CN105740509A - Method for optimizing flow distribution part two-stage type design spiral membrane element reverse osmosis seawater desalination system considering boron removal - Google Patents

Abstract

The invention discloses a method for optimizing a flow distribution part two-stage type spiral membrane element reverse osmosis seawater desalination system considering boron removal. According to the method, an accurate model of a reverse osmosis seawater desalination transfer mechanism considering boron removal is established in a strict mechanism mode. The flow distribution part two-stage design is introduced; by utilizing a characteristic that the yield and quality of producing water at the front end of a pressure container are higher than those of producing water at the back end of the pressure container, the producing water at the front end of the pressure container is directly conveyed to final producing water and the producing water at the back end enters a next stage to be treated again; and a flow adjustment valve is added, so that the ratio of outlet water at the two ends can be flexibly adjusted according to an actual condition. A superstructure model of the reverse osmosis system is established, the changes of saline water pressure, concentration and flow in an axial direction of the pressure container as well as the salinity rise caused by saline water mixing in a worker exchange are considered, operation condition constraints are added for ensuring the system to run safely, and a simultaneous solution technology is adopted for solving optimization systems. The method comprehensively considers the influences of various factors on the seawater desalination system to further reduce the water producing cost and energy consumption of seawater desalination and enable the producing water of the system to meet the boron content standard of boron in drinking water. Not only can the reverse osmosis system be designed but also operation parameters can be optimized in a system operation process, so that the method has very good application prospects.

Description

A kind of two grades of wound membrane element reverse osmosis seawater desalination system optimization methods of shunting part considering de-boron

Technical field

The invention belongs to the process field of sea water, bitter, be specifically related to by optimizing wound membrane element reverse osmosis seawater desalination system, ensureing that the water producing cost making system on the basis of boron-removing rate is minimum.

Background technology

Desalination technology is one of effective way solving shortage of fresh water, and the development through decades has become a kind of industrial technology reliably.Most widely used in current engineering it is divided into the way of distillation and hyperfiltration.Reverse osmosis, due to plurality of advantages such as technology maturation, applied widely, energy consumption constantly reductions, progressively becomes the first-selection of international desalinization project.But, reverse osmosis membrane is not satisfactory to the de-effect of boron of sea water, and it produces the too high meeting of Boron contents in water makes people reproduction, nervous system disease occur.Additionally, Boron contents is too high also some crops can be brought harm.In " drinking water sanitary standard GB5479-2006 " that China promulgates for 2012, in regulation drinking water, Boron contents should be less than 0.5mg/L.In natural sea-water, Boron contents is about 4～6mg/L, main with easily through the H of film under usual pH value (7.9～8.2)₃BO₃Boric acid molecular forms exists.Although the reverse osmosis membrane with excellent de-boron performance is continually developed, but in actual commercial system, it is only 78%～80% even lower (in its product water, Boron contents is more than 1.0mg/L), it is clear that the requirement of drinking water and other industrial or agricultural water can not be met.

In order to reduce water producing cost and energy consumption, counter-infiltration system optimization design is always up the focus of scholar's research.Early stage is reported more for the system optimization research of hollow fiber film assembly.Although it is relatively low that wound membrane element piles thorough density in contrast, but its pre-processing requirements is relatively low, can obtain the balance of permeant flux, Environmental capacity, reduces operation and maintenance cost, occupies leading position in desalinization market.But current existing counter-infiltration system optimizing research seldom considers the de-boron impact on Optimized System Design.There is chemical equilibrium due to boron in the seawater, add the complexity of its transmittance process, the system optimization research of the de-boron process of reverse osmosis is still in the starting stage.Although considering ocean temperature, pH value and the product water Boron contents requirement impact on the de-boron of counter-infiltration system in some optimizing research, but in its model, the elimination of boron being by simple numerical fitting relationship expression, does not ensure that the precision of its TRANSFER MODEL.

Summary of the invention

The invention discloses a kind of two grades of wound membrane element reverse osmosis seawater desalination system optimization methods of shunting part considering de-boron.Reverse osmosis mechanism according to seawater desalination system and the structure of whole flow process, adopt the mode of exact mechanism to set up the accurate model of the reverse osmosis transport mechanism considering de-boron, adopt differential and algebraic equation to be described.Introduce shunting part level two design, utilize that pressure vessel front end aquifer yield compared with rear end is bigger and water quality is better, being produced from pressure vessel front end water and is fed directly to finally produce water, rear end is produced water and is entered next stage reprocessing, and adding flow control valve can according to practical situation flexible two ends water outlet proportion.Establish the superstructure model of counter-infiltration system, consider the change along the axial brine pressure of pressure vessel, concentration and flow, and the salinity caused due to saline mixing in merit exchanger raises, add operating condition constraint and ensure system safety operation, adopt simultaneous solution technology that optimal problem is solved.The present invention has considered the many factors impact on seawater desalination system, tries hard to the water producing cost and the energy consumption that reduce desalinization further so that system is produced water and met the standard of Boron contents in drinking water.Not only counter-infiltration system can be designed, also in system operation, operating parameter can be optimized, there is extraordinary application prospect.

The present invention comprises the following steps:

Step 1: set up the wound membrane element desalting process model considering de-boron；

According to reverse osmosis process mechanism and quality and law of conservation of energy, adopt salinity, boron concentration, pressure, flow etc. in differential equation pressure vessel along the axial change of pressure vessel, and differential equation finite difference method is carried out discretization, then consider that the wound membrane element desalting process model of de-boron can be represented by following equations:

$J_{w,l}=A_{ref}{(1-{\mathrm{FF}}_d)}^{N_{mlp}}\exp \[\frac{e}{R}(\frac{1}{298.15}-\frac{1}{273.15+T})\](P_l-\mathrm{\σ}({\mathrm{\π}}_{ch,mw,l}-{\mathrm{\π}}_{ch,p,l}\left)\right)---\left(1\right)$

$J_{s,l}=B_{ref}{(1+B_{in})}^{N_{mlp}}(C_{ch,mw,l}-C_{ch,p,l})---\left(2\right)$

σ=0.997-4.98 × 10^-5T(3)

$B_{TB,l}={\mathrm{\α}}_{0,l}{B}_{boric}{e}^{\left(0.067\right(T-T_0\left)\right)}+{\mathrm{\α}}_{1,l}{B}_{borate}{e}^{\left(0049\right(T-T_0\left)\right)}---\left(4\right)$

σ_{TB, l}=α_{0, l}σ_boric+α_{1, l}σ_borate(5)

${\mathrm{pK}}_{a,l}=\frac{2291.90}{T}+0.01756T-3.3850-0.32051{\left(\frac{C_{ch,mw,l}}{1.80655}\right)}^{1/3}---\left(6\right)$

${\mathrm{\α}}_{0,l}={\mathrm{\α}}_{1,l}{10}^{{\mathrm{pK}}_{a,l}-pH}---\left(7\right)$

$V_{w,l}=\frac{J_{w,l}+J_{s,l}}{{\mathrm{\ρ}}_p}---\left(8\right)$

$C_{ch,p,l}=\frac{J_{s,l}}{V_{w,l}}---\left(9\right)$

$C_{TB,ch,p,l}=\frac{(C_{TB,ch,b,l}-C_{TB,ch,p,l})(1-{\mathrm{\σ}}_{TB,l})\exp (V_{w,l}/K_l)}{{\mathrm{\σ}}_{TB,l}(1-\exp (-\left(1-{\mathrm{\σ}}_{TB,l}\right)V_{w,l}/\left(B_{TB,l}{\left(1+B_{TB,in}\right)}^{N_{mlP}}\right)\left)\right)}---\left(10\right)$

$\frac{C_{TB,ch,mw,l}-C_{TB,ch,p,l}}{C_{TB,ch,b,l}-C_{TB,ch,p,l}}=\exp \left(\frac{V_{w,l}}{K_{TB,l}}\right)---\left(11\right)$

$K_l=0.068{{\mathrm{Re}}_l}^{0.875}{{\mathrm{Sc}}_l}^{025}\frac{D_s}{d_e}---\left(12\right)$

$\frac{C_{TB,ch,mw,l}-C_{TB,ch,p,l}}{C_{TB,ch,b,l}-C_{TB,ch,p,l}}=\exp \left(\frac{V_{w,l}}{K_{TB,l}}\right)---\left(13\right)$

K_l=0.97K_{TB, l}(14)

$P_{l+1}=P_l+\frac{\mathrm{\Δ}z}{2}(-K_{\mathrm{\λ}}6.23{{\mathrm{Re}}_l}^{-03}\frac{{\mathrm{\ρ}}_b}{d_e}\frac{{V_l}^2}{2}-K_{\mathrm{\λ}}6.23{{\mathrm{Re}}_{l+1}}^{-0.3}\frac{{\mathrm{\ρ}}_b}{d_e}\frac{{V_{l+1}}^2}{2})---\left(15\right)$

Wherein A, B, B_TBRespectively pure water and salt are through constant, and P represents that pressure, C represent salinity, and π represents osmotic pressure.ρ_pAnd V_wRepresent density and the flow velocity of fresh water respectively.J_wAnd J_sRespectively pure water flux and salt permeation flux, V_wFor seepage velocity, T is temperature, and K is mass tranfer coefficient, d_eFor the equivalent diameter of charging runner, S_lFor the area of one differentiation element of membrane component, S_l=S_m·n_m/ L, S_mFor the area of single membrane component, L_pvFor the length of pressure vessel, n_mFor the number of pressure vessel membrane component, L_mLength for single membrane component.L is total differentiation element nodes.Re is Reynolds (Reynold's) criterion (Re=ρ Vd_e/ μ), wherein μ is dynamic viscosity, and Sc is the quasi-number of Schmidt (Sc=μ/ρ D_s), D_sFor the diffusion coefficient of salt, Q is flow, and V is charging flow velocity, (V=Q/ (3600S_fcsε_sp), S_fcsFor charging runner cross-sectional area, ε_spFor charging runner filter porosity, Q_{P, n}For total permeant flux, C_{P, n}For on average producing salinity water.σ is reflection coefficient, α₀And α₁The respectively point rate of boric acid and borate ion.pK_aFirst ionization constant for boric acid.K_λFor coefficient of friction, Δ z is integration step, Y_lIt is used for describing the binary variable that in pressure vessel, each differentiation element flows to.FF_dFor contamination factor.E is the activation energy of film, as T≤298K, and e value 25,000J/mol^-1, as T > 298K, e value 22,000J/mol^-1.R is gas constant.B_inFor annual salt through increment rate, N_mlpAverage life for reverse osmosis membrane.Subscript ch is the charging of membrane component or produces water flow passage, and b is strong brine, and f is charging sea water, and p is for producing water, and mw is film surface, and TB is total boron, and boric is boric acid, and borate is borate, and ref is T₀The parameter of film when not polluting when 298K, l is differentiation element node.

The boundary condition of finite difference calculus: z=0, V=V_in, Q=Q_in, C_TB=C_{TB, in}, C=C_chP=P_in。

Step 2. sets up the pressure vessel numerical model of shunting part level two design

Utilize reverse osmotic pressure force container Inner Front End membrane component product water water quality to be better than rear end and flow is bigger, the product water of pressure vessel front end is fed directly to finally produce water, the product water of rear end enters next stage desalination again, and pressure vessel two ends add flow control valve can according to practical situation flexible two ends water outlet proportion (as shown in Figure 1).Its model can be expressed as:

Q_{Ch, b, l+1}=Q_{Ch, b, l}-3600V_{W, l}S_l(16)

Q_{Ch, b, l+1}C_{Ch, b, l+1}-Q_{Ch, b, l}C_{Ch, b, l}=-3600V_{W, l}S_lC_{Ch, p, l}(17)

Q_{Ch, b, l+1}C_{TB, ch, b, l+1}-Q_{Ch, b, l}C_{TB, ch, b, l}=-3600V_{W, l}S_lC_{TB, ch, p, l}(18)

$Q_{p,n,lc}=\underset{l}{\Σ}\left(3600V_{w,l}S{l}_{}{Y}_l\right)---\left(19\right)$

$Q_{p,n,hc}=\underset{l}{\Σ}\left(3600V_{w,l}{S}_l\right(1-Y_l\left)\right)---\left(20\right)$

$Q_{p,n,lc}{C}_{p,n,lc}=\underset{l}{\Σ}\left(3600V_{w,l}{S}_l{C}_{ch,p,l}{Y}_l\right)---\left(21\right)$

$Q_{p,n,lc}{C}_{TB,p,n,lc}=\underset{l}{\Σ}\left(3600V_{w,l}{S}_l{C}_{TB,ch,p,l}{Y}_l\right)---\left(22\right)$

$Q_{p,n,hc}{C}_{p,n,hc}=\underset{l}{\Σ}\left(3600V_{w,l}{S}_l{C}_{ch,p,l}\right(1-Y_l\left)\right)---\left(23\right)$

$Q_{p,n,hc}{C}_{TB,p,n,hc}=\underset{l}{\Σ}\left(3600V_{w,l}{S}_l{C}_{TB,ch,p,l}\right(1-Y_l\left)\right)---\left(24\right)$

Q_{F, n}=Q_{B, n}+Q_{P, n, lc}+Q_{P, n, hc}(25)

Q_{F, n}C_{F, n}=Q_{B, n}C_{B, n}+Q_{P, n, lc}C_{P, n, lc}+Q_{P, n, hc}C_{P, n, hc}(26)

Q_{F, n}C_{TB, f, n}=Q_{B, n}C_{TB, b, n}+Q_{P, n, lc}C_{TB, p, n, lc}+Q_{P, n, hc}C_{TB, p, n, hc}(27)

Wherein binary variable Y represents the product current direction of differentiation element in pressure vessel, and subscript lc represents that water is produced in pressure vessel front end, and hc represents that water is produced in pressure vessel rear end, and n represents the n-th pressure vessel.

The diffusion coefficient D of saline osmotic pressure π, dynamic viscosity μ and salt_sCan be calculated by following fitting formula:

π=4.54047 (10³C/M_sρ)^0.987(28)

μ=(1.4757 × 10^-3+2.4817×10^-6C+9.3287×10^-9C²)exp(-0.02008T)(29)

D_s=6.725 × 10^-6exp(0.1546×10^-3C-2513/(T+273.15))(30)

Wherein M_sMolal weight for solute.

Step 3. sets up the reverse osmosis superstructure model of shunting part level two design

The basic composition of one counter-infiltration system includes reverse osmosis membrane group, pump, energy recycle device, logistics blender and logistics separator etc..Reverse osmosis network packet shown in Fig. 2 is containing N_PSIndividual booster stage and N_ROIndividual reverse osmosis level is constituted.Total total N_PS+ 2 logistics nodes, 2 refer to saline and the fresh water of eventually off reverse osmosis network.N_PSEach node table in individual logistics node is shown with one logistics after high-pressure pump supercharging (or without high-pressure pump supercharging), is directly entered 1 reverse osmosis units.Each reverse osmosis level is made up of multiple parallel pressure vessels, and each pressure vessel is in series by 2～8 membrane components, works under identical operating conditions.One saline every and the fresh water that leave reverse osmosis level can enter N_PS+ 2 logistics nodes.

Each logistics in reverse osmosis superstructure is represented by the function of flow, salinity, boron concentration and pressure.Each charging M in flow distribution case_IN(Q_in, C_in, C_{TB, in,}P_in) M can be divided into through equipressure mixing_OUT(Q_out, C_out, C_{TB, out}, P_out) individual logistics.Introduce both subsidiary streams (Q_{In, out}, C_{In, out}, C_{TB, in, out}, P_{In, out}) represent logistics distributor.Then flow distribution case is expressed as:

$Q_{in}=\underset{out=1}{\overset{M_{OUT}}{\Σ}}{Q}_{in,out}---\left(31\right)$

C_{In, out}=C_inOut=1 ... M_OUT(32)

C_{TB, in, out}=C_{TB, in}Out=1 ... M_OUT(33)

P_{In, out}=P_inOut=1 ... M_OUT(34)

$Q_{out}=\underset{in=1}{\overset{M_{IN}}{\Σ}}{Q}_{in,out}---\left(35\right)$

$Q_{out}{C}_{out}=\underset{in=1}{\overset{M_{IN}}{\Σ}}{Q}_{in,out}{C}_{in}---\left(36\right)$

$Q_{out}{C}_{TB,out}=\underset{in=1}{\overset{M_{IN}}{\Σ}}{Q}_{in,out}{C}_{TB,in}---\left(37\right)$

0=(P_in-P_out)Q_{In, out}In=1 ... M_IN(38)

Formula (31)-(34) represent logistics distributor, formula (35)-(37) represent logistics blender, formula (38) represents isobaric mixed constraints, and in superstructure, water finally produces water to the product of permission reverse osmosis level with system, the strong brine of reverse osmosis level mixes with system feeding.

Contact at merit exchanger mesohigh saline and sea water can cause the mixing between logistics, has a degree of rising in its outlet through the seawater salinity of pressure-exchange.The material balance equation of high-pressure pump and merit exchanger is:

Q_{Ps, 1}=Q_hpp+Q_pxlin(39)

Q_{Ps, 1}C_{Ps, 1}=Q_hppC_hpp+Q_pxlinC_pxlin(40)

Q_{Ps, 1}C_{TB, ps, 1}=Q_hppC_{TB, hpp}+Q_pxlinC_{TB, pxlin}(41)

Q_{RO, 1}=Q_hpp+Q_pxhout(42)

Q_{RO, 1}C_{RO, 1}=Q_hppC_hpp+Q_pxhoutC_pxhout(43)

Q_{RO, 1}C_{TB, RO, 1}=Q_hppC_{TB, hpp}+Q_pxhoutC_{TB, pxhout}(44)

Q_pxhout=Q_pxlin(45)

Q_pxhin=Q_pxlout(46)

L_pxQ_pxhin/ 100=Q_pxhin-Q_pxhout(47)

L_px[%]=0.3924+0.01238P_pxhin(48)

C_pxhout=Mix (C_pxhin-C_pxlin)+C_pxlin(49)

C_{TB, pxhout}=Mix (C_{TB, pxhin}-C_{TB, pxlin})+C_{TB, pxlin}(50)

Mix=6.0057-0.3559OF+0.0084OF²(51)

OF [%]=100 × (Q_pxhin,-Q_pxhout)/Q_pxhin(52)

C_pxloutQ_pxlout=Q_pxlinC_pxlin+Q_pxhinC_pxhin-Q_pxhoutC_pxhout(53)

C_{BT, pxlout}Q_pxlout=Q_pxlinC_{BT, pxlin}+Q_pxhinC_{BT, pxhin}-Q_pxhoutC_{BT, pxhout}(54)

Wherein L_PXFor slip, Mix is volume mixing ratio, OF is lubrication flow, span is-10%≤OF≤15%, and subscript hpp, pxhin, pxlin, pxhout and pxhin represent high-pressure pump, the low pressure feed sea water entering merit exchanger and high-pressure thick saline, the pressurised seawater leaving merit exchanger and pressure release strong brine respectively.

The logistics leaving i-th booster stage is directly entered jth reverse osmosis level.Assuming that with the membrane component of the employing identical type in one-level reverse osmosis pressure container, (pure water passes through constant through constant, solute to its characteristic, boron reflection coefficient, membrane area, charging filter thickness and price etc.) remain unchanged, can be determined, by equation below, the membrane component model k that j-th stage reverse osmosis inner pressure vessel adopts:

$X_j=\underset{k=1}{\overset{K_i}{\mathrm{\Σ}}}{y}_{j,k}{X}_k,j=1,2,3,...,N_{RO},k=1,2---\left(55\right)$

P_j-P_{K, max}≤U(1-y_{J, k}) j=1,2 ..., N_RO, k=1,2 ..., K_t(56)

$\underset{k=1}{\overset{2}{\Σ}}{y}_{j,k}\≤1,j=1,2,3,...,N_{RO}---\left(57\right)$

Y_l-Y_l+1≥0(58)

Wherein y_{J, k}It is binary variable, represents the membrane component choosing kth kind type in j-th stage reverse osmosis when it takes 1, otherwise take 0.Formula (56) defines the maximum intake pressure that membrane component allows.U is a sufficiently large number.K_tIt it is the kind set of reverse-osmosis membrane element.Introduce formula (58) and guarantee that producing water at each differentiation element of pressure vessel Inner Front End or rear end has the consistent flow direction.

Whole reverse osmosis network meets following material balance relationship and the constraint of product water demand:

Q_f=Q_b+Q_p(59)

Q_fC_f=Q_bC_b+Q_pC_p(60)

Q_fC_{TB, f}=Q_bC_{TB, b}+Q_pC_{TB, p}(61)

$Q_b=\underset{j=1}{\overset{N_{RO}}{\Σ}}{Q}_{b,i,j}+Q_{pxlout}---\left(62\right)$

$Q_b{C}_b=\underset{j=1}{\overset{N_{RO}}{\Σ}}{Q}_{b,i,j}{C}_{b,i,j}+Q_{pxlout}{C}_{pxlout}---\left(63\right)$

$Q_b{C}_{TB,b}=\underset{j=1}{\overset{N_{RO}}{\Σ}}{Q}_{b,i,j}{C}_{TB,b,i,j}+Q_{pxlout}{C}_{TB,pxlout}---\left(64\right)$

$Q_p=\underset{j=1}{\overset{N_{RO}}{\Σ}}{Q}_{p,i,j}---\left(65\right)$

$Q_p{C}_p=\underset{j=1}{\overset{N_{RO}}{\Σ}}{Q}_{p,i,j}{C}_{p,i,j}---\left(66\right)$

$Q_p{C}_{TB,p}=\underset{j=1}{\overset{N_{RO}}{\Σ}}{Q}_{p,i,j}{C}_{TB,p,i,j}---\left(67\right)$

Q_p≥Q_{P, lo}(68)

C_p≤C_{P, up}(69)

C_{TB, p}≤C_{TB, p, up}(70)

Q in formula_b、C_bAnd C_{TB, b}Represent respectively and leave the brine flow of reverse osmosis network, salinity and boron concentration, Q_p、C_pAnd C_{TB, p}Represent the flow of product water, salinity and boron concentration respectively.Subscript lo and up represents Minimum requirements value and maximum permissible value respectively.

Step 4. flow system flow and operating condition constraint

For ensureing counter-infiltration system safe operation, set following constraint in a model: the concentration polarization factor is film surface salt concentration C_ch.mw.lWith bulk solution salinity C_{Ch, b.l}Ratio, first-stage reverse osmosis concentration polarization factor ultimate value is 1.2, two-pass reverse osmosis due to its water inlet salinity significantly reduce, the concentration polarization factor is 1.4 to the maximum；Single pressure vessel Max pressure loss is the average permeant flux maximum respectively 20L/ (m in 0.35MPa, the first order and the second level²H) with 40L/ (m²H), the first order and first of second level membrane component maximum permeant flux respectively 35L/ (m²H) with 48L/ (m²H), minimum strong brine flow respectively 3.6m in the first order and second level pressure vessel³/ h and 2.4m³/ h, strong brine concentration is less than 90kg/m³, reverse osmosis charging pH value range is 2～11；Step 5. pressure vessel and membrane component number Integer constrained characteristic

Below equation can by the quantity n of membrane component_{M, j}Pressure vessel number n with jth reverse osmosis level_{Pv, j}Convert binary variable to.

$n_{m,j}=n_{m,j,lo}+\underset{km=1}{\overset{N_b}{\Σ}}{2}^{km-1}{Z}_{km}---\left(71\right)$

$N_b=1+\mathrm{int}\left(\frac{log(n_{m,l,up}-n_{m,l,lo})}{\log \left(2\right)}\right)---\left(72\right)$

$n_{pv,j}=n_{pv,j,lo}+\underset{kpv=1}{\overset{N_n}{\Σ}}{2}^{kpv-1}{Z}_{kpv}+sv-svb---\left(73\right)$

$N_n=1+\mathrm{int}\left(\frac{log(n_{pv,l,up}-n_{pv,l,1o})}{1og\left(2\right)}\right)---\left(74\right)$

Wherein N_{B, j}And N_{Pv, j}Refer to the number of the minimum binary variable needed.n_{M, j, up}、n_{M, j, lo}、n_{Pv, j, up}And n_{Pv, j, lo}Maximum or the minimum membrane component number allowing to place and the maximum or minimum pressure vessel number allowing to place of jth reverse osmosis level in representative pressure container respectively.It is to be noted that formula (72) and formula (74) are used only to calculate N_bAnd N_nValue, not as the constraints of model.The infeasible solution caused in order to avoid being absent from when reverse osmosis level, formula (73) introduces slack variable sv and svb, and it can be used as the addition Item of object function, usual the two slack variable weight value only small (taking 0.001 herein).

Step 6. sets up counter-infiltration system mathematical optimization models

The optimization design problem of counter-infiltration system can be expressed as a mixed integer nonlinear programming (MINLP), with total annual cost minimum for object function, meet the constraints such as process thermodynamics, unit operation, designing requirement.The total annual cost TAC of reverse osmosis comprise year investment cost CC and year operating cost OC two parts, the expression formula of each function is as follows:

CC_SWIP=996 (Q_f24)^0.8(75)

CC_hpp=52 (Δ P_hppQ_hpp)(76)

CC_bp=52 (Δ P_bpQ_pxhin)(77)

CC_px=3134.7Q_hpp ^0.58(78)

${\mathrm{CC}}_m=\underset{j=1}{\overset{N_{RO}}{\Σ}}{C}_{k,j}{n}_{m,j}{n}_{pv,j}+\underset{j=1}{\overset{N_{RO}}{\Σ}}{C}_{pv}{n}_{pv,j}---\left(79\right)$

TCC=1.411 (CC_SWIP+CC_hpp+CC_px+CC_bp+CC_m)(80)

OC_m=0.2C_m(81)

${\mathrm{OC}}_e=C_e{f}_c\·24\·365\·(\frac{P_{SWIP}{Q}_f}{3.6{\mathrm{\η}}_{SWIP}{\mathrm{\η}}_{moter}}+\frac{P_{hpp}{Q}_{hpp}}{3.6{\mathrm{\η}}_{hpp}{\mathrm{\η}}_{moter}}+\frac{(P_{hpp}-P_{pxhout})Q_{pxhout}}{3.6{\mathrm{\η}}_{bp}{\mathrm{\η}}_{moter}})---\left(82\right)$

OC_insrce=0.005TCC (83)

OC_labor=Q_p·24·365·f_c·0.01(84)

OC_ch=Q_f·24·365·f_c·0.0225(85)

OC_maintQ_p·24·365·f_c·0.01(86)

OC_reag=Q_{RO, 2}·24·365·f_c·exp(-16.726+0.91357pH+0.06847pH²)·1.28(87)

OC_O&M=CO_insrce+CO_labor+CO_ch+CO_maint+CO_reag(88)

AOC=OC_m+OC_e+OC_O&M(89)

${\mathrm{\η}}_{px}=\frac{P_{pxhout}{Q}_{pxhout}+P_{pxlout}{Q}_{pxlout}}{P_{pxhin}{Q}_{pxhin}+P_{pxlin}{Q}_{pxlin}}\×100\%---\left(90\right)$

$TAC=TCC/crf+AOC+\underset{j}{\Σ}({\mathrm{sv}}_j+{\mathrm{svb}}_j)---\left(91\right)$

$upc=\frac{TCC/ccr+AOC}{Q_p\·24\·365}---\left(92\right)$

Formula (75) represents investment cost, CC to formula (80)_SWIP、CC_hpp、CC_bpAnd CC_pxRepresent the investment cost of sea water water intake system and early stage pretreatment, high-pressure pump, booster pump and merit exchanger, C respectively_mRepresent total membrane component expense, C_kFor the price of kth kind type membrane component, C_pvFor the price of single pressure vessel, n_jRepresenting the pressure vessel number that j-th stage reverse osmosis introduces, Δ P is pressure reduction, and formula (81) to formula (89) is operation and maintenance cost OC_o&mComputing formula, by manpower expense OC_labor, chemical reagent expense OC_ch, maintenance cost OC_maint, insurance OC_insrceThe expense OC of acid is needed with alkali and post processing needed for adjustment pH value_reagComposition, operating cost AOC includes membrane component renewal cost OC_m, energy consumption cost OC_eWith operation and maintenance expense OC_o&m, η_hpp、η_SWIP、η_bp、η_motor、η_pxRepresent the efficiency of water pump, high-pressure pump, booster pump, motor and merit exchanger, f respectively_cFor loading coefficient, C_eFor electricity price, P_SWIPFor water pump outlet pressure, year, operating cost was by formula (91) calculating, and fresh water cost is calculated by formula (92), and the wherein capital recovery factor is

The system optimization proposition formed is solved by step 7.

Adopt Mathematical Planning software to solve Integral nonlinear program-ming problem mixed above, by composing different initial values to variable, be iterated from multiple initial points, it is thus achieved that the flow process of system optimal and operating condition.

Beneficial effects of the present invention:

The structure of the method for the present invention reverse osmosis mechanism according to seawater desalination system and whole flow process, adopts the mode of exact mechanism to set up the accurate model of the reverse osmosis transport mechanism considering de-boron.Establish the superstructure model of the counter-infiltration system adopting shunting part level two design, model considers the change along pressure vessel brine pressure, concentration and flow, consider the pressure vessel inlet salinity caused due to saline mixing in merit (pressure) exchanger to raise, add system operating condition constraint and ensure the operation of security of system.The present invention has considered the impact of many factors during seawater desalination system optimizes, and introduces reverse osmosis shunting part level two design, it is possible to according to practical situation flexible two ends water outlet proportion.Set up systematic procedure model, by simultaneous solution technology, counter-infiltration system is optimized, water producing cost and the energy consumption of desalinization can be reduced further so that system is produced water and met the standard of Boron contents in drinking water.The present invention is possible not only to counter-infiltration system is designed, it is also possible in system operation, operating parameter is optimized, and has extraordinary application prospect.System model and method for solving that the present invention provides have the good suitability.

Accompanying drawing explanation

Fig. 1 taps part level two design reverse osmosis seawater desalting schematic diagram；

Fig. 2 counter-infiltration system superstructure schematic diagram；

Fig. 3 tradition two-pass reverse osmosis takes off boron seawater desalination system process optimization scheme；

Fig. 4 taps the de-boron seawater desalination system prioritization scheme of part level two design reverse osmosis.

Detailed description of the invention

Below in conjunction with accompanying drawing, the invention will be further described:

The present invention comprises the following steps:

Step 1: set up the wound membrane element desalting process model considering de-boron；

According to reverse osmosis process mechanism and quality and law of conservation of energy, adopt salinity, boron concentration, pressure, flow etc. in differential equation pressure vessel along the axial change of pressure vessel, and differential equation finite difference method is carried out discretization, then consider that the wound membrane element desalting process model of de-boron can be represented by following equations:

$J_{w,l}=A_{ref}{(1-{\mathrm{FF}}_d)}^{N_{mlp}}\exp \[\frac{e}{R}(\frac{1}{298.15}-\frac{1}{273.15+T})\](P_l-\mathrm{\σ}({\mathrm{\π}}_{ch,mw,l}-{\mathrm{\π}}_{ch,p,l}\left)\right)---\left(1\right)$

$J_{s,l}=B_{ref}{(1+B_{in})}^{N_{mlp}}(C_{ch,mw,l}-C_{ch,p,l})---\left(2\right)$

σ=0.997-4.98 × 10^-5T(3)

$B_{TB,l}={\mathrm{\α}}_{0,l}{B}_{bo\stackrel{\·}{n}c}{e}^{\left(0.067\right(T-T_0\left)\right)}+{\mathrm{\α}}_{1,l}{B}_{borate}{e}^{\left(0.049\right(T-T_0\left)\right)}---\left(4\right)$

σ_{TB, l}=α_{0, l}σ_boric+α_{1, l}σ_borate(5)

${\mathrm{pK}}_{a,l}=\frac{2291.90}{T}+0.01756T-3.3850-0.32051{\left(\frac{C_{ch,mw,l}}{1.80655}\right)}^{1/3}---\left(6\right)$

${\mathrm{\α}}_{0,l}={\mathrm{\α}}_{1,l}{10}^{{\mathrm{pK}}_{a,l}-pH}---\left(7\right)$

$V_{w,l}=\frac{J_{w,l}+J_{s,l}}{{\mathrm{\ρ}}_p}---\left(8\right)$

$C_{ch,p,l}=\frac{J_{s,l}}{V_{w,l}}---\left(9\right)$

$C_{TB,ch,p,l}=\frac{(C_{TB,ch,b,l}-C_{TB,ch,p,l})(1-{\mathrm{\σ}}_{TB,l})\exp (V_{w,l}/K_l)}{{\mathrm{\σ}}_{TB,l}(1-\exp (-\left(1-{\mathrm{\σ}}_{TB,l}\right)V_{w,l}/\left(B_{TB,l}{\left(1+B_{TB,in}\right)}^{N_{mlp}}\right)\left)\right)}---\left(10\right)$

$\frac{C_{TB,ch,mw,l}-C_{TB,ch,p,l}}{C_{TB,ch,b,l}-C_{TB,ch,p,l}}=\exp \left(\frac{V_{w,l}}{K_{TB,l}}\right)---\left(11\right)$

$K_l=0.068{\mathrm{Re}}_l^{0875}{{\mathrm{Sc}}_l}^{0.25}\frac{D_s}{d_e}---\left(12\right)$

$\frac{C_{TB,ch,mw,l}-C_{TB,ch,p,l}}{C_{TB,ch,b,l}-C_{TB,ch,p,l}}=\exp \left(\frac{V_{w,l}}{K_{TB,l}}\right)---\left(13\right)$

K_l=0.97K_{TB, l}(14)

$P_{l+1}=P_l+\frac{\mathrm{\Δ}z}{2}(-K_{\mathrm{\λ}}6.23{{\mathrm{Re}}_l}^{-0.3}\frac{{\mathrm{\ρ}}_b}{d_e}\frac{{V_l}^2}{2}-K_{\mathrm{\λ}}6.23{{\mathrm{Re}}_{l+1}}^{-03}\frac{{\mathrm{\ρ}}_b}{d_e}\frac{{V_{l+1}}^2}{2})---\left(15\right)$

Wherein A, B, B_TBRespectively pure water and salt are through constant, and P represents that pressure, C represent salinity, and π represents osmotic pressure.ρ_pAnd V_wRepresent density and the flow velocity of fresh water respectively.J_wAnd J_sRespectively pure water flux and salt permeation flux, V_wFor seepage velocity, T is temperature, and K is mass tranfer coefficient, d_eFor the equivalent diameter of charging runner, S_lFor the area of one differentiation element of membrane component, S_l=S_m·n_m/ L, S_mFor the area of single membrane component, L_pvFor the length of pressure vessel, n_mFor the number of pressure vessel membrane component, L_mLength for single membrane component.L is total differentiation element nodes.Re is Reynolds (Reynold's) criterion (Re=ρ Vd_e/ μ), wherein μ is dynamic viscosity, and Sc is the quasi-number of Schmidt (Sc=μ/ρ D_s), D_sFor the diffusion coefficient of salt, Q is flow, and V is charging flow velocity, (V=Q/ (3600S_fcsε_sp), S_fcsFor charging runner cross-sectional area, ε_spFor charging runner filter porosity, Q_{P, n}For total permeant flux, C_{P, n}For on average producing salinity water.σ is reflection coefficient, α₀And α₁The respectively point rate of boric acid and borate ion.pK_aFirst ionization constant for boric acid.K_λFor coefficient of friction, Δ z is integration step, Y_lIt is used for describing the binary variable that in pressure vessel, each differentiation element flows to.FF_dFor contamination factor.E is the activation energy of film, as T≤298K, and e value 25,000J/mol^-1, as T > 298K, e value 22,000J/mol^-1.R is gas constant.B_inFor annual salt through increment rate, N_mlpAverage life for reverse osmosis membrane.Subscript ch is the charging of membrane component or produces water flow passage, and b is strong brine, and f is charging sea water, and p is for producing water, and mw is film surface, and TB is total boron, and boric is boric acid, and borate is borate, and ref is T₀The parameter of film when not polluting when 298K, l is differentiation element node.

The boundary condition of finite difference calculus: z=0, V=V_in, Q=Q_in, C_TB=C_{TB, in}, C=C_chP=P_in。

Step 2. sets up the pressure vessel numerical model of shunting part level two design

Utilize reverse osmotic pressure force container Inner Front End membrane component product water water quality to be better than rear end and flow is bigger, the product water of pressure vessel front end is fed directly to finally produce water, the product water of rear end enters next stage desalination again, and pressure vessel two ends add flow control valve can according to practical situation flexible two ends water outlet proportion (as shown in Figure 1).Its model can be expressed as:

Q_{Ch, b, l+1}=Q_{Ch, b, l}-3600V_{W, l}S_l(16)

Q_{Ch, b, l+1}C_{Ch, b, l+1}-Q_{Ch, b, l}C_{Ch, b, l}=-3600V_{W, l}S_lC_{Ch, p, l}(17)

Q_{Ch, b, l+1}C_{TB, ch, b, l+1}-Q_{Ch, b, l}C_{TB, ch, b, l}=-3600V_{W, l}S_lC_{TB, ch, p, l}(18)

$Q_{p,n,lc}=\underset{l}{\Σ}\left(3600V_{w,l}{S}_l{Y}_l\right)---\left(19\right)$

$Q_{p,n,hc}=\underset{l}{\Σ}\left(3600V_{w,l}{S}_l\right(1-Y_l\left)\right)---\left(20\right)$

$Q_{p,n,lc}{C}_{p,n,lc}=\underset{l}{\Σ}\left(3600V_{w,l}{S}_l{C}_{ch,p,l}{Y}_l\right)---\left(21\right)$

$Q_{p,n,lc}{C}_{TB,p,n,lc}=\underset{l}{\Σ}\left(3600V_{w,l}{S}_l{C}_{TB,ch,p,l}{Y}_l\right)---\left(22\right)$

$Q_{p,n,hc}{C}_{p,n,hc}=\underset{l}{\Σ}\left(3600V_{w,l}{S}_l{C}_{ch,p,l}\right(1-Y_l\left)\right)---\left(23\right)$

$Q_{p,n,hc}{C}_{TB,p,n,hc}=\underset{l}{\Σ}\left(3600V_{w,l}{S}_l{C}_{TB,ch,p,l}\right(1-Y_l\left)\right)---\left(24\right)$

Q_{F, n}=Q_{B, n}+Q_{P, n, lc}+Q_{P, n, hc}(25)

Q_{F, n}C_{F, n}=Q_{B, n}C_{B, n}+Q_{P, n, lc}C_{P, n, lc}+Q_{P, n, hc}C_{P, n, hc}(26)

Q_{F, n}C_{TB, f, n}=Q_{B, n}C_{TB, b, n}+Q_{P, n, lc}C_{TB, p, n, lc}+Q_{P, n, hc}C_{TB, p, n, hc}(27)

Wherein binary variable Y represents the product current direction of differentiation element in pressure vessel, and subscript lc represents that water is produced in pressure vessel front end, and hc represents that water is produced in pressure vessel rear end, and n represents the n-th pressure vessel.

The diffusion coefficient D of saline osmotic pressure π, dynamic viscosity μ and salt_sCan be calculated by following fitting formula:

π=4.54047 (10³C/M_sρ)^0.987(28)

μ=(1.4757 × 10^-3+2.4817×10^-6C+9.3287×10^-9C²)exp(-0.02008T)(29)

D_s=6.725 × 10^-6exp(0.1546×10^-3C-2513/(T+273.15))(30)

Wherein M_sMolal weight for solute.

Step 3. sets up the reverse osmosis superstructure model of shunting part level two design

The basic composition of one counter-infiltration system includes reverse osmosis membrane group, pump, energy recycle device, logistics blender and logistics separator etc..Reverse osmosis network packet shown in Fig. 2 is containing N_PSIndividual booster stage and N_ROIndividual reverse osmosis level is constituted.Total total N_PS+ 2 logistics nodes, 2 refer to saline and the fresh water of eventually off reverse osmosis network.N_PSEach node table in individual logistics node is shown with one logistics after high-pressure pump supercharging (or without high-pressure pump supercharging), is directly entered 1 reverse osmosis units.Each reverse osmosis level is made up of multiple parallel pressure vessels, and each pressure vessel is in series by 2～8 membrane components, works under identical operating conditions.One saline every and the fresh water that leave reverse osmosis level can enter N_PS+ 2 logistics nodes.

Each logistics in reverse osmosis superstructure is represented by the function of flow, salinity, boron concentration and pressure.Each charging M in flow distribution case_IN(Q_in, C_in, C_{TB, in}, P_in) MOUT (Q can be divided into through equipressure mixing_out, C_out, C_{TB, out}, P_out) individual logistics.Introduce both subsidiary streams (Q_{In, out}, C_{In, out}, C_{TB, in, out}, P_{In, out}) represent logistics distributor.Then flow distribution case is expressed as:

$Q_{in}=\underset{out=1}{\overset{M_{OUT}}{\Σ}}{Q}_{in,out}---\left(31\right)$

C_{In, out}=C_inOut=1 ... M_OUT(32)

C_{TB, in, out}=C_{TB, in}Out=1 ... M_OUT(33)

P_{In, out}=P_inOut=1 ... M_OUT(34)

$Q_{out}=\underset{in=1}{\overset{M_{IN}}{\Σ}}{Q}_{in,out}---\left(35\right)$

$Q_{out}{C}_{out}=\underset{in=1}{\overset{M_{IN}}{\Σ}}{Q}_{in,out}{C}_{in}---\left(36\right)$

$Q_{out}{C}_{TB,out}=\underset{in=1}{\overset{M_{IN}}{\Σ}}{Q}_{in,out}{C}_{TB,in}---\left(37\right)$

0=(P_in-P_out)Q_{In, out}In=1 ... M_IN(38)

Formula (31)-(34) represent logistics distributor, formula (35)-(37) represent logistics blender, formula (38) represents isobaric mixed constraints, and in superstructure, water finally produces water to the product of permission reverse osmosis level with system, the strong brine of reverse osmosis level mixes with system feeding.

Contact at merit exchanger mesohigh saline and sea water can cause the mixing between logistics, has a degree of rising in its outlet through the seawater salinity of pressure-exchange.The material balance equation of high-pressure pump and merit exchanger is:

Contact at merit exchanger mesohigh saline and sea water can cause the mixing between logistics, has a degree of rising in its outlet through the seawater salinity of pressure-exchange.The material balance equation of high-pressure pump and merit exchanger PX-220 is:

Q_{Ps, 1}=Q_hpp+Q_pxlin(39)

Q_{Ps, 1}C_{Ps, 1}=Q_hppC_hpp+Q_pxlinC_pxlin(40)

Q_{Ps, 1}C_{TB, ps, 1}=Q_hppC_{RB, hpp}+Q_pxlinC_{TB, pxlin}(41)

Q_{RO, 1}=Q_hpp+Q_pxhout(42)

Q_{RO, 1}C_{RO, 1}=Q_hppC_hpp+Q_pxhoutC_pxhout(43)

Q_{RO, 1}C_{TB, RO, 1}=Q_hppC_{TB, hpp}+Q_pxhoutC_{TB, pxhout}(44)

Q_pxhout=Q_pxlin(45)

Q_pxhin=Q_pxlout(46)

L_pxQ_pxhin/ 100=Q_pxhin-Q_pxhout(47)

L_px[%]=0.3924+0.01238P_pxhin(48)

C_pxhout=Mix (C_pxhin-C_pxlin)+C_pxlin(49)

C_{TB, pxhout}=Mix (C_{TB, pxhin}-C_{TB, pxlin})+C_{TB, pxlin}(50)

Mix=6.0057-0.3559OF+0.0084OF²(51)

OF [%]=100 × (Q_pxhin,-Q_pxhout)/Q_pxhin(52)

C_pxloutQ_pxlout=Q_pxlinC_pxlin+Q_pxhinC_pxhin-Q_pxhoutC_pxhout(53)

C_{BT, pxlout}Q_pxlout=Q_pxlinC_{BT, pxlin}+Q_pxhinC_{BT, pxhin}-Q_pxhoutC_{BT, pxhout}(54)

Wherein L_pXFor slip, Mix is volume mixing ratio, OF is lubrication flow, span is-10%≤OF≤15%, and subscript hpp, pxhin, pxlin, pxhout and pxhin represent high-pressure pump, the low pressure feed sea water entering merit exchanger and high-pressure thick saline, the pressurised seawater leaving merit exchanger and pressure release strong brine respectively.

The logistics leaving i-th booster stage is directly entered jth reverse osmosis level.Assuming that with the membrane component of the employing identical type in one-level reverse osmosis pressure container, (pure water passes through constant through constant, solute to its characteristic, boron reflection coefficient, membrane area, charging filter thickness and price etc.) remain unchanged, can be determined, by equation below, the membrane component model k that j-th stage reverse osmosis inner pressure vessel adopts:

$X_j=\underset{k=1}{\overset{k_t}{\Σ}}{y}_{j,k}{X}_k,j=1,2,3,...,N_{RO},k=1,2---\left(55\right)$

P_j-P_{K, max}≤U(1-y_{J, k}) j=1,2 ..., N_RO, k=1,2 ..., K_t(56)

$\underset{k=1}{\overset{2}{\Σ}}{y}_{j,k}\≤1,j=1,2,3,...,N_{RO}---\left(57\right)$

Y_l-Y_l+1≥0(58)

Wherein y_{J, k}It is binary variable, represents the membrane component choosing kth kind type in j-th stage reverse osmosis when it takes 1, otherwise take 0.Formula (56) defines the maximum intake pressure that membrane component allows.U is a sufficiently large number.K_tIt it is the kind set of reverse-osmosis membrane element.Introduce formula (58) and guarantee that producing water at each differentiation element of pressure vessel Inner Front End or rear end has the consistent flow direction.

Whole reverse osmosis network meets following material balance relationship and the constraint of product water demand:

Q_f=Q_b+Q_p(59)

Q_fC_f=Q_bC_b+Q_pC_p(60)

Q_fC_{TB, f}=Q_bC_{TB, b}+Q_pC_{TB, p}(61)

$Q_b=\underset{j=1}{\overset{N_{RO}}{\Σ}}{Q}_{b,i,j}+Q_{pxlout}---\left(62\right)$

$Q_b{C}_b=\underset{j=1}{\overset{N_{RO}}{\Σ}}{Q}_{b,i,j}{C}_{b,i,j}+Q_{pxlout}{C}_{pxlout}---\left(63\right)$

$Q_b{C}_{TB,b}=\underset{j=1}{\overset{N_{RO}}{\Σ}}{Q}_{b,i,j}{C}_{TB,b,i,j}+Q_{pxlout}{C}_{TB,pxlout}---\left(64\right)$

$Q_p=\underset{j=1}{\overset{N_{RO}}{\Σ}}{Q}_{p,i,j}---\left(65\right)$

$Q_p{C}_p=\underset{j=1}{\overset{N_{RO}}{\Σ}}{Q}_{p,i,j}{C}_{p,i,j}---\left(66\right)$

$Q_p{C}_{TB,p}=\underset{j=1}{\overset{N_{RO}}{\Σ}}{Q}_{p,i,j}{C}_{TB,p,i,j}---\left(67\right)$

Q_p≥Q_{P, lo}(68)

C_p≤C_{P, up}(69)

C_{TB, p}≤C_{TB, p, up}(70)

Q in formula_b、C_bAnd C_{TB, b}Represent respectively and leave the brine flow of reverse osmosis network, salinity and boron concentration, Q_p、C_pAnd C_{TB, p}Represent the flow of product water, salinity and boron concentration respectively.Subscript lo and up represents Minimum requirements value and maximum permissible value respectively.

Step 4. flow system flow and operating condition constraint

For ensureing counter-infiltration system safe operation, set following constraint in a model: the concentration polarization factor is film surface salt concentration C_ch.mw.lWith bulk solution salinity C_{Ch, b.l}Ratio, first-stage reverse osmosis concentration polarization factor ultimate value is 1.2, two-pass reverse osmosis due to its water inlet salinity significantly reduce, the concentration polarization factor is 1.4 to the maximum；Single pressure vessel Max pressure loss is the average permeant flux maximum respectively 20L/ (m in 0.35MPa, the first order and the second level²H) with 40L/ (m²H), the first order and first of second level membrane component maximum permeant flux respectively 35L/ (m²H) with 48L/ (m²H), minimum strong brine flow respectively 3.6m in the first order and second level pressure vessel³/ h and 2.4m³/ h, strong brine concentration is less than 90kg/m³, reverse osmosis charging pH value range is 2～11.Step 5. pressure vessel and membrane component number Integer constrained characteristic

Below equation can by the quantity n of membrane component_{M, j}Pressure vessel number n with jth reverse osmosis level_{Pv, j}Convert binary variable to.

$n_{m,j}=n_{m,j,lo}+\underset{km=1}{\overset{N_b}{\Σ}}{2}^{km-1}{Z}_{km}---\left(71\right)$

$N_b=1+\mathrm{int}\left(\frac{log(n_{m,l,up}-n_{m,l,lo})}{1og\left(2\right)}\right)---\left(72\right)$

$n_{pv,j}=n_{pv,j,lo}+\underset{kpv=1}{\overset{N_n}{\Σ}}{2}^{kpv-1}{Z}_{kpv}+sv-svb---\left(73\right)$

$N_n=1+\mathrm{int}\left(\frac{log(n_{pv,l,up}-n_{pv,l,lo})}{log\left(2\right)}\right)---\left(74\right)$

Wherein N_{B, j}And N_{Pv, j}Refer to the number of the minimum binary variable needed.n_{M, j, up}、n_{M, j, lo}、n_{Pv, j, up}And n_{Pv, j, lo}Maximum or the minimum membrane component number allowing to place and the maximum or minimum pressure vessel number allowing to place of jth reverse osmosis level in representative pressure container respectively.It is to be noted that formula (72) and formula (74) are used only to calculate N_bAnd N_nValue, not as the constraints of model.The infeasible solution caused in order to avoid being absent from when reverse osmosis level, formula (73) introduces slack variable sv and svb, and it can be used as the addition Item of object function, usual the two slack variable weight value only small (taking 0.001 herein).

Step 6. sets up counter-infiltration system mathematical optimization models

The optimization design problem of counter-infiltration system can be expressed as a mixed integer nonlinear programming (MINLP), with total annual cost minimum for object function, meet the constraints such as process thermodynamics, unit operation, designing requirement.The total annual cost TAC of reverse osmosis comprise year investment cost CC and year operating cost OC two parts.The expression formula of each function is as follows:

CC_SWIP=996 (Q_f24)^0.8(75)

CC_hpp=52 (Δ P_hppQ_hpp)(76)

CC_bp=52 (Δ P_bpQ_pxhin)(77)

CC_px=3134.7Q_hpp ^0.58(78)

${\mathrm{CC}}_m=\underset{j=1}{\overset{N_{RO}}{\Σ}}{C}_{k,j}{n}_{m,j}{n}_{pv,j}+\underset{j=1}{\overset{N_{RO}}{\Σ}}{C}_{pv}{n}_{pv,j}---\left(79\right)$

TCC=1.411 (CC_SWTP+CC_hpp+CC_px+CC_bp+CC_m)(80)

OC_m=0.2C_m(81)

${\mathrm{OC}}_e=C_e{f}_c\·24\·365\·(\frac{P_{SWIP}{Q}_f}{3.6{\mathrm{\η}}_{SWIP}{\mathrm{\η}}_{moter}}+\frac{P_{hpp}{Q}_{hpp}}{3.6{\mathrm{\η}}_{hpp}{\mathrm{\η}}_{moter}}+\frac{(P_{hpp}-P_{pxhout})Q_{pxhout}}{3.6{\mathrm{\η}}_{bp}{\mathrm{\η}}_{moter}})---\left(82\right)$

OC_insrce=0.005TCC (83)

OC_labor=Q_p·24·365·f_c·0.01(84)

OC_ch=Q_f·24·365·f_c·0.0225(85)

OC_maint=Q_p·24·365·f_c·0.01(86)

OC_reag=Q_{RO, 2}·24·365·f_c·exp(-16.726+0.91357pH+0.06847pH²)·1.28(87)

OC_O&M=CO_insrce+CO_labor+CO_ch+CO_maint+CO_reag(88)

AOC=OC_m+OC_e+OC_O&M(89)

${\mathrm{\η}}_{px}=\frac{P_{pxhout}{Q}_{pxhout}+P_{pxlout}{Q}_{pxlout}}{P_{pxhin}{Q}_{pxhin}+P_{pxlin}{Q}_{pxlin}}\×100\%---\left(90\right)$

$TAC=TCC/crf+AOC+\underset{j}{\Σ}({\mathrm{sv}}_j+{\mathrm{svb}}_j)---\left(91\right)$

$upc=\frac{TCC/ccr+AOC}{Q_p\·24\·365}---\left(92\right)$

Formula (75) represents investment cost, CC to formula (80)_SWIP、CC_hpp、CC_bpAnd CC_pxRepresent the investment cost of sea water water intake system and early stage pretreatment, high-pressure pump, booster pump and merit exchanger, C respectively_mRepresent total membrane component expense, C_kFor the price of kth kind type membrane component, C_pvFor the price of single pressure vessel, n_jRepresenting the pressure vessel number that j-th stage reverse osmosis introduces, Δ P is pressure reduction, and formula (81) to formula (89) is operation and maintenance cost OC_o&mComputing formula, by manpower expense OC_labor, chemical reagent expense OC_ch, maintenance cost OC_maint, insurance OC_insrceThe expense OC of acid is needed with alkali and post processing needed for adjustment pH value_reagComposition, operating cost AOC includes membrane component renewal cost OC_m, energy consumption cost OC_eWith operation and maintenance expense OC_o&m, η_hpp、η_SWIP、η_bp、η_motor、η_pxRepresent the efficiency of water pump, high-pressure pump, booster pump, motor and merit exchanger, f respectively_cFor loading coefficient, C_eFor electricity price, P_SWIPFor water pump outlet pressure, year, operating cost was by formula (91) calculating, and fresh water cost is calculated by formula (92), and the wherein capital recovery factor is $ccr=({\left(ir+1\right)}^{n_{LT}}-1)/\left(ir{\left(ir+1\right)}^{n_{LT}}\right).$

The system optimization proposition formed is solved by step 7.

Adopt Mathematical Planning software to solve Integral nonlinear program-ming problem mixed above, by composing different initial values to variable, be iterated from multiple initial points, it is thus achieved that the flow process of system optimal and operating condition.

It is embodied as describing to the present invention below in conjunction with embodiment:

Certain wound membrane element reverse osmosis seawater desalination system is carried out case study by the present invention, and this system adopts the two-pass reverse osmosis flow process of merit exchanger energy recycle device.Membrane module adopts SW30XLE-400i and the BW30-440i of DOW Chemical, is expressed as SW and BW in instances.Traditional design and shunting part level two design are expressed as normal and PS.Table 1 gives the basic parameter of membrane component, and table 2 gives the relevant parameter of Optimized model.For solving this optimal problem, reverse osmotic pressure force container is divided into 30 finite difference nodes.Copenhagen water is studied, its salinity and Boron contents respectively 35kg/m³And 0.005kg/m³, investigate different Boron contents requirements respectively, to meet different water demands (irrigation water of drinking water or different crops).The DICOPT solver adopting universal algebra modeling GAMS software solves Integral nonlinear program-ming mixed above, and PROBLEM DECOMPOSITION is a series of Non-Linear Programming and mixed integer programming subproblem by this solution.By composing different initial values to variable, it is iterated from multiple initial points, filters out optimal case from obtaining multiple local minimum solution.

The basic parameter of table 1. membrane component

Table 2. reverse osmosis Optimized model parameter

Average strong brine density p [kg/m3]	1020
		Universal gas constant R [J/ (mol K)]	8.314
Molecular weight solute Ms	58.5
		SWIP outlet pressure Pswip[MPa]	0.5
Water intaking/high pressure/booster pump efficiency etaswip/ηhpp/ηbp	75%
		Merit exchanger efficiency ηpx	95%
Electric efficiency ηmotor	98%
		Reverse osmosis performance load coefficient fc	0.9
Electricity price Ce[$/(kWh)-1]	0.08
		Pressure vessel price [$]	1000
Friction factor, Kλ	2.4
		Interest rate, Ir	8%
Counter-infiltration system cycle of operation, nLT[year]	25

Model parameter general in example is as follows:

The reverse osmosis produced water yield: 120m³/h；Maximum allowable product water salinity: 0.50kg/m³；Annual film permeant flux is decayed: the first order 7%, the first order 2%；Annual film salt-stopping rate and boron rejection increase: the first order 10%, the first order 5%；Average film assembly service life: 5year；Design cycle: 0year.

First order reverse osmosis charging is sea water, improves pH value and can increase fouling risk, and therefore first order charging pH is set as 7.4, and second level charging is the product water of the first order, and such as calcium, magnesium ion content are relatively low for easy fouling components, thus allows for the second level and regulates pH increase boron-removing rate.By the binary variable Y in model_lWhen being fixed as 0, the scheme obtained is traditional design.

Below, difference will be produced water Boron contents requirement, charging ocean temperature and three aspects of operating condition and will be analyzed by the present invention.

Table 3 gives product water Boron contents requirement respectively 0.0003,0.0005 and 0.001kg/m³Optimum results, charging ocean temperature is 20 DEG C.Traditional design and shunting part level two design all adopt the two steps ro flow process of two grades of strong brine backflows.Require as 0.01kg/m when producing water Boron contents³Time, for traditional design (Fig. 3), 285.8m³The charging sea water of/h enters the first-stage reverse osmosis of 30 pressure vessel compositions after high-pressure pump pressurizes.Producing moisture is two strands, one 49.5m³The product water of/h (produces water salinity and Boron contents respectively 0.319kg/m³And 0.00135kg/m³) after the 10.45 of pH value raising, entering into second level desalination again, another stock is fed directly to finally produce water.The strong brine of two-pass reverse osmosis is relatively low due to its salinity, can be transported to charging sea water.Is produced from the first order pressure vessel rear end water and the second level produce water be mixed to get meet produce salinity water and Boron contents demand finally produce water.

For shunting part level two design (Fig. 4), 263.2m³The charging sea water of/h enters the first-stage reverse osmosis of 27 pressure vessel compositions after high-pressure pump adherence pressure.Maximum with traditional design it is distinctive in that product water (salinity and the Boron contents respectively 0.248kg/m of first-stage reverse osmosis pressure device front end³And 0.00116kg/m³) it is fed directly to finally produce water.The water that produces of pressure vessel rear end enters into, after the 10.34 of pH value raising, the two-pass reverse osmosis desalination again comprising 3 pressure vessels.The pressure vessel number adopting the counter-infiltration system tapping part level two design required compared with tradition two-pass reverse osmosis design is less.On the whole, shunting part level two design can save the water producing cost of 2.06～5.35% and the energy consumption of 1.90～4.43%.

Table 3. is different produces the counter-infiltration system prioritization scheme that water Boron contents requires.

Charging ocean temperature is to affect counter-infiltration system design and the important parameter run, and table 4 is the charging ocean temperature prioritization scheme when 15～35 DEG C.Physical property and the permeability of the membrane of sea water are all had impact by charging ocean temperature, and when temperature improves, permeability of the membrane increases, and seawater viscosity reduces, and water is easier to pass through film.Therefore system feeding pressure raises with ocean temperature and reduces, thus reducing system energy consumption.Water producing cost raises with temperature and first increases, and after temperature is more than 25 DEG C, water producing cost increases, and the Changing Pattern of the system response rate is contrary with water producing cost.The rejection of boron is had large effect by temperature equally, and when temperature improves, boron all increases through constant and boron mass tranfer coefficient.Boron mass tranfer coefficient increase can weaken the concentration polarization phenomenon on film surface, increases temperature and also can reduce the ionization constant pK of boric acid_a, increase the boratory ratio of high rejection, therefore the rejection of boron is the combined effect result of above-mentioned three kinds of factors.When raising with temperature, the reduction of water ratio is produced in pressure vessel front end, it was shown that boron rejection is gradually lowered.Part level two design is tapped no longer applicable when ocean temperature is 35 DEG C.

The counter-infiltration system prioritization scheme of table 4. different feeds ocean temperature

Reverse osmosis membrane can gradually degrade along with the increase performance of operating time, and the operating condition of counter-infiltration system needs corresponding adjustment.Table 5 gives when operation temperature is 25 DEG C, and producing the maximum allowable boron concentration of water is 0.0005kg/m³Time the annual operating condition of counter-infiltration system.Owing in pressure vessel in running, the number of membrane component is not easy to adjust, therefore in each grade pressure vessels the number of membrane component be fixed as operation year be optimum results when 0 year.

Optimum results shows, along with annual film properties deteriorates, film pure water through performance is gradually lowered, and the operation pressure of counter-infiltration system needs to be gradually increased.The response rate of counter-infiltration system and every one-level reverse osmosis pressure container number need to make to adjust to reduce water producing cost accordingly.Reduction along with film boron rejection, it is necessary to be gradually reduced pressure vessel front end product water and be delivered to the final flow producing water.Therefore, the water producing cost of system and energy consumption are all along with the operating time is gradually increased.

Table 5 counter-infiltration system operating condition situation over time

(^aIn every one-level reverse osmosis pressure container, the number of membrane component is fixed as operating time optimum results of (new membrane component) when being 0 year)

Instance analysis shows: compared with tradition two-stage reverse osmosis system, set forth herein that shunting part two-stage reverse osmosis system can effectively reduce water producing cost and the energy consumption of de-boron counter-infiltration system, can also reduce the membrane component number of two-pass reverse osmosis simultaneously.2. the reverse osmosis seawater desalination system considering de-boron is had large effect by charging ocean temperature, and along with charging ocean temperature raises, boron rejection is gradually lowered.3. reverse osmosis membrane can gradually degrade along with the increase performance of operating time, and the operating condition of counter-infiltration system can be optimized by model in this paper.The optimum results that difference is produced the requirement of water Boron contents, temperature and operating condition shows, system model and method for solving that the present invention provides have the good suitability.

Below the example of the invention has been illustrated, but the invention is not limited to described example, those of ordinary skill in the art can also make various equivalent modification or replacement, these equivalent modification or replacement under the premise without prejudice to the invention spirit and be all contained in the application claim limited range.

Unaccomplished matter of the present invention is known technology.

Claims (1)

1. two grades of wound membrane element reverse osmosis seawater desalting network systems optimum methods of shunting part considering de-boron, it is characterised in that the method comprises the following steps:

Step 1: set up the wound membrane element desalting process model considering de-boron；

According to reverse osmosis process mechanism and quality and law of conservation of energy, adopt salinity, boron concentration, pressure, flow etc. in differential equation pressure vessel along the axial change of pressure vessel, and differential equation finite difference method is carried out discretization, then consider that the wound membrane element desalting process model of de-boron can be represented by following equations:

$J_{w,l}=A_{ref}{(1-{\mathrm{FF}}_d)}^{N_{mlp}}\exp \[\frac{e}{R}(\frac{1}{298.15}-\frac{1}{273.15+T})\](P_l-\mathrm{\σ}({\mathrm{\π}}_{ch,mw,l}-{\mathrm{\π}}_{ch,p,l}\left)\right)---\left(1\right)$

$J_{s,l}=B_{ref}{(1+B_{in})}^{N_{mlp}}(C_{ch,mw,l}-C_{ch,p,l})---\left(2\right)$

σ=0.997-4.98 × 10^-5T(3)

$B_{TB,l}={\mathrm{\α}}_{0,l}{B}_{bonc}{e}^{\left(0.067\right(T-T_0\left)\right)}+{\mathrm{\α}}_{1,l}{B}_{borate}{e}^{\left(0.049\right(T-T_0\left)\right)}---\left(4\right)$

σ_{TB, l}=α_{0, l}σ_boric+α_{L, l}σ_borate(5)

${\mathrm{pK}}_{a,l}=\frac{2291.90}{T}+0.01756T-3.3850-0.32051{\left(\frac{C_{ch,mw,l}}{1.80655}\right)}^{1/3}---\left(6\right)$

${\mathrm{\α}}_{0,l}={\mathrm{\α}}_{1,l}{10}^{{\mathrm{pK}}_{a,l}-pH}---\left(7\right)$

$V_{w,l}=\frac{J_{w,l}+J_{s,l}}{{\mathrm{\ρ}}_p}---\left(8\right)$

$C_{ch,p,l}=\frac{J_{s,l}}{V_{w,l}}---\left(9\right)$

$C_{TB,ch,p,l}=\frac{(C_{TB,ch,b,l}-C_{TB,ch,p,l})(1-{\mathrm{\σ}}_{TB,l})\exp (V_{w,l}/K_l)}{{\mathrm{\σ}}_{TB,l}(1-\exp (-(1-{\mathrm{\σ}}_{TB,l})V_{w,l}/\left(B_{TB,l}{(1+B_{TB,m})}^{N_{mlp}}\right)\left)\right)}---\left(10\right)$

$\frac{C_{TB,ch,mw,l}-C_{TB,ch,p,l}}{C_{TB,ch,b,l}-C_{TB,ch,p,l}}=\exp \left(\frac{V_{w,l}}{K_{TB,l}}\right)---\left(11\right)$

$K_l=0.068{{\mathrm{Re}}_l}^{0.875}{{\mathrm{Sc}}_l}^{0.25}\frac{D_s}{d_e}---\left(12\right)$

$\frac{C_{TB,ch,mw,l}-C_{TB,ch,p,l}}{C_{TB,ch,b,l}-C_{TB,ch,p,l}}=\exp \left(\frac{V_{w,l}}{K_{TB,l}}\right)---\left(13\right)$

K_l=0.97K_{TB, l}(14)

$P_{l+1}=P_l+\frac{\mathrm{\Δ}z}{2}(-K_{\mathrm{\λ}}6.23{{\mathrm{Re}}_l}^{0.3}\frac{{\mathrm{\ρ}}_b}{d_e}\frac{{V_l}^2}{2}-K_{\mathrm{\λ}}6.23{{\mathrm{Re}}_{l+1}}^{-0.3}\frac{{\mathrm{\ρ}}_b}{d_e}\frac{{V_{l+1}}^2}{2})---\left(15\right)$

Wherein A, B, BTB respectively pure water and salt are through constant, and P represents that pressure, C represent that salinity, π represent osmotic pressure, ρ_pAnd V_wRepresent density and the flow velocity of fresh water, J respectively_wAnd J_sRespectively pure water flux and salt permeation flux, V_wFor seepage velocity, T is temperature, and K is mass tranfer coefficient, d_eFor the equivalent diameter of charging runner, S_lFor the area of one differentiation element of membrane component, S_l=S_m·n_m/ L, S_mFor the area of single membrane component, L_pvFor the length of pressure vessel, n_mFor the number of pressure vessel membrane component, L_mFor the length of single membrane component, L is total differentiation element nodes, and Re is Reynolds (Reynold's) criterion, Re=ρ Vd_e/ μ, wherein, for dynamic viscosity, Sc is the quasi-number of Schmidt, Sc=μ/ρ D_s, D_sFor the diffusion coefficient of salt, Q is flow, and V is charging flow velocity, V=Q/ (3600S_fcsε_sp, S_fcsFor charging runner cross-sectional area, ε_spFor charging runner filter porosity, Q_{P, n}For total permeant flux, C_{P, n}For on average producing salinity water, σ is reflection coefficient, α₀And α₁The respectively point rate of boric acid and borate ion, pK_aFor the first ionization constant of boric acid, K_λFor coefficient of friction, Δ z is integration step, Y_lIt is used for describing the binary variable that in pressure vessel, each differentiation element flows to, FF_dFor contamination factor, e is the activation energy of film, as T≤298K, and e value 25,000J/mol^-1, as T > 298K, e value 22,000J/mol^-1, R is gas constant, B_inFor annual salt through increment rate, N_mlpFor the average life of reverse osmosis membrane, subscript ch is the charging of membrane component or produces water flow passage, and b is strong brine, and f is charging sea water, and p is for producing water, and mw is film surface, and TB is total boron, and boric is boric acid, and borate is borate, and ref is T₀The parameter of film when not polluting when 298K, l is differentiation element node；

The boundary condition of finite difference calculus: z=0, V=V_m, Q=Q_in, C_TB=C_{TB, in}, C=C_chP=P_in；

Step 2. sets up the pressure vessel numerical model of shunting part level two design

Utilize reverse osmotic pressure force container Inner Front End membrane component product water water quality to be better than rear end and flow is bigger, the product water of pressure vessel front end is fed directly to finally produce water, the product water of rear end enters next stage desalination again, pressure vessel two ends add flow control valve can according to practical situation flexible two ends water outlet proportion, and its model can be expressed as:

Q_{Ch, b, l+1}=Q_{Ch, b, l}-3600V_{W, l}S_l(16)

Q_{Ch, b, l+1}C_{Ch, b, l+1}-Q_{Ch, b, l}C_{Ch, b, l}=-3600V_{W, l}S_lC_{Ch, p, l}(17)

Q_{Ch, b, l+1}C_{TB, ch, b, l+1}-Q_{Ch, b, l}C_{TB, ch, b, l}=-3600V_{W, l}S_lC_{TB, ch, p, l}(18)

$Q_{p,n,lc}=\underset{l}{\Σ}\left(3600V_{w,l}{S}_l{Y}_l\right)---\left(19\right)$

$Q_{p,n,hc}=\underset{l}{\Σ}\left(3600V_{w,l}{S}_l\right(1-Y_l\left)\right)---\left(20\right)$

$Q_{p,n,lc}{C}_{p,n,lc}=\underset{l}{\Σ}\left(3600V_{w,l}{S}_l{C}_{ch,p,l}{Y}_l\right)---\left(21\right)$

$Q_{p,n,lc}{C}_{TB,p,n,lc}=\underset{l}{\Σ}\left(3600V_{w,l}{S}_l{C}_{TB,ch,p,l}{Y}_l\right)---\left(22\right)$

$Q_{p,n,hc}{C}_{p,n,hc}=\underset{l}{\Σ}\left(3600V_{w,l}{S}_l{C}_{ch,p,l}\right(1-Y_l\left)\right)---\left(23\right)$

$Q_{p,n,hc}{C}_{TB,p,n,hc}=\underset{l}{\Σ}\left(3600V_{w,l}{S}_l{C}_{TB,ch,p,l}\right(1-Y_l\left)\right)---\left(24\right)$

Q_{F, n}=Q_{B, n}+Q_{P, n, lc}+Q_{P, n, hc}(25)

Q_{F, n}C_{F, n}=Q_{B, n}C_{B, n}+Q_{P, n, lc}C_{P, n, lc}+Q_{P, n, hc}C_{P, n, hc}(26)

Q_{F, n}C_{TB, f, n}=Q_{B, n}C_{TB, b, n}+Q_{P, n, lc}C_{TB, p, n, lc}+Q_{P, n, hc}C_{TB, p, n, hc}(27)

Wherein binary variable Y represents the product current direction of differentiation element in pressure vessel, and subscript lc represents that water is produced in pressure vessel front end, and hc represents that water is produced in pressure vessel rear end, and n represents the n-th pressure vessel；

The diffusion coefficient D of saline osmotic pressure π, dynamic viscosity μ and salt_sCan be calculated by following fitting formula:

π=4.54047 (10³C/M_sρ)^0.987(28)

μ=(1.4757 × 10^-3+2.4817×10^-6C+9.3287×10^-9C²)exp(-0.02008T)(29)

D_s=6.725 × 10^-6exp(0.1546×10^-3C-2513/(T+273.15))(30)

Wherein M_sMolal weight for solute；

Step 3. sets up the reverse osmosis superstructure model of shunting part level two design

The basic composition of one counter-infiltration system includes reverse osmosis membrane group, pump, energy recycle device, logistics blender and logistics separator etc., comprises N_PSIndividual booster stage and N_ROIndividual reverse osmosis level, total N_PS+ 2 logistics nodes, 2 refer to the saline and fresh water that leave reverse osmosis network, N_PSEach node table in individual logistics node is shown with one logistics after high-pressure pump supercharging, or without high-pressure pump supercharging, it is directly entered 1 reverse osmosis units, each reverse osmosis level is made up of multiple parallel pressure vessels, each pressure vessel is in series by 2～8 membrane components, working under identical operating conditions, one saline every and the fresh water that leave reverse osmosis level can enter N_PS+ 2 logistics nodes, each logistics in network is represented by the function of flow, salinity, boron concentration and pressure, each charging M in flow distribution case_INM can be divided into through equipressure mixing_OUTIndividual logistics, then flow distribution case is expressed as:

$Q_{in}=\underset{out=1}{\overset{M_{OUT}}{\Σ}}{Q}_{in,out}---\left(31\right)$

C_{In, out}=C_inOut=1 ... M_OUT(32)

C_{TB, in, out}=C_{TB, in}Out=1 ... M_OUT(33)

P_{In, out}=P_inOut=1 ... M_OUT(34)

$Q_{out}{C}_{TB,out}=\underset{in=1}{\overset{M_{IN}}{\Σ}}{Q}_{in,out}{C}_{TB,in}---\left(37\right)$

0=(P_in-P_out)Q_{In, out}In=1 ... M_IN(38)

Formula (31)-(34) represent logistics distributor, formula (35)-(37) represent logistics blender, formula (38) represents isobaric mixed constraints, and in superstructure, water finally produces water to the product of permission reverse osmosis level with system, the strong brine of reverse osmosis level mixes with system feeding；

Contact at merit exchanger mesohigh saline and sea water can cause the mixing between logistics, has a degree of rising in its outlet through the seawater salinity of pressure-exchange, and the material balance equation of high-pressure pump and merit exchanger is:

Q_{Ps, 1}=Q_hpp+Q_pxlin(39)

Q_{Ps, 1}C_{Ps, 1}=Q_hppC_hpp+Q_pxlinC_pxlm(40)

Q_{Ps, 1}C_{TB, ps, 1}=Q_hppC_{TB, hpp}+Q_pxlinC_{TB, pxlin}(41)

Q_{RO, 1}=Q_hpp+Q_pxhout(42)

Q_{RO, 1}C_{RO, 1}=Q_hppC_hpp+Q_pxhoutC_pxhout(43)

Q_{RO, 1}C_{TB, RO, 1}=Q_hppC_{TB, hpp}+Q_pxhoutC_{TB, pxhout}(44)

Q_pxhout=Q_pxlin(45)

Q_pxhin=Q_pxlout(46)

L_pxQ_pxhin/ 100=Q_pxhin-Q_pxhout(47)

L_px[%]=0.3924+0.01238P_pxhin(48)

C_pxhout=Mix (C_pxhin-C_pxlin)+C_pxlin(49)

C_{TB, pxhout}=Mix (C_{TB, pxhin}-C_{TB, pxlin})+C_{TB, pxlin}(50)

Mix=6.0057-0.3559OF+0.0084OF²(51)

OF [%]=100 × (Q_Pxhin,-Q_pxhout)/Q_pxhin(52)

C_pxloutQ_pxlout=Q_pxlinC_pxlin+Q_pxhinC_pxhin-Q_pxhoutC_pxhout(53)

C_{BT, pxlout}Q_pxlout=Q_pxlinC_{BT, pxlin}+Q_pxhinC_{BT, pxhin}-Q_pxhoutC_{BT, pxhout}(54)

Wherein L_PXFor slip, Mix is volume mixing ratio, OF is lubrication flow, span is-10%≤OF≤15%, and subscript hpp, pxhin, pxlin, pxhout and pxhin represent high-pressure pump, the low pressure feed sea water entering merit exchanger and high-pressure thick saline, the pressurised seawater leaving merit exchanger and pressure release strong brine respectively；

The logistics leaving i-th booster stage is directly entered jth reverse osmosis level, assuming that with the membrane component of the employing identical type in one-level reverse osmosis pressure container, its characteristic such as pure water passes through constant through constant, solute, boron reflection coefficient, membrane area, charging filter thickness and price etc. remain unchanged, and can be determined, by equation below, the membrane component model k that j-th stage reverse osmosis inner pressure vessel adopts:

$X_j=\underset{k=1}{\overset{K_t}{\Σ}}{y}_{j,k}{X}_k,j=1,2,3,\mathrm{...},N_{RO},k=1,2---\left(55\right)$

P_j-P_{K, max}≤U(1-y_{J, k}) j=1,2 ..., N_RO, k=1,2 ..., K_t(56)

$\underset{k=1}{\overset{2}{\Σ}}{y}_{j,k}\≤1,j=1,2,3,...,N_{RO}---\left(57\right)$

Y_l-Y_l+1≥0(58)

Introduce y_{J, k}It is binary variable, represents the membrane component choosing kth kind type in j-th stage reverse osmosis when it takes 1, otherwise take 0；Formula (56) defines the maximum intake pressure that membrane component allows, and U is a sufficiently large number, K_tIt is the kind set of reverse-osmosis membrane element, introduces formula (58) and guarantee that producing water at each differentiation element of pressure vessel Inner Front End or rear end has the consistent flow direction；

Whole reverse osmosis network meets following material balance relationship and product water constraint of demand:

Q_f=Q_b+Q_p(59)

Q_fC_f=Q_bC_b+Q_pC_p(60)

Q_fC_{TB, f}=Q_bC_TB,b+Q_pC_{TB, p}(61)

$Q_b=\underset{j=1}{\overset{N_{RO}}{\Σ}}{Q}_{b,i,j}+Q_{pxlout}---\left(62\right)$

$Q_b{C}_b=\underset{j=1}{\overset{N_{RO}}{\Σ}}{Q}_{b,i,j}{C}_{b,i,j}+Q_{pxlout}{C}_{pxlout}---\left(63\right)$

$Q_b{C}_{TB,b}=\underset{j=1}{\overset{N_{RO}}{\Σ}}{Q}_{b,i,j}{C}_{TB,b,i,j}+Q_{pxlout}{C}_{TB,pxlout}---\left(64\right)$

$Q_p=\underset{j=1}{\overset{N_{RO}}{\Σ}}{Q}_{p,i,j}---\left(65\right)$

$Q_p{C}_p=\underset{j=1}{\overset{N_{RO}}{\Σ}}{Q}_{p,i,j}{C}_{p,i,j}---\left(66\right)$

$Q_p{C}_{TB.p}=\underset{j=1}{\overset{N_{RO}}{\Σ}}{Q}_{p,i,j}{C}_{TB,p,i,j}---\left(67\right)$

Q_p≥Q_{P, lo}(68)

C_p≤C_{P, up}(69)

C_{TB, p}≤C_{TB, p, up}(70)

Q in formula_b、C_bAnd C_{TB, b}Represent respectively and leave the brine flow of reverse osmosis network, salinity and boron concentration, Q_p、C_pAnd C_{TB, p}Representing the flow of product water, salinity and boron concentration respectively, subscript lo and up represents Minimum requirements value and maximum permissible value respectively；

Step 4. flow system flow and operating condition constraint

For ensureing counter-infiltration system safe operation, set following constraint in a model: the concentration polarization factor is film surface salt concentration C_ch.mw.lWith bulk solution salinity C_{Ch, b.l}Ratio, first-stage reverse osmosis concentration polarization factor ultimate value is 1.2, two-pass reverse osmosis due to its water inlet salinity significantly reduce, the concentration polarization factor is 1.4 to the maximum；Single pressure vessel Max pressure loss is the average permeant flux maximum respectively 20L/ (m in 0.35MPa, the first order and the second level²H) with 40L/ (m²H), the first order and first of second level membrane component maximum permeant flux respectively 35L/ (m²H) with 48L/ (m²H), minimum strong brine flow respectively 3.6m in the first order and second level pressure vessel³/ h and 2.4m³/ h, strong brine concentration is less than 90kg/m³, reverse osmosis charging pH value range is 2～11；

Step 5. pressure vessel and membrane component number Integer constrained characteristic

Below equation can by the quantity n of membrane component_{M, j}Pressure vessel number n with jth reverse osmosis level_{Pv, j}Convert binary variable to:

$n_{m,j}=n_{m,j,lo}+\underset{km=1}{\overset{N_b}{\Σ}}{2}^{km-1}{Z}_{km}---\left(71\right)$

$N_b=1+\mathrm{int}\left(\frac{log(n_{m,l,up}-n_{m,l,lo})}{log\left(2\right)}\right)---\left(72\right)$

$n_{pv,j}=n_{pv,j,lo}+\underset{kpv=1}{\overset{N_n}{\Σ}}{2}^{kpv-1}{Z}_{kpv}+sv-svb---\left(73\right)$

$N_n=1+\mathrm{int}\left(\frac{log(n_{pv,l,up}-n_{pv,l,lo})}{log\left(2\right)}\right)---\left(74\right)$

Wherein N_{B, j}And N_{Pv, j}Refer to the number of the minimum binary variable needed, n_{M, j, up}、n_{M, j, lo}、n_{Pv, l, up}And n_{Pv, j, lo}Maximum or the minimum membrane component number allowing to place and the maximum or minimum pressure vessel number allowing to place of jth reverse osmosis level in representative pressure container respectively；It is to be noted that formula (72) and formula (74) are used only to calculate N_bAnd N_nValue, not as the constraints of model；The infeasible solution caused in order to avoid being absent from when reverse osmosis level, introduces slack variable sv and svb in formula (73), and it can be used as the addition Item of object function, and usual the two slack variable weight value is only small, takes 0.001 herein；

Step 6. sets up counter-infiltration system mathematical optimization models

The optimization design problem of counter-infiltration system can be expressed as a mixed integer nonlinear programming, with total annual cost minimum for object function, meet the constraints such as process thermodynamics, unit operation, designing requirement；The total annual cost TAC of reverse osmosis comprise year investment cost CC and year operating cost OC two parts, the expression formula of each function is as follows:

CC_SWIP=996 (Q_f24)^0.8(75)

CC_hpp=52 (Δ P_hppQ_hpp)(76)

CC_bp=52 (Δ P_bpQ_pxhin)(77)

CC_px=3134.7Q_hpp ^0.58(78)

${\mathrm{CC}}_m=\underset{j=1}{\overset{N_{RO}}{\Σ}}{C}_{k,j}{n}_{m,j}{n}_{pv,j}+\underset{j=1}{\overset{N_{RO}}{\Σ}}{C}_{pv}{n}_{pv,j}---\left(79\right)$

TCC=1.411 (CC_SWIP+CC_hpp+CC_px+CC_bp+CC_m)(80)

OC_m=0.2C_m(81)

${\mathrm{OC}}_e=C_e{f}_c\·24\·365\·(\frac{P_{SWIP}{Q}_f}{3.6{\mathrm{\η}}_{SWIP}{\mathrm{\η}}_{moter}}+\frac{P_{hpp}{Q}_{hpp}}{3.6{\mathrm{\η}}_{hpp}{\mathrm{\η}}_{moter}}+\frac{(P_{hpp}-P_{pxhout})Q_{pxhout}}{3.6{\mathrm{\η}}_{bp}{\mathrm{\η}}_{moter}})---\left(82\right)$

OC_insroe=0.005TCC (83)

OC_labor=Q_p·24·365·f_c·0.01(84)

OC_ch=Q_f·24·365·f_c·0.0225(85)

OC_maint=Q_p·24·365·f_c·0.01(86)

OC_reag=Q_{RO, 2}·24·365·f_c·exp(-16.726+0.91357pH+0.06847pH²)·1.28(87)

OC_O&M=CO_insrce+CO_labor+CO_ch+CO_maint+CO_reag(88)

AOC=OC_m+OC_e+OC_O&M(89)

${\mathrm{\η}}_{px}=\frac{P_{pxhout}{Q}_{pxhout}+P_{pxlout}{Q}_{pxlout}}{P_{pxhin}{Q}_{pxhin}+P_{pxlin}{Q}_{pxlin}}\×100\%---\left(90\right)$

$TAC=TCC/crf+AOC+\underset{j}{\Σ}({\mathrm{sv}}_j+{\mathrm{svb}}_j)---\left(91\right)$

$upc=\frac{TCC/ccr+AOC}{Q_p\·24\·365}---\left(92\right)$

Formula (75) represents investment cost, CC to formula (80)_SWIP、CC_hpp、CC_bpAnd CC_pxRepresent the investment cost of sea water water intake system and early stage pretreatment, high-pressure pump, booster pump and merit exchanger, C respectively_mRepresent total membrane component expense, C_kFor the price of kth kind type membrane component, C_pvFor the price of single pressure vessel, n_jRepresenting the pressure vessel number that j-th stage reverse osmosis introduces, Δ P is pressure reduction, and formula (81) to formula (89) is operation and maintenance cost OC_o&mComputing formula, by manpower expense OC_labor, chemical reagent expense OC_ch, maintenance cost OC_maint, insurance OC_insrceThe expense OC of acid is needed with alkali and post processing needed for adjustment pH value_reagComposition, operating cost AOC includes membrane component renewal cost OC_m, energy consumption cost OC_eWith operation and maintenance expense OC_o&m, η_hpp、η_SWIP、η_bp、η_motor、η_pxRepresent the efficiency of water pump, high-pressure pump, booster pump, motor and merit exchanger, f respectively_cFor loading coefficient, C_eFor electricity price, P_SWIPFor water pump outlet pressure, year, operating cost was by formula (91) calculating, and fresh water cost is calculated by formula (92), and the wherein capital recovery factor is $ccr=({\left(ir+1\right)}^{n_{LT}}-1)/\left(ir{\left(ir+1\right)}^{n_{LT}}\right);$

The system optimization proposition formed is solved by step 7.

Adopt Mathematical Planning software to solve Integral nonlinear program-ming problem mixed above, by composing different initial values to variable, be iterated from multiple initial points, it is thus achieved that the flow process of system optimal and operating condition.