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hydrochloric acid reaction for thermochemical hydrogen production
international journal of hydrogen energy 35 (2010) 4853–4860
Available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/he
Kinetics study of the copper/hydrochloric acid reaction for thermochemical hydrogen production C. Zamfirescu*, G.F. Naterer, I. Dincer Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, 2000 Simcoe Street North, Oshawa, ON, Canada L1H 74K
article info
abstract
Article history:
The exothermic reaction of hydrochloric acid with particulate copper occurs during the
Received 23 June 2009
hydrogen production step in the thermochemical copper–chlorine water splitting cycle. In
Received in revised form
this paper, this chemical reaction is modeled kinetically, and a parametric study is per-
29 August 2009
formed to determine the influences of particle size, temperature and molar ratios on the
Accepted 30 August 2009
hydrogen conversion aspects. It is obtained that the residence time of copper particles
Available online 30 March 2010
varies between 10 and 100 s, depending on the operating conditions. The hydrogen conversion at equilibrium varies between 55% and 85%, depending on the reaction
Keywords:
temperature. The heat flux at the particle surface, caused by the exothermic enthalpy of
Cu–Cl thermochemical cycle
reaction, reaches over 3000 W/m2 when the particle shrinks to 0.1% from its initial size. The
Cu–HCl reaction
estimated Biot number varies from 0.001 to 0.1, depending on the operating conditions and
Transport phenomena
the accuracy of thermophysical data of the substances. A numerical algorithm is developed
Fluidized bed reactors
to solve the moving boundary Stefan problem with a chemical reaction that models the
Hydrogen
shrinking of copper particles in the hypothesis that the chemical reaction and heat transfer are decoupled. The model allows for the estimation of the temperature of a copper particle, assumed spherical, in the radial direction on the hypothesis of large Biot numbers. For small Biot numbers, the transient heat transfer equation results in a lumped capacitance model. In all cases, the particle decomposes in about 10–20s. ª 2009 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Converting thermal energy from sustainable sources (e.g., nuclear, solar, biomass) to hydrogen fuel and oxygen by thermochemical water splitting is examined in this paper. Thermochemical cycles use a series of chemical reactions and intermediate chemical compounds to decompose the water molecule, as highlighted in recent studies [2,10]. The Sandia National Laboratory and Japan Atomic Energy Agency have focused on the development of the sulfur-iodine water splitting cycle [15], which requires about 900 C temperature heat input. Such a high temperature provokes some concerns
about the safety of nuclear reactors. Some novel inorganic separation membranes can be used to lower it to 700 C and make the cycle more adaptable to various types of nuclear reactors. This includes conventional light water reactors, high temperature gas cooled reactors, liquid metal-cooled fast reactors, the Very High Temperature Reactor (VHTR), and the Generation IV reactor design of Atomic Energy of Canada Limited [14], as well as the Advanced High Temperature Reactor (AHTR). There are various types of thermochemical water splitting cycles, with most of them requiring high temperature heat for driving chemical reactions and recycling the intermediate
* Corresponding author. E-mail addresses: [email protected] (C. Zamfirescu), [email protected] (G.F. Naterer), [email protected] (I. Dincer). 0360-3199/$ – see front matter ª 2009 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2009.08.077
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international journal of hydrogen energy 35 (2010) 4853–4860
Nomenclature a Bi C Fo h k K n p q" r R R t T X Y
2 1
thermal diffusivity, m s Biot number chemical conversion Fourier number heat transfer coefficient, Wm2K1 -1 (forward), reaction constant, mmol1 atm0:5 h1 gCu 1 1 -1 mmol atm,h gCu (backward) equilibrium constant, atm0.5 molar ratio pressure, bars heat flux, Wm2 rate (of consumption, of production, of reaction) radius, m radius, as integration variable, m time, s temperature, oC fractional HCl conversion fractional H2 production
compounds. About 290 of those cycles were screened by Ref. [1]. Some of these cycles operate at very high temperatures, i.e., from point focus solar concentrators (Zn–ZnO cycle requires 2600 C as indicated by Ref. [13]). Three of the referenced cycles operate at low temperatures, namely the Cu–Cl (<550 C), Li–N–I (<475 C) and Fe–S–I cycle (<450 C). It is advantageous if the required peak temperature is lower because a greater range of thermal sources can be utilized. Among the low temperature water splitting cycles, the copper–chlorine (Cu–Cl) cycle has been developed extensively by Atomic Energy of Canada Limited (AECL), because it links well with Canada’s Generation IV nuclear reactor. Significant progress has been recently reported by a consortium of North American institutions [8,18,24–28]. The predicted efficiency of the Cu–Cl process is about 50% with respect to the higher heating value of hydrogen, which compares favorably to the overall efficiency of electrolysis, which is typically 24% [10]. This important gain in efficiency occurs because electrical generation and its associated losses are partially avoided since the process requires mainly heat as input. Moreover, a series of past studies demonstrated that it is possible to link this cycle with heat sources at lower temperatures than 550 C. This can be accomplished by using heat pumps, and one of the possibilities is using heat rejected by the moderator of CANDU nuclear power plants at 80 C [19,20]. A more general model by Ref. [21] proposed and analyzed an integrated system including the Cu–Cl water splitting cycle, a heat pump and heat engines for generating hydrogen and oxygen from sustainable thermal energy sources available at temperatures in the range of 40–350 C. The model showed that the thermodynamic upper limits of the hydrogen production efficiency is about twice the typical efficiency of water electrolysis. But several challenges arise with the development of the copper–chlorine cycle. Firstly, thermodynamic properties of intermediate compounds are not accurately known [22]. Other challenges include material resistance to corrosion of chemicals, and unknowns regarding chemical kinetics and heat and
Greek letters enthalpy of reaction, kJ/mol DrH q dimensionless temperature k thermal conductivity, Wm1K1 m molecular mass, kg.kmol1 n number of mols, mol x dimensionless radial coordinate r density, kg.m3 Subscripts N surroundings 0 initial b backward Cu copper CuCl cuprous chloride e exterior (outer) eq equilibrium f forward H2 hydrogen HCl hydrochloric acid
mass transfer associated with certain reaction steps. These make the hydrogen production reaction very complex. One of the key challenges is that three phases are present in the chemical reactor – molten (liquid) CuCl, gaseous HCl and H2, and solid copper. This paper examines the kinetics of the hydrogen production reaction in which hydrochloric gas is reacted with particulate copper to form gaseous hydrogen and cuprous chloride (CuCl). A study of this reaction that calculates the exergetic efficiency has been conducted by Ref. [9]. This reaction is exothermic and generates 46.8 kJ/molH2 at 450 C according to Cu(s)þHCl(g)/CuCl(molten)þ1/2H2(g). More heat can be recovered from this reaction by quenching and cooling the molten cuprous chloride, and this heat can be used internally within the cycle [16,17]. The kinetics of this reaction has been studied by Ref. [11], which determined the reaction rate in a fixed bed reactor. It was shown that the gas solid mass transfer is controlled by chemical reactions at the interface. The forward reaction is of order 0.5 and the backward reaction is of order one. The reaction is reversible and the reaction constant varies in the range 0.85 to 2.5 atm when the temperature falls from 475 C to 400 C. Ref. [11] fit the experimental results on a ‘‘lnK vs 1/T ‘‘ curve and determined the Arrhenius equation for the reaction rate constant. The results by Ref. [11] are used by Ref. [23] to perform a parametric study that is extended in this present paper. A possible implementation of the hydrogen production reactor is described by Ref. [16]. It consists of a moving particle exchange bed where hydrochloric gas is circulated in excess to react with copper particles. The particles are moved by a screw mechanism and the reaction heat is absorbed by cooling water that embeds the reactor at the outer shell. The products are molten cuprous chloride (CuCl) and gaseous H2 and HCl. It is suggested that HCl is absorbed in an alkaline solution that is discharged out of the cycle and not recycled. Cuprous chloride is quenched in water in a separate reactor. In brief, in this reactor enters particulate copper and
international journal of hydrogen energy 35 (2010) 4853–4860
hydrochloric acid and exits particulate CuCl and a mixture of HCl and hydrogen (some hydrochloric acid is unused). Note however that it would be desirable to recycle all HCl, because the intention of any thermochemical water splitting cycle is to recycle all chemicals except water, hydrogen and oxygen. The objective of this study is to provide some new information and model regarding the chemical kinetics, to allow for a conceptual design of the reactor with the best possible HCl recycling. More specifically, the paper examines the influence of reaction temperature, particle size, residence time, and heat flux at the particle surface. The results are expected to be valuable for purposes of equipment design and scale-up in the Cu–Cl water splitting plant.
2.
Analysis of reaction kinetics
This section analyzes the relevant transport phenomena at the gas/solid interface, namely heat and mass transfer and the chemical reaction. Fig. 1 shows a conceptual model of the reactor. The reactor is of constant-pressure, isothermal batch type and it can be viewed as a thermodynamic system of variable volume V(t), where t 0 is time. At the initial moment, t ¼ 0, in the reactor one finds only nCu mols of copper and nHCl ¼ n0 mols of gaseous hydrochloric gas. At any later moment, in addition to the two reactants in the reactor, there are nH2 moles of hydrogen and nCuCl moles of cupric chloride (assumed here in the solid state). The figure suggests that the reactor volume shrinks, because 1 mol of hydrochloric gas converts to a half mol of hydrogen. We introduce the fractional conversion X of hydrochloric gas which is the ratio of converted reactant to the initial molar content, n0. Since the converted HCl at the current time t is n0 – nHCl, (1)
X ¼ 1 nHCl =n0
Using the fractional conversion of HCl, one expresses for any t, 9 nHCl ¼ n0 ð1 XÞ > > = nH2 ¼ n0 Y Y ¼ 0:5X > > ; n ¼ nHCl þ nH2 ¼ n0 ð1 0:5XÞ
(2)
where Y is the fractional hydrogen production and n is the total number of mols in the gas phase. Fig. 1 also shows the evolution of copper particles while reacting with hydrochloric gas. Initially, copper presents a bare surface exposed to HCl reactant. We represent the particle with a sphere, of 3–100 mm diameter. Dendritic Cu particles of 3mm diameter can be obtained commercially. Past kinetics experiments by Ref. [11] were performed with this size of Cu particles. Through electrochemical procedures, copper particles can be obtained in sizes smaller than 100mm diameter. During the reaction, at the surface of the particle, the CuCl product is formed (see Fig. 1). The reaction heat will increase the particle temperature up to the melting point of CuCl, which is 709 K [4]. As saturated liquid, cuprous chloride partially evaporates, while its vapor pressure is about 10 Pa close to the melting point [7]. Through the two-phase CuCl shell, gaseous HCl diffuses toward the copper surface and generated gaseous hydrogen diffuses toward the exterior. This depicted situation suggests that the outer shell that embeds the copper core is unstable and thus facilitates good mass transfer. The results by Ref. [11] confirm this assumption because they showed that the mass transport at the particle is controlled by the reaction. For gas-solid non-catalytic reactions that evolve according to a shrinking core model, the mass transfer mechanism may be controlled [5,6] by: diffusion through the gas film, diffusion through the outer layer, or the chemical reaction. In the last case, which is assumed to represent the present situation, the mass transfer depends on the concentrations in the bulk flow (HCl) and at the copper surface (H2). At the same time, the molar consumption rate of copper is the same as that of hydrochloric gas. Thus, dnCu dnHCl ¼ ¼ rHCl pHCl ; pH2 dt dt
(3)
where rHCl is the rate of HCl consumption due to the reaction and pHCl and pH2 are the partial pressures of participating gases, as a measure of the molar concentration. The rate of HCl consumption is opposite (negative) to the reaction rate. It has been found by Ref. [11] as being of order 0.5 for the forward reaction (H2 production) and first order for the backward reaction (HCl production). Therefore, the total reaction rate is
P,T,V0
HCl(g)
ν0
Cu(s) 3-100μm
Cu(s)
P,T,V(t) HCl(g)
Q
νHCl
H 2(g) νH2 νH2+ νHCl=ν
t=0
νCu,0
4855
Cu(s) CuCl(s)
ν Cu νCuCl
t>0
HCl(g)
H 2(g) CuCl(l,v)
Fig. 1 – Conceptual model of constant pressure batch reactor for hydrogen production.
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international journal of hydrogen energy 35 (2010) 4853–4860
Fig. 2 – Fractional production of hydrogen (a) and the time to reach chemical equilibrium (b).
r ¼ kf p0:5 HCl kb pH2
(4)
where k is the reaction constant and the index ‘‘f’’ stands for forward and the index ‘‘b’’ refers to backward reactions, respectively. As the equilibrium constant is defined by Keq ¼ kf/kb (see e.g., [12]) and r¼– rHCL, one can write
R3 R30 ¼
3mCu 4prCu
Z t dnHCl dt: dt 0
(6)
Eq. (5) can be solved to determine both the HCl consumption and the shrinkage of the copper particle. For example, if one denotes R0 as the initial radius and R as the current radius of the copper particle, assumed spherical for simplicity, then one can show that
For our situation, the RHS of Eq. (6) is always negative (HCl is consumed) and the radius of the copper particle diminishes until it vanishes. If the RHS could be calculated, by setting R ¼ 0 one may determine the time to complete the reaction, sc. Calculation of the RHS implies integration of Eq. (5) for HCl. This can be accomplished as follows below. One expresses the partial pressure based on the fractional HCl consumption defined by Eq. (2) and the total pressure P as follows: 9 nHCl 1X > = P¼ P> pHCl ¼ n 1 0:5X (7) nH2 0:5X > P¼ P > pH2 ¼ ; n 1 0:5X
Fig. 3 – Conversion at equilibrium for various operating conditions.
Fig. 4 – Shrinking of copper particle for three molar ratios n at a 700 K reaction temperature.
dnCu dnHCl ¼ ¼ kf p0:5 HCl pH2 =Keq dt dt
(5)
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The solution X(t) of Eq.(8) is essential in the reactor design because it allows for calculation of other quantities, e.g., dnHCL/dt as a function of time. This leads to obtaining a particle radius variation R(t), but also allows for the calculation of heat generation at the particle surface: q}ðtÞ ¼
Dr HðTÞ dnHCl 4pRðtÞ2 dt
(9)
where DrH(T ) is the enthalpy of reaction at a temperature T. The heat conduction equation through the copper spherical particle is 1 v vT 1 vT R2 ¼ ;R ¼ 0 R 2 vR aCu vt R vR
(10)
where aCu is the thermal diffusivity of Cu, assumed constant at an average value for the range of temperatures of interest. The boundary condition written at the sphere surface is kCu Fig. 5 – Residence time of Cu particles for a range of n and three temperatures.
Using Eq. (2) to express nHCl and replacing Eq. (7) in Eq. (5) leads to dX ¼ kf dt
1X 1 0:5X
0:5
1 0:5X Keq 1 0:5X
(8)
Assume that the reaction constant and equilibrium constant are determined as by Ref. [11] for 1 g of Cu, 1 mmol of HCl and 1 atm total pressure. Eq. (8) can be integrated numerically for a given operating temperature at which the constants are known. The fractional HCl conversion at equilibrium can also be computed by setting dX/dt ¼ 0 and solving for X. It results in the time to reach chemical equilibrium in the batch reactor.
vT þ q}ðtÞ ¼ hðT TN Þ vR
(11)
where kCu is the thermal conductivity of copper, h is the heat transfer between the sphere and the multiphase shell (including molten CuCl and gases) and TN is the temperature at the outer side shell. As detailed later, assumptions will be needed to derive values for h and TN and integrate Eqs. (9–11) which form a special kind of Stefan problem (see e.g., [3]).
3.
Results and discussion
In the previous section, the analysis led to the development of a mathematical model that describes heat and mass transport with a chemical reaction, which occurs during the hydrogen production reaction. In this section, this model will be applied to conduct a parametric study of the reaction and determine the influence of various operating conditions relevant to the conceptual design of the reactor. Consider deriving an expression for the equilibrium constant of the forward reaction kf, needed for integration of Eq. (8). In this respect, we regressed the data published by Ref. [11] and obtained the following expression for the equilibrium constant: Keq ¼ 2:26 þ ðT 673:15Þ=ð351:59 0:54TÞ
(12)
which is valid for T ¼ 650–800 K. We also used the following Arrhenius equation for the reaction rate constant, based on [11], kf ¼ 1737573:23expð7515:5=TÞ
Fig. 6 – Heat flux caused by the reaction.
(13)
where kf is given for 1 atm, 1 g of copper and 1 mmol of HCl and it has units of h1. In Fig. 2a, it is presented in terms of the fractional hydrogen production Y, resulting from integration of Eq. (8) for three reaction temperatures. It is observed that the magnitude of the time to equilibrium teq varies from 0.06 to 0.14 h. Fig. 2b shows also the variation of time to reach equilibrium. Note also that the results from Fig. 2 are applicable to particle sizes of 3–100 mm, which lies in the range of the experimental determinations by Ref. [11], where the rate of reaction and equilibrium constant have been derived.
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international journal of hydrogen energy 35 (2010) 4853–4860
The hydrogen conversion at equilibrium is defined by Ceq ¼ nH2eq/(nH2eq þ nHCleq). Using the definition for the fractional conversion of HCl and fractional production of hydrogen, as introduced in Eq. (2), one has Ceq ¼ 0:5Xeq = 1 0:5Xeq
(14)
Fig. 3 presents the hydrogen conversion at equilibrium and fractional conversions for a range of temperatures. Obtaining good conversions (over 80%) are possible at the lowest temperatures, but this leads to larger equilibrium times, or in other words larger residence times of particles in the reactor. The influence of particle size can be studied by integrating Eq. (6). Consider the ratio of initial mols of HCl and Cu, n¼n0/ nCu,o. Based on Eqs. (2) and (6), it can be shown that Z t 1=3 dX R=R0 ¼ 1 n : dt dt 0
(15)
Fig. 4 presents the results regarding the particle radius variation with time for a fixed reaction temperature of 700 K and three values of n. The particle radius is given with reference to the initial radius R0. From this plot, one can also observe the particle residence time in the reactor, which is 20.5 s for n ¼ 5, 9.9 s for n ¼ 10 and 6.5 s for n ¼ 15. The residence time for a range of n and three reaction temperatures, namely 650, 700 and 750 K, can be observed in Fig. 5. Regarding the heat transfer during the reaction, in order to integrate Eqs. (9) and (11) one needs to estimate first a realistic range of heat transfer coefficient at the outer side of the copper particle. In this respect, one can assume that a copper particle is surrounded by a layer of molten CuCl, which, in general, embeds migrating vapor/gas molecules or even bubbles of various species. Based on a material balance at the particle level, it can be shown that the outer radius Re of the particle, formed from the copper core and the shell containing mainly molten CuCl, is 3 3 3 Re r m R R þ ¼ Cu CuCl 1 R0 rCuCl mCu R0 R0
(16)
When the particle is consumed, by setting R ¼ 0 in the above equation, one obtains Re/R0 ¼ 1.5. If one assumes that the
molten layer is viscous enough so that heat transfer occurs mainly by conduction, then h in Eq. (11) is approximated with kCuCl/(Re-R). Note that this approximates the lowest value of h which yields on the order of 1000 W/m2K. In a real situation the heat transfer coefficient can be higher because the outer layer may detach since it is in a molten state. Because the CuCl shell melts in the process, one may assume that at the outer radius, the temperature is about the same as the melting point temperature, TN ¼ 709 K. The superficial heat flux caused by the reaction heat has been calculated with Eq. (9) for an assumed temperature at the surface of 700 K and three molar ratios, n ¼ 5, 10 and 15. The results are shown in Fig. 6 and reveal that heating is very intense by the end of the reaction, i.e., when the copper particle becomes small. This occurs due to the reduction of the particle surface area. The plot presents the heat flux up to 99.9% from the particle disappearance time. In order to integrate heat Eqs. (10)–(11) they are made first dimensionless. This is done by introducing q¼
TCu T0 R aCu t hR ; z ¼ ; Fo ¼ 2 ; Bi ¼ : TN T0 R R kCu
(17)
where TCu is the temperature of the copper particle, T0 is the initial temperature, TN ¼ 709 K is the surroundings temperature, Fo is Fourier and Bi is the Biot number. The resulting dimensionless equation is 1 v 2 vq vq z ¼ : (18) 2 vz vFo z vz with the following initial and boundary conditions 8 q00 ðFoÞRðFoÞ vq > < vzjz¼1 ¼ kCu ðTN T0 Þ Biq vq : > vzjz¼0 ¼ 0 : qðR; 0Þ ¼ 1
(19)
Here, the first equation expresses the energy balance at the particle surface, the second represents the symmetry condition at the particle center and the third is the initial condition stating that the particle temperature is uniform at a value higher than that of the ambient but lower than that of the melting point of CuCl.
Fig. 7 – Dimensionless temperature along the radius of the copper particle at increasing times.
international journal of hydrogen energy 35 (2010) 4853–4860
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study has been performed to determine the influences of particle size, temperature and molar ratios on the reaction kinetics. The results provide valuable new data for equipment design in the Cu–Cl cycle. The specific conclusions are listed as follows. The residence time of copper particles varies between 10 and 100 s, depending on the operating conditions. The hydrogen conversion at equilibrium varies between 55 and 85%, depending on the reaction temperature. The heat flux at the particle surface can reach up to 3 kW/m2 when the particle size reduces to 0.1% of its initial size. The particle temperature can increase by up to 200 C during the exothermic reaction.
Acknowledgement Support provided by Atomic Energy of Canada Limited and the Ontario Research Excellence Fund is gratefully acknowledged. Fig. 8 – Particle temperature variation calculated with a lumped capacity model for Bi [ 0.001, T0 [ 350 8C.
references Based on considerations presented above, we estimated that the Biot number for the copper particles can be in the range 103 to 0.1. Thus we integrated Eqs. (17)–(19) first for Bi ¼ 0.1. The results presented in Fig. 7a give the evolution of radial temperature for a spherical copper particle that shrinks during the reaction. For this case we took n ¼ 15 and determined the variation of sphere radius and heat flux from the results obtained in Figs. 4 and 6, respectively. These results were inserted into Eq. (19) that is then solved with a centered, implicit finite difference scheme. Fig. 7b presents the lumped capacitance model method for the Bi ¼ 0.01 case. The importance of the Bi number is crucial for the evolution of the temperature profile across the particle. It is expected that the Bi number should take values in the lower end of the specified range. Therefore the result depicted in Fig. 7b, showing that the maximum temperature is reached at the particle surface (where the reaction occurs), is more likely to represent the actual situation. Moreover, since the particle is very small, the temperature profile is flat for very low Bi numbers. In the example presented in Fig. 8, the Bi number is 0.001. In this case, the heat transfer equations can be simplified to a lumped capacitance model which shows that the temperature of the particle may increase by up to 200 C during the reaction. All three heat transfer cases, namely for Bi numbers of 0.1, 0.01 and 0.001, represent limiting scenarios; in practice, the particle temperature could lie between the extreme results predicted in this paper.
4.
Conclusions
This paper analyzed the reaction kinetics of the hydrogen production step of a Cu–Cl water splitting cycle. A parametric
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[14] Torgerson DF, Shalaby BA, Pang S. CANDU technology for Generation IIIþ and IV reactors. Nuclear Engineering and Design 2006;236:1565–72. [15] Uhrig RE. Producing hydrogen using nuclear energy. International Journal of Nuclear Hydrogen Production and Applications 2008;1:179–93. [16] Wang Z, Naterer GF, Gabriel K. Multiphase reactor scale-up for Cu–Cl thermochemical hydrogen production. International Journal of Hydrogen Energy 2008a;33:6934–46. [17] Wang Z, Naterer GF, Gabriel K. Thermochemical process heat requirements of the Copper–Chlorine cycle for nuclear-based hydrogen production. 29th Conference of the Canadian Nuclear Society, Toronto ON, June 1–4, 2008b. [18] Wang ZL, Naterer GF, Gabriel KS, Gravelsins R, Daggupati VN. Comparison of different copper–chlorine thermochemical cycles for hydrogen production. International Journal of Hydrogen Energy 2009;34:3267–76. [19] Zamfirescu C, Naterer GF, Dincer I. Upgrading of waste heat for combined power and hydrogen production with nuclear reactors. Journal of Engineering for Gas Turbines and Power 2009a (accepted). [20] Zamfirescu C, Dincer I, Naterer GF. Performance evaluation of organic and titanium based working fluids for high temperature heat pumps. Thermochimica Acta 2009b;. doi: 10.1016/j.tca.2009.06.021. [21] Zamfirescu C, Naterer GF, Dincer I. Reducing greenhouse gas emissions by a copper–chlorine water splitting cycle driven by sustainable energy sources for hydrogen production. Global Conference on Global Warming, Istanbul 5–9 July, 2009c, paper #537.
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Available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/he
Kinetics study of the copper/hydrochloric acid reaction for thermochemical hydrogen production C. Zamfirescu*, G.F. Naterer, I. Dincer Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, 2000 Simcoe Street North, Oshawa, ON, Canada L1H 74K
article info
abstract
Article history:
The exothermic reaction of hydrochloric acid with particulate copper occurs during the
Received 23 June 2009
hydrogen production step in the thermochemical copper–chlorine water splitting cycle. In
Received in revised form
this paper, this chemical reaction is modeled kinetically, and a parametric study is per-
29 August 2009
formed to determine the influences of particle size, temperature and molar ratios on the
Accepted 30 August 2009
hydrogen conversion aspects. It is obtained that the residence time of copper particles
Available online 30 March 2010
varies between 10 and 100 s, depending on the operating conditions. The hydrogen conversion at equilibrium varies between 55% and 85%, depending on the reaction
Keywords:
temperature. The heat flux at the particle surface, caused by the exothermic enthalpy of
Cu–Cl thermochemical cycle
reaction, reaches over 3000 W/m2 when the particle shrinks to 0.1% from its initial size. The
Cu–HCl reaction
estimated Biot number varies from 0.001 to 0.1, depending on the operating conditions and
Transport phenomena
the accuracy of thermophysical data of the substances. A numerical algorithm is developed
Fluidized bed reactors
to solve the moving boundary Stefan problem with a chemical reaction that models the
Hydrogen
shrinking of copper particles in the hypothesis that the chemical reaction and heat transfer are decoupled. The model allows for the estimation of the temperature of a copper particle, assumed spherical, in the radial direction on the hypothesis of large Biot numbers. For small Biot numbers, the transient heat transfer equation results in a lumped capacitance model. In all cases, the particle decomposes in about 10–20s. ª 2009 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Converting thermal energy from sustainable sources (e.g., nuclear, solar, biomass) to hydrogen fuel and oxygen by thermochemical water splitting is examined in this paper. Thermochemical cycles use a series of chemical reactions and intermediate chemical compounds to decompose the water molecule, as highlighted in recent studies [2,10]. The Sandia National Laboratory and Japan Atomic Energy Agency have focused on the development of the sulfur-iodine water splitting cycle [15], which requires about 900 C temperature heat input. Such a high temperature provokes some concerns
about the safety of nuclear reactors. Some novel inorganic separation membranes can be used to lower it to 700 C and make the cycle more adaptable to various types of nuclear reactors. This includes conventional light water reactors, high temperature gas cooled reactors, liquid metal-cooled fast reactors, the Very High Temperature Reactor (VHTR), and the Generation IV reactor design of Atomic Energy of Canada Limited [14], as well as the Advanced High Temperature Reactor (AHTR). There are various types of thermochemical water splitting cycles, with most of them requiring high temperature heat for driving chemical reactions and recycling the intermediate
* Corresponding author. E-mail addresses: [email protected] (C. Zamfirescu), [email protected] (G.F. Naterer), [email protected] (I. Dincer). 0360-3199/$ – see front matter ª 2009 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2009.08.077
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Nomenclature a Bi C Fo h k K n p q" r R R t T X Y
2 1
thermal diffusivity, m s Biot number chemical conversion Fourier number heat transfer coefficient, Wm2K1 -1 (forward), reaction constant, mmol1 atm0:5 h1 gCu 1 1 -1 mmol atm,h gCu (backward) equilibrium constant, atm0.5 molar ratio pressure, bars heat flux, Wm2 rate (of consumption, of production, of reaction) radius, m radius, as integration variable, m time, s temperature, oC fractional HCl conversion fractional H2 production
compounds. About 290 of those cycles were screened by Ref. [1]. Some of these cycles operate at very high temperatures, i.e., from point focus solar concentrators (Zn–ZnO cycle requires 2600 C as indicated by Ref. [13]). Three of the referenced cycles operate at low temperatures, namely the Cu–Cl (<550 C), Li–N–I (<475 C) and Fe–S–I cycle (<450 C). It is advantageous if the required peak temperature is lower because a greater range of thermal sources can be utilized. Among the low temperature water splitting cycles, the copper–chlorine (Cu–Cl) cycle has been developed extensively by Atomic Energy of Canada Limited (AECL), because it links well with Canada’s Generation IV nuclear reactor. Significant progress has been recently reported by a consortium of North American institutions [8,18,24–28]. The predicted efficiency of the Cu–Cl process is about 50% with respect to the higher heating value of hydrogen, which compares favorably to the overall efficiency of electrolysis, which is typically 24% [10]. This important gain in efficiency occurs because electrical generation and its associated losses are partially avoided since the process requires mainly heat as input. Moreover, a series of past studies demonstrated that it is possible to link this cycle with heat sources at lower temperatures than 550 C. This can be accomplished by using heat pumps, and one of the possibilities is using heat rejected by the moderator of CANDU nuclear power plants at 80 C [19,20]. A more general model by Ref. [21] proposed and analyzed an integrated system including the Cu–Cl water splitting cycle, a heat pump and heat engines for generating hydrogen and oxygen from sustainable thermal energy sources available at temperatures in the range of 40–350 C. The model showed that the thermodynamic upper limits of the hydrogen production efficiency is about twice the typical efficiency of water electrolysis. But several challenges arise with the development of the copper–chlorine cycle. Firstly, thermodynamic properties of intermediate compounds are not accurately known [22]. Other challenges include material resistance to corrosion of chemicals, and unknowns regarding chemical kinetics and heat and
Greek letters enthalpy of reaction, kJ/mol DrH q dimensionless temperature k thermal conductivity, Wm1K1 m molecular mass, kg.kmol1 n number of mols, mol x dimensionless radial coordinate r density, kg.m3 Subscripts N surroundings 0 initial b backward Cu copper CuCl cuprous chloride e exterior (outer) eq equilibrium f forward H2 hydrogen HCl hydrochloric acid
mass transfer associated with certain reaction steps. These make the hydrogen production reaction very complex. One of the key challenges is that three phases are present in the chemical reactor – molten (liquid) CuCl, gaseous HCl and H2, and solid copper. This paper examines the kinetics of the hydrogen production reaction in which hydrochloric gas is reacted with particulate copper to form gaseous hydrogen and cuprous chloride (CuCl). A study of this reaction that calculates the exergetic efficiency has been conducted by Ref. [9]. This reaction is exothermic and generates 46.8 kJ/molH2 at 450 C according to Cu(s)þHCl(g)/CuCl(molten)þ1/2H2(g). More heat can be recovered from this reaction by quenching and cooling the molten cuprous chloride, and this heat can be used internally within the cycle [16,17]. The kinetics of this reaction has been studied by Ref. [11], which determined the reaction rate in a fixed bed reactor. It was shown that the gas solid mass transfer is controlled by chemical reactions at the interface. The forward reaction is of order 0.5 and the backward reaction is of order one. The reaction is reversible and the reaction constant varies in the range 0.85 to 2.5 atm when the temperature falls from 475 C to 400 C. Ref. [11] fit the experimental results on a ‘‘lnK vs 1/T ‘‘ curve and determined the Arrhenius equation for the reaction rate constant. The results by Ref. [11] are used by Ref. [23] to perform a parametric study that is extended in this present paper. A possible implementation of the hydrogen production reactor is described by Ref. [16]. It consists of a moving particle exchange bed where hydrochloric gas is circulated in excess to react with copper particles. The particles are moved by a screw mechanism and the reaction heat is absorbed by cooling water that embeds the reactor at the outer shell. The products are molten cuprous chloride (CuCl) and gaseous H2 and HCl. It is suggested that HCl is absorbed in an alkaline solution that is discharged out of the cycle and not recycled. Cuprous chloride is quenched in water in a separate reactor. In brief, in this reactor enters particulate copper and
international journal of hydrogen energy 35 (2010) 4853–4860
hydrochloric acid and exits particulate CuCl and a mixture of HCl and hydrogen (some hydrochloric acid is unused). Note however that it would be desirable to recycle all HCl, because the intention of any thermochemical water splitting cycle is to recycle all chemicals except water, hydrogen and oxygen. The objective of this study is to provide some new information and model regarding the chemical kinetics, to allow for a conceptual design of the reactor with the best possible HCl recycling. More specifically, the paper examines the influence of reaction temperature, particle size, residence time, and heat flux at the particle surface. The results are expected to be valuable for purposes of equipment design and scale-up in the Cu–Cl water splitting plant.
2.
Analysis of reaction kinetics
This section analyzes the relevant transport phenomena at the gas/solid interface, namely heat and mass transfer and the chemical reaction. Fig. 1 shows a conceptual model of the reactor. The reactor is of constant-pressure, isothermal batch type and it can be viewed as a thermodynamic system of variable volume V(t), where t 0 is time. At the initial moment, t ¼ 0, in the reactor one finds only nCu mols of copper and nHCl ¼ n0 mols of gaseous hydrochloric gas. At any later moment, in addition to the two reactants in the reactor, there are nH2 moles of hydrogen and nCuCl moles of cupric chloride (assumed here in the solid state). The figure suggests that the reactor volume shrinks, because 1 mol of hydrochloric gas converts to a half mol of hydrogen. We introduce the fractional conversion X of hydrochloric gas which is the ratio of converted reactant to the initial molar content, n0. Since the converted HCl at the current time t is n0 – nHCl, (1)
X ¼ 1 nHCl =n0
Using the fractional conversion of HCl, one expresses for any t, 9 nHCl ¼ n0 ð1 XÞ > > = nH2 ¼ n0 Y Y ¼ 0:5X > > ; n ¼ nHCl þ nH2 ¼ n0 ð1 0:5XÞ
(2)
where Y is the fractional hydrogen production and n is the total number of mols in the gas phase. Fig. 1 also shows the evolution of copper particles while reacting with hydrochloric gas. Initially, copper presents a bare surface exposed to HCl reactant. We represent the particle with a sphere, of 3–100 mm diameter. Dendritic Cu particles of 3mm diameter can be obtained commercially. Past kinetics experiments by Ref. [11] were performed with this size of Cu particles. Through electrochemical procedures, copper particles can be obtained in sizes smaller than 100mm diameter. During the reaction, at the surface of the particle, the CuCl product is formed (see Fig. 1). The reaction heat will increase the particle temperature up to the melting point of CuCl, which is 709 K [4]. As saturated liquid, cuprous chloride partially evaporates, while its vapor pressure is about 10 Pa close to the melting point [7]. Through the two-phase CuCl shell, gaseous HCl diffuses toward the copper surface and generated gaseous hydrogen diffuses toward the exterior. This depicted situation suggests that the outer shell that embeds the copper core is unstable and thus facilitates good mass transfer. The results by Ref. [11] confirm this assumption because they showed that the mass transport at the particle is controlled by the reaction. For gas-solid non-catalytic reactions that evolve according to a shrinking core model, the mass transfer mechanism may be controlled [5,6] by: diffusion through the gas film, diffusion through the outer layer, or the chemical reaction. In the last case, which is assumed to represent the present situation, the mass transfer depends on the concentrations in the bulk flow (HCl) and at the copper surface (H2). At the same time, the molar consumption rate of copper is the same as that of hydrochloric gas. Thus, dnCu dnHCl ¼ ¼ rHCl pHCl ; pH2 dt dt
(3)
where rHCl is the rate of HCl consumption due to the reaction and pHCl and pH2 are the partial pressures of participating gases, as a measure of the molar concentration. The rate of HCl consumption is opposite (negative) to the reaction rate. It has been found by Ref. [11] as being of order 0.5 for the forward reaction (H2 production) and first order for the backward reaction (HCl production). Therefore, the total reaction rate is
P,T,V0
HCl(g)
ν0
Cu(s) 3-100μm
Cu(s)
P,T,V(t) HCl(g)
Q
νHCl
H 2(g) νH2 νH2+ νHCl=ν
t=0
νCu,0
4855
Cu(s) CuCl(s)
ν Cu νCuCl
t>0
HCl(g)
H 2(g) CuCl(l,v)
Fig. 1 – Conceptual model of constant pressure batch reactor for hydrogen production.
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Fig. 2 – Fractional production of hydrogen (a) and the time to reach chemical equilibrium (b).
r ¼ kf p0:5 HCl kb pH2
(4)
where k is the reaction constant and the index ‘‘f’’ stands for forward and the index ‘‘b’’ refers to backward reactions, respectively. As the equilibrium constant is defined by Keq ¼ kf/kb (see e.g., [12]) and r¼– rHCL, one can write
R3 R30 ¼
3mCu 4prCu
Z t dnHCl dt: dt 0
(6)
Eq. (5) can be solved to determine both the HCl consumption and the shrinkage of the copper particle. For example, if one denotes R0 as the initial radius and R as the current radius of the copper particle, assumed spherical for simplicity, then one can show that
For our situation, the RHS of Eq. (6) is always negative (HCl is consumed) and the radius of the copper particle diminishes until it vanishes. If the RHS could be calculated, by setting R ¼ 0 one may determine the time to complete the reaction, sc. Calculation of the RHS implies integration of Eq. (5) for HCl. This can be accomplished as follows below. One expresses the partial pressure based on the fractional HCl consumption defined by Eq. (2) and the total pressure P as follows: 9 nHCl 1X > = P¼ P> pHCl ¼ n 1 0:5X (7) nH2 0:5X > P¼ P > pH2 ¼ ; n 1 0:5X
Fig. 3 – Conversion at equilibrium for various operating conditions.
Fig. 4 – Shrinking of copper particle for three molar ratios n at a 700 K reaction temperature.
dnCu dnHCl ¼ ¼ kf p0:5 HCl pH2 =Keq dt dt
(5)
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The solution X(t) of Eq.(8) is essential in the reactor design because it allows for calculation of other quantities, e.g., dnHCL/dt as a function of time. This leads to obtaining a particle radius variation R(t), but also allows for the calculation of heat generation at the particle surface: q}ðtÞ ¼
Dr HðTÞ dnHCl 4pRðtÞ2 dt
(9)
where DrH(T ) is the enthalpy of reaction at a temperature T. The heat conduction equation through the copper spherical particle is 1 v vT 1 vT R2 ¼ ;R ¼ 0 R 2 vR aCu vt R vR
(10)
where aCu is the thermal diffusivity of Cu, assumed constant at an average value for the range of temperatures of interest. The boundary condition written at the sphere surface is kCu Fig. 5 – Residence time of Cu particles for a range of n and three temperatures.
Using Eq. (2) to express nHCl and replacing Eq. (7) in Eq. (5) leads to dX ¼ kf dt
1X 1 0:5X
0:5
1 0:5X Keq 1 0:5X
(8)
Assume that the reaction constant and equilibrium constant are determined as by Ref. [11] for 1 g of Cu, 1 mmol of HCl and 1 atm total pressure. Eq. (8) can be integrated numerically for a given operating temperature at which the constants are known. The fractional HCl conversion at equilibrium can also be computed by setting dX/dt ¼ 0 and solving for X. It results in the time to reach chemical equilibrium in the batch reactor.
vT þ q}ðtÞ ¼ hðT TN Þ vR
(11)
where kCu is the thermal conductivity of copper, h is the heat transfer between the sphere and the multiphase shell (including molten CuCl and gases) and TN is the temperature at the outer side shell. As detailed later, assumptions will be needed to derive values for h and TN and integrate Eqs. (9–11) which form a special kind of Stefan problem (see e.g., [3]).
3.
Results and discussion
In the previous section, the analysis led to the development of a mathematical model that describes heat and mass transport with a chemical reaction, which occurs during the hydrogen production reaction. In this section, this model will be applied to conduct a parametric study of the reaction and determine the influence of various operating conditions relevant to the conceptual design of the reactor. Consider deriving an expression for the equilibrium constant of the forward reaction kf, needed for integration of Eq. (8). In this respect, we regressed the data published by Ref. [11] and obtained the following expression for the equilibrium constant: Keq ¼ 2:26 þ ðT 673:15Þ=ð351:59 0:54TÞ
(12)
which is valid for T ¼ 650–800 K. We also used the following Arrhenius equation for the reaction rate constant, based on [11], kf ¼ 1737573:23expð7515:5=TÞ
Fig. 6 – Heat flux caused by the reaction.
(13)
where kf is given for 1 atm, 1 g of copper and 1 mmol of HCl and it has units of h1. In Fig. 2a, it is presented in terms of the fractional hydrogen production Y, resulting from integration of Eq. (8) for three reaction temperatures. It is observed that the magnitude of the time to equilibrium teq varies from 0.06 to 0.14 h. Fig. 2b shows also the variation of time to reach equilibrium. Note also that the results from Fig. 2 are applicable to particle sizes of 3–100 mm, which lies in the range of the experimental determinations by Ref. [11], where the rate of reaction and equilibrium constant have been derived.
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The hydrogen conversion at equilibrium is defined by Ceq ¼ nH2eq/(nH2eq þ nHCleq). Using the definition for the fractional conversion of HCl and fractional production of hydrogen, as introduced in Eq. (2), one has Ceq ¼ 0:5Xeq = 1 0:5Xeq
(14)
Fig. 3 presents the hydrogen conversion at equilibrium and fractional conversions for a range of temperatures. Obtaining good conversions (over 80%) are possible at the lowest temperatures, but this leads to larger equilibrium times, or in other words larger residence times of particles in the reactor. The influence of particle size can be studied by integrating Eq. (6). Consider the ratio of initial mols of HCl and Cu, n¼n0/ nCu,o. Based on Eqs. (2) and (6), it can be shown that Z t 1=3 dX R=R0 ¼ 1 n : dt dt 0
(15)
Fig. 4 presents the results regarding the particle radius variation with time for a fixed reaction temperature of 700 K and three values of n. The particle radius is given with reference to the initial radius R0. From this plot, one can also observe the particle residence time in the reactor, which is 20.5 s for n ¼ 5, 9.9 s for n ¼ 10 and 6.5 s for n ¼ 15. The residence time for a range of n and three reaction temperatures, namely 650, 700 and 750 K, can be observed in Fig. 5. Regarding the heat transfer during the reaction, in order to integrate Eqs. (9) and (11) one needs to estimate first a realistic range of heat transfer coefficient at the outer side of the copper particle. In this respect, one can assume that a copper particle is surrounded by a layer of molten CuCl, which, in general, embeds migrating vapor/gas molecules or even bubbles of various species. Based on a material balance at the particle level, it can be shown that the outer radius Re of the particle, formed from the copper core and the shell containing mainly molten CuCl, is 3 3 3 Re r m R R þ ¼ Cu CuCl 1 R0 rCuCl mCu R0 R0
(16)
When the particle is consumed, by setting R ¼ 0 in the above equation, one obtains Re/R0 ¼ 1.5. If one assumes that the
molten layer is viscous enough so that heat transfer occurs mainly by conduction, then h in Eq. (11) is approximated with kCuCl/(Re-R). Note that this approximates the lowest value of h which yields on the order of 1000 W/m2K. In a real situation the heat transfer coefficient can be higher because the outer layer may detach since it is in a molten state. Because the CuCl shell melts in the process, one may assume that at the outer radius, the temperature is about the same as the melting point temperature, TN ¼ 709 K. The superficial heat flux caused by the reaction heat has been calculated with Eq. (9) for an assumed temperature at the surface of 700 K and three molar ratios, n ¼ 5, 10 and 15. The results are shown in Fig. 6 and reveal that heating is very intense by the end of the reaction, i.e., when the copper particle becomes small. This occurs due to the reduction of the particle surface area. The plot presents the heat flux up to 99.9% from the particle disappearance time. In order to integrate heat Eqs. (10)–(11) they are made first dimensionless. This is done by introducing q¼
TCu T0 R aCu t hR ; z ¼ ; Fo ¼ 2 ; Bi ¼ : TN T0 R R kCu
(17)
where TCu is the temperature of the copper particle, T0 is the initial temperature, TN ¼ 709 K is the surroundings temperature, Fo is Fourier and Bi is the Biot number. The resulting dimensionless equation is 1 v 2 vq vq z ¼ : (18) 2 vz vFo z vz with the following initial and boundary conditions 8 q00 ðFoÞRðFoÞ vq > < vzjz¼1 ¼ kCu ðTN T0 Þ Biq vq : > vzjz¼0 ¼ 0 : qðR; 0Þ ¼ 1
(19)
Here, the first equation expresses the energy balance at the particle surface, the second represents the symmetry condition at the particle center and the third is the initial condition stating that the particle temperature is uniform at a value higher than that of the ambient but lower than that of the melting point of CuCl.
Fig. 7 – Dimensionless temperature along the radius of the copper particle at increasing times.
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study has been performed to determine the influences of particle size, temperature and molar ratios on the reaction kinetics. The results provide valuable new data for equipment design in the Cu–Cl cycle. The specific conclusions are listed as follows. The residence time of copper particles varies between 10 and 100 s, depending on the operating conditions. The hydrogen conversion at equilibrium varies between 55 and 85%, depending on the reaction temperature. The heat flux at the particle surface can reach up to 3 kW/m2 when the particle size reduces to 0.1% of its initial size. The particle temperature can increase by up to 200 C during the exothermic reaction.
Acknowledgement Support provided by Atomic Energy of Canada Limited and the Ontario Research Excellence Fund is gratefully acknowledged. Fig. 8 – Particle temperature variation calculated with a lumped capacity model for Bi [ 0.001, T0 [ 350 8C.
references Based on considerations presented above, we estimated that the Biot number for the copper particles can be in the range 103 to 0.1. Thus we integrated Eqs. (17)–(19) first for Bi ¼ 0.1. The results presented in Fig. 7a give the evolution of radial temperature for a spherical copper particle that shrinks during the reaction. For this case we took n ¼ 15 and determined the variation of sphere radius and heat flux from the results obtained in Figs. 4 and 6, respectively. These results were inserted into Eq. (19) that is then solved with a centered, implicit finite difference scheme. Fig. 7b presents the lumped capacitance model method for the Bi ¼ 0.01 case. The importance of the Bi number is crucial for the evolution of the temperature profile across the particle. It is expected that the Bi number should take values in the lower end of the specified range. Therefore the result depicted in Fig. 7b, showing that the maximum temperature is reached at the particle surface (where the reaction occurs), is more likely to represent the actual situation. Moreover, since the particle is very small, the temperature profile is flat for very low Bi numbers. In the example presented in Fig. 8, the Bi number is 0.001. In this case, the heat transfer equations can be simplified to a lumped capacitance model which shows that the temperature of the particle may increase by up to 200 C during the reaction. All three heat transfer cases, namely for Bi numbers of 0.1, 0.01 and 0.001, represent limiting scenarios; in practice, the particle temperature could lie between the extreme results predicted in this paper.
4.
Conclusions
This paper analyzed the reaction kinetics of the hydrogen production step of a Cu–Cl water splitting cycle. A parametric
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