Methods for determining local state variables of an electrochemical cell and system with an electrochemical cell

Abstract

The invention relates to a method for determining local state variables of an electrochemical cell. The method comprises the steps of: dividing the electrochemical cell into levels (13), each comprising several segments (14); determining a distribution of a state variable of the electrochemical cell over the segments (14) of at least one of the levels (13) using a physical module; and determining at least a further distribution of at least a further state variable of the electrochemical cell over the segments (14) of at least one of the levels (13) using at least a further physical module. The steps aimed at determining distributions of state variables are repeated alternately until a convergence criterion is reached. In each repetition, the most recently determined state variable distribution is processed as the input. The invention further relates to a system with an electrochemical cell.

Description

[0001] The invention relates to a method for determining local state variables of an electrochemical cell. Furthermore, the invention relates to a system comprising an electrochemical cell.

[0002] From DE 10 2025 115 470 A1 a model for determining the aging of a polymer membrane electrolysis cell is known.

[0003] The inventive method for determining local state variables of an electrochemical cell comprises the following steps: - Dividing the electrochemical cell into layers, each comprising several segments; - Determining a distribution of a state variable of the electrochemical cell across the segments of at least one of the planes using a physical module; and - Determining at least one further distribution of at least one further state variable of the electrochemical cell across the segments of at least one of the planes using at least one further physical module.

[0004] The steps aimed at determining distributions of state variables are repeated alternately until a convergence criterion is reached. In each repetition, the most recently determined distribution of state variables is processed as the input.

[0005] The method can be used to determine various state variables of fuel cells, electrolyzers or similar devices, for example electrolyzers that operate on the principle of proton exchange membrane electrolysis (PEM-EL), anion exchange membrane electrolysis (AEM-EL), alkaline electrolysis (AEL) or solid oxide electrolysis (SOE).

[0006] The division of the electrochemical cell into segmented planes is done virtually, i.e., not physically real, but simulated, for example, by computer technology.

[0007] By dividing the electrochemical cell into planes with several segments each, spatial variations in the electrochemical cell, such as channels and ribs, can be represented in a model and taken into account when determining the different state variables.

[0008] The division of the cell into segmented levels and the alternating use of different physical modules enables the determination of relevant state variables without the need for computationally intensive fully coupled solvers. This makes the method resource-efficient and flexibly adaptable to various cell architectures. The method allows for both single-cell and stack analyses, for example, to determine local aging states, for design optimization purposes, and / or for optimized operation.

[0009] Preferably, in the first process step, the electrochemical cell is divided into several layers, each characterizing a layer or intermediate layer of the electrochemical cell. For this purpose, the electrochemical cell is virtually divided, for example, in the z-direction into its layered components such as bipolar plates, porous support layers, catalyst layers and / or membranes.

[0010] Segmentation is preferably performed perpendicular to the z-direction in the xy-plane of the electrochemical cell across its respective active surface. This achieves a structured three-dimensional discretization of the electrochemical cell, which in turn enables a detailed simulation of local electrochemical, thermal, fluid-dynamic, and mechanical phenomena within the electrochemical cell.

[0011] Depending on the electrochemical cell's structure, at least one of the layers can characterize a bipolar plate, an interconnect, a porous transport layer, a catalyst layer, an electrode layer, or a separator layer, such as a membrane, diaphragm, or electrolyte layer. This variability makes the method highly adaptable to different cell designs and technologies. Consequently, the method's range of applications is broad.

[0012] In principle, the method is not limited to the three explicitly mentioned process steps and the use of only two different physical modules. It is possible to use three, four, five, or even more different physical modules repeatedly and alternately to determine more than two state variables of the electrochemical cell.

[0013] One aspect of the invention provides that data is transferred between the physical modules in a standardized format via a standardized interface. This has the advantage that changes or adjustments to one of the physical modules do not affect the other physical module(s). The method can therefore be adapted flexibly and with minimal technical effort to the specific requirements and constraints at hand.

[0014] In one variant of the method, a current density distribution in at least one of the levels and / or between the levels is determined as a state variable in one of the process steps. For this purpose, a physical module designed as an electrochemical module is used, which calculates the current density distribution using Butler-Volmer kinetics by evaluating a media flow in at least one of the levels and / or between the levels. Concentration overpotentials and / or gas covering effects, for example, can be taken into account in the calculation.

[0015] In another variant of the method, the distribution of an electrical potential in at least one of the levels and / or between the levels is determined as a state variable in one of the process steps. For this purpose, a physical module designed as a charge transport module is used, for example, which calculates the potential distribution by applying Ohm's law, taking local electrical conductivities into account. The local electrical conductivities, in turn, can be determined, for example, based on local temperatures, hydration states, and local gas saturation.

[0016] Both current density and potential distribution are essential indicators for the function of an electrochemical cell. Determining these parameters is important for both optimization and functional testing.

[0017] Another aspect involves determining the concentration distribution of at least one medium in at least one of the layers and / or between the layers as a state variable in one of the process steps. For this purpose, a physical module designed as a mass transport module is used, which calculates media concentration fields for dissolved and / or gaseous phases of the at least one medium using convection and / or diffusion equations. To increase the prediction accuracy, phase equilibrium models and / or gas bubble transport and barrier layer penetration phenomena can be considered in the calculation.

[0018] Furthermore, it is possible that a temperature distribution in at least one of the levels and / or between the levels is determined as a state variable in one of the process steps. For this purpose, a physical module designed as a temperature module is used, which calculates the temperature distribution using heat conduction equations, taking into account electrochemical and ohmic heat sources and / or convection cooling effects. By using the temperature module, local temperatures within the electrochemical cell can be determined with high accuracy, which in turn influence the course of chemical reactions and local resistances, and are therefore important for the function of the electrochemical cell.

[0019] Furthermore, it may be provided that in one of the process steps, a pressure distribution and / or mass flow distribution and / or flow distribution of at least one medium in at least one of the levels and / or between the levels is determined as a state variable. For this purpose, for example, a physical module designed as a pressure and / or flow module is used, which calculates the aforementioned distributions using a simplified momentum balance. To increase the prediction accuracy, corrections for the geometry of the flow field of the at least one medium can be made, and two-phase flow effects and / or local gas evolution can be taken into account.

[0020] The system according to the invention comprises at least one electrochemical cell and a computing unit configured to execute a computer program product that causes the computing unit to carry out a method according to the invention.

[0021] The advantages mentioned for the method apply equally to the system according to the invention.

[0022] Preferred embodiments are explained in more detail with reference to the following figures. These show - Fig. 1 a schematic representation of an embodiment of a system according to the invention; - Fig. 2 a schematic representation of a model for determining local state variables of an electrochemical cell; - Fig. 3 a schematic representation of an embodiment of a method according to the invention for determining local state variables of an electrochemical cell; - Fig. 4 a schematic representation of an electrochemical cell divided into planes; and - Fig. 5 A schematic representation of several levels of an electrochemical cell divided into segments.

[0023] In Fig. Figure 1 is a schematic representation of an embodiment of a system 1 according to the invention. The system 1 comprises at least one electrochemical cell 2 and a computing unit 3.

[0024] The computing unit 3 is trained to execute a computer program product 4 that causes the computing unit 3 to perform a procedure for determining local state variables of the electrochemical cell 2 using a model 5 of the electrochemical cell 2.

[0025] The Model 5 is in Fig. 2 shown schematically. It works with five consecutive physical modules 6.

[0026] The first of the physical modules 6 is configured as an electrochemical module 7, a second as a charge transport module 8, a third as a mass transport module 9, a fourth as a temperature module 10, and a fifth as a pressure and flow module 11. This is not to be understood as a limitation. In principle, the model 5 can also comprise fewer or more than five physical modules 6.

[0027] Standardized interfaces 12 are provided between the physical modules 6, via which the physical modules 6 can exchange data in a standardized form.

[0028] The in Fig. Model 5, shown in Figure 2, is used to... Fig. to carry out the 3 shown procedures to determine local state variables of the electrochemical cell 2.

[0029] In a first step S1 of the process, the computing unit 3 divides the electrochemical cell 2, as in the Fig. 4 and Fig. 5 shown schematically, virtually into several parallel planes 13, each of which in turn comprises several segments 14.

[0030] Each of the levels 13 characterizes a layer 15 or intermediate layer of the electrochemical cell 2.

[0031] At the in Fig. In the variant shown in Figure 4, the electrochemical cell 2 is a polymer proton exchange membrane electrolyzer cell (PEM-EL). This is not to be understood as a limitation. The method and model 5 can, in principle, also be used to determine state variables of any other type of electrochemical cell 2.

[0032] The in Fig. The electrochemical cell 2 shown in Figure 4 comprises two bipolar plates 16, between which porous transport layers 17, catalyst layers 18, and a separator layer 19 are arranged. The separator layer 19 is designed as a polymer proton exchange membrane.

[0033] The subdivision in step S1 of the procedure is such that each of the levels 13 characterizes one of the aforementioned layers 15 of the electrochemical cell 2. In other words, each of the bipolar plates 16, each of the porous transport layers 17, each of the catalyst layers 18, and the separator layer 19 of the electrochemical cell 2 are represented in model 5 as an individual level 13. This is, of course, not to be understood as a limitation. In principle, a layer 15 of the electrochemical cell 2, for example, the separator layer 19, can also be divided into several levels 13. Furthermore, it is possible for one or more levels 13 to characterize an interconnect layer (not shown), an electrode layer (not shown), or any other type of layer, if the electrochemical cell 2 includes one.

[0034] The individual levels 13 are, as in Fig. 5 shown, each divided into an equal number of segments 14.

[0035] Segmentation enables spatially resolved modeling of the electrochemical cell 2. Spatial variations in the layers 15 of the electrochemical cell 2, such as wall structures 20, channel structures 21, inlets 22 and outlets 23, can be represented in the respective planes 13.

[0036] After the subdivision of the electrochemical cell 2 into segmented levels 13 is completed, the computing unit 3 determines, in a second step S2 of the procedure, a distribution of a first state variable of the electrochemical cell 2 over the segments 14 of at least one of the levels 13 by means of one of the physical modules 6. For example, the computing unit 3 determines, by means of the electrochemical module 7, as a first state variable a distribution of a current density in at least one of the levels 13 and / or between the levels 13 by evaluating a medium flow.

[0037] In a third step S3 of the procedure, the computing unit 3 determines a distribution of a second state variable of the electrochemical cell 2 over the segments 14 of at least one of the levels 13 by means of a further physical module 6. For example, the computing unit 3 determines, by means of the charge transport module 8 as a second state variable, a distribution of an electric potential in at least one of the levels 13 and / or between the levels 13 by applying Ohm's law, taking into account local electrical conductivities and the previously determined current density distribution.

[0038] In a fourth step S4 of the procedure, the computing unit 3 determines a distribution of a third state variable of the electrochemical cell 2 over the segments 14 of at least one of the levels 13 by means of a further physical module 6. For example, the computing unit 3 determines a media concentration distribution or media concentration fields for dissolved and / or gaseous phases of at least one medium flowing through the electrochemical cell 2 by means of the mass transport module 9 as a third state variable using convection and / or diffusion equations.

[0039] In a fifth step S5 of the procedure, the computing unit 3 determines a distribution of a fourth state variable of the electrochemical cell 2 over the segments 14 of at least one of the levels 13 by means of a further physical module 6. For example, the computing unit 3 determines a temperature distribution in one or more of the levels 13 by means of the temperature module 10 as the fourth state variable using heat conduction equations and taking into account electrochemical and ohmic heat sources as well as convection cooling effects.

[0040] In a sixth step S6 of the procedure, the computing unit 3 determines a distribution of a fifth state variable of the electrochemical cell 2 over the segments 14 of at least one of the levels 13 by means of a further physical module 6. For example, the computing unit 3 determines a pressure distribution, mass flow distribution and / or flow distribution in one or more of the levels 13 by means of the pressure and flow module 11 as the fifth state variable using a simplified momentum balance.

[0041] The examples given for the defined state variables are, of course, not to be understood as limiting. Further and / or other types of physical modules 6 can also be used to determine any other types of state variables. Determining multiple state variables using a single physical module 6 is also fundamentally possible.

[0042] Steps S2 to S6 of the procedure are repeated alternately until a convergence criterion is reached. With each repetition, the most recently determined state variable distribution is transmitted as standardized data via the standardized interface 12 to the subsequent physical module(s) 6 and processed by them as input. In simplified terms, the state variables are thus coupled or determined in relation to one another until sufficient accuracy is ensured by reaching the convergence criterion.

[0043] To carry out the procedure, it is not absolutely necessary to use all of the physical modules 6 mentioned. For example, it is possible to dispense with the use of the temperature module 10 and to assume a constant temperature or a specific temperature distribution over one or more of the levels 13, which can then be used as an input variable in the subsequent process steps to determine further state variable distributions.

[0044] In the simplest case, it is sufficient to use only two of the aforementioned physical modules 6 to alternately determine only two state variables of the electrochemical cell 2 until the specified convergence criterion is reached.

[0045] Through the use of the in Fig. 2 shown model 5 as well as the one in Fig. The methods shown in section 3 allow for the technically simple analysis of complex interactions between materials, operating conditions, and the cell geometry of the electrochemical cell 2 under consideration. For example, the spatially resolved modeling of the electrochemical cell 2 makes it possible to investigate local phenomena such as hotspot formation, gas accumulation patterns, power inconsistencies, and their relationship to the cell geometry and operating conditions.

[0046] A balance suitable for the respective application between the computational effort and the achievable spatial resolution can be set via the fineness of the segmentation of the individual levels 13.

[0047] This means that in Fig. 2 shown model 5 as well as the one in Fig.The 3 methods shown can be used for numerous different applications, for example for optimizing cell design in an early phase of a cell development process, for online monitoring purposes or for use in model predictive control and / or regulation systems. QUOTES INCLUDED IN THE DESCRIPTION

[0000] This list of documents cited by the applicant was automatically generated and is included solely for the reader's convenience. The list is not part of the German patent or utility model application. The DPMA accepts no liability for any errors or omissions. Cited patent literature

[0000] DE 10 2025 115 470 A1

[0002]

Claims

[1] Method for determining local state variables of an electrochemical cell (2) comprising the steps: - Dividing the electrochemical cell (2) into levels (13), each comprising several segments (14); - Determining a distribution of a state variable of the electrochemical cell (2) over the segments (14) of at least one of the levels (13) using a physical module (6); and - Determining at least one further distribution of at least one further state variable of the electrochemical cell (2) over the segments (14) of at least one of the levels (13) by means of at least one further physical module (6), wherein the steps directed towards the determination of distributions of state variables are repeated alternately until a convergence criterion is reached and wherein, in each repetition, the last determined state variable distribution is processed as input. [2] Method according to claim 1, wherein the electrochemical cell (2) is divided into several levels (13) which each characterize a layer (15) or intermediate layer of the electrochemical cell (2). [3] Method according to claim 1 or 2, wherein at least one of the levels (13) - a bipolar plate (16) of the electrochemical cell (2), - an interconnect of the electrochemical cell (2), - a porous transport layer (17) of the electrochemical cell (2), - a catalyst layer (18) of the electrochemical cell (2), - an electrode layer of the electrochemical cell (2) or - a separator layer (19) of the electrochemical cell (2) is characterized. [4] Method according to one of the preceding claims, wherein data is transferred between the physical modules (6) in a standardized form via a standardized interface (12). [5] Method according to one of the preceding claims, wherein in one of the method steps a distribution of a current density in at least one of the planes (13) and / or between the planes (13) is determined as a state variable. [6] Method according to one of the preceding claims, wherein in one of the method steps a distribution of an electric potential in at least one of the levels (13) and / or between the levels (13) is determined as a state variable. [7] Method according to one of the preceding claims, wherein in one of the method steps a concentration distribution of at least one medium in at least one of the levels (13) and / or between the levels (13) is determined as a state variable. [8] Method according to one of the preceding claims, wherein in one of the method steps a temperature distribution in at least one of the levels (13) and / or between the levels (13) is determined as a state variable. [9] Method according to one of the preceding claims, wherein in one of the method steps a pressure distribution and / or mass flow distribution and / or flow distribution of at least one medium in at least one of the levels (13) and / or between the levels (13) is determined as a state variable. [10] System comprising at least one electrochemical cell (2) and a computing unit (3) configured to execute a computer program product (4) that causes the computing unit (3) to perform a method according to any of the preceding claims.

Images