Iron-chromium flow battery aging modeling method

Abstract

The invention relates to the technical field of iron-chromium flow battery energy storage, and provides an iron-chromium flow battery aging modeling method, which comprises the following steps: exploring the reaction principle of an iron-chromium flow battery; building an iron-chromium flow battery reaction kinetic model (two-dimensional steady state) based on the reaction principle of the iron-chromium flow battery; and based on the reaction kinetic model (two-dimensional steady state) of the iron-chromium flow battery, constructing a reaction kinetic model (two-dimensional transient state) of the iron-chromium flow battery, which couples the reaction kinetic model (two-dimensional steady state) of the iron-chromium flow battery with the mass balance of an external storage tank. The method achieves the quick prediction of the aging of the battery through simulation, thereby laying a solid simulation analysis foundation for exploring how to slow down the aging, improve the cycle life of the battery and improve the economical efficiency of the battery. Meanwhile, a relation between macroscopic battery capacity attenuation and microscopic chromium ion concentration change is established, so that a battery aging mechanism is disclosed, and theoretical guidance is provided for battery aging research and development.

Description

Technical Field

[0001] This invention relates to the field of iron-chromium redox flow battery energy storage technology, and in particular to an aging modeling method for iron-chromium redox flow batteries. Background Technology

[0002] In the context of addressing the depletion of fossil fuels and environmental challenges, accelerating the deployment of renewable energy is imperative. However, its inherent intermittency and volatility pose significant operational risks when directly integrated into the grid. Therefore, developing large-scale, long-duration energy storage technologies has become a crucial step in ensuring grid stability and enhancing the absorption capacity of renewable energy.

[0003] Redox flow batteries, with their inherent safety, excellent cycle life, decoupled energy and power design, and environmental friendliness, have become ideal candidate technologies for large-scale energy storage, with broad application prospects. In recent years, flow battery technology has made significant progress, with vanadium redox flow batteries achieving the highest level of commercialization. However, their large-scale promotion is constrained by the high cost of vanadium resources. Against this backdrop, iron-chromium flow batteries demonstrate outstanding potential: utilizing the Earth's abundant iron and chromium elements as active materials, their theoretical cost is significantly lower than other systems; simultaneously, their aqueous electrolyte has low toxicity and corrosiveness. These characteristics make iron-chromium flow batteries one of the most promising technological routes for achieving low-cost, large-scale energy storage.

[0004] However, the practical application of iron-chromium flow batteries still faces performance bottlenecks. Chromium ion couple (Cr...) 3+ / Cr 2+ The slow reaction kinetics at the electrode interface restrict the power density and charge / discharge efficiency of the battery; during charge and discharge, the hydrogen evolution side reaction, especially at the negative electrode, reduces the coulombic efficiency of the battery; and the aging problem of iron-chromium flow batteries is more significant compared to that of vanadium redox flow batteries.

[0005] Therefore, it is of great significance to explore a method for modeling the aging of iron-chromium redox flow batteries. Summary of the Invention

[0006] The purpose of this invention is to provide a method for modeling the aging of iron-chromium redox flow batteries. This method first constructs a two-dimensional steady-state reaction kinetic model of the iron-chromium redox flow battery based on the battery's reaction principle. Then, it couples this model with the mass balance of an external storage tank to construct a two-dimensional transient reaction kinetic model of the iron-chromium redox flow battery. This addresses the problem of insufficient exploration of battery aging mechanisms in existing research.

[0007] This invention provides a method for aging modeling of iron-chromium redox flow batteries, comprising:

[0008] To investigate the reaction principle of iron-chromium redox flow batteries.

[0009] A two-dimensional steady-state reaction kinetic model of an iron-chromium flow battery was constructed based on the reaction principle of the iron-chromium flow battery.

[0010] Based on the aforementioned iron-chromium redox flow battery reaction kinetic model (two-dimensional steady state), a two-dimensional transient iron-chromium redox flow battery reaction kinetic model is constructed that couples the iron-chromium redox flow battery reaction kinetic model (two-dimensional steady state) with the mass balance of the external storage tank.

[0011] According to the aging modeling method for iron-chromium flow batteries of the present invention, the step of building a reaction kinetic model (two-dimensional steady state) of the iron-chromium flow battery based on the reaction principle of the iron-chromium flow battery includes:

[0012] Based on the reaction principle of iron-chromium redox flow batteries, a two-dimensional steady-state iron-chromium redox flow battery model with porous electrode domain, deionization membrane domain, inlet domain and outlet domain is established, and electrochemical reaction control equations are coupled in the two-dimensional steady-state iron-chromium redox flow battery model.

[0013] The coupling boundary conditions use a constant electrode current input, and the initial ion concentration value is set based on empirical data. The geometric model is discretized using the finite element method, and the nonlinear equations are solved by the Newton-Raphson iterative method. The iterative solver processes the linear sub-equations.

[0014] According to the iron-chromium redox flow battery aging modeling method of the present invention, the electrochemical reaction governing equations include: the Nernst equation, the Butler-Volmer type kinetic expression, and the overpotential equation. (in It is the solid-state potential of the electrode. It is the electrolyte potential, E eq These include equilibrium potential, the Nernst-Planck equation, and the charge conservation equation.

[0015] According to the aging modeling method for iron-chromium redox flow batteries of the present invention, the step of constructing an iron-chromium redox flow battery reaction kinetic model (two-dimensional steady state) that couples the iron-chromium redox flow battery reaction kinetic model (two-dimensional steady state) with the mass balance of the external storage tank, based on the aforementioned iron-chromium redox flow battery reaction kinetic model (two-dimensional steady state), includes:

[0016] The global ordinary differential and differential algebraic equation model is coupled with the reaction kinetic model, and the finite element method is used to achieve co-computation during the coupled solution process.

[0017] A load of 1-100 charge-discharge cycles (30 minutes of constant current charging + 30 minutes of constant current discharging) is applied, with the initial concentration value output from the global ordinary differential and differential-algebraic equation model. The geometric model is discretized using the finite element method, and the nonlinear equation system is solved using the Newton-Raphson iterative method, while the linear sub-equations are handled by the iterative solver.

[0018] According to the iron-chromium redox flow battery aging modeling method of the present invention, the global ordinary differential and differential algebraic equation model includes:

[0019]

[0020] Where V is the total volume of the flowing electrolyte in the electrolyte tank, and L is the electrode height (N). X (n represents the molar flux of each electrolyte substance upwards via the boundary method)

[0021] The present invention also provides an iron-chromium redox flow battery model that uses any of the above-described iron-chromium redox flow battery aging modeling methods for aging modeling.

[0022] This invention provides an aging modeling method for iron-chromium redox flow batteries. It explores the reaction principle of iron-chromium redox flow batteries; constructs a two-dimensional steady-state reaction kinetic model based on this principle; and builds a two-dimensional transient reaction kinetic model that couples this model with the mass balance of an external storage tank. This enables rapid prediction of battery aging through simulation, laying a solid foundation for simulation analysis to explore ways to slow down aging, improve battery cycle life, and enhance economic efficiency. Simultaneously, it establishes the relationship between macroscopic battery capacity decay and microscopic chromium ion concentration changes, revealing the battery aging mechanism and providing theoretical guidance for battery aging research and development. Attached Figure Description

[0023] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0024] Figure 1 This is a flowchart illustrating an aging modeling method for an iron-chromium redox flow battery provided in an embodiment of the present invention.

[0025] Figure 2 This is a schematic diagram of the reaction principle of a single iron-chromium redox flow cell provided in an embodiment of the present invention;

[0026] Figure 3 This is a graph showing the concentration distribution of trivalent chromium ions during the first charge-discharge cycle, provided by an embodiment of the present invention, as a function of charging time.

[0027] Figure 4This is a graph showing the distribution of trivalent chromium ion concentration as a function of the number of charge-discharge cycles, provided in an embodiment of the present invention. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0029] The following is combined Figures 1 to 4 This invention describes an aging modeling method for iron-chromium redox flow batteries. For example... Figure 1 As shown, the method includes the following steps:

[0030] S1. Investigate the reaction principle of iron-chromium redox flow batteries.

[0031] like Figure 2 As shown, the iron-chromium flow battery is an aqueous flow battery that stores energy based on the reversible redox reaction of iron (Fe) and chromium (Cr) ions. Its core principle lies in the valence state transformation of the active materials in the acidic electrolyte: during charging, Fe... 2+ Oxidation reaction produces Fe 3+ The reaction occurs at the negative electrode; Cr undergoes the reaction at the negative electrode. 3+ The reduction reaction produces Cr 2+ The reaction. The discharge process is the opposite, Fe 3+ Reduction and Cr 2+ Oxidation releases electrical energy. Positive and negative electrode electrolytes (containing Cr) 3+ / Cr 2+ with Fe 2+ / Fe 3+ The fuel cell reactor (FCR) is stored in an external tank and circulated through the reactor's reaction zone via a pump. Ion exchange membranes (such as proton exchange membranes) separate the two electrodes, allowing H₂ to pass through. + Migration maintains charge balance while preventing cross-contamination of iron and chromium ions.

[0032] S2. Based on the reaction principle of the iron-chromium redox flow battery, a reaction kinetic model (two-dimensional steady state) of the iron-chromium redox flow battery is constructed.

[0033] First, the iron-chromium redox flow battery aging modeling method of the present invention is based on the reaction principle of iron-chromium redox flow battery, and establishes a two-dimensional steady-state iron-chromium redox flow battery model with porous electrode domain, deionization membrane domain, inlet domain and outlet domain, and couples electrochemical reaction control equations in the two-dimensional steady-state iron-chromium redox flow battery model.

[0034] Specifically, the governing equations for the electrochemical reaction are based on the Nernst equation, Butler-Volmer type kinetic expressions, and overpotential equations. (in It is the solid-state potential of the electrode. It is the electrolyte potential, E eq These include equilibrium potential, the Nernst-Planck equation, and the charge conservation equation.

[0035] Specifically, the Nernst equation, the Butler-Volmer type kinetic expression, and the overpotential equation are used to describe the redox reaction kinetics on the electrode surface in the battery, while the Nernst-Planck equation and the charge conservation equation are used to calculate the flux of the substance near the electrode surface and the electrolyte potential in the porous electrode.

[0036] Furthermore, the boundary conditions of the model are set according to the battery operating principle: the negative electrode boundary is grounded, and an electrode current is applied to the positive electrode boundary, with the applied value being a constant value; and initial values ​​for each ion concentration are given, which are obtained based on empirical data.

[0037] Furthermore, the geometric model of the entire iron-chromium flow battery is discretized using the finite element method, that is, the battery components are divided into small elements. Then, the governing equations describing the physical fields are solved locally and approximated on each element. Finally, all element equations are assembled into a global equation set and numerically solved: an iterative solver is selected for the linear sub-equations, while the Newton-Raphson iterative method is used for the nonlinear parts.

[0038] S3. Based on the aforementioned iron-chromium redox flow battery reaction kinetic model (two-dimensional steady state), construct an iron-chromium redox flow battery reaction kinetic model (two-dimensional transient state) that couples the iron-chromium redox flow battery reaction kinetic model (two-dimensional steady state) with the mass balance of the external storage tank.

[0039] In this embodiment, the global ordinary differential equation and differential algebraic equation model are mainly used to couple with the reaction kinetic model, and the finite element method is used to achieve co-calculation during the coupling solution process.

[0040] Specifically, the global ordinary differential and differential-algebraic equation models mainly include:

[0041]

[0042]

[0043] Where V is the total volume of the flowing electrolyte in the electrolyte tank, and L is the electrode height (N). X ﹒ n represents the molar flux of each electrolyte substance upwards via the boundary method.

[0044] Furthermore, the boundary conditions of the model are set according to the battery operating principle. The negative electrode boundary is grounded, and an electrode current is applied to the positive electrode boundary. The applied electrode current is for 20 load cycles: charging at a constant current density for 30 minutes, then discharging at the same current density for 30 minutes, and repeating this cycle 20 times. Initial values ​​for each ion concentration are given, which are provided by the global ordinary differential and differential algebraic equation model to achieve overall coupling.

[0045] Furthermore, the geometric model of the entire iron-chromium flow battery is discretized using the finite element method, that is, the battery components are divided into small elements. Then, the governing equations describing the physical fields are solved locally and approximated on each element. Finally, all element equations are assembled into a global equation set and numerically solved: an iterative solver is selected for the linear sub-equations, while the Newton-Raphson iterative method is used for the nonlinear parts.

[0046] This invention reveals in detail the process of chromium ions (Cr) at the negative electrode during a single charge-discharge cycle of an iron-chromium redox flow battery. 3+ / Cr 2+ The dynamic evolution of the concentration field. Key findings include: Figure 3 Simulation results show that significant concentration fluctuations occur at the reaction interface regions on both sides of the electrode, while the concentration distribution remains relatively uniform and stable in the middle region of the electrode. Notably, with continued charge-discharge cycles, these concentration fluctuations not only persist but also intensify, exhibiting a clear time dependence. This concentration fluctuation is one of the core causes of impaired ion mass transfer within the system. It limits the supply / removal rate of the active materials required for the reaction, thus directly constituting a key local bottleneck region restricting electrochemical reaction efficiency and battery performance.

[0047] Furthermore, this invention investigated the evolution characteristics of chromium ion concentration at the negative electrode under long-term operation (multiple cycles) through multiphysics field coupling simulation. For example... Figure 4 As shown, at the same specific spatial location, the negative electrode chromium ions (in the form of Cr) 3+ The local concentration of the electrolyte (mainly electrolyte) shows a significant and continuous decreasing trend with the accumulation of cycles. This phenomenon suggests that there may be irreversible consumption or transformation of the active components of the electrolyte.

[0048] The model analyzes the dynamic heterogeneity of the concentration field and its chain effect on performance (fluctuation → mass transfer obstruction → reaction limitation; decay → loss of active material → capacity degradation) in both spatial and temporal dimensions, establishing a key theoretical foundation for electrode structure optimization, electrolyte management strategies, and lifetime prediction.

[0049] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for modeling the aging of iron-chromium redox flow batteries, characterized in that, include: To investigate the reaction principle of iron-chromium redox flow batteries. A two-dimensional steady-state reaction kinetic model of an iron-chromium flow battery was constructed based on the reaction principle of the iron-chromium flow battery. Based on the aforementioned iron-chromium redox flow battery reaction kinetic model (two-dimensional steady state), a two-dimensional transient iron-chromium redox flow battery reaction kinetic model is constructed that couples the iron-chromium redox flow battery reaction kinetic model (two-dimensional steady state) with the mass balance of the external storage tank.

2. The aging modeling method for iron-chromium redox flow batteries according to claim 1, characterized in that, The proposed reaction kinetic model (two-dimensional steady state) of the iron-chromium flow battery, based on its reaction principle, includes: Based on the reaction principle of iron-chromium redox flow batteries, a two-dimensional steady-state iron-chromium redox flow battery model with porous electrode domain, deionization membrane domain, inlet domain and outlet domain is established, and electrochemical reaction control equations are coupled in the two-dimensional steady-state iron-chromium redox flow battery model. The coupling boundary conditions use a constant electrode current input, and the initial ion concentration value is set based on empirical data. The geometric model is discretized using the finite element method, and the nonlinear equations are solved by the Newton-Raphson iterative method. The iterative solver processes the linear sub-equations.

3. The aging modeling method for iron-chromium redox flow batteries according to claim 2, characterized in that, The governing equations for the electrochemical reaction include: the Nernst equation, the Butler-Volmer type kinetic expression, and the overpotential equation η = φ. s -φ l -E eq (where φ) s It is the solid-state potential of the electrode, φ l It is the electrolyte potential, E eq These include equilibrium potential, the Nernst-Planck equation, and the charge conservation equation.

4. The method for modeling the aging of iron-chromium redox flow batteries according to claim 1, characterized in that, Based on the aforementioned iron-chromium redox flow battery reaction kinetic model (two-dimensional steady state), a two-dimensional transient iron-chromium redox flow battery reaction kinetic model is constructed, coupling the two-dimensional steady state model with the mass balance of the external storage tank, including: The global ordinary differential and differential algebraic equation model is coupled with the reaction kinetic model, and the finite element method is used to achieve co-computation during the coupled solution process. The load was subjected to 1-100 charge-discharge cycles (30 minutes of constant current charging + 30 minutes of constant current discharging). The initial concentration value was output by the global ordinary differential and differential-algebraic equation model. The geometric model was discretized using the finite element method, and the nonlinear equation system was solved by the Newton-Raphson iterative method. The iterative solver handled the linear sub-equations.

5. The aging modeling method for iron-chromium redox flow batteries according to claim 4, characterized in that, The global ordinary differential and differential algebraic equation model includes: Where V is the total volume of the flowing electrolyte in the electrolyte tank, and L is the electrode height (N). X ﹒ n represents the molar flux of each electrolyte substance upwards via the boundary method.

6. A model of an iron-chromium redox flow battery, characterized in that, An iron-chromium redox flow battery model for aging modeling using the iron-chromium redox flow battery aging modeling method as described in any one of claims 1 to 5.

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