CN110231141B - Method for simulating membrane module in membrane bioreactor by using porous medium model - Google Patents

Method for simulating membrane module in membrane bioreactor by using porous medium model Download PDF

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CN110231141B
CN110231141B CN201910508837.XA CN201910508837A CN110231141B CN 110231141 B CN110231141 B CN 110231141B CN 201910508837 A CN201910508837 A CN 201910508837A CN 110231141 B CN110231141 B CN 110231141B
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刘雪菲
王远
大卫·韦特
纪超
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Jiangsu Xinyi China Australia Environmental Technology Co ltd
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Abstract

The invention discloses a method for simulating a membrane module in a membrane bioreactor by using a porous medium model, which is used for solving the problem that the influence of accurately simulating the membrane module on the water flow in a membrane pool is the key of the whole simulation and the difficult point in a computational fluid mechanics model; according to the method, unit head loss data are obtained and are led into Matlab, mathematical expressions of horizontal direction and vertical direction flow of the hollow fiber bundle are respectively synthesized, firstly, a porous medium model is built, secondly, a friction loss coefficient of the porous medium model is determined through a tube bundle empirical formula and a fluid resistance experiment, finally, two head loss data obtained through the experiment are led into Matlab, and a set of brand new porous medium model is built to simulate the hydraulics of the hollow fiber membrane module in the membrane bioreactor through the mathematical expressions of horizontal direction and vertical direction flow of the hollow fiber bundle.

Description

Method for simulating membrane module in membrane bioreactor by using porous medium model
Technical Field
The invention relates to the technical field of simulating the hydraulic characteristics of a hollow fiber membrane module in a membrane bioreactor, in particular to a method for simulating a membrane module in a membrane bioreactor by using a porous medium model.
Background
The flow field property in the membrane bioreactor can be effectively reproduced by computational fluid mechanics simulation, so that the hydraulic performance of the membrane bioreactor is researched. The actual topography of the hollow fiber membrane module device is complex, a large number of grids are needed to take local topography into consideration, and the corresponding calculation amount is large. Thereby greatly limiting the application of computational fluid dynamics simulation technology in the actual engineering design. In the computational fluid dynamics model, the accurate simulation of the influence of the membrane group device on the water flow in the membrane pool is a key and difficult point of the whole simulation. The invention establishes a set of brand new porous medium model to simulate the hydraulics characteristics of the hollow fiber membrane module in the membrane bioreactor by an experimental method. The model fully considers the design variables and the design range of the hollow fiber membrane module in the current market, and can be widely applied to simulating the hydraulic performance of different membrane modules.
Disclosure of Invention
The invention aims to provide a method for simulating a membrane bioreactor in a membrane bioreactor by using a porous medium model; the method is used for solving the problem that the influence of accurately simulating the membrane group device on the water flow in the membrane pool is the key of the whole simulation and the problem of difficulty in a computational fluid mechanics model; the invention establishes a set of brand new porous medium models by an experimental method to simulate the hydraulics characteristics of the hollow fiber membrane module in the membrane bioreactor;
the purpose of the invention can be realized by the following technical scheme: a method for simulating a membrane module in a membrane bioreactor by using a porous medium model comprises the following specific steps of obtaining unit head loss data, guiding the data into Matlab, and respectively fitting mathematical expressions of horizontal and vertical flows of hollow fiber bundles, wherein the mathematical expressions are as follows:
u1: determining the fiber bundle characteristics and the influence of the membrane flow direction on the water head loss coefficient of unit length through a module structure; the head loss coefficient per unit length is expressed by a function related to the flow rate and the viscosity;
u2: changing the rheological property of the mixed solution by adding an iron flocculating agent to obtain that the local speed among fibers is higher under the same flow velocity, thereby generating larger turbulence and resistance; the pressure drop of the membrane module is influenced by the characteristics of the fiber bundle, and for the hollow fiber bundle which flows perpendicular to the fluid, the pressure drop is related to the free volume in the hollow fiber membrane module device;
u3: when the axial direction of the hollow fiber membrane filaments is parallel to the fluid flow direction, the head loss along the unit length is a function related to the Reynolds number, and the mathematical expression is as follows:
Figure BDA0002091192720000021
wherein DH is the hydraulic diameter of the hollow fiber membrane bundle; re is Reynolds number; ρ is the fluid density; μ is the fluid viscosity;
u4: when the filament direction of the hollow fiber membrane is perpendicular to the flowing direction, the head loss per unit length is expressed by an equation of fluid viscosity and cross sectional area and free volume, and the mathematical expression is as follows:
Figure BDA0002091192720000022
wherein A is the cross-sectional area of the hollow fiber membrane module, and V is the free volume of the hollow fiber membrane module; Δ P is the pressure drop; l is the length along the water flow direction.
Before the unit head loss data obtained as described above is introduced into Matlab, the following steps are also required:
s1: the pressure loss of the hollow fiber membrane bundle is simulated by a porous medium method, and the specific steps are as follows:
SS 1: adding a momentum source item to a momentum control equation;
SS 2: in the laminar flow of the porous medium, the porous medium model is simplified into Darcy's law; recording the head pressure loss per unit length in the flow direction as an inertial resistance factor under the condition of high flow velocity;
SS 3: eliminating a viscosity term by using a tube bundle modeling method to obtain a simplified form of a porous medium equation;
s2: determining the friction loss coefficient of the hollow fiber membrane bundle by using a tube bundle empirical formula;
s3: determining the friction loss coefficient of the porous medium model by using a fluid resistance experiment;
s4: introducing the friction loss coefficient of the porous medium model determined by a tube bundle empirical formula and a fluid resistance experiment into Matlab;
preferably, the momentum control equation described in step SS1 is:
Figure BDA0002091192720000031
wherein, KpermTo a permeability, KlossD and C are defined matrices for the coefficient of friction loss; ρ is the fluid density, vjIs the fluid velocity; v. ofmagIs the viscosity of the fluid; first term on the equation
Figure BDA0002091192720000032
As a viscosity loss term, the second term
Figure BDA0002091192720000033
Is an inertial loss term;
preferably, the friction loss coefficient measurement of the hollow fiber membrane bundle described in steps S2 and S3 is performed in a single-phase flow in which aeration is not performed and the membrane flux is zero.
The invention has the beneficial effects that:
(1) the pressure loss of the hollow fiber membrane bundle is simulated by a porous medium method; firstly, establishing a porous medium model, secondly, determining the friction loss coefficient of the porous medium model through a tube bundle empirical formula and a fluid resistance experiment, finally, introducing two water head loss data obtained by the experiment into Matlab, respectively fitting into mathematical expressions of the flow of the hollow fiber bundle in the horizontal direction and the vertical direction, and establishing a brand-new porous medium model to simulate the hydraulics of the hollow fiber membrane module in the membrane bioreactor through fitting into the mathematical expressions of the flow of the hollow fiber bundle in the horizontal direction and the vertical direction;
(2) according to the invention, the rheological property of the mixed solution is changed by adding the iron flocculant, so that the local speed among fibers is higher under the same flow velocity, and thus, larger turbulence and resistance are generated; the pressure drop of the membrane module is influenced by the characteristics of the fiber bundle, and for hollow fiber bundles flowing perpendicular to the fluid, the pressure drop is related to the free volume in the hollow fiber membrane module.
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The invention will be further described with reference to the accompanying drawings.
FIG. 1 is a schematic view of the cross-distribution and size of the tube bundle of the present invention;
FIG. 2 is a schematic view of the series arrangement and size of the tube bundle of the present invention;
FIG. 3 is a schematic structural diagram of a fluid resistance testing apparatus according to the present invention;
FIG. 4 is a graph of pressure loss versus flow rate for hollow fiber bundles of varying fluid viscosity with constant packing density and fiber diameter according to the present invention;
FIG. 5 is a graph of pressure loss versus flow rate for hollow fiber bundles of varying packing density with constant fiber diameter and fluid viscosity according to the present invention;
FIG. 6 is a graph of pressure loss versus flow rate for hollow fiber bundles of varying fiber diameter with constant packing density and fluid viscosity according to the present invention;
FIG. 7 is a graph of pressure loss as a function of flow velocity for hollow fiber modules of the present invention having the same free volume and different fiber diameters and packing densities, perpendicular to the flow direction.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention relates to a method for simulating a membrane module in a membrane bioreactor by a porous medium model, which simulates the pressure loss of a hollow fiber membrane bundle by a porous medium method and comprises the following specific steps:
s1: adding a momentum source item to a momentum control equation;
it is very difficult to simulate the flow in a bundle of hollow fiber membranes with a discretized grid; therefore, the pressure loss of the hollow fiber membrane bundle can be simulated by a porous medium method, and a momentum source term Si is added into a momentum control equation:
Figure BDA0002091192720000051
wherein, KpermTo a permeability, KlossD and C are defined matrices for the coefficient of friction loss; ρ is the fluid density, vjIs the fluid velocity; v. ofmagIs the viscosity of the fluid; first term on the equation
Figure BDA0002091192720000052
As a viscosity loss term, the second term
Figure BDA0002091192720000053
Is an inertial loss term;
s2: in a laminar flow of porous media, the pressure drop is generally proportional to the velocity, and neglecting the effects of convective acceleration and diffusion, the porous media model can be simplified to darcy's law:
Figure BDA0002091192720000061
wherein α represents a magnetic permeability;
in the case of very high flow rates, the head pressure loss per unit length in the flow direction is taken as the inertial resistance factor, C2ijThe pressure drop can therefore be expressed as a function of the dynamic head;
s3: the pressure drop caused by viscous losses in the hollow fiber membrane module is not determined by the permeability of the membrane, but by the permeability of the entire module, and therefore, the viscous term can be eliminated in a similar way to tube bundle modeling, resulting in a simplified form of the porous media equation,
Figure BDA0002091192720000062
in the formula, coefficient of inertial loss
Figure BDA0002091192720000063
Is related to Reynolds number (i.e. flow)Bulk density ρ, velocity vj and viscosity vmag) A function of (a);
the friction loss coefficient of the hollow fiber membrane bundle is determined by using a tube bundle empirical formula, and the difficulty of using a porous medium model is that the flow resistance and the pressure drop caused by different membrane components are different, so that the inertia resistance coefficient is difficult to determine; because the hollow fibers and the tube bundle are similar in structure, the pressure drop of the hollow fiber bundle can be estimated by using an empirical formula for estimating the pressure drop of the tube bundle;
as shown in fig. 1-2, the pressure drop of the hollow fiber bundle is estimated using an empirical formula for estimating the pressure drop of the bundle; the pressure drop is influenced by factors such as the space between the tube bundles and the arrangement mode of the tube bundles;
expressing the pressure drop of the tube bundle by the change of the friction coefficient along with the Reynolds number and determining the pressure drop vertical to the flow direction of the tube bundle and parallel to the flow direction of the tube bundle; for turbulence perpendicular to the flow direction of the tube bundle:
Figure BDA0002091192720000071
wherein N istF is the friction factor; the structure of the hollow fiber membrane bundle is similar to that of the staggered tube bundle; the coefficient of friction for the staggered arrangement can be written as:
Figure BDA0002091192720000072
where Dc is the distance between the tube bundles, μmaxTo pass through DcThe speed of time; in the formula (5), when the tube bundle distance is within the range of 1.25-1.50mm, the accuracy is +/-25%;
as shown in fig. 1, the pitch of the hollow fiber membrane bundle may be determined by equation (6):
Figure BDA0002091192720000073
when the DHF is 0.1114m, n is 1692, the bundle spacing a is 0.0026m, and therefore, the inter-fiber spacing Dc is 0.0013 m;
for flow parallel to the tube bundle, determining the pressure drop from the pressure drop of the flow in the tube bundle;
Figure BDA0002091192720000074
wherein the friction coefficient f of the turbulent flow is a function related to the Reynolds number R:
f＝0.079Re-0.25 (8)
the hydraulic diameter DH of the hollow fiber bundle can be obtained from equation (9):
Figure BDA0002091192720000075
wherein a is a cross-sectional area of the hollow fiber membrane module, which can be obtained by the formula (10):
Figure BDA0002091192720000076
l represents a wet cycle, and can be obtained by the following equation (11):
L＝πDHF+nπd (11)
as shown in fig. 3, the friction loss coefficient of the porous medium model is determined by a fluid resistance experiment, and the specific steps are as follows:
establishing an experimental device for measuring the inertial resistance coefficient; the experimental device comprises a delivery pump 101 with the flow rate of 225L/min, a branch pipe loop 102, two valves 103, a pressure gauge 104, a pressure regulating tank 110, a cooling water system 105 and a hollow fiber membrane bundle 109 with the same filling density as that of the membrane bioreactor in use; both sides of the pressure regulating tank 110 are connected to the cooling water system 105 through the branch pipe circuit 102, and the pressure gauge 104 is used for measuring the pressure of the hollow fiber membrane bundle 109; a cooling water inlet 108 and a cooling water outlet 106 are respectively arranged on two sides of the cooling water system 105; a buffer tank 107 is arranged in the cooling water system 105, one side of the buffer tank 107 is connected with one side of the delivery pump 101, and the other side of the delivery pump 101 is connected with the branch pipe loop 102 through a valve 103;
controlling the packing density of the fibers in the hollow fiber membrane bundle; in order to control the filling density of the fibers, the two ends of the fibers are fixed on two screens;
selecting a solution capable of representing the rheological property of sludge in the membrane bioreactor in an experiment; respectively measuring flow resistance vertical and parallel to the hollow fiber membrane to obtain data in three directions in space; measuring the pressure drop of different flow rates within the range of 12-200L/min; determining and calculating results from the CFD simulation results, higher flow rates are difficult to achieve due to pump limitations and large water volumes; three different test solutions, namely tap water, 0.5g/L xanthan gum solution and 1g/L xanthan gum solution, are adopted to represent different mixed solution concentrations; as shown in table 1:
table 1 table of experimental conditions of fluid resistance
Figure BDA0002091192720000081
Figure BDA0002091192720000091
From table 1, it can be seen that the xanthan gum solution can represent the rheological properties of the sludge in the membrane bioreactor;
determining the friction loss coefficient of the porous medium model through an experimental method; the test method is obtained in the Wang, y., Brannock, m., Cox, s., Leslie, g., 2010.CFD interactions of membrane filtration zone in a sub-sized porous fiber membrane bioreactor using a pore media approach.j.membrane. sci.363(1e2), 57e66 literature, and important parameters of the friction loss coefficient are measured for experiments and the pressure loss of the hollow fiber membrane bundle is measured; table 2 is an important parameter for determining the coefficient of friction loss;
TABLE 2 parameters for determining the coefficient of friction loss
Figure BDA0002091192720000092
Figure BDA0002091192720000101
Wherein the outer diameters of the hollow fibers are respectively 1.3mm, 1.5mm and 2.4mm, and the filling density is between 200 and 560m2/m 3; measuring the pressure loss of the hollow fiber membrane bundle at a flow velocity of 0 to 0.35 m/s; this velocity range covers 90% of the particle flow rate in the hollow fiber membrane bioreactor; mixtures of drinking water and xanthan gum at concentrations of 0.5g/L, 0.75g/L and 1.0g/L were used to simulate the effect of viscosity on inertial loss;
as shown in fig. 4-6, the head loss data obtained by the experiment is introduced into Matlab, and mathematical expressions for horizontal and vertical flows of the hollow fiber bundle are respectively fitted, and the specific steps are as follows:
u1: FIG. 4 shows the packing density of 340m2/m3The fiber diameter is 1.5mm and is kept unchanged, and the fluid viscosity is different; FIG. 5 shows the case of a fiber having a diameter of 2.4mm, a fluid viscosity of 0.8cp remaining unchanged, and a filler having a different density; FIG. 6 shows the packing density of 340m2/m3The fluid viscosity is kept constant at 0.8cp, and the fiber diameters are different; from 9 sets of pressure loss data, the effect of the module structure (hollow fiber packing density and fiber diameter) and the membrane flow direction (parallel or perpendicular) on the friction loss coefficient, expressed as pressure drop per unit length, expressed as a function of flow rate and viscosity, was determined;
u2: changing the rheological property of the mixed solution by adding an iron flocculating agent to obtain that the local speed among fibers is higher under the same flow velocity, thereby generating larger turbulence and resistance; the pressure drop of the membrane module is influenced by the characteristics of the fiber bundle, and for the hollow fiber bundle which flows perpendicular to the fluid, the pressure drop is related to the free volume in the hollow fiber membrane module device;
TABLE 3 influence of flocculant addition on mixed liquor suspension (MLSS) and viscosity
Figure BDA0002091192720000111
As can be seen from table 3, the addition of the iron flocculant changed the rheological properties of the mixed solution; as the fluid viscosity increases from 0.8cp to 2.1cp, the resistance of the membrane assembly increases; as shown in fig. 4, the effect of viscosity on pressure loss is more pronounced for fibers flowing perpendicular to the fluid relative to fibers flowing parallel to the fluid; as shown in FIG. 5, when the flow rate is in the range of 0.05 to 0.4m/s, the packing density is from 280m2/m3Increased to 340m2/m3The effect of the fibers on the friction loss perpendicular to the fluid flow direction is much greater than if the fibers were parallel to the fluid flow direction; also, as can be seen from FIG. 6, as the fiber diameter increases from 1.5mm to 2.4mm, the friction loss increases; this is because the presence of large diameter fibers results in a smaller free volume (the volume of the bundle not occupied by fibers); thus, at the same flow velocity, the local velocity between the fibers is higher, resulting in greater turbulence and drag;
as shown in fig. 7, the pressure drop of the membrane module is affected by the fiber bundle characteristics (fiber diameter and packing density); for a hollow fiber bundle flowing perpendicular to the fluid, the pressure drop is related to the free volume within the hollow fiber membrane module;
u3: when the hollow fiber is horizontal to the fluid flow direction, the friction loss is equal to the Reynolds number (R)20.913), the expression is as follows: :
Figure BDA0002091192720000121
wherein DH is the hydraulic diameter of the hollow fiber membrane bundle; re is Reynolds number; ρ is the fluid density; μ is the fluid viscosity;
u4: when the filament direction of the hollow fiber membrane is perpendicular to the flowing direction, the head loss per unit length is expressed by an equation of fluid viscosity and cross sectional area and free volume, and the mathematical expression is as follows:
Figure BDA0002091192720000122
wherein A is the cross-sectional area of the hollow fiber membrane module, and V is the free volume of the hollow fiber membrane module; Δ P is the pressure drop; l is the length along the water flow direction;
the tube bundle empirical formula and the fluid resistance experiment can be applied to various hollow fiber membrane structures; the measurement of the pressure loss was carried out in a single-phase flow with no aeration and zero membrane flux; in this case, the hydraulic characteristics of the fluid flow have the greatest effect on the pressure loss of the fiber bundle; applying two empirical formulas, namely a tube bundle empirical formula and a fluid resistance experiment, to the porous medium model, considering the aeration effect, establishing a multiphase flow model, and simulating the fluid dynamics characteristic in the membrane bioreactor; due to the existence of the iron flocculant, the influence of viscosity increase is fully considered in the porous medium model, so that the porous medium model can be taken as a source term of a momentum equation in the CFD simulation;
the working principle of the invention is as follows: simulating the pressure loss of the hollow fiber membrane bundle by a porous medium method; firstly, establishing a porous medium model, secondly, determining the friction loss coefficient of the porous medium model through a tube bundle empirical formula and a fluid resistance experiment, finally, introducing two water head loss data obtained by the experiment into Matlab, respectively fitting into mathematical expressions of the flow of the hollow fiber bundle in the horizontal direction and the vertical direction, and establishing a brand-new porous medium model to simulate the hydraulics of the hollow fiber membrane module in the membrane bioreactor through fitting into the mathematical expressions of the flow of the hollow fiber bundle in the horizontal direction and the vertical direction; changing the rheological property of the mixed solution by adding an iron flocculating agent to obtain that the local speed among fibers is higher under the same flow velocity, thereby generating larger turbulence and resistance; the pressure drop of the membrane module is influenced by the characteristics of the fiber bundle, and for hollow fiber bundles flowing perpendicular to the fluid, the pressure drop is related to the free volume in the hollow fiber membrane module.
The foregoing is merely exemplary and illustrative of the present invention and various modifications, additions and substitutions may be made by those skilled in the art to the specific embodiments described without departing from the scope of the invention as defined in the following claims.

Claims (1)

1. A method for simulating a membrane module in a membrane bioreactor by using a porous medium model is characterized in that the method comprises the following specific steps of obtaining unit head loss data, leading the data into Matlab, respectively fitting mathematical expressions of horizontal and vertical flows of hollow fiber bundles, and fitting the mathematical expressions:
u1: determining the fiber bundle characteristics and the influence of the membrane flow direction on the water head loss coefficient of unit length through a module structure; the head loss coefficient per unit length is expressed by a function related to the flow rate and the viscosity;
u2: changing the rheological property of the mixed solution by adding an iron flocculating agent to obtain that the local speed among fibers is higher under the same flow velocity, thereby generating larger turbulence and resistance; the pressure drop of the membrane module is influenced by the characteristics of the fiber bundle, and for the hollow fiber bundle which flows perpendicular to the fluid, the pressure drop is related to the free volume in the hollow fiber membrane module device;
u3: when the axial direction of the hollow fiber membrane filaments is parallel to the fluid flow direction, the head loss along the unit length is a function related to the Reynolds number, and the mathematical expression is as follows:
Figure FDA0002716601330000011
wherein D isHIs the hydraulic diameter of the hollow fiber membrane bundle; re is Reynolds number; ρ is the fluid density; μ is the fluid viscosity;
u4: when the filament direction of the hollow fiber membrane is perpendicular to the flowing direction, the head loss per unit length is expressed by an equation of fluid viscosity and cross sectional area and free volume, and the mathematical expression is as follows:
Figure FDA0002716601330000012
wherein A is the cross-sectional area of the hollow fiber membrane module, and V is the free volume of the hollow fiber membrane module; Δ P is the pressure drop; l is the length along the water flow direction;
before acquiring the unit head loss data and importing the unit head loss data into Matlab, the following steps are required:
s1: the pressure loss of the hollow fiber membrane bundle is simulated by a porous medium method, and the specific steps are as follows:
SS 1: adding a momentum source item to a momentum control equation;
SS 2: in the laminar flow of the porous medium, the porous medium model is simplified into Darcy's law; recording the head pressure loss per unit length in the flow direction as an inertial resistance factor under the condition of high flow velocity;
SS 3: eliminating a viscosity term by using a tube bundle modeling method to obtain a simplified form of a porous medium equation;
s2: determining the friction loss coefficient of the hollow fiber membrane bundle by using a tube bundle empirical formula;
s3: determining the friction loss coefficient of the porous medium model by using a fluid resistance experiment;
s4: introducing the friction loss coefficient of the porous medium model determined by a tube bundle empirical formula and a fluid resistance experiment into Matlab;
the momentum control equation described in step SS1 is:
Figure FDA0002716601330000021
wherein, KpermTo a permeability, KlossD and C are defined matrices for the coefficient of friction loss; ρ is the fluid density, vjIs the fluid velocity; v. ofmagIs the viscosity of the fluid; first term on the equation
Figure FDA0002716601330000022
As a viscosity loss term, the second term
Figure FDA0002716601330000023
Is an inertial loss term;
the friction loss coefficient measurements of the hollow fiber membrane bundles of steps S2 and S3 were both performed in a single-phase flow with no aeration and zero membrane flux;
determining the friction loss coefficient of the porous medium model by using a fluid resistance experiment, and specifically comprising the following steps of:
establishing an experimental device for measuring the inertial resistance coefficient; the experimental device comprises a delivery pump (101) with the flow rate of 225L/min, a branch pipe loop (102), two valves (103), a pressure gauge (104), a pressure regulating tank (110), a cooling water system (105) and a hollow fiber membrane bundle (109) with the same filling density as that of a membrane bioreactor in use; two sides of the pressure regulating tank (110) are connected with a cooling water system (105) through a branch pipe loop (102), and a pressure gauge (104) is used for measuring the pressure of the hollow fiber membrane bundle (109); a cooling water inlet (108) and a cooling water outlet (106) are respectively arranged on two sides of the cooling water system (105); a buffer tank (107) is arranged in the cooling water system (105), one side of the buffer tank (107) is connected with one side of the delivery pump (101), and the other side of the delivery pump (101) is connected with the branch pipe loop (102) through a valve (103).
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