Performance Modeling and Flow Rate Optimization of Vanadium Redox Flow Batteries

Table of Contents

Chapter 1
INTRODUCTION
1.1 Electrochemical Energy Storage Systems
1.2 Redox Flow Batteries (RFB)
1.3 All-Vanadium Redox Flow Battery (VRFB)
1.4 Structure of the Thesis

Chapter 2
LITERATURE REVIEW
2.1 Electrochemistry and Electrode Kinetics of VRFB
2.2 Conservation Equations
2.3 Fundamental Flow Batteries

Chapter3 Performance Modeling of VRFB
3.1 Membrane Analysis
3.2 Impact of Mass Transfer Rates
3.3 Effect of Current Density
3.4 Effect of Electrode Morphology
3.4.1 Effect of electrodes on Ion transport
3.4.2 Effect of electrodes on Electron transport
3.4.3 Effect of electrodes on Mass transport

Chapter 4
Flow Rate Optimization
4.1 Impact of Flow Rate
4.2 Experimental Flow Rate Control
4.3 Flow Rate Control Model Review.
4.4 Model Assumptions
4.5 Electrochemical Model
4.5.1 Activation Over-potential:
4.5.2 Ohmic Over-potential:
4.5.3 Concentration Over-potential:
4.6 Ion Concentration
4.7 Electrolyte Properties
4.8 Hydraulic Model

Chapter 5 Flow Rate Control Strategy
5.1 Strategy 1: Minimum Flow Rate Operation
5.2 Strategy 2: Maximum Applied Flow Rate
5.3 Strategy 3: Flow Factor Optimization
5.4 Model Parameters

Chapter 6 Results and Discussions

Chapter 7

CONCLUSION AND FUTURE SCOPE

APPENDIX

LITERATURE CITED

Abstract

There is a drastic capacity increase in the ocean, solar, and wind power based energy generation in recent years. Moreover, a larger increase is predicted in future years. Hence, we need a reliable, efficient, and cost-effective energy storage system to match up with the intermittent nature of renewable energy sources. Vanadium redox flow batteries are a promising option and are fast approaching commercialization owing to their unique characteristics like including independent scaling of power and energy density. However, there are various losses associated with the membrane, electrodes, and also due to mass transfer which limit its performance and further decrease battery capacity and efficiency. The first part of this study focusses on membrane thickness, mass transfer coefficients, electrode morphology, and current density to analyze the performance of the battery. The latter part describes the effect of flow rate on concentration over-potential, pressure losses, and pumping power to come up with an optimal variable flow rate strategy to maximize the battery capacity and system efficiency.

Keywords : Electrochemical Energy Storage, Vanadium Redox Flow Batteries, Flow Rate optimization, Performance Modeling, Polarization Curves, Over-potential, Hydraulic Model, Variable flow rate, system efficiency, mass transfer, membrane thickness, current density, limiting current density, tortuosity, porosity, electrode compression, catalysis, specific surface area

List of Figures

Figure 1 Ragone plot comparing the energy and power densities of energy storage system2

Figure 2 Schematic diagram of all-vanadium flow battery 4

Figure 3 Performance Improving aspects of all-vanadium flow battery29

Figure 4 Polarization Curves at different values of membrane thickness at 100 mAcm-2 40

Figure 5 Polarization Curves at different values of membrane thickness at 200 mA/cm2 40

Figure 6 Coulombic Efficiency as a function of membrane thickness at the various current densities46

Figure 7 Voltage Efficiency as a function of membrane thickness at the various current densities46

Figure 8 Polarization Curves showing the limiting current density54

Figure 9 Polarization Curves comparing mass transfer coefficients59

Figure 10 Polarization Curves for electrodes with varying thickness67

Figure 11 Schematic of electrode-electrolyte processes103

Figure 12 Polarization Curves at different values of flow factor93

Figure 13 Variation of pressure losses and pump power at different values of flow factor59

Figure 14 Variation of efficiencies with flow factor93

Figure 15 Variation of capacity and energy density with flow factor59

Figure 16 Polarization plot showing a decrease of average discharge voltage with current density

Figure 17 Comparing energy and power density with variation in current density

Figure 18 Discharge Curves at three different values of current density

Figure 19 Tortuosity vs Porosity relation for carbon paper and carbon cloth

Figure 20 Variation of ASR with porosity for a different electrode material

List of Tables

Table 1 Source heat terms for energy balance10

Table 2 Coefficients for density and viscosity relation 96

Table 3 Values of minor loss coefficient across various component96

Table 4 Model parameters for VRFB system

Nomenclature

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Chapter 1

INTRODUCTION

1.1 Electrochemical Energy Storage Systems

Here is a huge demand for eco-friendly, renewable energy sources like PV, and wind in the market because there is a need to replace fossil fuels and nuclear energy. However, a significant issue with them is their intermittent and fluctuating nature which poses a problem of storing the electrical energy generated. Hence, they have to depend on energy storage systems (ESS) which also mitigate the demand and supply problem in the form of grid storage, flexibility, and economic viability. Among the various methods of energy storage include the likes of chemical, electrical, thermal, biological, and mechanical. However electrochemical energy storage is efficient as it provides direct conversion between chemical and electrical energy, and has a low carbon footprint and short response time.1

The significant advantage of them is that they are pollution-free (non-toxic), the storage system can be located near the loads and the system energy losses are negligible. However, a major disadvantage is of their high cost of the membranes, electrolyte and also their bulky nature

1.2 Redox Flow Batteries (RFB)

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Figure 1 Ragone plot comparing the energy and power densities of energy storage system2

In redox flow batteries, the ion-exchange membrane separates the electrodes, they differ from the conventional batteries in the sense that here the reaction takes place between the anolyte and catholyte rather than the electrolyte and electrode. Another point to note is that the electrolytes are stored in external tanks and pumped through pumps into the stack.

Examples of flow batteries are redox flow batteries3, hybrid flow batteries, and redox fuel cell. There are many types of redox flow batteries like V-poly halides, Br2-polysulphides, Fe-Cr, Zn-Br2, all- VRFB, Ce-Zn.

High power density is a useful characteristic of super-capacitors as they have short discharge time enabling them to provide instant energy for a short duration of time (starting application) while high energy, high discharge time is crucial for power management applications and this is where secondary batteries are handy. A fundamental aspect of redox flow batteries is that they have a decoupling of power and energy. Power density can be modulated by varying the number of cells in tanks and the size of electrodes while energy density is varied by increasing the size of electrolyte tanks and concentration of electrolytes.

1.3 All-Vanadium Redox Flow Battery (VRFB)

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Figure 2 Schematic diagram of all-vanadium flow battery 4

All-VRFB exploits the ability of vanadium to exist in four stable oxidation states. Kazacos and co-workers5 first developed them in the 1970s in UNSW, Australia.

The VRFB electrolyte is a mixture of vanadium with dilute H2SO4. It has an indefinite life span and is reusable providing VRFB with a high depth of discharge and extended cycle capability (20,000). Since the electrolyte is a non-flammable aqueous solution with high thermal heat capacity enables the battery to withstand the temperature rise and hence there is no problem of ignition or explosion. Also, there is no risk of cross-contamination as the electrolyte is the same in both half-cells. Other advantages include low maintenance and quick response time. Hence, they can be used in grid storage.

However, a major disadvantage associated with them is that the vanadium has very low solubility which leads to a low energy density (25 Wh/kg), (though by using precipitation inhibitors, increasing electrolyte concentration and controlling electrolyte temperature, a higher energy density can be achieved). Further, due to electrolyte cross-over across the membrane, there is a capacity imbalance that leads to a decrease in efficiency and capacity. Appropriate rebalancing techniques can be used to counter this. The primary concern is the high cost of the membrane, electrolyte, pumps, and other components6

1.4 Structure of the Thesis

Chapter 2 consists of the literature review of VRFB models. The governing and conservation equation of mass transfer, charge, momentum, and energy balance are described in this part including the electrochemical kinetics. And, the key terminologies, their formulae, the physical significance is also explained. The question: “How and Why to model?” is answered along with an analysis of the basic models developed.

Chapter 3 describes the performance modeling of the VRFB system dealing with four aspects. It deals with membrane properties and its function in the system, to come up with a membrane of the optimal thickness followed by the impact of mass transfer on battery performance. Then the next section analyzes the effect of current density on cell performance and finally, there is an analysis of the impact of electrode morphology on the over-potential losses

Chapter 4 focusses on flow rate optimization techniques, A review of models developed, and experiments conducted for flow rate control is done in this section. Then, the equations of the electrochemical model, ion concentration changes, transport properties of electrolyte, current density, over-potential are explained here. Then, it is combined with a hydraulic model dealing with pressure losses and pump power requirements.

Chapter 5 presents the model parameters and flow rate control strategy to come up with higher system efficiency and battery capacity.

Chapter 2

LITERATURE REVIEW

2.1 Electrochemistry and Electrode Kinetics of VRFB

When the electricity is applied, V (III) is reduced to V (II) while V (IV) is oxidized to V (V).

The discharge reactions are as follows:

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There are also crossover reactions across the membrane which decrease the capacity.

Additionally, there are self dis-charge reactions which are prevalent in the system:

Positive Electrode:

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Negative Electrode:

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Also, the gases are evolved when the battery is over-charged at high over-potential.

At the Negative Electrode, a hydrogen evolution reaction occurs.

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While at the Positive Electrode there is Oxygen Evolution

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The ­equilibrium cell voltage is calculated by the Nernst Equation,

The current flowing at equilibrium is called as exchange current and is given by:

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The current at positive and negative electrodes are given Buttler-Volmer Equation

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The following metrics analyze the performance of VRFB:

- Coulombic Efficiency (CE)-

It indicates how much loss is there in capacity during the charge-discharge process.

It is calculated by dividing the amount of usable charge to the total stored charge. In order words, it is nothing However the ratio of discharge capacity and charge capacity. It is hugely affected by Vanadium crossover, side reactions (gassing and evolution of H2 and O2), and shunt currents as well as battery design and operation.

- Voltage Efficiency (VE)-

It is the ratio of average discharge voltage and average charge voltage. It is indicative of ohmic losses, polarization properties, and over-potential of the battery.

- Energy Efficiency (EE)-

It is the ratio of discharge energy (withdrawn) and charging energy (fed). It can also be calculated by the product of voltage and coulombic efficiency.

- The State of Charge (SoC)-

It denotes the amount of battery capacity which can be utilized. It lies mostly in the range of 20-90%.

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2.2 Conservation Equations

Flow batteries are fast approaching commercialization However the process is limited by certain technological barriers.7 Modeling and simulation is an effective way not only to analyze the issues associated with the system. It also predicts and improves the performance of the battery. Here we have the governing equations describing mass, momentum, heat, and charge transfer.

- Conservation equations for fluid flow

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The effective permeability of electrode is given as by Kozeny-Carman equation:

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- Conservation equations for mass transfer

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Since the current is due to protons, the charge balance equation is:

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- Conservation equations for heat transfer (Energy Balance)

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Where, is the source term.

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Table 1 Source heat terms for energy balance8

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- Methodology for solving a VRFB system

The first step includes the distribution of pressure and flow velocity within the cell, then the concentration of species is modeled by considering electrochemical reactions and lastly, we get the current density and electric fields.9-10

2.3 Fundamental Flow Batteries

- Li and Hikihara11 developed the first-ever model for VRFB. He developed a zero-dimensional, transient model to demonstrate the concentration of vanadium ions based on electrochemical reactions and the flow of electrolysis solutions.
- Shah et al. 12- 13 developed a 2D transient model based on mass, charge, momentum balance to analyze the effect of variation in ion concentration, flow rate, and electrode porosity by modeling porous electrode, membrane, and current collectors. They also modeled the effects of hydrogen and oxygen evolution in subsequent research.
- You et al.14 further improved Shah’s model by a two-dimensional mathematical model of a flow-through porous electrode, in which the electrolyte flow is perpendicular to the current flow to study the combined effects of mass transfer, ohmic resistance, kinetic and operational factors on the performance of flow-through porous electrode, including the distribution of current density and concentration, the overall electrode polarization, the thickness of effective reaction layer and the concentration polarization in a lengthened electrode
- Tang et al.15 developed a dynamic model based on mass balance with the application of Nernst equation to analyze the effects of V ion diffusion across membrane, hydrogen evolution at high SoC and large current density, air oxidation of bivalent V ion which leads to electrolyte imbalance and capacity fade by studying the three different membranes (Selemion CMV, Selemion AMV and Nafion 115) with consideration of electrolyte flow and pressure losses. The direction and magnitude of cross-over are dependent on SoC, properties of the membrane (Ion Exchange Capability, and types of ion-exchange groups whether anionic or cationic).
- Kumbur et al.16 were the first to develop a 2D transient, an isothermal model that predicts cross-over and capacity loss due to all three phenomena: convection, migration, and diffusion, it also explains the water transfer to understand the volume changes in half-cells and it also includes the transfer of “all” ions including hydrogen and bi-sulfate.
- Vynky et al.17,18 further simplified the Shah’s model was incorporating scaling and asymptotic measures to analyze large scale Vanadium Redox Flow Battery stacks.
- Ma et al.19 developed a 3D transient model for the analysis of electrolyte velocity on cell performance. He studied distributions of velocity, concentration, over-potential, and transfer current density in the sections that are perpendicular and parallel to the applied current are studied.
- Kazacoss et al.20 developed a thermal model using energy balance to do a stack network-level analysis to show that the electrolyte temperatures in both the tanks and stack are influenced by multiple effects of charge/discharge current, flow rate, surrounding temperature and the heat generated by cell resistance.

Chapter 3 Performance Modeling of VRFB

The majority of literature is concerning the performance improving aspects of VRFBs21. The most extensively researched materials include electrode22, redox-active electrolyte23, flow field design24, membrane25, temperature aspects26, aging, electrolyte rebalancing27, and hydrogen evolution28. However, the problem with VRFB is that they have low energy efficiency as compared to others. Hence, operation based performance improvement strategies can be useful for this purpose. My thesis focusses on flow rate measures to improve the overall system efficiency and capacity of the battery.

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