, Δ L ₂Δ L _iDeng filtering layer, unit: rice;

Said the 4th the step in to the coefficient lambda in the function of said formula (8) ₁And λ ₂Carry out identification and find the solution, the method with identified parameters of being meant is to the coefficient lambda in the function of said formula (8) ₁And λ ₂Carrying out identification finds the solution; The method of said identified parameters is meant differential evolution algorithm or nonlinear regression function algorithm.

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