APPROVED: Tae-Youl Choi, Major Professor Wongbong Choi, Committee Member Weihuan Zhao, Committee Member Kuruvilla John, Chair of the Department of

Mechanical Engineering Hanchen Huang, Dean of the College of

Engineering Victor Prybutok, Dean of Toulouse Graduate

School

A NOVEL THERMAL REGENERATIVE ELECTROCHEMICAL SYSTEM

FOR ENERGY RECOVERY FROM WASTE HEAT

David B. Gray

Thesis Prepared for the Degree of

MASTER OF SCIENCE

UNIVERSITY OF NORTH TEXAS

May 2021

Gray, David B. A Novel Thermal Regenerative Electrochemical System for Energy

Recovery from Waste Heat. Master of Science (Mechanical and Energy Engineering), May 2021,

54 pp., 1 table, 32 figures, 1 appendix, 23 numbered references.

Waste-heat-to-power (WHP) recovers electrical power from exhaust heat emitted by

industrial and commercial facilities. Waste heat is available in enormous quantities. The U.S.

Department of Energy estimates 5-13 quadrillion BTUs/yr with a technical potential of 14.6 GW

are available and could be utilized to generate power by converting the heat into electricity.

The research proposed here will define a system that can economically recover energy from

waste heat through a thermal regenerative electrochemical system. The primary motivation

came from a patent and the research sponsored by the National Renewable Energy Laboratory

(NREL). The proposed system improves on this patent in four major ways: by using air/oxygen,

rather than hydrogen; by eliminating the cross diffusion of counter ions and using a dual

membrane cell design; and by using high concentrations of electrolytes that have boiling points

below water. Therefore, this system also works at difficult-to-recover low temperatures.

Electrochemical power is estimated at 0.2W/cm2, and for a 4.2 M solution at 1 L/s, the power of

a 100 kW system is 425 kW. Distillation energy costs are simulated and found to be 504 kJ/s for

a 1 kg/s feed stream. The conversion efficiency is then calculated at 84%. The Carnot efficiency

for a conservative 50% conversion efficiency is compared to the ideal Carnot efficiency.

Preliminary work suggests an LCOE of 0.6¢/kWh. Industrial energy efficiency could be boosted

by up to 10%. Potential markets include power stations, industrial plants, facilities at

institutions like universities, geothermal conversion plants, and even thermal energy storage.

ii

Copyright 2021

by

David B. Gray

iii

ACKNOWLEDGMENTS

Thanks to my wife Nancy Bateman for believing in me and allowing the time and

financing to “go back to school”.

Thanks to Dr. Tae-Youl Choi for accepting and approving my application to graduate

school, for mentoring my research efforts, for financial support out of his own budget, for

listening to my concerns and problems, and for encouraging my often unorthodox way of doing

things.

Thanks to Dr. Wonbong Choi for listening to my proposals and expecting me to show the

numbers and present the data.

Thanks to Dr. Zhao for her enthusiasm about my project and for agreeing to join my

committee at a late date.

Thanks to Richard Pierson for his skill, patience in training me in machine shop skills, for

repeatedly explaining to me how the machines work, and for actually completing some of the

tasks for me.

Thanks to Robbin Shull and the ME staff for assisting me with laboratory access and

supplies, supplemental work income, and administrative support.

Thanks to Lorne Hinz and Michael Hinz for helping me fabricate and debug a DIY

potentiometer and other research circuits.

iv

TABLE OF CONTENTS

Page

ACKNOWLEDGMENTS ..................................................................................................................... iii

LIST OF TABLES ................................................................................................................................. v

LIST OF FIGURES .............................................................................................................................. vi

CHAPTER 1. INTRODUCTION ........................................................................................................... 1

CHAPTER 2. BACKGROUND ............................................................................................................. 3

CHAPTER 3. SYSTEM OVERVIEW ..................................................................................................... 5

3.1 Mass Flow ............................................................................................................... 6

3.2 Energy Balance ........................................................................................................ 7 CHAPTER 4. ELECTROCHEMICAL CELL ............................................................................................. 8

4.1 Electrolytes ............................................................................................................. 9

4.2 Open Circuit Potential ........................................................................................... 10

4.3 Current .................................................................................................................. 14

4.4 Other Features ...................................................................................................... 17

4.5 Later Experiments ................................................................................................. 21 CHAPTER 5. DISTILLATION ............................................................................................................ 27

5.1 Fractional Distillation ............................................................................................ 27

5.2 Simulation ............................................................................................................. 31

5.3 Laboratory Demonstration ................................................................................... 37

5.4 Optional Concentration by Filtration .................................................................... 38 CHAPTER 6. COST OF ENERGY ....................................................................................................... 40 CHAPTER 7. CONCLUSION ............................................................................................................. 45

7.1 Efficiency ............................................................................................................... 46

7.2 Future Research .................................................................................................... 48 APPENDIX: COST OF ENERGY CALCULATIONS .............................................................................. 50

REFERENCES .................................................................................................................................. 53

v

LIST OF TABLES

Page

Table 4.1: Selected acid and base electrolyte candidates. ........................................................... 10

vi

LIST OF FIGURES

Page

Figure 3.1: TRES system components and flows. ........................................................................... 5

Figure 4.1: The 3-compartment design. ......................................................................................... 8

Figure 4.2: A half U-cell in a beaker of water with Pt and glassy carbon electrodes. .................. 11

Figure 4.3: W-cell with Pt and glassy carbon electrodes. ............................................................. 11

Figure 4.4: OCV of acetic acid half-cell in water with platinum cathode and glassy carbon anode and Fumasep anion membrane. ................................................................................................... 13

Figure 4.5: OCV of ammonia half-cell in water with two glassy carbon electrodes and a Nafion cation membrane. ......................................................................................................................... 13

Figure 4.6: OCV of full cell with a platinum electrode in acetic acid and a glassy carbon electrode in ammonia. .................................................................................................................................. 14

Figure 4.7: Chronoamperometry graph for a potential of 0.6 V. ................................................. 15

Figure 4.8: Impedance graphs for an ammonia Nafion half-cell. ................................................. 16

Figure 4.9: Chronopotentiometry of a half-cell with a current of 0.001 A................................... 16

Figure 4.10: Chronopotentiometry of a half-cell with varying distances of the electrode, (a) 1, 2, 4, 6, and 8 centimeters from the membrane, (b) 1 and 8 centimeters distances. ...................... 18

Figure 4.11: OCV of a half-cell with a supporting electrolyte of NaCl. ......................................... 19

Figure 4.12: Three examples of stirred convection, (a) no stir, (b) stir setting at 2, (c) stir setting at 8. ............................................................................................................................................... 20

Figure 4.13: Open circuit potention of HCl and NaOH in W-cell. ................................................. 23

Figure 4.14: Current of 3.2 mA/cm2 at 1 V for a 1M HCl half-cell. ............................................... 24

Figure 4.15: 17.3 mA/cm2 at 1 V for a 1M NaOH solution. .......................................................... 25

Figure 5.1: Diagram of a distillation column showing feed, reflux, and reboiler. ........................ 28

Figure 5.2: A Txy plot of a benzene-toluene mixture. .................................................................. 29

Figure 5.3: An xy plot for benzene in a benzene-toluene mixture. .............................................. 30

vii

Figure 5.4: An xy plot showing the vapor-liquid steps for a total reflux operating condition. .... 30

Figure 5.5: An illustration of the COCO flowsheet for distillation simulation. ............................. 32

Figure 5.6:The feed specifications for the distillation simulation. ............................................... 32

Figure 5.7: The column specifications for the molar case, case 1.The column specifications for the molar case, case 1. .................................................................................................................. 33

Figure 5.8: The Streams report for the molar case, case 1. .......................................................... 34

Figure 5.9: The Mass and Energy Balance report for the molar case. .......................................... 34

Figure 5.10: Column specification for product rate case, case 2. ................................................ 35

Figure 5.11: Stream report for product rate case, case 2. ........................................................... 36

Figure 5.12: Mass and Energy Balance report for case 2. ............................................................ 37

Figure 5.13: The laboratory setup for distilling DEA from an acetic-acid-DEA mixture ............... 38

Figure 6.1: Cost structure of 250kW VFRB stack with Nafion (after Minke[2017], Fig. 5). .......... 41

Figure 6.2: Model system and cost structure of system with E/P = 4 h (after Minke[2017], Fig. 6)........................................................................................................................................................ 42

Figure 7.1: Comparison of Carnot TRES and ORC efficiencies to the ideal................................... 47

1

CHAPTER 1

INTRODUCTION

The world is finally accepting the full implications of dangers caused by climate change.

According to the International Panel for Climate Change1, a 2° C rise in average world

temperatures is a threshold beyond which extreme climactic conditions will cause untold

damage and misery, especially to the world’s marginalized and poorer populations. To reduce

the greenhouse gas emissions that cause climate change, the world’s energy sources must be

de-carbonized to the fullest extent possible. My research is aimed at providing additional clean

energy through energy efficiency utilizing what is called waste-heat-to-power. Waste-heat-to-

power recovers electrical power from exhaust heat emitted by industrial and commercial

facilities that would otherwise be released directly into the atmosphere.

Waste heat is available in tremendous quantities from power plants to industrial

processes to institutions like hospitals and universities. The U.S. Department of Energy (DOE)

estimates 5-13 quadrillion BTUs/yr. with a technical potential of 14.6 GW are available and

could be utilized to generate power by converting the heat into electricity2. The DOE and clean

energy companies are extremely interested in utilizing this energy to significantly increase the

county's energy efficiency which in turn saves money, increases our energy independence, and

provides pollution-free, non-CO2 power that will reduce greenhouse gases and help limit

climate change.

The research presented here demonstrates a system that can recover energy from

waste heat through a thermally regenerative electrochemical system (TRES). The idea is

deceptively simple: a chemical reaction powered by an acid-base neutralization powers an

2

electrochemical battery. The battery type used here is known as a flow battery in which the

liquid electrolyte or electrolytes flow into the battery in one state or the other—charged or

uncharged—and flow out of the battery in the opposite state. In research presented here, the

acid and base electrolytes flow in only with a charged state, and the neutralized and discharged

electrolytes flow out. Then the neutralized electrolytes are regenerated chemically into the

charged acid and base electrolytes through the application of the available waste heat.

The components of the TRES presented include the cells of the battery, a distillation

column to regenerate the electrolytes, various heat transfer components including heat

exchangers and fans, and an optional molecular sieve to concentrate the discharged

electrolyte. This paper presents on overview of the complete system, investigates each

component in turn, and provides a cost estimate for manufacturing such a system. I show such

a system can recover waste heat at temperatures only slightly above 100°C.

3

CHAPTER 2

BACKGROUND

Some of the earliest work on TRES’s is presented in Chum[1981a]3 and Chum[1981b]4,

published by the Solar Energy Research Institute which is now the National Renewable Energy

Laboratory (NREL). In Vol. 1 of [3], four types of TRESs are presented where A, B, C, D, and E are

substances as well as compound CA.

In Type 1 TRES, compound CA is formed from C and A in an electrochemical cell at temperature T1

with concomitant production of electrical work in the external load. Compound CA is sent to a regenerator unit through a heat exchanger. In the regenerator, compound CA is decomposed into C and A, which are separated and redirected to the electrochemical cell via a heat exchanger, thus closing the cycle…. Type 2 is similar to Type 1, but the products C and E of the electrochemical cell reaction A + D → C + E are regenerated in a two-step process (C → A + B; E + B → D)…. Type 3 is also similar to Type 1 and involves a one-step regeneration. Liquid metal electrodes are composed of one electroactive metal C and one electroinactive metal B…. In Type 4 systems , compound CA, formed in the electrochemical cell at temperature T1 is sent to a regenerator, which is an electrolysis cell at temperature T2• In the regenerator, reactions opposite to those occurring at T1 re generate C and A by using two energy inputs--electric and thermal….

None of the 4 types reported were very practical, and most of them were high temperature

systems. The most successful Type 1 was a lithium-hydride at temperatures from 500°C to

900°C.

My system is of Type 1, and the primary motivation for the initial version of my system

came from a patent5.

A thermoelectrochemical system in which a continuous electrical current is generated from a heat input below about 250° C. A hydrogen ion reacting cathode is immersed in a chosen Bronsted acid and a hydrogen ion reacting anode is immersed in a chosen Bronsted base. Reactants consumed at the electrodes during the electrochemical

4

reaction are directly regenerated thermally below about 250° C. and recycled to the electrodes to provide continuous operation of the system.

While this patent formed the basis for the current invention, it did not present any sort of full

system results. The research leading to the patent was sponsored by NREL6, however the full

report is not available. The current invention improves on this patent in three major ways: by

using air/oxygen as the working gas instead of hydrogen, using a three compartment cell which

also eliminates the cross diffusion of counter ions, and by using a strong acid and base that

both have boiling points lower than water.

A more recent TRES uses ammonia along with copper electrolytes7 with a peak power

production of 136 W m-2 (0.0136 W cm-2). The difficulty with this system is the cathode

compartment has to be switched with the anode compartment after each discharge cycle.

Another variation uses a dual loop, and it requires three electrochemical cells and two

regenerators.8 Clearly, this system is of unreasonable complexity.

A review of electrochemical and membrane systems for conversion of low grade heat

has been published by Rahimi et al. [2018]9.

5

CHAPTER 3

SYSTEM OVERVIEW

As mentioned previously, the system proposed here is conceptually simple. Figure 1

presents a high level illustration of the main system components and primary flows.

Figure 3.1: TRES system components and flows.

At the center right is the battery powered by the acid and base electrolytes. The acid and base

neutralization reaction into a salt generate the electrochemical reactions at the cathode and

anode. Then the salt along with the water solvent is pumped out of the battery to the stripper

(a distillation column). The externally supplied waste heat is transferred to the stripper and

boils the salt solution. The distillation is a continuous, fractional process that separates the acid

and base from the solvent in two fractions. The acid and base vapors are condensed, and the

liquids are returned to the battery in the cathode and anode compartments, respectively. The

bottoms of the distillation (the unvaporized component) is the leftover water, and it is returned

to the center compartment of the battery.

6

Chemical oxidation takes place at the anode generating electrons and making the anode

the negative terminal. Reduction takes place at the cathode where the electrons are

consumed, making the cathode the positive terminal.

3.1 Mass Flow

The mass flow of ions (multiplied by their charge) through the membranes separating

the compartments and into the neutral water must balance the flow of electronic current

through the external circuit of the battery. The molar flow of negative ions 𝑁𝑁𝐴𝐴− and positive

ions 𝑁𝑁𝐵𝐵𝐵𝐵+ in moles/s across the membranes and neutralized in the pure water make up the

ionic current. The salt flow out of the cell must contain the same amount of neutralized ions in

the solvent as flow in, [𝐵𝐵𝐵𝐵𝐴𝐴] × 𝐿𝐿𝐵𝐵𝐵𝐵𝐴𝐴𝐵𝐵, where [𝐵𝐵𝐵𝐵𝐴𝐴] is the molar concentration of the salt in

the solvent and 𝐿𝐿𝐵𝐵𝐵𝐵𝐴𝐴𝐵𝐵 is the flow of solution (salt in water) in L/s; and the return flow of each

electrolyte, 𝑁𝑁𝐵𝐵 and 𝑁𝑁𝐴𝐴, must equal the amount removed in the salt:

𝑁𝑁𝐵𝐵𝐵𝐵+ = 𝑁𝑁𝐴𝐴− = 𝑁𝑁𝑋𝑋 = [𝐵𝐵𝐵𝐵𝐴𝐴] × 𝐿𝐿𝐵𝐵𝐵𝐵𝐴𝐴𝐵𝐵 = 𝑁𝑁𝐵𝐵 = 𝑁𝑁𝐴𝐴

The power out is the work rate in Watts for current I and potential V

𝑃𝑃 = 𝐼𝐼 × 𝑉𝑉 = 𝐶𝐶/𝑠𝑠 × 𝑉𝑉

where C/s is Coulombs per second. The ionic flow can be expressed in molar terms with the

help of the Faraday constant, F ≅ 100,000 C/mole:

𝐶𝐶/𝑠𝑠 × 𝑉𝑉 = 𝐹𝐹 × 𝑉𝑉 × 𝑁𝑁𝑥𝑥

Solving for 𝐿𝐿𝐵𝐵𝐵𝐵𝐴𝐴𝐵𝐵,

𝐿𝐿𝐵𝐵𝐵𝐵𝐴𝐴𝐵𝐵 = 𝑃𝑃/(𝐹𝐹 × 𝑉𝑉× [𝐵𝐵𝐵𝐵𝐴𝐴])

Assuming a 100% distillation (not really possible), the flow rate for a 100 kW system with a 1 V

battery cell and a 1 Molar salt concentration is ~1.0 L/s (where P units are C/s x V).

7

3.2 Energy Balance

This system is driven by heat delivered from an external source such as waste heat from

a furnace or boiler exhaust. As a heat engine, its efficiency is constrained by Carnot’s Law. As

shown in Figure 1, the incoming heat at temperature T2 heats the salt solution and then is

exhausted at the boiling temperature of the solution, T1. For example, if T2 were a relatively low

temperature of 200°C and T1 were 100°C, the Carnot efficiency would be

𝜂𝜂 = 1 −373473

= 0.21 𝑜𝑜𝑜𝑜 21%

This relatively low efficiency could be addressed by an extension of this system to a series of

cascading systems, each similar in design but using electrolytes that work at lower

temperatures. Though that is beyond the scope of the present system, it is the reason I prefer

to measure the conversion efficiency

𝜁𝜁 = 𝑊/(𝑄2−𝑄1),

where W is the electrical energy output and Q2 and Q1 are the incoming and outgoing heat,

respectively.

8

CHAPTER 4

ELECTROCHEMICAL CELL

The two main components of the system under study are the electrochemical battery

and the stripper or distillation column. A battery is composed of multiple cells arranged in

series and in parallel in order to provide the appropriate voltage and current. We take a close

look at the electrochemical cell in this chapter and distillation in the next chapter.

The electrochemical cell is driven by an acid-base neutralization reaction, and is

expected to generate 0.8 V at OCV and 0.3 A/cm2 working current with an estimated 0.2 W/cm2

working power. The following from Chan10 is for a hydrogen recycling reaction,

… a cell voltage of 0.828 V will be generated [by hydroxide and protons] if the neutralization of acid and base can be carried out electrochemically…

and it corroborates the chemical potential and thus voltage possible from an acid-base

neutralization.

Figure 4.1: The 3-compartment design.

9

The cell is a key component making up the battery for this system, and it is a novel

design intended to take advantage of the unusual properties of an acid/base-powered cell. As

described by Chan et al. [2014]10, a three compartment cell can lead to higher overall

efficiencies for an acid-alkaline battery. Figure 4.1 illustrates the 3-compartment design. The

cathode compartment contains the acid where chemical reduction of the H+ ion takes place

along with an anion-selective membrane that allows the anion to diffuse into the center

compartment. Conversely, the anode compartment contains the base where the OH- ion is

oxidized along with a cation-selective membrane that allows the cation to diffuse into the

center. The center compartment contains the neutralized salt solution. Flows across both ion-

selective membranes make up the ionic current. The reactions in each compartment are aided

by the addition of Gas Diffusion Electrodes (GDEs)—carbon felts with a high degree of surface

area coated with the appropriate metal catalysts.

4.1 Electrolytes

The choice of electrolytes is important in minimizing the distillation costs, and

maximizing the power. Almost all the electrolytes reported in the 1988 Ludwig patent5 have

boiling points above 100°C, and are weak acids and bases. An acid, trifluoroacetic acid, and a

base, diethylamine, both have boiling points less than 100°C. Trifluoroacetic acid also has a

very low pKa or a high disassociation and is a strong acid. Diethylamine is a weak base, but

guanidine is a strong base with a pKb of 0.4. Unfortunately, guanidine has a higher than 100°

boiling point. Table 4.1 lists several potential acid and base electrolytes and their properties.

10

Table 4.1: Selected acid and base electrolyte candidates.

Chemical Ion no pKa/pKb Density

g/ml g/mol Boiling point

∆Gf

kJ/mol ∆Hv

kJ/mol

Acid

s

Trifluoroacetic acid 1 0.23 1.5 114 72.4

Oxalic Acid 2 1.25 /4.27 1.9 90 189

Acetic Acid 1 4.76 1.05 60 118 -300 -483

Base

s

Piperazine 2 5.35/9.73 pKb 86 146

Ethylenediamine 2 4.1/7.1 pKb 0.9 60 116 -98

Ammonia (aq) 1 11.6 4.75 pKb

0.7 0.91 (25%) 35 -33

37.7 aq -27 -80

Diethylamine (CH3CH2)2NH 1 3.29 pKb 0.707 73 55 -131

Acetamidine (C2H6N2)

1 12.1 pKa 1.03 94.5 62

Guanidine 1 0.4 pKb 1.1 77 132? -615

Water 0 18 100 -37

4.2 Open Circuit Potential

A comprehensive theoretical framework for the system under study is beyond the scope

of this thesis. To help explain future work, I introduce some basic electrochemical theory for

background. One important starting point is the Nernst equation

𝐸𝐸 = 𝐸𝐸0 + 𝑅𝑅𝑅𝑅𝑛𝑛𝑛𝑛

ln 𝐶𝐶0𝐶𝐶𝑅𝑅

(4.1)

for the reaction at an electrode

𝑂𝑂 + 𝑛𝑛𝑒𝑒− ↔ 𝑅𝑅 (4.2)

where C0 and CR are the concentrations of the oxidant and reductant, respectively, and E0 is the

standard reduction potential of the reaction of one half cell. The overall potential of the cell is

the difference of the potentials of the two half-cell reactions

11

𝐸𝐸𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 𝐸𝐸𝑐𝑐𝑐𝑐𝑐𝑐ℎ𝑜𝑜𝑜𝑜𝑐𝑐 − 𝐸𝐸𝑐𝑐𝑛𝑛𝑜𝑜𝑜𝑜𝑐𝑐 (4.3)

where for a galvanostatic cell (spontaneous discharge) the cathode has a positive potential and

the anode has a negative potential.

I have measured the open circuit voltage (OCV) for both half-cell and full cell potentials

with acetic acid (distilled vinegar) and household ammonia using simple laboratory H-cell and

W-cell glassware (Figures 4.2 and 4.3).

Figure 4.2: A half U-cell in a beaker of water with Pt and glassy carbon electrodes.

Figure 4.3: W-cell with Pt and glassy carbon electrodes.

12

For both electrolytes, the volume concentration was around 8% or roughly one molar for acetic

acid and around 5 molar for ammonia. The cation membrane was a Nafion 115 product and

the anion membrane was a Fumasep FAP-450 product available from The Fuel Cell Store. I

experimented with several electrode types, but the plain graphite electrodes worked well in

both the acid and the base electrolytes.

The reactions for these measurements are for the anode

𝐵𝐵 + 𝐵𝐵2𝑂𝑂 → 𝐵𝐵𝐵𝐵+ + 𝑂𝑂𝐵𝐵− (4.4)

4𝑂𝑂𝐵𝐵− ← 2𝐵𝐵2𝑂𝑂 + 𝑂𝑂2 + 4𝑒𝑒−, 𝐸𝐸0 = 0.44 𝑉𝑉 (4.5)

where B is the base or NH3 in this case. For the cathode, the reactions are

𝐵𝐵𝐴𝐴𝐻𝐻 → 𝐵𝐵+ + 𝐴𝐴𝐻𝐻− (4.6)

4𝐵𝐵+ + 𝑂𝑂2 + 4𝑒𝑒− → 2𝐵𝐵2𝑂𝑂, 𝐸𝐸0 = 1.21 𝑉𝑉 (4.7)

where Ac is the acetate ion. Note that oxygen is consumed at the anode and generated at the

cathode. Also note the anode reaction does not favor the reduction of the hydroxide ions, but

because the cathode standard reduction is much higher at 1.21 V, the theoretical full cell

voltage would be 1.21 – 0.44 ≅ 0.7 V. I have measured OCVs approaching 0.6 V and above as

shown for example in Figures 4.4, 4.5 and 4.6 with both a W-cell arrangement and two half-cells

in a beaker of water. Note that the STP solubility of oxygen in water is 8 mg/L or 0.00025

mol/L. This low concentration favors the anode reaction of hydroxide oxidation, but disfavors

the oxygen reduction in the cathode. By oxygenating the acetic acid (I simply blew air into the

acetic acid), I increased the OCV of the acid cell by 10% or more.

Acetic acid and ammonia are a weak acid and base, respectively. Increasing the

concentrations of hydroxide (OH-) and hydronium (H3O+) ions would also raise the OCV. The

13

electrolytes mentioned above, trifluoroacetic acid and guanidine (or acetamidine), would give

strong concentrations. Investigating strong ion concentrations is on my research To-Do list.

Also, the chemical behavior of these stronger electrolytes under these working

conditions is unknown.

Figure 4.4: OCV of acetic acid half-cell in water with platinum cathode and glassy carbon anode and

Fumasep anion membrane.

Figure 4.5: OCV of ammonia half-cell in water with two glassy carbon electrodes and a Nafion cation

membrane.

14

Figure 4.6: OCV of full cell with a platinum electrode in acetic acid and a glassy carbon electrode in

ammonia.

4.3 Current

When current is allowed to discharge a cell, many electrochemical behaviors are

introduced. Derived from the Arrhenius equation and transition state theory, the Butler-

Volmer equation is the first approximation to the current flowing into or out of the electrode

𝑖𝑖 = 𝑖𝑖𝑜𝑜𝑒𝑒−𝛼𝛼𝛼𝛼𝛼𝛼 − 𝑒𝑒(1−𝛼𝛼)𝛼𝛼𝛼𝛼 (4.8)

where η = E – E0 and is known as the overpotential or the potential above the equilibrium

potential or OCV, α is the transfer coefficient, f = F/RT, and i0 is known as the exchange-current

or the balanced back and forth equilibrium current. When current is allowed to flow through

an external circuit, internal resistances to the ionic flow and from the reaction kinetics create

opposing voltages known as polarizations that create the overpotential.

I have made current measurements, however the laboratory apparatus I use is not really

suitable for realistic current and current density values. But I show that through additional

15

measurements a current density of 0.3 A/cm2 is possibly achievable.

Direct amperometry measurements yield current density around 1e-5 A/cm2 falling off

to a diffusion resistance limit of 1e-6/cm2 for the ammonia/Nafion/water half-cell (see Figure

4.7 where the polarity is shown as negative). Impedance measurements show an internal ionic

resistance of 2e4 Ohms (see Figure 4.8) of the glassware half-cell. Furthermore,

chronopotentiometry measures the voltage for a fixed current setting. In Figure 4.9, we see the

change of voltage after a current of 0.001 A is started. The initial voltage change is known to be

the Faradaic response or the pure resistance of the ionic flow. The later voltage approaches the

full resistance that includes the current-opposing polarization from the reaction kinetics. If we

measure the linear change of the initial response in Figure 4.9 and divide by the current of

0.001 A, we get the Faradaic resistance of R = V/I = 1.8/0.001 = 1800 Ω. We also see from

Figure 4.9 that the total effective resistance is about 2.7 V/0.001 A = 2800 Ω.

Figure 4.7: Chronoamperometry graph for a potential of 0.6 V.

16

Figure 4.8: Impedance graphs for an ammonia Nafion half-cell.

Figure 4.9: Chronopotentiometry of a half-cell with a current of 0.001 A.

I have measured the internal resistance of a realistic cell model and found the direct

internal resistance to be on the order of 1 Ω which is also found in the literature. If we make

the impedance correction by increasing the resistance to 1800 and substitute a realistic voltage

of 0.3 for a half-cell, we get a corrected current of 1e-3 X iC = 0.3 V/1800 Ω or simply iC = 0.3

V/1.8 Ω = 0.166 A where 0.3 V is about the voltage of the half-cell. If we double the current to

17

account for voltage of both half-cells and measure the opening of the glassware at 1 cm2, we

can conservatively estimate a working current of 0.33 A/cm2 which is less than a PEM fuel cell,

but significantly more than that reported in published works of TRES. More about the

resistance in the next section.

4.4 Other Features

The ionic portion of the current flow taking place in the cell is caused by mass transfer.

The modes of mass transfer in a cell are migration, diffusion, and convection. Mass transfer

with three terms for each mode, respectively, is governed by the Nernst-Planck equation

𝑁𝑁𝑖𝑖 = − 𝑧𝑧𝑖𝑖𝑛𝑛𝑅𝑅𝑅𝑅

𝐷𝐷𝑖𝑖𝐻𝐻𝑖𝑖∇𝜑𝜑 − 𝐷𝐷𝑖𝑖∇𝐻𝐻𝑖𝑖 + 𝐻𝐻𝑖𝑖𝑣𝑣 (4.9)

where Ni is the flux of species i at distance x from the electrode surface, Di is the diffusion

coefficient, ∇ci is the concentration gradient, ∇φ is the potential gradient, zi and ci are the

charge and concentration, respectively, and v is the velocity of a volume element.11

The resistance of the cell solution to the flow of ions induces an iR drop in the cell

potential.

When the potential of an electrode is measured against a nonpolarizable reference electrode during the passage of current, a voltage drop equal to iRs is always included in the measured value. Here, Rs is the solution resistance between the electrodes, which, … actually behaves as a true resistance over a wide range of conditions.12

The electrodes in my glassware are quite far apart compared to a conventional cell model.

Typically a model cell has a pair of GDEs laid right up against or formed on the ion-permeable

membrane as shown in Figure 4.1 (without the third middle water compartment) so that the

distance between electrodes approaches zero. I demonstrated the effect of distance between

electrodes by placing one electrode in the half-U-tube cell and another one in a large beaker of

18

water along with the half-cell. This allowed me to vary the distance slightly between the

electrodes as seen in Figure 4.10. As shown, both the OCV and the working voltage for the

0.001 current is higher for the 8 cm distance than for the 1 cm distance which means the

resistance is higher for the 8 cm distance. However, those distances do not include the

distance of the electrode in the half-U-cell from the ion-selective membrane (which is roughly 6

cm).

(a) (b)

Figure 4.10: Chronopotentiometry of a half-cell with varying distances of the electrode, (a) 1, 2, 4, 6, and 8 centimeters from the membrane, (b) 1 and 8 centimeters distances.

Diffusion depends on temperature and the concentration gradient as described by Fick’s

Law

𝐽𝐽𝑖𝑖 = −𝐷𝐷𝑖𝑖∇𝐻𝐻𝑖𝑖 (4.10)

where Ji is the molar flux relative to the average bulk velocity. Protons or H+ have a high

conductivity, and OH- is even higher. The conductivity for H+, for example, is 67.3 X 10-4

m2S/mol with a diffusion coefficient of 0.597 x 10-5 cm2/s at 25°C in dilute aqueous solution.

19

However, maintaining a large concentration difference between the electrolyte compartment

and the center neutral water compartment across the membrane is important to maintain both

the cell potential and the ionic current flow. From Figure 4(b) in Shimpalee et al.13, we can see

that the conductivity of protons through a Nafion membrane is about 0.1 S/cm, and from their

experiments in Figure 6(b), we see a current density ranging up to 1500 ma/cm2. Note that we

see that the ionic diffusion is more limiting than diffusion through a Nafion membrane. Note

also that the battery in the present system is proposed to operate at least at 55°C to minimize

the amount of cooling required after the distillation process which is (328-298)/298 = 0.101 or

10% higher than STP.

Figure 4.11: OCV of a half-cell with a supporting electrolyte of NaCl.

The migration mode of transport comes from the force of charged species in an electric

field, and since, for example, positive charges must be transported to the positive electrode in

20

order to be reduced by electrons, the migration force opposes the necessary current flow of

ionic charges. By adding a non-reacting salt, the electric field strength is reduced and the

opposing force on migration is lowered thereby increasing the ionic current flow and lowering

the overpotential. I added a small amount of NaCl to an ammonia anodic half-cell and recorded

a significantly higher OCV of 0.5 V, see Figure 4.11.

A flow battery’s design intrinsically includes convection through all cells of the battery

from the flow of electrolytes, and my example is no different. Convection overcomes some of

the limitations of simple diffusion since the flow brings the fresh, higher concentrated

electrolyte directly to the electrode. I demonstrated convection by putting an anionic half U-

cell into a large beaker of water with a stir rod on the bottom of the beaker. I placed the

beaker on a stirring hot plate (with no heat), and measured the OCV. In Figure 4.12 is shown

from 3.1 V for no-stir down to 2.6 V for the setting at 8. The reduction in potential for the same

current indicates the ionic current resistance is lower or alternatively the overpotential is lower.

Note the convection is only occurring in the neutral beaker of water and not in the half U-cell.

(a) (b) (c)

Figure 4.12: Three examples of stirred convection, (a) no stir, (b) stir setting at 2, (c) stir setting at 8.

Electrodes can play a big role in reducing overpotential and increasing cell power. The

oxygen reduction and oxygen generation reactions proposed for this system, while well studied,

21

are complex reactions involving a chain of several reactions and four electrons. Catalysts are

almost always used to promote faster reactions with less overpotential. According to

Kinoshita14, one of the best catalysts for oxygen reduction is platinum, and some of the best for

generation is iridium or ruthenium oxide. Practically speaking, these precious materials are

expensive, but there is abundant research into cheaper alternatives like nickel and copper

alloys. These catalysts are often loaded with carbon black onto a carbon cloth support. I have

ordered 5 cm X 5 cm 2mg/cm2 Pt Black Carbon Cloth and a 2 mg/cm2 Ruthenium Oxide GDEs for

oxygen reduction and oxygen generation testing, respectively.

I plan to test many of the additional features mentioned above in the glass U- and W-

cells. The potentiometer is the standard instrument used by electrochemists to measure the

characteristics of cells. Unfortunately, the UNT Mechanical Engineering laboratory does not

currently have access to a potentiometer. I am currently working on assembling a simple DIY

version of such an instrument that should suffice to give basic measurements.

From foregoing discussion and results, I can estimate that the basic electrochemical cell

will reach 0.8 OCV with working current of 0.3 A/cm2. So a conservative estimate for the

working power density of the cell would be 0.2 W/cm2.

4.5 Later Experiments

In order to test the new GDE’s and further investigate the current characteristics, I

resorted to building a Do-It-Yourself potentiostat15 although it has limited functionality and

range. I also wanted to test the higher concentrations of strong acids and bases as suggested

by the proposed electrolytes. To do so, I used a substitute acid and base, hydrochloric acid and

sodium hydroxide, which were easy to obtain and easy to manage in the lab. To verify that the

22

GDE was working and to isolate any potential problems, I tested each of the acid and base in

separate “half-cells” with a “standard reference” half-cell on the opposite side of the cell. For

opposite the base half-cell, I used a copper electrode in copper sulfate, and for the acid, I used

a silver foil electrode in silver nitrate. Then I tested both half-cells together in the W-cell with

the third, central, neutral water compartment.

I learned two things from these tests. Firstly and most importantly, the three

compartment W-cell is never going to provide reasonable current production. I believe this is

due to at least two things: 1) the distance between the two membranes and electrode impedes

the ionic flow of the two ion species and represents a high impedance to ionic current flow, and

discourages chemical and electrical neutralization, and 2) the membranes actually have their

own potential difference across the membrane which, in the absence of ionic neutralization,

sets up a polarization from the static charges that accumulate on each side of the membrane as

one ionic species diffuses across the membrane.

Secondly, I learned that concentrations absolutely make a difference. From Equation

4.1, we see that the OCV increases with the logarithm of the ratio between oxidant and

reductant electrolytes. Concentration and concentration gradient also effect ionic current

which is caused by mass transfer as seen in Equation 4.9.

Additionally, I learned from an e-mail conversation with Fuel Cells Etc. that the anode

ion membrane that I purchased was not the best choice of membrane for my purposes. There

are several others recommended to me by Fuel Cells Etc. that have been conductivity ratings

almost comparable to the Nafion cation membrane.

23

Although the 3-compartment W-cell was not conducive to current flow, it did exhibit

consistently high OCV when configured with the new GDEs. Not surprisingly, with the low pKa

of HCl acid and the low pKb of NaOH, the concentrations of ions were exceedingly high which in

turn leads to higher voltage as we see in Equation 4.1. In Figure 4.13 is shown an OCV of 0.74 V

with a 1M solution of HCl on one side and 1M NaOH on the other side.

Figure 4.13: Open circuit potention of HCl and NaOH in W-cell.

As stated above, the W-cell did not generate any appreciable current, possibly because

of the width of the neutral compartment and membrane polarization. To get an idea of

potential current capability assuming those aforementioned limitations could be overcome, I

tested the NaOH half-cell against an Ag/AgNO4 half-cell and the HCl half-cell against a Cu/CuSO4

half-cell with the platinum-on-carbon GDE and a Fumasep anion membrane. The configuration

is notated as CuSO4/Cu||Fuma/PtC/HCl. As seen if Figure 4.14, a 1M solution of HCl generated

3.2 mA/cm2 at 1 V. Interestingly, when I quadrupled the HCl solution to 4M, the current went

24

up to 10 mA/cm2 or a three-fold increase. For the NaOH half-cell I used a Ag/AgNO4 counter

half-cell with a ruthenium-oxide GDE and a Nafion cation membrane,

NaOH/RuO/Nafion||Ag/AgNO4. Figure 4.15 shows a current of 17.3 mA/cm2 at 1 V with a 1M

solution of NaOH. Using the same three-fold increase as for the HCl half-cell, we could expect a

51 mA/cm2 reading with a 4M NaOH solution.

Figure 4.14: Current of 3.2 mA/cm2 at 1 V for a 1M HCl half-cell.

25

Figure 4.15: 17.3 mA/cm2 at 1 V for a 1M NaOH solution.

I investigated the difference in measured between the acid and base half-cells with an

inquiry to Fuel Cells Etc. about the conductivity of the Fumasep anion membrane. They

recommended several other membranes with much better conductivity than the tested one,

almost matching the rated conductivity of the Nafion membrane. Thus we could expect a

comparable current of about 50 mA/cm2 from the HCl half-cell with a better anion membrane.

These results certainly do not reach the 300 mA/cm2 projected in the previous section.

However, a new, conventional model cell needs to be built to overcome the W-cell limitations

described above. This new cell would include several features that could dramatically increase

the current capability such as proper neutralization in the third compartment with a supporting

electrolyte and convection to overcome the W-cell limitations, a thicker GDE similar to a fuel

cell’s PEM, no cross-diffusion across the ion membrane, as well as the more conductive anion

membrane. Furthermore, it appears that increasing the concentrations of acid and base will

26

increase the current until reaching some unknown diffusion limit. All this should be

investigated with the construction of a new conventional, model cell.

27

CHAPTER 5

DISTILLATION

The process of distillation has many various forms, and all are based on the relative

volatility differences of the components in the mixture to be separated. For this system,

fractional, continuous distillation is the form of interest. In this form, a distillation column with

many “trays” is used to separate the lighter components (higher vapor pressure) from the

heavier ones (lower vapor pressure). For example, the suggested electrolytes, trifluoroacetic

acid and diethylamine (DEA), would be the lighter fractions to be separated from water, since

they both have lower boiling points and thus higher vapor pressures than water.

Below I introduce distillation theory and present two cases simulating the distillation of

DEA from water. These cases are representative of the heat required to separate the lighter

fractions of acid and base from water. The two cases differ markedly in results, yet they both

show that the energy required for distillation is much less than or about the same as the

electrical work done by the electrochemical system (at 4.2 M, 1 L/s is 4.2 x 100 kW = 420 kW).

The work from the electrochemical cell is represented by the ions making up the salt solution

which in turn represent the actual current flow. Ignoring the heat losses from the closed

system, entropy losses, and irreversible losses, the results show from almost no input energy

for the molar case up to over 100% input required in the product rate case. I also report on the

laboratory demonstration of distilling DEA from an acetic-acid/DEA mixture which achieved a

DEA distillate with pH 12, close to pure DEA, as measured by a pH meter.

5.1 Fractional Distillation

A fractional distillation column is a sophisticated device designed to separate lighter

28

components of a mixture from heavier ones. Figure 5.1 from Luyben16 shows a schematic

diagram of a distillation column. The mixture is fed into the column at the “Feed” location and

the heavier liquid drops to the bottom where it is labeled “Bottoms” as the lighter vapor floats

to the top and is labeled “Distillate”. At the bottom a reboiler reheats a part of the bottoms

and returns the heated mixture to the column, and the other part is extracted as the purified

heavy fraction. At the top, vapor is condensed and part of it is returned to the column (known

as the reflux), and the other part is extracted as the purified lighter fraction. Both the reboiling

and the refluxing can be controlled as degrees of freedom to meet various distillation

requirements. Another degree of freedom is the number of “trays” (NT in the figure) or

locations within the column where condensations and re-vaporizations take place with each

additional location increasing the purity of the fractions.

Figure 5.1: Diagram of a distillation column showing feed, reflux, and reboiler.

Distillation is based on the vapor-liquid equilibrium (VLE) which can be explained with

the help of the Txy diagram. Figure 5.2 from Luyben shows the VLE at 1 atm for a binary system

29

of benzene and toluene where the temperature is plotted as a function of the mole fraction of

benzene. The lower curve is the saturated benzene liquid as a mole fraction of the liquid phase

x. The upper curve is the saturated benzene vapor curve as a mole fraction of the vapor phase

y. Drawing a horizontal line at a given temperature, say for example 370°K, gives the mole

fraction of benzene in each phase—in this case 0.375 for the vapor phase and 0.586 for the

liquid phase. This shows that indeed the heavier component, benzene, is less rich in the vapor

phase.

Figure 5.2: A Txy plot of a benzene-toluene mixture.

Another useful plot is the xy diagram where the vapor phase mole fraction is plotted

against the liquid phase mole fraction as shown in Figure 5.3. In the McCabe-Thiele analysis,

operating lines are determined for the rectifying section (ROL) and the stripping section (SOL)

where the slope for the ROL = LR/VR and LR and VR are the liquid and vapor flow rates in the

rectifying section and similarly for SOL. The feed location can be determined from the

intersection of the two lines. Assuming a full reflux ratio (and then the distillate rate is zero),

30

the ROL and SOL slopes are unity and lie along the 45° line. In this case, the minimum number

of trays can be determined by stepping up between the 45° line and the VLE as show in Figure

5.4.

Figure 5.3: An xy plot for benzene in a benzene-toluene mixture.

Figure 5.4: An xy plot showing the vapor-liquid steps for a total reflux operating condition.

31

Moving vertically from point xB on the 45° line and representing the reboiler

composition to the VLE gives the vapor composition leaving the reboiler. Moving horizontally

from the point on the VLE to the 45° line gives the composition of the liquid leaving tray 1. By

repeating this stepping up all the way up, we reach the vapor composition required by the

distillation. The number of steps equals the minimum number of trays.

A complete multi-tray column distillation represents a complex process with a large

number of variables. In a two-component, binary system considering a normal situation, the

feed rate, feed pressure, feed composition, temperature and pressure are usually given along

with the compositions of the product streams. The only remaining degrees of freedom are the

number of trays, NT and the location of the feed tray, NF. Solving the problem theoretically is

difficult, but modeling systems exist that allow the user to specify a number of the operating

parameters and solve for the rest.

5.2 Simulation

I used the ChemSep17 distillation modeling package embedded in the COCO18 open

source software package and open standard modeling system to model the distillation of

diethylamine from water.

COCO (CAPE-OPEN to CAPE-OPEN) is a free-of-charge CAPE-OPEN compliant steady-state simulation environment consisting of the following components:

COFE - the CAPE-OPEN Flowsheet Environment is an intuitive graphical user interface to chemical flowsheeting. COFE has sequential solution algorithm using automatic tear streams. COFE displays properties of streams, deals with unit-conversion and provides plotting facilities.

COFE flowsheets can be used as CAPE-OPEN unit operations; so you can use COFE Flowsheets as unit operation inside COFE (flowsheets in flowsheets) or inside other simulators.18

32

Figure 5.5 shows a simple COCO flowsheet containing the feed stream, a distillation

column, and two product outflowing streams. Figure 5.6 shows the definition of Feed 1 on the

flowsheet with a molar fraction of diethylamine (DEA) of 0.1 and water 0.9 (the two must sum

to one), an incoming temperature of 95°C, pressure of 1.2 atms, and a flow rate of 1 kg/s ≅ 1

L/s. The distillation column is defined with 32 trays with the feed at tray 16.

Figure 5.5: An illustration of the COCO flowsheet for distillation simulation.

Figure 5.6:The feed specifications for the distillation simulation.

33

Discovering the heat input required to distill the DEA is the key to the conversion

efficiency of the entire system. Unfortunately, two similar but different column specifications

give two widely different results. In addition, the only energy report is difficult to understand.

For the first case, in Figure 5.7, the Molar Fraction case, I show the column

specifications defining product molar fractions of 0.995 for both the DEA top and the water

bottom products. The simulation solves easily and gives the Streams report shown in Figure

5.8. Indeed, the molar fraction of the top product flow, the DEA, is 0.995 with very little water,

while the bottom product flow, water, is 0.984. As I understand it, the reboiler is the only

external heat requirement which apparently assumes that all the outgoing heat is exchanged

into the incoming feeds. In order to match the second case, the incoming feed pressure is set

at 1.2 atm with a temperature of 95°C.

Figure 5.7: The column specifications for the molar case, case 1.The column specifications for the

molar case, case 1.

34

Figure 5.8: The Streams report for the molar case, case 1.

The Mass and Energy report shown in Figure 5.9 shows a Reboiler input of only 1.5 X 10-5 KJ/s.

The reported reflux ratio was 3.42. It appears that most of the heat comes in with the feed

stream and goes out with the water bottom product. Assuming the bottom product is put

through a heat exchanger with the incoming feed stream, there should be little external heat

required except to maintain the temperature of the incoming feed stream.

Figure 5.9: The Mass and Energy Balance report for the molar case.

35

I communicated with the authors of ChemSep by e-mail and inquired about the low

energy requirement. Their response was that the column specification was incorrect and

suggested I use a Product Rate specification instead of Molar Fraction. They were unable to

explain the Mass and Energy Balance report accounting. Figure 5.10 shows the column

specification with a Product Rate set for the bottom product that matches the rate computed in

the first case. I had difficulty getting this case to solve successfully. For both cases, I tried many

solutions “manually” trying to optimize the energy demand. For this case, the energy seems

sensitive to the reflux ratio, but I could not lower it beyond the 6 shown in Figure 5.10. and still

get a solution. The flow profile for this case shows much more liquid and vapor flowing both up

and down the column while the first case has almost no vapor flowing down.

Figure 5.10: Column specification for product rate case, case 2.

The Streams output is shown in Figure 5.11. The Mass and Energy Balance is quite

different too, see Figure 5.12. The external reboiler input is now 504 kJ/s compared to almost

none for the first case. For both cases, the vapor molar flow rate corresponds to 0.00425

36

kmol/s X 100,000 C/mol = 425,000 W or 425,000 J/s which is much more than the energy input

in the first case and slightly less than that of the second case. Also note that the molar fraction

of 0.1 for diethylamine equates to about a 4.5 molar concentration for the input feed (there are

about 55 moles of water in a liter, and a dissolved salt adds almost no volume). This

concentration is too high for the resultant salt in the neutral chamber of the electrochemical

cell since the electrochemical potential relies on the concentration gradient for its voltage.

However, again I was unable to lower the molar fraction in this simulator and still get solutions

consistently. Lower concentrations will probably increase the required heat input, but there is

a third system feature discussed below about how to increase the concentration using a

molecular sieve. I do not know why these cases are so different. A commerical, professional

software package like Aspen19 might have better documentation, reporting and optimizing

options.

Figure 5.11: Stream report for product rate case, case 2.

37

Figure 5.12: Mass and Energy Balance report for case 2.

This simulation distills only diethylamine where as the proposed system requires both a

base and acid to be distilled. Adding another component like trifluoroacetic acid with a boiling

point below water will probably not require additional heat since the mixture boiling point will

be lower with a lower water vapor pressure. However, a fractioning distillation column will be

required to separate the diethylamine base from the trifluoroacetic acid.

5.3 Laboratory Demonstration

Distilling a weak base component like diethylamine is not dissimilar from distilling a pH-

neutral substance since most of the base is not disassociated. Below I report on a laboratory

experiment demonstrating this result. However, distilling a salt formed from a strong acid like

trifluoroacetic acid and a strong base like guanadine may be more difficult and needs further

investigation into the chemical thermodynamic ramifications of this kind of mixture.

38

Finally, I did demonstrate the distillation DEA from an acetic acid-diethylamine salt

solution in the laboratory with a distillation column and condenser. The column was packed

with glass beads serving as trays. The condenser was cooled with tap water pumped from and

to a bucket. I prepared a 440 ml soution of 1 M acetic acid and 1 M DEA in water and

measured a pH of 6.04 with a pH meter. I placed the solution in an Erlehmmeyer flask and set it

heating in the mantle (see Figure 5.13) and plugged it in. The solution began boiling after 12

minutes.

Figure 5.13: The laboratory setup for distilling DEA from an acetic-acid-DEA mixture

The top column thermometer measured 90-92° C at its peak. The first drops condensed after

22 minutes. After turning off the heat, I measured the boiling temperature in the flask at 105°

C (acetic acid has a 118° C boiling point). I recovered 47 ml of DEA (and water) in 30 minutes

and measured the pH with the pH meter of 12.05 which is fairly close to pure DEA.

5.4 Optional Concentration by Filtration

I found by simulation that the distillation energy required to recharge the

39

electrochemical electrolytes was either much less or about the same as the power provided by

discharge of those electrolytes, at least in an ideal and theoretical sense. However, that

simulation could not be done with a solution less than 0.1 molar fraction equal to about a 4.5

molar solution of electrolyte salt. This concentration coming out of the neutral third cell

compartment is much too high for adequate voltage and power generation from the cell. One

possible addition to the system under study is the use of ultra- or nanofiltration or reverse

osmosis to concentrate a much more dilute, outflowing discharged electrolyte salt before

feeding it into the distillation.

There is an energy cost associated with filtration or reverse osmosis, however it is much

less than the required distillation energy. For mechanical filtration, the solution has to be

pressurized from 2 to 7 bar or about 200-700 kPa to force it through the filter. Reverse osmosis

can filter the solution to almost purity but requires up to 27 bar or 2700 kPa of pressure. As

mentioned above, a 100 kW system requires a flow of about 1 L/s so the ideal, reversible

energy required for filtration at 200 kPa would be

500 kPa X 1000 Pa/kPa X 1 (J/m3)/Pa X 0.001 kJ/J X (0.001 m3/L)/s = 0.5 (kJ/L)/s = 0.5 kW/L.

There is also associated maintenance of the filters to contend with and the added capital cost

of the filtration unit.

The tradeoff between distillation energy costs and mechanical filtration costs depends

on the optimized distillation parameters and the maximum allowable concentration of the

discharged, outflowing electrolytes. Ideally, the energy costs for distillation for the optimal

allowable concentration would be less than or about the same as the electrochemical energy

discharged by the electrolytes thus avoiding the need for filtration.

40

CHAPTER 6

COST OF ENERGY

For new technology to be viable, it must be affordable. In this section, I estimate the

costs of building and running the system under study. Cost estimates at this stage are

uncertain and can only be approximated within ranges. I use a technoeconomic study of

vanadium redox flow batteries (VRFB) as a guide.

In Minke and Turek [2018]20, cost studies of VRFB over two decades were reviewed, and

estimates for the past 10 years were normalized into a range of cost estimates. The included

studies had different bases, objectives, and technology models in addition to being spread out

over many years with subsequent cost fluctuations. As a result, a wide range of costs is

reported.

Costs were broken down into component costs including manufacturing and generalized

into system costs on a kW and kWh basis.

• electrolyte: 45-334 €/kWh

• membranes: 16-451 €/m2, estimated average 300 €/ m2

• bi-polar plates (BPP): 37-418 €/ m2, estimated average 100 €/ m2

• carbon felt: 14-63 €/ m2, estimated average 53 €/ m2

Cost models were proposed in the reviewed literature and normalized in the review, and these

give rise to estimated system costs as a function of power $/kW or energy $/kWh. The cost

models are valid for systems in the range of 250 kW to 1 MW and an energy/power ration of 4-

8 h. Minke gives a range of 884-12931 €/kW for present day system costs, and 564-2355 €/kW

41

for optimistic and future costs. As noted by Minke, “These wide ranges of data cannot be

discussed without reference to the technical configuration of systems”.

In an earlier paper21, Minke et al. [2017] provides a more detailed techno-economic

assessment of 4-8 MWh VRFBs. That reference describes the costs based on 2.7 m2

electrochemical cells assembled into 250 kW modular stacks. The costs are broken down first

for the power system and the energy system.

Figure 6.1 shows the cost structure of the 250 kW VFRB stack assembly. The Nafion

membrane dominates the cost at 37%. The total stack cost is €218,800 and comprise 80% of

the power system cost with the rest being related to electronics and the control system. The

total specific cost of the power system is €1125/kW for systems less than 4 MW.

Figure 6.1: Cost structure of 250kW VFRB stack with Nafion (after Minke[2017], Fig. 5).

Figure 6.2 shows the cost structure for a complete VRFB with an energy-to-power ratio

of E/P = 4. The cost is heavily dominated by the vanadium electrolyte, vanadium being an

expensive material. The specific total system cost is €655/kWh. The system proposed in this

37%

11%19%

21%

12% Nafion

Electrodes

Bipolar plates

Current collector, gasket,frames

Assembly

42

document is not intended for energy storage although electrolyte reserves could be

regenerated and used as standby power.

Figure 6.2: Model system and cost structure of system with E/P = 4 h (after Minke[2017], Fig. 6).

The the cost of energy estimate for the proposed system is based on the

technoeconomic assessment done by Minke [2017]21. Figure A.1 in the appendix shows the

spreadsheet for the system cost breakdown. The first line “Case” identifies the case being

estimated. The case “VRFB Minke (2017)” is an attempt to reproduce the detailed costs

reported in that reference. The other three cases are for the system-under-study: the current

estimate, an optimistic estimate (following Minke [2017]), and a futuristic estimate. The VRFB

Minke (2017) case is worked up for a 250 kW system while for my TRES system, I use a 100 kW

output.

The first section under Components is an estimate of the stack costs which make up the

power system costs. For all four systems, the costs are dominated by the membrane or

12% 4%

6%

7%

8%

43%

4%

16%

Membranes ElectrodesBipolar plates Stack misc.Power electronics ElectrolyteTanks, pumps, piping, heat exchangers Assembly

43

membranes—31% for the VRFB and 48% for the TRES. There are two membranes in the

proposed system—I used the same cost of the Nafion membrane for the anion membrane.

That next highest cost are the bipolar plates (BPP). For this TRES, there are two stack frames

per cell. I also added the cost of the platinum catalyst to the TRES estimates but no cost for a

nickel catalyst since it is relatively inexpensive. The “per unit” component costs were scaled by

the fraction of power, 100/250. The stack cost for VRFB Minke(2017) here worked out to

€788/kW and for the three TRES’s respectively, €800/kW, €560/kW, and €507/kW.

Additional system costs related to the stack are the converter, cabling, and control

system (PCS). I omitted the converter costs from the TRES because the application of the TRES

is project dependent and difficult to estimate. I also omitted the costs of microprocessors on

each cell because the TRES only needs sensors instead on each cell. The total specific stack

costs are then €1192/kW (VRFB), €1304/kW, €814/kW, and €611/kW. The roughly equal

specific costs come from same “per system” costs of a 250 kW system and a 100 kW system.

The VRFB requires storage of its electrolytes sinces it is flow battery, and that feature

constitutes the energy system. The TRES is not configured for storage although it could be.

Hence no estimates for the VRFB energy costs are shown, but the component costs are used to

complete the system costs for the TRES. The largest cost of non-stack components of the TRES

is the distillation tower, estimated at €27,273. The remaining costs include the 2 electrolytes,

pumps, heat exchangers, pipes and fitting, and assembly coming to €15,758. I used four times

the cost of acetic acid as an estimate for the trifluoroacetic acid (when manufactured in bulk),

and the cost of DEA for the base chemical. The total specific costs of the TRES are €173/kW,

€124/kW, and €95/kW for the current, optimistic, and futuristic cases.

44

Based on the costs for a VFRB, the estimated the costs for a 100 kW system as proposed

here have been calculated, as well as an optimistic estimate following that of Minke[2017]. The

total system costs are €156,000 with specific costs of €1.56/W. For the optimistic case and a

futuristic case, the costs are €119,000 and €90,000 respectively, with specific costs of €1.19/W

and €0.90/W. The cost for the primary heat source and heat exchanger, the inverter and

connection to the grid, and the cost for transportation and installation are not included since

this system would typically be included as part of a larger scale project, and each project would

have unique and different requirements.

Figure A.2 in the appendix shows the calculation for the Levelized Cost of Energy (LCOE).

This spreadsheet is taken from the NREL web site. The system cost figures given above are

discounted into dollars based on a generic conversion factor of 1.1 dollar per euro. The inputs

for this calculation include the Net Capacity Factor (95%), Annual Energy Production (8,322

kWh/kW), Capital Expenditure ($190/kW for the Current case, $136 for Optimistic, and $104 for

Futuristic), Fixed Operating and Maintenance Expenses ($15/kW same as the NREL example),

and Weighted Average Cost of Capital (7.9% same as NREL example). The LCOE is then calcuted

at $5.5/MWh ($0.006/kWh), $3.9/MWh, and $3.0/MWh for the Current, Optimistic, and

Futuristic cases.

45

CHAPTER 7

CONCLUSION

In this thesis, I present the framework for a cost-effective clean energy system utilizing

waste heat (or other heat sources) that is converted into power by a TRES. I found that the

power provided the discharge of the electrochemical system was slightly less to much less than

energy required to recharge the electrochemical electrolytes by distillation. I also found that

the cost of the energy provided by the system was very small.

In Chapter 2, I give some background on the TRES and list the improvements made with

the current system. In Chapter 3, I introduce the current TRES as a type of flow battery that

only discharges, while the discharged electrolytes are regenerated by a chemical distillation and

then flow back into the battery cells. The electrochemical reaction is a neutralization reaction

wherein an acid and base react to form a salt and water. The neutralized salt is then pumped

to a distillation stripper where a fractional and continuous distillation separate the acid, base,

and water into three fractions, and each component is returned to its respective battery cell

compartment.

In Chapter 4 and Chapter 5, we look closely at the battery and the distillation process. I

show that the electrochemical cell is estimated to generate about 0.2 W/cm2. For the

distillation process, I use a simulation with mixed results and limited parameters that indicate

the heat energy per second required to distill the neutralized electrolytes was about the same

or much less than the power generated by those discharged electrolytes.

The OCV is partially dependent on the concentration difference between the neutral

water in the middle compartment and the acid and base solutions in the other two

46

compartments. The greater the difference and the lower the concentration in the water, the

higher the OCV is. However there is a tradeoff between the lower salt solution concentration

and greater energy required for distillation. Therefore I introduce the option of filtration to

increase the salt concentration before distillation at the cost of a small amount of pumping

energy and increased capital costs.

In Chapter 6, I analyze the cost of energy of my TRES with the results provided by a

technoeconomic assessment of a VRFB. I provide estimates for three cases—current,

optimistic, and futuristic—following the suggestions made in the VRFB study. The specific costs

for the three cases are €1.73/W, €1.24/W and €0.95/W, respectively. Using a spreadsheet

found at NREL, I then calculate the LCOE. The LCOE for the three cases are 0.6¢/kWh,

0.4¢/kWh, and 0.3¢/kWh, respectively which is quite inexpensive compared to conventional

and renewable energy sources.

7.1 Efficiency

The mass flow for a 100 kW system with an OCV of 1.0 and 1 M neutralized salt

concentration was calculated at approximately 1 L/s. We see that a Carnot efficiency for T1 and

T2 equal to 100°C and 200°C is 21%. However I am interested in the conversion efficiency. The

Product Case distillation simulation calculated an input heat requirement of 504 kJ/s for a 4.2 M

salt solution. Since a 1 M solution provides 100 kW, a 4.2 M solution would provide 420 kW

because the ionic content of the salt is from neutralized and discharged ions of the

electrochemical reactions. Thus the conversion efficiency is 420 kW/504 kJ/s X 100% = 84%.

The conversion efficiency for the Molar Case appears to be even higher but it is unclear how

much it really is.

47

If we assume conservatively after deducting heat losses, entropy, pumping costs, and

other energy costs that the conversion efficiency is 50%, than we can calculate the Carnot

efficiency. Where Wa is the actual work done, we have

𝜁𝜁 = 𝑊𝑐𝑐/(𝑄2−𝑄1) = 1/2

and

2𝑊𝑐𝑐 = (𝑄2−𝑄1)

So if ηc is the ideal Carnot efficiency and ηa the actual Carnot efficiency,

2𝑊𝑊𝑐𝑐/ 𝑄2 = 2(𝑄2−𝑄1)/𝑄2 = 2𝜂𝜂𝑐𝑐 = 𝜂𝜂𝑐𝑐

then the actual efficiency is half the ideal efficiency.

If we cascade a second system after the first, the second efficiency would be half of the

first half, so the overall Carnot efficiency would be ¾ of the ideal.

Figure 7.1: Comparison of Carnot TRES and ORC efficiencies to the ideal.

Figure 7.1 graphs the Carnot efficiency of the TRES with a 50% conversion efficiency and

T1 = 95°C for a single stage and for a cascaded stage, both in comparison with the ideal Carnot

efficiency. A comparison is also made for the Organic Rankine Cycle (ORC) turbine. The

0.0

10.0

20.0

30.0

40.0

50.0

60.0

Carn

ot E

ffici

ency

%

Ideal Actual Cascaded ORC

48

performance and operating range of an ORC depends on many variables and especially the

working fluid.

Typically an ORC has an optimal operating state. I have seen various estimates of ORC

thermal efficiency ranging from 7% to 16%, and efficiency estimates have varying definitions.

The 12% figure in Figure 7.1 comes a parametric simulation and optimization study22 that

calculated the efficiency for 10 different fluids at optimal operating parameters for a waste

heat source at 145°C and a condensing temperature of 25°C. The operating range is shown

only up to 220°C because it is limited by the boiling point of many of the working fluids and

performance drops significantly after that. A suggested LCOE for ORC power is 6¢/kWh.23

7.2 Future Research

As the reader has probably noticed, there are still many unanswered questions about

the technology reported here. There are at least three important areas of research to be

investigated. In particular, the behavior and capability of the newly introduced acid and base

electrolytes is unknown. In addition, overcoming difficulties with the three-cell compartment

design needs to be understood. Finally, the design of a bipolar plate or separator that allows

generated oxygen to diffuse to the oxygen reduction reaction while also providing sufficient air

needs to be considered.

A high voltage electrochemical cell powered by acid-base neutralization with sizable

power is possible with organic, high-strength (low pKa and pKb) electrolytes which have boiling

temperatures lower than water. The candidate electrolytes that can be distilled without

decomposing or degrading and with a minimum of heat needs to be determined, and this type

of distillation is not well known. For successful candidates, long term stability is needed.

49

This project uses a three-compartment electrochemical cell with a cation ion-selective

membrane as well as an anion membrane. This has several advantages over a conventional cell

when applied here: 1) the ionic crossover is minimized since each membrane prevents the

diffusion of counter ions into the active cell compartments, disallowing any unwanted

neutralization, 2) the two concentration gradients between the active compartments and the

third neutral compartment help maintain a high OCV, 3) while a third compartment is a

necessary complication, it does allow convection in the neutral compartment to maintain the

high concentration gradients. How narrow the third compartment needs to be, how much

convection is necessary, and what concentration of supporting electrolyte is optimal—all need

to be determined to overcome the polarization of the membranes by the membrane potential.

The distillation simulation must be improved and optimized to get a true understanding

of the conversion efficiency.

In contrast to previous work, this proposed TRES uses oxygen as the “working” gas

instead of hydrogen. This makes the system safer and easier to manage. “Working” gas refers

to the combination of oxygen reduction at the cathode and oxygen generation at the anode.

Ideally, the bi-polar plate in a conventional flow battery would be replaced with a porous plate

or separator that allows only the generated oxygen gas to diffuse from the anodic

compartment into the adjoining cathodic compartment while restricting any flow of electrolyte.

But the plate or separator should also allow additional oxygen or air to reach the cathode in

order to be sure the cathodic reaction is not starved. Such a design needs to be investigated.

Successful research in these areas (and others) will ensure the proposed TRES can

provide inexpensive power from waste heat and other thermal sources.

50

APPENDIX

COST OF ENERGY CALCULATIONS

51

Figure A.1: Cost breakdown for the Minke(2017) VRFB and the TRES with 3 cases.

52

Figure A.2: LCOE of the TRES system.

53

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