Proceedings of the 23rd National Heat and Mass Transfer Conference and
1st International ISHMT-ASTFE Heat and Mass Transfer Conference
IHMTC2015
17-20 December, 2015, Thiruvananthapuram, India
Paper No. IHMTC2015-1120
MODELING THERMAL DECOMPOSITION OF SALT HYDRATES
FOR THERMAL ENERGY STORAGE SYSTEMS
Ashok J
Department of Mechanical Engineering
IIT Kanpur
Email: [email protected]
Arvind Kumar
Department of Mechanical Engineering
IIT Kanpur
Email: [email protected]
ABSTRACT
Salt hydrates are chemical thermal energy
storage materials which rely on reversible chemical
reactions. On heating, they dissociate into a lower hydrate
or anhydrate and evolve water vapor. The chemical energy
spent on dissociation gets stored in the lower hydrate or
anhydrate in the form of bond formation internal energy
and can be recovered back by passing water vapor. Salt
hydrates have high volumetric heat storage capacity,
moderate reaction temperature, good reversibility and
most importantly the low cost. Also, they can store energy
for long durations at ambient conditions with little or no
losses. Even with all these advantages, their application is
not widespread because of their complex decomposition
process. In this paper, we present a macroscopic transient
model to solve the decomposition of salt hydrate by
considering solid state kinetics and the associated
transport phenomena. The model predicts Temperature,
species concentrations, flow field as the decomposition
process occurs.
universal gas constant (J/K-mol)
Temperature (K)
rate of reaction (s-1)
time (s)
𝑢̃
βT
κ
μ
ρ
velocity (m/s)
thermal expansion coefficient (K-1)
intrinsic permeability of the medium (m2)
viscosity (kg/m-s)
density (kg/m3)
SUBSCRIPTS
h
g
s
salt hydrate
water vapor
anhydrous salt
INTRODUCTION
We depend on energy for almost everything in our
lives. We rely on coal, oil and natural gas for over 80% of
our energy needs [1]. But fossil fuels reserves are limited
in nature and their excess exploitation leads to various
environmental hazards and also there has been a steep
increase in their prices. Many new renewable sources have
been identified and is being used today but their large-scale
utilization is restricted due to their intermittent and time
dependent nature. Energy Storage technology appears to be
a feasible solution for more rational and efficient utilization
of renewable resources by helping to adjust the instability
and time discrepancy between supply and demand of
energy [1, 2].
Keywords: Salt Hydrate, Thermal Energy Storage,
Numerical Modelling
NOMENCLATURE
A
c
E
ΔH
λ
M
N
P
R
T
r
t
frequency factor in Arrhenius equation (s-1)
specific heat capacity (J/kg-K)
activation Energy (kJ/mol)
enthalpy of dehydration (J/kg)
thermal conductivity (W/m-K)
molar mass (g/mol)
concentration (mol/m3)
Pressure (N/m2)
The basic idea is to store excess energy that would
have been wasted otherwise. Energy can be stored in
mechanical, electrical or thermal forms. We focus on
storage in thermal form using reversible chemical
1
Assumptions
reactions. In Thermal Energy Storage (TES), energy is
stored as internal energy of the material either in the form
of sensible, latent, chemical heat or a combination of these.
TES systems are capable of improving the efficiency of
thermal systems and can facilitate solar thermal
applications and many other low grade heat recovery and
utilization. Among different TES Systems, chemical
energy storage systems have been found to have the
advantage of high energy density, low heat losses, longterm storage for low and medium temperature applications
[3, 4].
The salt hydrate is spread uniformly on a
stationary domain. Physical properties such as specific heat
capacities, conductivities are taken to be constant. Water
vapor is considered as an ideal gas. Size of the salt particles
do not change as the reaction occurs. Porosity of the salt
bed is uniform and constant. At any given location in the
domain, gas and solid temperatures are considered the
same since both the phases co-exist. Decomposition of salt
hydrate is considered as a single step elementary reaction.
Salt Hydrates have been identified as potential
materials for compact and efficient chemical TES systems
[5, 6]. They are inorganic salts containing water molecules
combined in a definite ratio as an integral part of the salt
crystal that are either bound to a metal center or that have
crystallized with the metal complex. They generally remain
in either of the following equilibria,
Chemical Kinetics and Stoichiometry
A chemical kinetic model describes a particular
reaction type and translates it mathematically into a rate
equation. Many models have been proposed in solid-state
kinetics, mostly developed on mechanistic assumptions
taking into account the nucleation, diffusion, geometric
properties of the material [6]. The actual rate law for any
chemical reaction can only be found through experiments.
Since we try to formulate a generic model, we assume the
decomposition reaction to occur in a single step and of
basic first order type. Generally, elementary single step
reactions do have reaction order equal to the stoichiometric
coefficients of the reactant. An earlier modeling done by
Ganesh et al., 2010 [7] has also considered a similar
approach.
Salt.nH2O (s) + Heat ⇌ Salt (s) + nH2O (g)
Salt.nH2O (s) + Heat ⇌ Salt.(n-m)H2O (s) + mH2O (g)
The forward reaction is the charging phase, during
which the salt hydrate is heated and is dissociated into its
anhydrous or lower hydrate and water vapor. Then the
products are separated, cooled and stored at ambient
conditions. There is little or no energy loss during the
storage period. When energy is required, water vapor is
passed through the anhydrate and the backward reaction
occurs and it being exothermic, stored energy is
discharged. The backward reaction is also called the
discharge phase. A list of few promising salt hydrates and
their relevant properties are listed in Table 1.
According to the first order kinetics, the rate of
reaction is proportional to concentration of the reactant and
the rate constant is given by Arrhenius equation.
Mathematically,
TABLE 1: PROPERTIES OF FEW SALT HYDRATES
[4, 5]
Thermochemical
material
CaSO4.2H2O
MgSO4.7H2O
CaCl2.2H2O
Energy Storage
density (GJ/m3)
1.4
2.8
1.9
𝜕𝑁ℎ
(1)
= −𝑟𝑁ℎ = −𝐴𝑒 −(𝐸/𝑅𝑇) 𝑁ℎ
𝜕𝑡
Stoichiometry requires dehydration of x moles of
salt hydrate to produce x moles of anhydrous salt. So the
rate of decrease in molar concentration of salt hydrate
should be equal to the rate of increase in molar
concentration of anhydrate. Hence,
Charging reaction
temperature(oC)
89
122
200
In this paper, we develop a generic model and use
MgSO4.7H2O as the candidate material to present our
results.
𝜕𝑁ℎ
𝜕𝑁𝑠
=−
𝜕𝑡
𝜕𝑡
MATHEMATICAL MODELING
We model the charging phase of chemical TES
systems. We develop a set of partial differential equations
which can depict the chemical kinetics, stoichiometry,
energy and mass balances as the forward reaction occurs.
(2)
Flow Regime
As the reaction occurs, water vapor is released and
it flows through the salt particles. This can formulated as
fluid flow through porous media of salt particles.
2
Following Darcy’s law, the velocity of fluid particles is
proportional to the pressure gradient and is given by,
𝑢̃ = −
𝜅
. 𝛻(𝑃)
µ
in mass balance, the final energy balance equation
becomes,
𝜕((𝑀𝑔 𝑁𝑔 𝑐𝑔 + 𝑀𝑠 𝑁𝑠 𝑐𝑠 + 𝑀ℎ 𝑁ℎ 𝑐ℎ )𝑇)
+ ∇(𝑁𝑔 𝑐𝑔 𝑢̃𝑇)
𝜕𝑡
= ∇. (𝜆∇𝑇) + 𝑟𝑀𝑔 𝑁𝑔 ∆𝐻
(3)
Using ideal gas law, Eqn. (3) can be rewritten in
terms of Temperature and molar concentration of water
vapor. Further, the effects of natural convection of vapor
particles can be incorporated using Boussinesq
Approximation. The final form of velocity is given by,
𝑢̃ = −
𝜅
. ( 𝛻(𝑅𝑇𝑁𝑔 ) − 𝜌0 𝛽𝑇 (𝑇 − 𝑇0 )𝑔 )
µ
NUMERICAL IMPLEMENTATION
In order to simulate the thermal decomposition,
we need to solve the coupled Eqns. (1), (2), (6), (10)
simultaneously with appropriate initial and boundary
conditions.
(4)
Discretization of Governing Equations
Mass Balance
Equations (1) and (2) are simple scalar partial
differential equations and their transient terms are
discretized using forward difference scheme.
The general mass balance equation is given by,
𝜕𝜌
𝜕𝑡
(5)
+ 𝛻. (𝜌𝑢̃) = 0
Equation (4) is used to calculate the velocity and
the gradient term is calculated by spatially discretizing it
using central difference. Then using the velocity values at
grid points, we interpolate the velocity at staggered grid
points giving equal weightage to neighbor grid point
values. These values at staggered grid points are latter used
in computations for solving Eqns. (6) and (10).
In our case, we have three different materials, salt
hydrate, anhydrate and water vapor. Salt Hydrate and
anhydrate are solid and immobile. But the vapor molecules
have velocity and move around. Hence the mass
conservation equation should have transient terms for salt
hydrate, anhydrate and water vapor and convection term
associated only with water vapor. Rewriting Eqn. (5) and
stating densities as a relative density in the domain, that is
product of concentration of species and corresponding
molar masses, we get,
𝑀𝑔
𝜕𝑁𝑔
𝜕𝑁𝑠
𝜕𝑁ℎ
+ 𝑀𝑠
+ 𝑀ℎ
+ 𝑀𝑔 𝑢.
̃ ∇𝑁𝑔 = 0
𝜕𝑡
𝜕𝑡
𝜕𝑡
Equation (10) resembles the general convectiondiffusion transport equation after considering the transient
terms associated with salt hydrate and anhydrate and the
chemical energy term as source terms. It is discretized
using a fully implicit time-stepping scheme and solved
using finite volume method. Power law scheme was used
to evaluate the finite volume coefficients [8]. The transient
terms are discretized using forward difference and
diffusion terms using central difference method. Equation
(6) is discretized similar to Equation (10) considering the
diffusion term to be zero. Finally, a Line-by-Line TriDiagonal Matrix Algorithm Solver is used to solve
iteratively solve the resultant system of algebraic
equations.
(6)
Energy Balance
The general conservation
Temperature notation is given by,
of
energy
in
𝜕(𝜌𝑐𝑝 𝑇)
(7)
+ 𝛻. (𝜌𝑐𝑝 𝑢̃𝑇) = 𝛻. (𝜆𝛻𝑇) + 𝑄
𝜕𝑡
The thermal conductivity (λ) is defined as a
combined property of the three different species as,
𝜆=
𝑀ℎ 𝑁ℎ 𝜆ℎ 𝑀𝑠 𝑁𝑠 𝜆𝑠 𝑀𝑔 𝑁𝑔 𝜆𝑔
+
+
𝜌ℎ
𝜌𝑠
𝜌𝑔
Convergence in the inner iterations is declared on
the basis of relative error of variables to be solved and a
tolerance limit of 10-6 is prescribed.
(8)
The source term Q in Eq. (7) is used to represent
the chemical reaction energy and is given by,
𝑄 = 𝑟𝑀𝑔 𝑁𝑔 ∆𝐻
(10)
Numerical Setup
(9)
Considering similar contributions by different
species to different terms in Eq. (7) and rewriting as done
FIGURE 1. COMPUTATION DOMAIN
3
We consider a square 2D cavity of dimensions
0.01m × 0.01m as the computational domain (Fig. 1). The
cavity is filled with MgSO4.7H2O particles uniformly. The
domain is discretized spatially using a uniform grid
approach. A number of simulations are conducted with
varying number of control volumes in the domain to
suitably define an appropriate control volume size and
ensure grid independency. The material properties relevant
to problem are listed in Table 2.
behavior. The temperature plot shows that, first the domain
gets heated from the input heat flux and the temperature in
the domain increases gradually. Once the temperature
attains around 395 K at t = 236 s, which is the forward
reaction temperature, the reaction starts, proceeds
exponentially and ends in the next few seconds. The steep
increase in temperature is attributed mainly to the
movement and increasing concentrations of water vapor as
the reaction occurs. By observing the plots at different
locations, we can infer that the reaction proceeds from right
to the left.
TABLE 2: MATERIAL PROPERTIES [7]
Symbol
Mh
Ms
Mg
ρh
ρs
ρg
ch
cs
cg
λh
λs
λg
ΔH
A
E
R
κ
μ
βT
Description
Molecular Mass of MgSO4.7H2O (gm/mol)
Molecular Mass of MgSO4 (gm/mol)
Molecular Mass of H2O (vapor) (gm/mol)
Density of MgSO4.7H2O (kg/m3)
Density of MgSO4 (kg/m3)
Density of H2O (vapor) (kg/m3)
Specific heat of MgSO4.7H2O (J/kg-K)
Specific heat of MgSO4 (J/kg-K)
Specific heat of H2O (vapor) (J/kg-K)
Thermal conductivity of MgSO4.7H2O (W/m-K)
Thermal conductivity of MgSO4 (W/m-K)
Thermal conductivity of H2O (vapor) (W/m-K)
Enthalpy of dehydration (J/kg)
Frequency factor in Arrhenius Equation (s-1)
Activation energy (kJ/mol)
Universal gas constant (J/K-mol)
intrinsic permeability of the medium (m2)
viscosity (kg/m-s)
thermal expansion coefficient (K-1)
Value
246
120
18
1680
2660
0.4664
1546
800
1975
0.48
0.48
0.026
8536.18
1.67×105
55
8.314
1×10-15
3×10-5
8.6×10-4
FIGURE 2. TEMPERATURE VS TIME PLOT AT
THREE DIFFERENT LOCATIONS
Initial and Boundary Conditions
The simulation uses the following initial
conditions,
T (at time t=0) = 300 K
Nh (at time t=0) = 3400 mol/m3
Ng (at time t=0) = 0 mol/m3
Ns (at time t=0) = 0 mol/m3
A constant heat flux of 1000 W/m2 on the right
boundary of the domain is imposed, the other three
boundaries are perfectly insulated. There is no mass
transport between the system and surrounding.
RESULTS AND DISCUSSION
The simulation predicts transient temperature,
concentrations of all the species, velocity of water vapor,
and pressure distribution in the domain.
FIGURE 3. SALT HYDRATE CONCENTRATION VS
TIME PLOT AT THREE DIFFERENT LOCATIONS
Figures (2)-(5) show time evolution of various
variables at three different locations. These plots can be
used to explain the overall thermal decomposition
4
FIGURE 4. WATER VAPOR CONCENTRATION VS
TIME PLOT AT THREE DIFFERENT LOCATIONS
FIGURE 7. VAPOR CONCENTRATION MAP AND
VELOCITY FIELD AT t=239.4 s
FIGURE 5. SALT ANHYDRATE CONCENTRATION
VS TIME PLOT AT THREE DIFFERENT LOCATIONS
A deeper understanding of the vapor flow field in
the system can be obtained by observing the vapor
concentration map and velocities as the reaction occurs.
Figures (6)-(10) show the same at different time instants
after the reaction has started.
FIGURE 8. VAPOR CONCENTRATION MAP AND
VELOCITY FIELD AT t=239.62 s
FIGURE 9. VAPOR CONCENTRATION MAP AND
VELOCITY FIELD AT t=239.69 s
FIGURE 6. VAPOR CONCENTRATION MAP AND
VELOCITY FIELD AT t=237.5 s
5
reaction gets completed and the system starts heating
uniformly again due to the input heat flux.
CONCLUSIONS
In this work we developed an in-depth
understanding of the thermal decomposition of salt
hydrates. We presented a one-domain macroscopic model
to simulate the reaction progress and associated transport
phenomena. In the model the chemical kinetics, heat
transfer without neglecting the water vapor transport by
using Darcy law and Boussinesq approximation are
appropriately incorporated. The variation of temperature
and species concentrations as the reaction proceeds is
presented. The domain is initially getting heated up slowly
till it reaches the dissociation reaction temperature and
after that it the reaction progresses rapidly and ends in the
next few seconds. Concentration maps along with velocity
field have been shown to analyse the water vapor
movement occurring in the domain. The results provide an
overall picture of the decomposition process and can help
in developing lab-scale experiments for thermal energy
storage systems using salt hydrates.
FIGURE 10. VAPOR CONCENTRATION MAP AND
VELOCITY FIELD AT t=239.71 s
As the reaction starts, vapor molecules start
gaining velocities due to the pressure gradient and thermal
buoyancy. They first move from right to left and start
accumulating towards the left boundary. This trend
continues till the time when the pressure gradient near the
right boundary becomes zero. Then the line along which
the pressure gradient is zero moves from right to left
reversing the flow on the right part of it. During this time,
the accumulated vapor gets dispersed throughout the
system. The reason for the zero pressure gradient line can
be seen from the plot of Pressure along a horizontal line in
the domain at a time instant. Figures 9 and 11 were plotted
at the same time instant, t=239.69 s. A local maxima,
meaning zero pressure gradient, is found at the same
location as of the line of separation in Fig. 9.
REFERENCES
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and Sustainable Energy Reviews 16, pp.2394-2433.
[3] Wim van Helden. Materials for Compact Seasonal Heat
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thermochemical storage”. Energy Procedia, vol.48, pp.
447-452.
FIGURE 11. PRESSURE VARIATION ALONG A
HORIZONTAL LINE THROUGH MIDDLE OF THE
DOMAIN AT t=239.69 s
After the line of zero pressure gradient reaches the
left boundary, vapor gets completely redistributed and the
6
[7] Ganesh, B., Mehdi, G., Muhammad, R.H., William,
P.W., Jennifer, A.T., and Ishwar, K.P., 2010. “Modelling
of thermochemical energy storage by salt hydrates”.
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7