CN114186438A - Method for establishing proton exchange membrane electrolytic cell performance prediction model for hydrogen production - Google Patents

Method for establishing proton exchange membrane electrolytic cell performance prediction model for hydrogen production Download PDF

Info

Publication number
CN114186438A
CN114186438A CN202111634997.2A CN202111634997A CN114186438A CN 114186438 A CN114186438 A CN 114186438A CN 202111634997 A CN202111634997 A CN 202111634997A CN 114186438 A CN114186438 A CN 114186438A
Authority
CN
China
Prior art keywords
anode
cathode
electrolytic cell
proton exchange
exchange membrane
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202111634997.2A
Other languages
Chinese (zh)
Other versions
CN114186438B (en
Inventor
王博文
焦魁
倪萌
杜青
刘智
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Tianjin University
Original Assignee
Tianjin University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Tianjin University filed Critical Tianjin University
Priority to CN202111634997.2A priority Critical patent/CN114186438B/en
Publication of CN114186438A publication Critical patent/CN114186438A/en
Application granted granted Critical
Publication of CN114186438B publication Critical patent/CN114186438B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • C—CHEMISTRY; METALLURGY
    • C25—ELECTROLYTIC OR ELECTROPHORETIC PROCESSES; APPARATUS THEREFOR
    • C25B—ELECTROLYTIC OR ELECTROPHORETIC PROCESSES FOR THE PRODUCTION OF COMPOUNDS OR NON-METALS; APPARATUS THEREFOR
    • C25B1/00—Electrolytic production of inorganic compounds or non-metals
    • C25B1/01—Products
    • C25B1/02—Hydrogen or oxygen
    • C25B1/04—Hydrogen or oxygen by electrolysis of water
    • C—CHEMISTRY; METALLURGY
    • C25—ELECTROLYTIC OR ELECTROPHORETIC PROCESSES; APPARATUS THEREFOR
    • C25B—ELECTROLYTIC OR ELECTROPHORETIC PROCESSES FOR THE PRODUCTION OF COMPOUNDS OR NON-METALS; APPARATUS THEREFOR
    • C25B9/00—Cells or assemblies of cells; Constructional parts of cells; Assemblies of constructional parts, e.g. electrode-diaphragm assemblies; Process-related cell features
    • C25B9/17—Cells comprising dimensionally-stable non-movable electrodes; Assemblies of constructional parts thereof
    • C25B9/19—Cells comprising dimensionally-stable non-movable electrodes; Assemblies of constructional parts thereof with diaphragms
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y02E60/30—Hydrogen technology
    • Y02E60/36—Hydrogen production from non-carbon containing sources, e.g. by water electrolysis
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P20/00—Technologies relating to chemical industry
    • Y02P20/10—Process efficiency
    • Y02P20/133—Renewable energy sources, e.g. sunlight

Landscapes

  • Engineering & Computer Science (AREA)
  • Chemical & Material Sciences (AREA)
  • Physics & Mathematics (AREA)
  • Chemical Kinetics & Catalysis (AREA)
  • Electrochemistry (AREA)
  • Materials Engineering (AREA)
  • Metallurgy (AREA)
  • Organic Chemistry (AREA)
  • Theoretical Computer Science (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • Geometry (AREA)
  • General Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Inorganic Chemistry (AREA)
  • Electrolytic Production Of Non-Metals, Compounds, Apparatuses Therefor (AREA)

Abstract

The invention discloses a method for establishing a proton exchange membrane electrolytic cell performance prediction model for hydrogen production, which realizes the prediction of input voltage required by an electrolytic cell under different operating conditions. The method for establishing the performance prediction model of the constructed proton exchange membrane electrolytic cell for hydrogen production comprises 5 parts: solving the required input voltage of the electrolytic cell, solving the activation overpotential of the anode and the cathode, solving the mass transfer overpotential, solving the ohm overpotential and calculating the mass transfer of the two-phase flow. The modeling method provided by the invention accurately describes the electrochemical reaction mechanism and the internal mass transfer characteristic of the proton exchange membrane electrolytic cell, and simultaneously considers the two-phase transmission characteristic in the electrolytic cell. The method has high practical significance and accuracy for predicting the performance of the proton exchange membrane electrolytic cell. The input parameters of the model cover various operating condition parameters and battery material design parameters in the operation of the electrolytic cell, and the influence of the core parameters on the performance of the electrolytic cell can be effectively predicted.

Description

Method for establishing proton exchange membrane electrolytic cell performance prediction model for hydrogen production
Technical Field
The invention belongs to the field of electrochemical hydrogen production, and particularly relates to a calculation method for predicting the performance of an electrolytic cell.
Background
The hydrogen is an energy medium which is clean, renewable and widely available, and the development and the utilization of the hydrogen energy have very important significance for reducing the emission of greenhouse gases, realizing carbon peak reaching, realizing energy diversification and ensuring energy safety. The hydrogen is prepared by electrolyzing water, and can be combined with various renewable energy sources.
The hydrogen production by utilizing the proton exchange membrane electrolytic cell has the advantages of high hydrogen purity, low gas transmembrane rate, suitability for high current density operation and the like. However, the proton exchange membrane electrolytic cell also has the problems of high cost, insufficient performance (efficiency) and the like, and a complex two-phase (reactant liquid water and resultant hydrogen and oxygen) flow process exists inside the proton exchange membrane electrolytic cell, which directly affects the performance (required input voltage) of the proton exchange membrane electrolytic cell. Through reasonable design of operation conditions and optimization of key parameters of the electrolytic cell, the method is very important for improving the performance of the electrolytic cell and reducing energy consumption. The simulation modeling is a key technology which can effectively predict and optimize the performance of the electrolytic cell at lower economic cost. The method for establishing the proton exchange membrane electrolytic cell performance prediction model is mainly applied to the design and development stages of electrolytic cells and provides a method for the optimal design of predicting the electrolytic cell performance.
Disclosure of Invention
The invention aims to provide a method for establishing a proton exchange membrane electrolytic cell performance prediction model for hydrogen production, which can realize the prediction of input voltage required by an electrolytic cell under different operating conditions.
The method for establishing the performance prediction model of the constructed proton exchange membrane electrolytic cell for hydrogen production comprises 5 parts: solving the required input voltage of the electrolytic cell, solving the activation overpotential of the anode and the cathode, solving the mass transfer overpotential, solving the ohm overpotential and calculating the mass transfer of the two-phase flow. The method comprises the following specific steps:
(1) solving for the required input voltage of the cell
V＝Voc+Vact_a+Vact_c+Vcon_a+Vcon_c+Vohm 1-1
Wherein a reversible voltage VocThe calculation formula of (A) is as follows:
Figure BDA0003435308520000011
(2) solving for the activation overpotentials of the anode and cathode
Figure BDA0003435308520000012
Figure BDA0003435308520000013
Figure BDA0003435308520000021
Figure BDA0003435308520000022
(3) Solving mass transfer overpotentials for anode and cathode
Figure BDA0003435308520000023
Figure BDA0003435308520000024
Figure BDA0003435308520000025
Figure BDA0003435308520000026
(4) Solving for ohmic overpotentials
Figure BDA0003435308520000027
Figure BDA0003435308520000028
(5) Two-phase flow mass transfer calculation
The step comprises the step (3) above
Figure BDA0003435308520000029
sg,cl,cAnd solving λ in step (4), specifically comprising: (5.1) parameters to be calculated in the anode flow channel:
Jlq,inAin-(Jlq,reac+Jlq,cro)Aact＝uout,aclqAinslq,out,a 5-1
Figure BDA00034353085200000210
Figure BDA00034353085200000211
Figure BDA00034353085200000212
Figure BDA00034353085200000213
wherein
Figure BDA00034353085200000214
Jlq,reacThe following equation is obtained:
Figure BDA00034353085200000215
Figure BDA00034353085200000216
Figure BDA00034353085200000217
(5.2) parameters to be calculated in the cathode flow channel:
Jlq,croAact＝uout,cclqAinslq,out,c-Nvp,out,c 5-9
Figure BDA0003435308520000031
Nvp,out,c＝uout,ccvpAinsg,out,c 5-11
slq,out,c+sg,out,c＝1 5-12
Figure BDA0003435308520000032
Figure BDA0003435308520000033
wherein c isvp、
Figure BDA0003435308520000034
Can be obtained by the following formula:
Figure BDA0003435308520000035
Figure BDA0003435308520000036
Figure BDA0003435308520000037
(5.3) parameters to be calculated in the anode and cathode porous electrodes:
Figure BDA0003435308520000038
Figure BDA0003435308520000039
the relationship between hydraulic pressure and liquid water saturation is described by the Leverett equation in the porous electrode, i.e. plq,ch,a、plq,cl,a、plq,ch,c、plq,cl,cCorresponding solution slq,ch,a、slq,cl,a、slq,ch,c、slq,cl,c. At the same time
Figure BDA00034353085200000310
And slq,cl,a、sg,cl,cAnd slq,cl,cThe following relationships exist:
Figure BDA00034353085200000311
sg,cl,c＝1-slq,cl,c 5-21
(5.4) parameters to be calculated for the water transport across the membrane are as follows:
Jlq,cro＝Jlq,hyd+Jlq,dmw+Jlq,nd 5-22
Figure BDA00034353085200000312
Figure BDA00034353085200000313
Figure BDA00034353085200000314
Figure BDA0003435308520000041
simultaneous solution of equations 5-1 to 5-26, combined with well-known mathematical fits, can be used to obtain
Figure BDA0003435308520000042
sg,cl,c，λ。
Will be provided with
Figure BDA0003435308520000043
sg,cl,cCarrying out the step (3) to obtain the mass transfer overpotential; substituting lambda into step (4) to obtain ohmic overpotential, and further adding V solved in steps (2), (3) and (4)act,a、Vact,c、Vcon_a、Vcon_c、VohmAnd (4) substituting each overpotential into the step (1), and obtaining the required input voltage of the electrolytic cell.
In the process of calculating the voltage required by the electrolytic cell, the invention considers the voltage loss caused by various overpotentials in the operation process of the electrolytic cell, analyzes the mass transfer characteristics in the electrolytic cell by solving the two-phase flow mass transfer part in the step (5), and realizes the accurate solution of the mass transfer overpotential and the ohmic overpotential of the electrolytic cell.
The invention has the characteristics and beneficial effects that: the provided modeling method accurately describes the electrochemical reaction mechanism and the internal mass transfer characteristic of the proton exchange membrane electrolytic cell, and simultaneously considers the two-phase transmission characteristic in the electrolytic cell, so that the method has high practical significance and accuracy for predicting the performance (input voltage) of the proton exchange membrane electrolytic cell. The input parameters of the model cover various operating condition parameters (such as temperature, pressure and the like) and battery material design parameters (proton exchange membrane physical properties, porous electrode physical properties and the like) in the running process of the electrolytic cell, namely, the influence of the core parameters on the performance of the electrolytic cell can be effectively predicted, so that a large amount of economic and time cost consumed by experimental tests can be avoided, and the efficiency of the design and optimization process of the electrolytic cell is improved.
Drawings
FIG. 1 shows that the current density I is 0 to 2.0A cm-2The corresponding input voltage of the electrolytic cell changes.
FIG. 2 is a polarization curve for an electrolytic cell operated at a temperature of 313K, 333K, 353K in an example of the invention.
Detailed Description
The method steps of the present invention are further described by the following specific calculation examples, which should be construed as illustrative and not limiting, and the scope of the present invention is not limited thereby.
The model parameters designed in the embodiment of the invention are given in a specific calculation process.
(1) Solving the required input voltage of the electrolytic cell:
V＝Voc+Vact_a+Vact_c+Vcon_a+Vcon_c+Vohm 1-1
reversible voltage VocThe calculation can be expressed as:
Figure BDA0003435308520000044
T＝353K,F＝96485C mol-1，R＝8.314J mol-1K-1，pa＝1.0atm，pc＝1.0atm，
Figure BDA0003435308520000045
calculating to obtain Voc＝1.1795V。
(2) Solving for the activation overpotentials of the anode and cathode:
Figure BDA0003435308520000051
Figure BDA0003435308520000052
Figure BDA0003435308520000053
Figure BDA0003435308520000054
the required input voltage increases with increasing operating current density due to the polarization characteristics of the cell, and in one operating regime, the current density-voltage curve of the cell is referred to as the polarization curve, the primary manifestation describing cell performance.
To form the polarization curve, the current density I is set in the range of 0 to 20000A m-2(2.0A cm-2). In the following description of the present embodiment, I is 10000A m-2(1.0A cm-2) The calculation is performed as an example.
αa＝αc＝0.5，i0,a＝0.1A cm-2,i0,c＝1000A cm-2. Calculating to obtain Vact,a＝0.4096V,Vact,c＝0.0764V。
(3) Solving the mass transfer overpotentials of the anode and cathode:
Figure BDA0003435308520000055
Figure BDA0003435308520000056
Figure BDA0003435308520000057
Figure BDA0003435308520000058
Figure BDA0003435308520000059
εadl＝εcdl0.3, wherein
Figure BDA00034353085200000510
sg,cl,cThe values are determined by the formulas 5-6, 5-16, 5-5 and 5-21 in the step (5).
(4) Solving for ohmic overpotential:
Figure BDA00034353085200000511
Figure BDA00034353085200000512
in the formula ofmem＝50.4×10-6m，δadl＝δcdl＝300×10-6m，σs＝200S m-1，Rcon＝10-5Ωm2. Wherein lambda is obtained by the two-phase flow mass transfer calculation part (5).
(5) Two-phase flow mass transfer calculation
(5.1) anode flow channel:
Jlq,inAin-(Jlq,reac+Jlq,cro)Aact＝uout,aclqAinslq,out,a 5-1
Figure BDA0003435308520000061
Figure BDA0003435308520000062
Figure BDA0003435308520000063
Figure BDA0003435308520000064
Figure BDA0003435308520000065
Figure BDA0003435308520000066
Figure BDA0003435308520000067
slq,in,a＝1，
Figure BDA0003435308520000068
Aact＝10-4m2，Ain＝10-6m2，clq＝5.56×104mol m-3，uout,a＝2.0×10-4m s-1to obtain
Figure BDA0003435308520000069
The other parameters are intermediate variables which can be eliminated in the simultaneous solution with the subsequent formula.
(5.2) cathode flow channel:
Jlq,croAact＝uout,cclqAinslq,out,c-Nvp,out,c 5-9
Figure BDA00034353085200000610
Nvp,out,c＝uout,ccvpAinsg,out,c 5-11
slq,out,c+sg,out,c＝1 5-12
Figure BDA00034353085200000611
Figure BDA00034353085200000612
Figure BDA00034353085200000613
Figure BDA00034353085200000614
Figure BDA00034353085200000615
water saturation vapor pressure psatThe following relationship exists with temperature:
Figure BDA0003435308520000071
to obtain
Figure BDA0003435308520000072
(5.3) anode and cathode porous electrodes:
Figure BDA0003435308520000073
Figure BDA0003435308520000074
Figure BDA0003435308520000075
Figure BDA0003435308520000076
Figure BDA0003435308520000077
sg,cl,c＝1-slq,cl,c 5-21
Kadl＝Kcdl＝10-11m2，μlq＝4.05×10-4kg m-1s-1。
(5.4) water transmembrane transport process:
Jlq,cro＝Jlq,hyd+Jlq,dmw+Jlq,nd 5-22
Figure BDA0003435308520000078
Figure BDA0003435308520000079
Figure BDA00034353085200000710
Km＝10-19m2，ρm＝1980kg m-3，EW＝1.1kg mol-1，ωa＝ωc＝0.2。
the relationship between hydraulic pressure and liquid water saturation is described by the Leverett equation in porous electrodes:
Figure BDA00034353085200000711
at the anode: p is a radical ofg＝pap0(ii) a At the cathode: p is a radical ofg＝pcp0；σlq＝0.0626N m-1。
An empirical fitting formula of the film water content in the catalytic layer and the liquid water saturation in the catalytic layer is as follows:
λa＝14+2.8×slq,cl,a 6-5
λc＝14+2.8×slq,cl,c 6-6
the water content lambda of the proton exchange membrane in a membrane state can be approximately equal to the average value of the water content of the membrane state in the catalytic layers of the anode and the cathode:
Figure BDA0003435308520000081
Dmwfitting an empirical formula with the membrane water content lambda of the proton exchange membrane:
Figure BDA0003435308520000082
ndfitting an empirical formula with the membrane water content lambda of the proton exchange membrane:
Figure BDA0003435308520000083
in the above process, the formula 6-1 to 6-8 is a well-known mathematical fitting formula, and the combined formula 5-1 to 5-26 and the formula 6-1 to 6-8 are used to obtain
Figure BDA0003435308520000084
sg,cl,c＝0.9238，λ＝14.8043。
Solving in step (5)
Figure BDA0003435308520000085
sg,cl,cCarry over to step (3), find Vcon_a＝2.9332×10-4V,Vcon_c＝3.026×10-4V。
Substituting the lambda solved in the step (5) into the step (4) to obtain Vohm＝0.2277V。
V obtained in the step (2)act,a、Vact,cIn step (3), V is obtainedcon_a、Vcon_cIn step (4), V is obtainedohmSubstituting the formula 1-1 in the step (1), the input voltage required for obtaining the electrolytic cell is V-1.8938V.
The above process calculates that I is 1.0A cm-2The required input voltage of the electrolytic cell. The calculated current density I is in the range of 0 to 2.0A cm-2Then, the corresponding cell input voltage forms the polarization curve of the cell, as shown in fig. 1. Therefore, by using the modeling method, the input voltage required by the electrolytic cell under different current densities can be effectively predicted.
Further, the water electrolysis cell can be set to operate at different operating temperatures, namely, the input quantity T of the model is changed, and fig. 2 shows the polarization curves of the electrolysis cell operating at the temperatures of 313K, 333K and 353K, so that the input voltage required by the operation of the electrolysis cell can be found to be gradually reduced along with the increase of the operating temperature. Therefore, by increasing the operation temperature of the electrolytic cell, the voltage required by the electrolytic cell can be effectively reduced, and the energy consumption is increased.
Through the simulation modeling mode, the performance of various electrolytic cell operation conditions can be effectively predicted, a large amount of economic and time cost consumed by experimental tests is avoided, and the efficiency of the electrolytic cell design and optimization process is improved.

Claims (1)

1. The method for establishing the proton exchange membrane electrolytic cell performance prediction model for hydrogen production is characterized by comprising the following steps:
(1) solving for the required input voltage of the cell
V＝Voc+Vact_a+Vact_c+Vcon_a+Vcon_c+Vohm 1-1
Wherein V represents the input voltage of the electrolytic cell; vocCan representA reverse voltage; vact_aAnd Vact_cRespectively representing the activation overpotentials of the anode and the cathode; vcon_aAnd Vcon_cRespectively representing the mass transfer overpotential of the anode and the cathode; vohmWhich represents an ohmic over-potential,
wherein a reversible voltage VocThe calculation formula of (A) is as follows:
Figure FDA0003435308510000011
wherein T is temperature; f is a Faraday constant; r is an ideal gas constant; p is a radical ofaAnd pcAnode oxygen partial pressure and cathode hydrogen partial pressure, respectively;
Figure FDA00034353085100000113
in order to obtain the water activity,
(2) solving for the activation overpotentials of the anode and cathode
Figure FDA0003435308510000012
Figure FDA0003435308510000013
Figure FDA0003435308510000014
Figure FDA0003435308510000015
Wherein I is the current density; alpha is alphaaAnd alphacThe charge exchange coefficients of the anode and the cathode respectively; i in formulae 2-3 and 2-40,a、i0,cExchange current densities of the anode and cathode, respectively; wherein iref,a、iref,cAre respectively yangReference exchange current densities of the pole and cathode.
(3) Solving mass transfer overpotentials for anode and cathode
Figure FDA0003435308510000016
Figure FDA0003435308510000017
Figure FDA0003435308510000018
Figure FDA0003435308510000019
In formula 3-3
Figure FDA00034353085100000110
Is the effective oxygen concentration in the anode catalytic layer,
Figure FDA00034353085100000111
is the oxygen concentration; in formulas 3 to 4
Figure FDA00034353085100000112
Is the concentration of hydrogen in the cathode catalytic layer,
Figure FDA0003435308510000021
is the hydrogen concentration;
Figure FDA0003435308510000022
is an oxygen reference concentration;
Figure FDA0003435308510000023
is a hydrogen reference concentration; epsilonadlAnd εcdlAnode and cathode porous electrode porosities, respectively;
Figure FDA0003435308510000024
the oxygen saturation in the porous electrode of the anode; sg,dl-cl,cIs the gas saturation in the porous electrode of the cathode,
(4) solving for ohmic overpotentials
Figure FDA0003435308510000025
Figure FDA0003435308510000026
In the formula ofmem、δadl、δcdlThe thicknesses of the anode porous electrode and the cathode porous electrode of the proton exchange membrane respectively; sigmasElectron conductivity for porous electrodes; rconIs a contact resistance; sigmamIs the ionic conductivity of the proton exchange membrane; lambda is the water content of the proton exchange membrane, lambda needs to be solved by the two-phase flow mass transfer calculation part in the step (5),
(5) two-phase flow mass transfer calculation
The step comprises the step (3) above
Figure FDA0003435308510000027
sg,cl,cThe solution of (a) is carried out,
(5.1) the parameters to be calculated in the anode flow channel are as follows:
Jlq,inAin-(Jlq,reac+Jlq,cro)Aact＝uout,aclqAinslq,out,a 5-1
Figure FDA0003435308510000028
Figure FDA0003435308510000029
Figure FDA00034353085100000210
Figure FDA00034353085100000211
in the formula Jlq,inRepresenting the liquid water flux supplied into the anode flow channels; j. the design is a squarelq,reacRepresents the flux of liquid water consumed by the electrochemical reaction; j. the design is a squarelq,croRepresents the flux of water across the membrane from the anode to the cathode;
Figure FDA00034353085100000212
represents the flux of oxygen generated by the electrochemical reaction; slq,ch,aIndicating the average saturation of liquid water in the anode flow channel; slq,in,a、slq,out,aRespectively representing the liquid water saturation at the inlet and the outlet of the anode runner;
Figure FDA00034353085100000213
represents the average saturation of oxygen in the anode flow channel;
Figure FDA00034353085100000214
respectively representing the oxygen saturation at the inlet and the outlet of the anode runner; a. theinRepresenting the anode flow channel inlet area; a. theactRepresenting the activation area of the electrolytic cell; u. ofout,aRepresenting the flow velocity in the anode flow channel; c. ClqIs liquid water concentration; wherein
Figure FDA00034353085100000215
Jlq,reac、Jlq,croThe following equation is obtained:
Figure FDA00034353085100000216
Figure FDA0003435308510000031
Figure FDA0003435308510000032
in the formula p0Which is indicative of the normal atmospheric pressure,
(5.2) the parameters to be calculated in the cathode flow channel are as follows:
Jlq,croAact＝uout,cclqAinslq,out,c-Nvp,out,c 5-9
Figure FDA0003435308510000033
Nvp,out,c＝uout,ccvpAinsg,out,c 5-11
slq,out,c+sg,out,c＝1 5-12
Figure FDA0003435308510000034
Figure FDA0003435308510000035
in the formula Nvp,out,cRepresents the molar flow of water vapor discharged from the outlet of the cathode flow channel;
Figure FDA0003435308510000036
represents the flux of hydrogen gas generated by the electrochemical reaction; u. ofout,cRepresenting the flow rate in the cathode flow channel; slq,ch,cIndicating the liquid in the cathode flow channelState level mean saturation; slq,out,cRespectively representing the liquid water saturation at the outlet of the cathode flow channel; sg,ch,cRepresents the average saturation of the gas in the cathode flow channel; sg,out,cRespectively representing the gas saturation at the outlet of the cathode flow channel; c. CvpIs the water vapor concentration; wherein c isvp、
Figure FDA00034353085100000313
Can be obtained by the following formula:
Figure FDA0003435308510000037
Figure FDA0003435308510000038
Figure FDA0003435308510000039
in the formula psatWhich represents the saturated vapor pressure of water,
(5.3) the parameters to be calculated in the anode and cathode porous electrodes are as follows:
Figure FDA00034353085100000310
Figure FDA00034353085100000311
in the formula
Figure FDA00034353085100000312
Represents the effective permeability of the anode and cathode porous electrodes, respectively; mu.slqRepresents the dynamic viscosity of liquid water; p is a radical oflq,ch,a、plq,ch,aRespectively represent an anode flow channel and a catalyst layerInternal hydraulic pressure; p is a radical oflq,ch,c、plq,ch,cRespectively representing the hydraulic pressure in the cathode flow channel and the catalytic layer, and describing the relation between the hydraulic pressure and the liquid water saturation by a Leverett equation in the porous electrode, namely plq,ch,a、plq,cl,a、plq,ch,c、plq,cl,cCorresponding solution slq,ch,a、slq,cl,a、slq,ch,c、slq,cl,cAt the same time sO2,cl,a、slq,cl,a、sg,cl,c、slq,cl,cThe following relationships exist:
Figure FDA0003435308510000041
sg,cl,c＝1-slq,cl,c 5-21
(5.4) parameters to be calculated for the water transport across the membrane are as follows:
Jlq,cro＝Jlq,hyd+Jlq,dmw+Jlq,nd 5-22
Figure FDA0003435308510000042
Figure FDA0003435308510000043
Figure FDA0003435308510000044
in the formula Jlq,hydRepresenting the flux of water transport across the membrane by hydraulic osmosis; j. the design is a squarelq,dmwFlux of water transport across membrane due to diffusion of water in membrane state, Jlq,ndRepresenting the flux transported by water across the membrane due to the electroosmotic drag effect; kmRepresents the permeability of the proton exchange membrane; rhomRepresents the density of the proton exchange membrane, EW represents the equivalent mass of the proton exchange membrane; dmwRepresents the water diffusivity of the proton exchange membrane，DmwThe correlation with the membrane state water content lambda of the proton exchange membrane can be calculated by a corresponding empirical fitting formula; lambda [ alpha ]a、λcRespectively representing the membrane state water content in the anode and cathode catalytic layers, the numerical value of the membrane state water content and the liquid water saturation s in the catalytic layerslq,cl,a、slq,cl,cCorrelation, which can be calculated by a corresponding empirical fit formula; omegaaAnd ωcRespectively representing the electrolyte content in the anode and cathode catalytic layers; n isdDenotes the electroosmotic drag coefficient, ndThe correlation with the membrane state water content lambda of the proton exchange membrane can be calculated by a corresponding empirical fitting formula; the water content lambda of the proton exchange membrane is equal to the average value of the water content of the membrane in the anode catalytic layer and the cathode catalytic layer:
Figure FDA0003435308510000045
from 5-1 to 5-26 in tandem, in combination with well-known mathematical fits, can be found
Figure FDA0003435308510000046
sg,cl,c，λ，
Will be provided with
Figure FDA0003435308510000047
sg,cl,cThe step (3) is carried out to obtain the mass transfer overpotential Vcon_a、Vcon_c(ii) a Substituting lambda into step (4) to determine the ohmic overpotential VohmFurther, V solved in steps (2), (3) and (4)act,a、Vact,c、Vcon_a、Vcon_c、VohmAnd (3) carrying out the step (1) by each overpotential, so as to obtain the required input voltage of the electrolytic cell.
CN202111634997.2A 2021-12-27 2021-12-27 Method for establishing proton exchange membrane electrolytic cell performance prediction model for hydrogen production Active CN114186438B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202111634997.2A CN114186438B (en) 2021-12-27 2021-12-27 Method for establishing proton exchange membrane electrolytic cell performance prediction model for hydrogen production

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202111634997.2A CN114186438B (en) 2021-12-27 2021-12-27 Method for establishing proton exchange membrane electrolytic cell performance prediction model for hydrogen production

Publications (2)

Publication Number Publication Date
CN114186438A true CN114186438A (en) 2022-03-15
CN114186438B CN114186438B (en) 2022-10-25

Family

ID=80606362

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202111634997.2A Active CN114186438B (en) 2021-12-27 2021-12-27 Method for establishing proton exchange membrane electrolytic cell performance prediction model for hydrogen production

Country Status (1)

Country Link
CN (1) CN114186438B (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115000464A (en) * 2022-08-02 2022-09-02 中车工业研究院(青岛)有限公司 Parameter regulation and control method, device, equipment and medium of PEMFC

Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20030091878A1 (en) * 2001-11-13 2003-05-15 Eldat Communication Ltd. Hydrogen generators for fuel cells
CN106848351A (en) * 2016-12-26 2017-06-13 天津大学 The method that proton exchange film fuel battery performance forecast model is set up
CN106960970A (en) * 2017-02-23 2017-07-18 天津大学 Proton Exchange Membrane Fuel Cells internal water distribution forecasting method
GB201905475D0 (en) * 2018-04-17 2019-05-29 Xergy Incorporated Electrolysis cell assembly utilizing an anion exchange membrane
CN112909303A (en) * 2020-12-21 2021-06-04 天津大学 Method for establishing transient real-time model of proton exchange membrane fuel cell
WO2021142883A1 (en) * 2020-01-13 2021-07-22 清华大学 Fuel cell low-temperature starting performance prediction method and system
CN113704961A (en) * 2021-07-14 2021-11-26 湖南大学 Method for predicting transient operation performance of proton exchange membrane fuel cell

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20030091878A1 (en) * 2001-11-13 2003-05-15 Eldat Communication Ltd. Hydrogen generators for fuel cells
CN106848351A (en) * 2016-12-26 2017-06-13 天津大学 The method that proton exchange film fuel battery performance forecast model is set up
CN106960970A (en) * 2017-02-23 2017-07-18 天津大学 Proton Exchange Membrane Fuel Cells internal water distribution forecasting method
GB201905475D0 (en) * 2018-04-17 2019-05-29 Xergy Incorporated Electrolysis cell assembly utilizing an anion exchange membrane
WO2021142883A1 (en) * 2020-01-13 2021-07-22 清华大学 Fuel cell low-temperature starting performance prediction method and system
CN112909303A (en) * 2020-12-21 2021-06-04 天津大学 Method for establishing transient real-time model of proton exchange membrane fuel cell
CN113704961A (en) * 2021-07-14 2021-11-26 湖南大学 Method for predicting transient operation performance of proton exchange membrane fuel cell

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
刘杰等: "质子交换膜燃料电池的稳态分析", 《能源研究与信息》 *
张亚等: "质子交换膜燃料电池二维全电池两相流综合数值模型", 《化工学报》 *
戚志东等: "基于模糊PID的质子交换膜燃料电池输出电压控制", 《南京理工大学学报》 *

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115000464A (en) * 2022-08-02 2022-09-02 中车工业研究院(青岛)有限公司 Parameter regulation and control method, device, equipment and medium of PEMFC

Also Published As

Publication number Publication date
CN114186438B (en) 2022-10-25

Similar Documents

Publication Publication Date Title
Roshandel et al. The effects of porosity distribution variation on PEM fuel cell performance
Nafchi et al. A parametric study of polymer membrane electrolyser performance, energy and exergy analyses
CN112909303B (en) Method for establishing transient real-time model of proton exchange membrane fuel cell
CN109657348B (en) Modeling method for proton exchange membrane fuel cell
Barragán et al. Estimation of the membrane methanol diffusion coefficient from open circuit voltage measurements in a direct methanol fuel cell
CN108875166B (en) Modeling method for recycling fuel cell anode hydrogen by adopting electrochemical hydrogen pump
Sudaroli et al. An experimental study on the effect of membrane thickness and PTFE (polytetrafluoroethylene) loading on methanol crossover in direct methanol fuel cell
Ni et al. Electrochemistry modeling of proton exchange membrane (PEM) water electrolysis for hydrogen production
CN112635783B (en) Fuel cell based on metal foam with differential permeability and without gas diffusion layer
CN114006009B (en) Modeling method of proton exchange membrane fuel cell coupled with agglomeration of catalytic layer
Zhao et al. Dynamic behaviour and control strategy of high temperature proton exchange membrane electrolyzer cells (HT-PEMECs) for hydrogen production
CN114186438B (en) Method for establishing proton exchange membrane electrolytic cell performance prediction model for hydrogen production
Yuan et al. Voltage response and two-phase flow during mode switching from fuel cell to water electrolyser in a unitized regenerative fuel cell
Kareemulla et al. Comprehensive one-dimensional, semi-analytical, mathematical model for liquid-feed polymer electrolyte membrane direct methanol fuel cells
Diaz et al. A component-level model of polymer electrolyte membrane electrolysis cells for hydrogen production
Ying et al. Simulation study on the microscopic characteristics of electrochemical Bunsen reaction in the sulfur–iodine cycle for renewable hydrogen production
Sone et al. Water electrolysis by the direct water supply to the solid polymer electrolyte through the interdigitated structure of the electrode
CA2561634A1 (en) Fuel cell
Hu et al. Diffusion–convection/electrochemical model studies on polybenzimidazole (PBI) fuel cell based on AC impedance technique
Han et al. Modeling of interfacial resistance effects on the performance and efficiency for electrolyzer energy storage
CN103151547A (en) Composite fuel cell
Ying et al. Modeling and numerical study of SO2-depolarized electrolysis for hydrogen production in the hybrid sulfur cycle
Dedigama et al. An electrochemical impedance spectroscopy study and two phase flow analysis of the anode of polymer electrolyte membrane water electrolyser
Cespedes et al. Effect of Water Content in the Gas Diffusion Layer of H 2/O 2 PEM Fuel Cell
Wang et al. Optimization of channel dimensions and gas diffusion layer thickness based on mass transfer characteristics of proton exchange membrane fuel cell

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant