TY - JOUR
AU - Lokhat, David
AB - Abstract Calcium-looping process was simulated by solution of one-dimensional mass and energy balance equations for both interconnected fluidized bed reactors. Kinetics for the carbonator and calciner were derived from literature sources and were revised to include the effects of sulphation. The degree of apparent carbonation was compared to the actual level of carbon dioxide removal through a series of sensitivity analyses. It has been found that carbonation decreases with an increase in temperature. Sulphation increases with an increase in temperature. The activity of calcium oxide decreases with an increase in carbonation–calcination cycles. Neglecting the effect of sulphation during the design of the calcium-looping system leads to overestimation of active calcium particles that will react with carbon dioxide. 1. INTRODUCTION The commencement of industrialization saw the marked increase of greenhouse gases in the atmosphere compared to pre-industrialization levels. Carbon dioxide, methane and oxides of nitrogen levels have increased in the atmosphere [1]. Although natural processes like respiration add carbon dioxide into the atmosphere, man’s activities are the ones that add a greater fraction of carbon dioxide in the atmosphere [2]. According to the United Nation’s Sustainable Development Goal number 13 [3], all should take urgent action to fight climate change and its impacts, which mainly include combating greenhouse gas emissions. Carbon capture and storage is one of the ways that are used to reduce greenhouse gases emission into the atmosphere [4]. There are various methods of capturing greenhouse gases from the atmosphere, which include separation with sorbents or solvents [5–7], separation with membranes and separation by cryogenic distillation. In this paper, the modelling and simulation of a calcium-looping system for carbon dioxide removal from flue gases were considered. The calcium-looping method was proposed in 1999 [8] and it is a method for carbon dioxide capture from flue gases using two coupled fluidized bed reactors. A limestone sorbent, calcium oxide, is used for carbon dioxide capture. Carbon dioxide is captured through a chemical reaction resulting in the formation of calcium carbonate. Carbon dioxide capture takes place in the carbonator after which the carbonate is passed to the calciner for regenerating the sorbent and carbon dioxide separation. The separated carbon dioxide is then compressed and stored. Most of the studies on calcium-looping reactor modelling have concentrated on the carbonator, which is the most innovative component. Different models of the carbonator have been proposed in literature with the first models being the bubbling fluidized bed reactors [9]. The carbonator models that have been suggested by researchers considered the carbonator as a circulating fluidized bed [10–12], which has two compartments: the bottom dense zone and the lean zone. Most of the models proposed in literature have concluded that the calcium particles that react in the fast regime influence carbonator efficiency. The percentage of the calcium particles that react in the fast regime is defined by the amount of fresh sorbent being introduced into the system and the solid circulation between the calciner and carbonator. It has been proposed in literature to design a model that considers the actual activity of the calcium particles in the system according to their carrying capacity, regardless of their preceding history of partial or full carbonation–calcination cycles [13]. True results would be obtained about the carbonator and general plant performance. It is also important to measure the effect of sulphation and the amount of non-active calcium particles that react with sulphur dioxide in the calcium-looping system. 2. CALCIUM-LOOPING PROCESS Calcium looping is a method that can be used for carbon dioxide capture in pre-combustion and post-combustion. Calcium looping involves carbon dioxide capture in a reactor, carbonator, in a process called carbonation where carbon dioxide reacts with calcium oxide to form calcium carbonate. The calcium carbonate is passed into the second reactor, calciner, where the calcination process takes place. Calcination is an endothermic reaction where calcium carbonate is decomposed to carbon dioxide and calcium oxide. The main advantage of calcium-looping technology is that the calcium-looping reactors have already been established commercially in large scale [14]. Shimizu et al. [8] first proposed calcium looping. It involves the carbon dioxide separation from flue gas making use of the reversible reaction of calcium oxide and carbon dioxide and the calcination of calcium carbonate to regenerate calcium oxide. Important steps have been taken in the past to demonstrate the viability of the calcium-looping technology. Experimental testwork to test the viability of using calcium oxide as carbon dioxide absorber in a calcium-looping system has been carried out. Carbon dioxide capture efficiencies ranging from 70 to 97% have been achieved in different test facilities at lab-scale from 10 to 30 KWth [9,14,15]. Several approaches have been made towards the development of carbonator reactor models integrated into a calcium-looping system. Shimizu et al. [8] and Abanades et al. [9] used the bubbling bed model proposed by Kunii and Levenspiel [16] to predict the carbon dioxide captured in a bubbling bed absorber that consisted of calcium oxide particles. Circulating fluidized bed carbonators are the most common choice for large-scale systems when high volumes of flue gases are expected to enter the carbonator on condition that it operates at atmospheric pressure. The first approach to modelling of a CFB reactor acting as carbonator was proposed by Hawthorne et al. [10] and Alonso et al. [11]. The models projected that capture efficiencies above 80% can be achieved under reasonable conditions. The main components in the calcium-looping technology are the carbonator and regenerator (calciner). Flue gas is fed into the carbonator, which operates between 600 and 700°C where carbon dioxide reacts with calcium oxide to form calcium carbonate. Lime is carbonated and passes through the cyclone where the stream is separated into a carbon dioxide-depleted gas stream and a stream of solids that are passed to the calciner for regeneration of the sorbent at a temperature around 850 to 950°C [14]. Limestone releases the carbon dioxide at high temperature in the calciner. The products from the calciner pass through a cyclone, where carbon dioxide is separated from solids. Calcination uses a great amount of energy, almost 50% of energy used in the calcium-looping system, because there is need of heating up the solids from carbonator and calcination is an endothermic reaction [17]. Figure 1 (above) is a simplified diagram of the calcium-looping process, flue gas containing carbon dioxide and sulphur dioxide (Stream S-1) enters the carbonator (Unit E-1), which contains calcium oxide as the sorbent. In the carbonator, carbon dioxide reacts with calcium oxide as shown in equation 1 (below) forming calcium carbonate. A side reaction called sulphation also occurs in the carbonator as sulphur dioxide reacts with either calcium oxide or the formed carbonate, as shown in equations 8 and 9,forming calcium sulphate. The carbon dioxide- and sulphur dioxide-depleted gases exit the carbonator as stream S-2. Calcium carbonate and calcium sulphate leave the carbonator into the calciner (Unit E-2) as stream S-3. Stream S-3 will combine with stream S-5, which makes up calcium carbon, to replace deactivated calcium oxide from the carbonator. In the calciner, calcium oxide is regenerated from calcium carbonate as shown by equation 5. Reaction conditions in the calciner do not allow for regeneration of calcium sulphate to calcium oxide. This is because generation of calcium oxide from calcium sulphate requires temperatures high enough to cause sintering and deactivation of the calcium oxide. Calcium sulphate together with deactivated calcium oxide will be removed from the calciner as stream S-7 while the regenerated calcium oxide is taken back to the carbonator as stream S-4. The concentrated carbon dioxide stream, ready for storage, exits the calciner as stream S-6. Side reactions such as sulphation and sintering result in the sorbent being inactive. Fresh sorbent will have to be added to compensate for the loss. Figure 1 Open in new tabDownload slide Calcium-looping process. Figure 1 Open in new tabDownload slide Calcium-looping process. In the carbonator, the reaction below takes place: $$\begin{equation} CaO+{CO}_2\leftrightarrow{CaCO}_3\kern2.25em \Delta H=-178 KJ/ mol \end{equation}$$(1) Calcium oxide also reacts with sulphur dioxide in flue gas. Calcination and sulphation reactions can limit the carbonator temperature to a maximum of 700°C, above which sulphation rate increases and the calcium carbonate decomposes releasing carbon dioxide [18]. The two stages involved in carbonation are the following: the fast carbonation stage where the carbon dioxide is bound on the surface of the calcium oxide and the slow carbonation stage where diffusion occurs and carbon dioxide is bound in the calcium oxide particle. The carbonation reaction may be represented by the following empirical correlation modelled by Ylätalo [19]: $$\begin{equation} {r}_{carb}={m}_s{S}_{ave}\left({W}_{max}-W\right){k}_{carb}\left({C}_{C{O}_2}-{C}_{C{O}_{2e}}\right) \end{equation}$$(2) where |${m}_s$| is mass of solid, |${S}_{ave}$| is the reaction surface area, |${W}_{max}-W$| represents the active fraction of the solid material, |${k}_{carb}$| represents the kinetic constant for the carbonation reaction and |${C}_{C{O}_2}$| is carbon dioxide concentration in the flue gas. The active fraction of the solid material is given by $$\begin{equation} {W}_{max}-W={f}_a=1-{e}_{\tau}^{-{t}^{\ast }} \end{equation}$$(3) where |${t}^{\ast }$| is the characteristic time at which the reaction rate becomes zero and |$\tau$| is average residence time in the carbonator. The reaction surface area is given by Alonso et al. [11] as $$\begin{equation} {S}_{ave}=\frac{X_{ave}\frac{\rho_{CaO}}{PM_{Cao}}}{e_{max}\frac{\rho_{CaC{O}_3}}{PM_{CaC{O}_3}}} \end{equation}$$(4) where |${\rho}_{CaO}$| and |${\rho}_{CaC{O}_3}$| are densities of calcium oxide and calcium carbonate, |${X}_{ave}$| is the average conversion of solids, |${PM}_{Cao}$| and |${PM}_{CaC{O}_3}$| are molecular weights of calcium oxide and calcium carbonate and |${e}_{max}$| is maximum thickness of the layer of calcium carbonate on the pore wall. The average value of the carbonation rate constant was calculated by Bhatia and Permutter for temperatures ranging from 550 to 725°C [20] as 5.95 × 10−10 m4(mol s)−1. In the regenerator, limestone is calcined releasing carbon dioxide: $$\begin{equation} Ca{CO}_3\leftrightarrow Ca O+{CO}_2\kern3em \Delta H=178 KJ/ mol \end{equation}$$(5) Because calcination reaction is endothermic, heat must be supplied. Calcination is carried out at higher temperature than carbonation. Due to sintering and sulphation reactions, and the sorbent deactivation caused by these reactions, the maximum recommended temperature for calcination is 900°C [18]. Calcination process normally takes 0 to 15 minutes to complete. If the sorbent is exposed to high temperatures for a longer period, it will end up deviating from the required process (calcination) and is sintered. Calcination is mainly affected by surrounding temperature and carbon dioxide partial pressure at the calcium oxide/calcium/carbonate/carbon dioxide interface. Calcination rate depends on the properties of the limestone used and the relation of carbon dioxide partial pressure, |${P}_{CO_2}$| to equilibrium partial pressure [21]. Calcination is modelled by Ylätalo et al. [19] as given below: $$\begin{equation} {r}_{calc}={m}_sW{S}_{ave}\frac{M_{CaCO_3}}{\rho_{CaCO_3}}{k}_{calc}\left(1-\frac{P_{{\mathrm{C}O}_2}}{P_{CO_{2e}}}\right) \end{equation}$$(6) where |${S}_{ave}$| represents the reaction surface area, |${\rho}_{CaCO_3}$| represents the density of calcium carbonate, |${M}_{CaCO_3}$| represents the molar mass of calcium carbonate and |${k}_{calc}$| represents the kinetic parameter for the calcination reaction of the selected limestone. The kinetic parameter for calcination was modelled by Silcox et al. [22] as given below: $$\begin{equation} {k}_{calc}=1.22\exp \left(-4026/T\right) \end{equation}$$(7) (mol.m−2.s−1.atm−1) The evaluation of the kinetics of calcination can be complicated by the following: The concentration of carbon dioxide, which hinder the reaction Particle size which may cause mass transfer limitations Catalysis or inhibition by impurities. Vanadium pentoxide and fly ash are commonly known to inhibit calcination while lithium carbonate accelerates it. When a fuel with a sulphur content burns, sulphur dioxide is formed, which competes with carbon dioxide on reaction with calcium oxide. Sulphur dioxide reacts with calcium oxide in two possible ways: $$\begin{equation} Ca O+{SO}_2+\frac{1}{2}{O}_2\to Ca{SO}_4\Delta H=-502 KJ/ mol \end{equation}$$(8) $$\begin{equation} Ca{CO}_3+{SO}_2+\frac{1}{2}{O}_2\to Ca{SO}_4+{CO}_2\kern0.75em \Delta H=-324 KJ/ mol \end{equation}$$(9) These reactions take over the formation of calcium carbonate due to the differences in heat of reaction. The significance of their influence depends on the sulphur dioxide content of the flue gas. Sulphation reaction can also take place in the calciner if heat is supplied using oxy-fuel combustion. Heating solid particles at high temperatures but below their melting point will cause them to start to merge. Porous materials like calcium oxide will shrink and the pores close as al the grains that initially formed the sorbent will fuse together to form larger grains. This is known as sintering and is more evident at high temperatures and long periods of reaction. It will cause a drop in the reactivity of the sorbent. If temperatures become too high (above 900°C for calcium oxide), sintering occurs at a high rate. This means the make-up flow will have to be increased too. Conditions in fluidized bed allow for sintering to occur. Sintering reduces the porosity and surface area of the sorbent. Sintering is accelerated by presence of carbon dioxide and water [23]. 3. CALCIUM-LOOPING MODELLING Most of the information from this section was adapted from Ylätalo et al. [19]. Two solids, calcium oxide and calcium carbonate, form the most part of carbonator and calciner. The required lime mass flow rate is calculated depending on the carbon dioxide mass flow rate and the absorption efficiency. Change in mass = total mass flows in-total mass flows out + amount of material regenerated The solid mass balance is given by $$\begin{equation} \frac{d{m}_s}{dt}=\sum{\dot{m}}_{s, in}-\sum{\dot{m}}_{s, out}+\sum{r}_s \end{equation}$$(10) where |${m}_s$| is the total mass in the reactor, |${\dot{m}}_{s, in}$| is mass of solids entering the reactor, |${\dot{m}}_{s, out}$| is mass of solids exiting the reactor and |${r}_s$| represents solid mass change due to chemical reaction. The gas mass derivative is much smaller than the solid mass derivative and for this reason, the mass of the gas in the domain can be assumed constant and therefore the change in gas mass to the element is neglected. $$\begin{equation} \frac{d{m}_{g,i}}{dt}=\sum{\dot{m}}_{g, in,i}-{\dot{m}}_{g, out,j}+{r}_{g,i} \end{equation}$$(11) There is no gas deposition into the control volume: $$\begin{equation} {\dot{m}}_{g, out,i}=\sum{\dot{m}}_{g, in,\kern0.5em i}+{r}_{g,i} \end{equation}$$(12) $$\begin{equation} \sum{\dot{m}}_{g, in,i}={\dot{m}}_{g,i-1} \end{equation}$$(13) where |${m}_{g,i}$| is the total gas mass in the domain, |${\dot{m}}_{g, in,i}$| is gas flow into the element, |${\dot{m}}_{g, out,j}$| is gas flows out of the element and |${r}_{g,i}$| is the combined effect of chemical reactions such as calcination, carbonation, sulphation, combustion of char and volatiles. The exiting gas either enters the succeeding control volume or leaves the reactor if the control volume was located at the exit of the reactor. The one-dimensional gas balance for a single gas component a is given by $$\begin{equation} \frac{d{m}_{a,i}}{dt}=\sum{\dot{m}}_{a, in,\mathrm{i}}-{\dot{m}}_{a, out,i}+\sum{r}_{a,i}=\sum{\dot{m}}_{a, in,i}-{w}_{a,i}{\dot{m}}_{a, out,i}+\sum{r}_{a,i} \end{equation}$$(14) where |${m}_{a,i}$| is the mass of the gas component, |${\dot{m}}_{a, in,i}$| represents gas component entering a control volume, |${\dot{m}}_{a, out}$| represents the gas component exiting the control volume and |${r}_{a,i}$| is the term for chemical reaction term for the gas component. $$\begin{equation} \frac{d{w}_i}{dt}=\frac{1}{m_{gi}}\left({\dot{m}}_{i, in}-{\dot{m}}_{i, out}+{r}_i\right) \end{equation}$$(15) The energy present in a control volume equals the energy associated with total convective flows in solids and gases and total energy by dispersion, total heat transfer and chemical reactions. $$\begin{equation} \frac{d{E}_i}{dt}=\sum{q}_{conv,s}+\sum{q}_{conv,g}+\sum{q}_{disp}+\sum{q}_{ht}+\sum{q}_{chem} \end{equation}$$(16) where |${E}_i$| is energy present in the control volume, |${q}_{conv,s}$| is energy associated with convective flows in solids, |${q}_{conv,g}$| is energy associated with convective flows in gases, |${q}_{disp}$| is energy associated with dispersion between elements, |${q}_{ht}$| is heat transfer and |${q}_{chem}$| is energy associated with chemical reactions. The left-hand side of equation 16 can be further expanded as follows: $$\begin{align} \frac{d{E}_i}{dt}&=\frac{d{U}_{s,i}}{dt}+\frac{d{U}_{g,i}}{dt}=\frac{d\left({m}_{s,i}{u}_{s,i}\right)}{dt}+\frac{d\left({m}_{g,i}{u}_{g,i}\right)}{dt}\nonumber\\&=\frac{d\left({m}_{s,i}\left({h}_{s,i}-{p}_i{v}_i\right)\right)}{dt}+\frac{d\left({m}_{g,i}\left({h}_{g,i}-{p}_i{v}_i\right)\right)}{dt}\nonumber\\&=\frac{d\left({m}_{s,i}{c}_{p,s}{T}_i\right)}{dt}+\frac{\left({m}_{g,i}{h}_{g,i}\right)}{dt}=\frac{d{m}_{s,i}}{dt}{c}_{p,s}{T}_i+\frac{d{T}_i}{dt}{m}_{s,i}{c}_{p,s}\nonumber\\&+\frac{d{m}_{g,i}}{dt}{h}_{g,i}+\frac{d{h}_{g,i}}{dt}{m}_{g,i} \end{align}$$(17) Assuming that gas mass is very small, $$ \frac{d{m}_{g,i}}{dt}{h}_{g,i}=0 $$ where |${U}_{s,i}$| is the internal energy of the solid, |${U}_{g,i}$| is the internal energy of the gas, |${u}_{s,i}$| is specific internal energy of solid phase, |${u}_{g,i}$| is the specific internal solid and gas phase enthalpies energy of gas phase, |${h}_{s,i}$| and |${h}_{g,i}$| are solid and gas phase enthalpies, |${p}_i{v}_i$| is work done by phase and |${c}_{p,s}$| is specific heat capacity of the solids. Solving the temperature derivative from equation 14 results in $$\begin{equation} \frac{d{T}_i}{dt}=\frac{\sum{q}_{conv,s+g}+\sum{q}_{disp}+\sum{q}_{ht}+\sum{q}_{chem}-\frac{d{m}_{s,i}}{dt}{c}_{p,s}{T}_i-\frac{d{h}_{g,i}}{dt}{m}_{g,i}}{m_{s,i}{c}_{p,s}} \end{equation}$$(18) From the mass balance, the convective flow of solids can be written as $$\begin{align} \sum{q}_{conv,s}&=\sum{q}_{conv,s, in}-\sum{q}_{conv,s, out}\nonumber\\&=\sum{\dot{m}}_{s, in,i}{c}_{p,s}\left(\!{T}_{s, in}\!-\!{T}_{NTP}\!\right)\!-\!\sum \!{\dot{m}}_{s, out}{c}_{p,s}\big(\!{T}_i\!-\!{T}_{NTP}\!\big) \end{align}$$(19) where |${q}_{conv,s, in}$| represents the convective flows of energy in control volume, |${q}_{conv,s, out}$| represents the convective flows of energy out of the control volume, |${T}_{s, in}$| represents temperature of the incoming mass flows and |${T}_{NTP}$| is reference temperature of the system. Substituting equation 18 into equation 16 gives $$\begin{equation} \sum{q}_{conv,s}-\frac{d{m}_{s,i}}{dt}{c}_{p,s}{T}_i={c}_{p,s}\left(\sum{\dot{m}}_{s, in,i}{T}_{s, in}-\sum{\dot{m}}_{s, out,i}{T}_i-\frac{d{m}_{s,i}}{dt}{T}_i\right) \end{equation}$$(20) For solids with different heat capacities, equation 20 can be written as $$\begin{equation} \sum{q}_{conv,s}-\frac{d{m}_{s,i}}{dt}{c}_{p,s}{T}_i=\sum{c}_{p,s}{\dot{m}}_{s, in,i}\left({T}_{\mathrm{s}, in}-{T}_{NTP}\right)-\sum{c}_{p,s}{\dot{m}}_{s, in,i}\left({T}_i-{T}_{NTP}\right) \end{equation}$$(21) The convective flows of the gas can be written as shown below: $$\begin{equation} \sum{q}_{conv,g}=\sum{q}_{conv,g, in}-\sum{q}_{conv,g, out}=\sum{\dot{m}}_{g, in,\mathfrak{i}}{h}_{g,\mathfrak{i}n}-\sum{\dot{m}}_{g, out,\mathfrak{i}}{h}_{g,i} \end{equation}$$(22) where |${q}_{conv,g, in}$| is convective energy flows of gases into the control volume and |${q}_{conv,g, out}$| is convective energy flows of gases out of the control volume. Substituting equation 18 to equation 22 gives $$\begin{equation} \sum{q}_{conv,g}-\frac{d{h}_{g,i}}{dt}{m}_{g,i}=\sum{\dot{m}}_{g, in,i}{h}_{g, in}-\sum{\dot{m}}_{g, out,i}{h}_{\mathrm{g},i}-\frac{d{h}_{g,i}}{dt}{m}_{g,i} \end{equation}$$(23) where |${h}_{g, in}$| is the enthalpy of the incoming flows. The enthalpy change in time can be written as $$\begin{equation} \frac{d{h}_{g,i}}{dt}{m}_{g,i}={m}_{g,i}\sum \frac{d{w}_i}{dt}{h}_{a,i} \end{equation}$$(24) where |${h}_{a,i}$| is the gas component enthalpy. Chemical reactions that can be considered include evaporation, carbonation, sulphation and the combustion of char and volatiles. $$\begin{equation} \sum{q}_{chem}=\sum{r}_{c,i}{Q}_i \end{equation}$$(25) where |${r}_{c,i}$| is the rate of reaction and |${Q}_i$| is the general reaction enthalpy. Applying Fick’s law of diffusion to the modelling approach, the following equation for dispersion is obtained [24]: $$\begin{equation} \sum{q}_{disp}={D}_s{c}_{p,s}{A}_b{\rho}_{ave}^{-}\frac{d{T}_i^{-}}{dz}+{D}_s{c}_{p,s}{A}_t{\rho}_{ave}^{+}\frac{d{T}_i^{+}}{dz} \end{equation}$$(26) where |${D}_s$| is the dispersion coefficient, |${A}_{b/t}$| is the cross section of the bottom/top element boundary and |${\rho}_{ave}^{+/-}$| is the average density between calculation element and siding element. Heat transfer to the surfaces is given by the expression $$\begin{equation} \sum{q}_{ht}={\alpha}_{tot}{A}_x\left({T}_i-{T}_x\right) \end{equation}$$(27) where |${\alpha}_{tot}$| is the total heat transfer coefficient $$\begin{equation} {\alpha}_{tot}=5.0{\rho}_s^{0.391}{T}_i^{0.408} \end{equation}$$(28) Substituting equations 21, 23, 25 and 26 into equation 18 give $$\begin{align} \frac{d{T}_i}{dt}{m}_{s,i}{c}_{p,s}&=\sum{c}_{p,s}{\dot{m}}_{s, in,i}\left({T}_{s, in}-{T}_{NTP}\right)\nonumber\\&-\sum{c}_{p,s}{\dot{m}}_{s, in,i}\left({T}_i-{T}_{NTP}\right)+\sum{\dot{m}}_{g, in,i}{h}_{g, in}\nonumber\\&-\sum{\dot{m}}_{g, out,i}{h}_{\mathrm{g},i}-{m}_{g,i}\sum \frac{d{w}_i}{dt}{h}_{j,i}\nonumber\\&+{D}_s{c}_{p,s}{A}_b{\rho}_{ave}^{-}\frac{d{T}_i^{-}}{dz}+{D}_s{c}_{p,s}{A}_t{\rho}_{ave}^{+}\frac{d{T}_i^{+}}{dz}\nonumber\\&+5.0{\rho}_s^{0.391}{T}_i^{0.408}{A}_x\left({T}_i-{T}_x\right) + \sum{r}_{c,i}{Q}_i \end{align}$$(29) Each reactor was divided into one-dimensional control volumes. Time-dependent mass and energy balances were solved numerically using appropriate ODE tools in MATLAB. Figure 2, below, shows the calculation procedure for the reactor model. Figure 2 Open in new tabDownload slide Calculation procedure for reactor model. Figure 2 Open in new tabDownload slide Calculation procedure for reactor model. The output variables (mass fraction of exit gases, mass of exiting solids and energy adsorbed or released by the system) were extracted from the MATLAB solution of the time-dependent mass and energy balances. These values were then transferred to an excel spreadsheet for plotting and analysing. Mass flow rate of sorbent, carbon dioxide partial pressure at the calcium oxide-calcium carbonate interface, temperature of incoming solid flows and concentration of carbon dioxide and sulphur dioxide in the flue gas stream were varied based on literature data, using values above and below those stipulated by different researchers. While one variable was being varied, all the other variables were being kept constant. The following assumptions were made: Instant and complete mixing of solids in both reactors Plug-flow of the gas phase in the carbonator Calcination goes to completion instantaneously in the calciner The input conditions for the laboratory simulation are shown in Table 1 below. Table 1 Laboratory simulation input variables. Variable . Value . Flue gas mass flow (kg/s) 0.403 Flue gas temperature (°C) 25 CO2 in flue gas (w-%) 14.4–43.2 O2 in flue gas (w-%) 5.00 N2 in flue gas (w-%) 51.76–80.56 SO2 in flue gas (w-%) 0.04–0.08 Solid mass in reactor (kg) 1.83 Variable . Value . Flue gas mass flow (kg/s) 0.403 Flue gas temperature (°C) 25 CO2 in flue gas (w-%) 14.4–43.2 O2 in flue gas (w-%) 5.00 N2 in flue gas (w-%) 51.76–80.56 SO2 in flue gas (w-%) 0.04–0.08 Solid mass in reactor (kg) 1.83 Open in new tab Table 1 Laboratory simulation input variables. Variable . Value . Flue gas mass flow (kg/s) 0.403 Flue gas temperature (°C) 25 CO2 in flue gas (w-%) 14.4–43.2 O2 in flue gas (w-%) 5.00 N2 in flue gas (w-%) 51.76–80.56 SO2 in flue gas (w-%) 0.04–0.08 Solid mass in reactor (kg) 1.83 Variable . Value . Flue gas mass flow (kg/s) 0.403 Flue gas temperature (°C) 25 CO2 in flue gas (w-%) 14.4–43.2 O2 in flue gas (w-%) 5.00 N2 in flue gas (w-%) 51.76–80.56 SO2 in flue gas (w-%) 0.04–0.08 Solid mass in reactor (kg) 1.83 Open in new tab Table 2, below, shows the input parameters for the different simulations done. Table 2 Input variables for the different simulations done. Simulation number . Sorbent flowrate (kg/s) . Input sorbent temperature (°C) (carbonator) . Input solid temperature (°C) (calciner) . Carbon dioxide concentration in flue gas (mol/m3) . Carbon dioxide partial pressure (kPa) . Flue gas composition (w-%) . . . . . . . SO2 . CO2 . O2 . 1 100.000 610–690 900–990 1.320–3.961 2.026–9.119 0.04–0.08 10.0–30.0 5.0 2 1.743 610–690 900–990 1.320–3.961 2.026–9.119 0.04–0.08 10.0–30.0 5.0 3 1.743 500–590 900–990 1.320–3.961 2.026–9.119 0.04–0.08 10.0–30.0 5.0 4 0.116 610–690 900–990 1.320–3.961 2.026–9.119 0.04–0.08 10.0–30.0 5.0 5 0.011 610–690 900–990 1.320–3.961 2.026–9.119 0.04–0.08 10.0–30.0 5.0 6 1.743 610–690 900–990 1.320–3.961 2.026–9.119 0 10.0–30.0 5.0 Simulation number . Sorbent flowrate (kg/s) . Input sorbent temperature (°C) (carbonator) . Input solid temperature (°C) (calciner) . Carbon dioxide concentration in flue gas (mol/m3) . Carbon dioxide partial pressure (kPa) . Flue gas composition (w-%) . . . . . . . SO2 . CO2 . O2 . 1 100.000 610–690 900–990 1.320–3.961 2.026–9.119 0.04–0.08 10.0–30.0 5.0 2 1.743 610–690 900–990 1.320–3.961 2.026–9.119 0.04–0.08 10.0–30.0 5.0 3 1.743 500–590 900–990 1.320–3.961 2.026–9.119 0.04–0.08 10.0–30.0 5.0 4 0.116 610–690 900–990 1.320–3.961 2.026–9.119 0.04–0.08 10.0–30.0 5.0 5 0.011 610–690 900–990 1.320–3.961 2.026–9.119 0.04–0.08 10.0–30.0 5.0 6 1.743 610–690 900–990 1.320–3.961 2.026–9.119 0 10.0–30.0 5.0 Open in new tab Table 2 Input variables for the different simulations done. Simulation number . Sorbent flowrate (kg/s) . Input sorbent temperature (°C) (carbonator) . Input solid temperature (°C) (calciner) . Carbon dioxide concentration in flue gas (mol/m3) . Carbon dioxide partial pressure (kPa) . Flue gas composition (w-%) . . . . . . . SO2 . CO2 . O2 . 1 100.000 610–690 900–990 1.320–3.961 2.026–9.119 0.04–0.08 10.0–30.0 5.0 2 1.743 610–690 900–990 1.320–3.961 2.026–9.119 0.04–0.08 10.0–30.0 5.0 3 1.743 500–590 900–990 1.320–3.961 2.026–9.119 0.04–0.08 10.0–30.0 5.0 4 0.116 610–690 900–990 1.320–3.961 2.026–9.119 0.04–0.08 10.0–30.0 5.0 5 0.011 610–690 900–990 1.320–3.961 2.026–9.119 0.04–0.08 10.0–30.0 5.0 6 1.743 610–690 900–990 1.320–3.961 2.026–9.119 0 10.0–30.0 5.0 Simulation number . Sorbent flowrate (kg/s) . Input sorbent temperature (°C) (carbonator) . Input solid temperature (°C) (calciner) . Carbon dioxide concentration in flue gas (mol/m3) . Carbon dioxide partial pressure (kPa) . Flue gas composition (w-%) . . . . . . . SO2 . CO2 . O2 . 1 100.000 610–690 900–990 1.320–3.961 2.026–9.119 0.04–0.08 10.0–30.0 5.0 2 1.743 610–690 900–990 1.320–3.961 2.026–9.119 0.04–0.08 10.0–30.0 5.0 3 1.743 500–590 900–990 1.320–3.961 2.026–9.119 0.04–0.08 10.0–30.0 5.0 4 0.116 610–690 900–990 1.320–3.961 2.026–9.119 0.04–0.08 10.0–30.0 5.0 5 0.011 610–690 900–990 1.320–3.961 2.026–9.119 0.04–0.08 10.0–30.0 5.0 6 1.743 610–690 900–990 1.320–3.961 2.026–9.119 0 10.0–30.0 5.0 Open in new tab 4. RESULTS AND DISCUSSION 4.1. Effect of temperature Figure 3a shows the effect of temperature on carbonation, between 600 and 700°C. As the temperature increases, the mass of carbonate formed or rate of carbonation decreases. Figure 3b shows the mass of solid formed at different temperatures, from a lower temperature of 500°C. For temperatures below 600°C, the decrease in amount of carbonate formed (carbonation) is less than it is after 600°C. The optimal temperature for carbonation would be approximately 600°C for it is high enough to drive the carbonation reaction and not too high to accelerate the sulphation reaction. Figure 3c shows the mass of solid formed at different temperatures from 600 to 900°C. Carbonation decreases as temperature increases and carbonation falls to zero after 790°C. Carbonation and sulphation reactions can limit the carbonator temperature to a maximum of 700°C, above which sulphation rate increases and the calcium carbonate decomposes releasing carbon dioxide. Figure 3 Open in new tabDownload slide Mass of solid formed versus temperature at constant flue gas composition for first carbonation–calcination cycle: (a) for temperatures above 500°C, (b) from 500°C and (c) for temperatures up to 900°C. Figure 3 Open in new tabDownload slide Mass of solid formed versus temperature at constant flue gas composition for first carbonation–calcination cycle: (a) for temperatures above 500°C, (b) from 500°C and (c) for temperatures up to 900°C. Figure 4 shows the changes exit mass fractions of carbon dioxide, oxygen and sulphur dioxide with increase in carbonation temperature. In the exit stream, mass fractions of carbon dioxide increase and mass fraction of sulphur dioxide (defined as the mass of gas element in the exit stream divided by the total amount of gas in the exit stream) decrease as temperature increase. According to Le Chatelier, if a constraint (such as a change in pressure, temperature or concentration of a reactant) is applied on a system in equilibrium, the equilibrium will move so as to tend to counter the effect of the constraint [25]. Carbonation is an exothermic reaction therefore increasing the temperature will favour the reverse reaction thus lowering the rate of carbonation. According to Lu et al. [26], there is an increase in carbonation as temperature decreases but temperatures below 500°C are too low to drive the carbonation reaction. Figure 4 Open in new tabDownload slide Exit gases mass fraction versus temperature at constant flue gas composition for first carbonation–calcination cycle. Figure 4 Open in new tabDownload slide Exit gases mass fraction versus temperature at constant flue gas composition for first carbonation–calcination cycle. The rate of sulphation increases as temperature increases. Unfortunately, increase in temperature accelerates sulphation because of the higher activation energy needed for the sulphation reaction [27]. With low amounts of sulphur dioxide in the flue gas, sulphation goes to completion and no sulphur dioxide will be found in the exit stream. Figure 5a shows the change in mass fraction of carbon dioxide in the calciner exit stream as temperature increases while Figure 5b shows the variation in carbon dioxide mass fraction in the calciner exit gas as a function of temperature and sorbent to carbon dioxide flow ratio in the carbonator. It can be seen that as sorbent to carbon dioxide flow ratio increases, carbon dioxide mass fraction in the calciner exit stream increases. An increase in the sorbent to carbon dioxide ratio in the carbonator means more active calcium oxide for carbon dioxide absorption, hence more bound carbon dioxide being carried over to the calciner. Figure 5 Open in new tabDownload slide Carbon dioxide mass fraction in the exit gas versus temperature: (a) at constant carbon dioxide partial pressure (9119.25 Pa) and (b) as a function of temperature and sorbent to carbon dioxide flow ratio to the carbonator. Figure 5 Open in new tabDownload slide Carbon dioxide mass fraction in the exit gas versus temperature: (a) at constant carbon dioxide partial pressure (9119.25 Pa) and (b) as a function of temperature and sorbent to carbon dioxide flow ratio to the carbonator. Figure 6 shows that as temperature increases, carbon dioxide mass fraction in the calciner also increases. This shows that calcination rate will be also increasing thus more carbon dioxide being formed. Calcination is an endothermic reaction, therefore increasing the temperature will favour the forward reaction, which if is formation of products (carbon dioxide and calcium oxide). Figure 6 Open in new tabDownload slide Bed mass versus number of carbonation–calcination cycles at constant temperature (610oC) and flue gas composition: (a) for up to 500 cycles and (b) for up to 100 cycle. Figure 6 Open in new tabDownload slide Bed mass versus number of carbonation–calcination cycles at constant temperature (610oC) and flue gas composition: (a) for up to 500 cycles and (b) for up to 100 cycle. Figure 7 Open in new tabDownload slide Mass of carbonate formed versus carbon dioxide concentration in flue gas at constant temperature (6000C). Figure 7 Open in new tabDownload slide Mass of carbonate formed versus carbon dioxide concentration in flue gas at constant temperature (6000C). It can be seen from Figure 5b that as amount of sorbent increases, the calciner exit stream will be containing more carbon dioxide. This is because more carbon dioxide would have been absorbed by the sorbent. It is therefore recommended to use high sorbent to carbon dioxide flow rates (above 10 000) so that a more concentrated stream of carbon dioxide will be produced and collected for storage. 4.2. Bed mass versus number of carbonation–calcination cycles From Figure 6a, the amount of active calcium oxide decreases as number of carbonation–calcination cycles increase. Figure 6b shows the changes in bed mass composition versus carbonation–calcination cycles, up to 100 cycles. There is a sharp decrease in active calcium oxide in the first 10 cycles and after about 100 cycles, the active calcium particles remain constant. This is caused by the decay in activity of calcium oxide as the number of carbonation–calcination cycles increases [28]. The amount of calcium oxide not reacted (inactive) increases as number of carbonation–calcination cycles increases because of the decay in activity of calcium oxide with an increase in number of carbonation–calcination cycles. Calcium carbonate recycled into the system also decreases with increasing number of carbonation–calcination cycles. The optimum number of carbonation–calcination cycles from Figure 6a and b is less than 20 after which the most part (more than 75%) of the sorbent will be inactive. 4.3. Effect of changing carbon dioxide concentration in the flue gas Rate of carbonation, which is directly proportional to rate of formation of calcium carbonate, increases as carbon dioxide concentration in the feed stream increase. The increase in rate of carbonation is due to an increase in reactant available for reaction. There is a linear correlation between carbonation and amount of carbon dioxide in flue gas because the rate of carbonation is directly proportional to carbon dioxide concentration in the flue gas as proposed by Ylätalo et al. [19] in the equation 2. 4.4. Change in sorbent to carbon dioxide flow ratio Increase in sorbent to carbon dioxide flow rate ratios leads to higher reaction rate in the carbonator. The sulphation reaction also increases as shown by the decrease in mass fraction of sulphur dioxide leaving the reactor as sorbent to carbon dioxide flow ratios increase. As the amount of sorbent increases, there will more sorbent available for reaction with the carbon dioxide as well as the sulphur dioxide hence an increase in rate of reaction. Figure 8b shows that sulphur dioxide is depleted instantly as sorbent to carbon dioxide flow rate ratios increase. This is because sulphur dioxide will be present in very small quantities in the feed gas and hence will be totally absorbed by the sorbent. As sorbent to carbon dioxide flow rate ratio decreases to below 1, sulphur dioxide depletion becomes slow and only goes up at elevated temperature (above 640°C) because of the higher activation energy needed for the sulphation reaction. Figure 8 Open in new tabDownload slide Variation of mass fraction in the carbonator exit gas as a function of temperature and sorbent to carbon dioxide flow ratio (Fr/Fco2): (a) carbon dioxide, (b) sulphur dioxide and (c) oxygen. Figure 8 Open in new tabDownload slide Variation of mass fraction in the carbonator exit gas as a function of temperature and sorbent to carbon dioxide flow ratio (Fr/Fco2): (a) carbon dioxide, (b) sulphur dioxide and (c) oxygen. A higher sorbent to carbon dioxide flow rate ratio (Figure 8a) allows for higher absorption of carbon dioxide and sorbent to carbon dioxide ratios above 20 are optimal. It can clearly be seen that at this ratio, the mass fraction of the gas in the exit goes down rapidly. Lower sorbent to carbon dioxide flow rates (<20) result in high carbon dioxide mass fractions in the exit gas stream. The challenge of higher sorbent to carbon dioxide flow rate ratios is that they also allow for higher adsorption of sulphur dioxide. 4.5. Effect of change in carbon dioxide partial pressure Figure 9 shows the change in carbon dioxide mass fraction with partial pressure at constant temperature. As carbon dioxide partial pressure (at the calcium oxide–calcium carbonate interface) increases in the calciner, the rate of calcination, which is directly proportional to increase in carbon dioxide mass fraction in the exit gas stream, decreases. More calcium carbonate is recycled to carbonator without conversion to calcium oxide. Maybe sorption effects at the calcium oxide/calcium carbonate/carbon dioxide interface are the reason for the decay [29]. Figure 9 Open in new tabDownload slide Carbon dioxide mass fraction versus partial pressure at constant temperature (900°C). Figure 9 Open in new tabDownload slide Carbon dioxide mass fraction versus partial pressure at constant temperature (900°C). 4.6. No sulphation Simulations were also performed for the case in which the effect of sulphation was ignored. Figures 10 and 11 show a comparison of carbonation reaction taking place in the presence as well as in the absence of sulphur dioxide. When carbonation takes place in the absence of sulphur dioxide, more calcium oxide will be in the bed and available for reaction with carbon dioxide. When sulphur dioxide is taken into account, more active calcium oxide is consumed by both reactions (carbonation and sulphation) but when sulphation is ignored, one reaction, carbonation, consumes the active calcium oxide thus a bigger amount of calcium oxide will be in the bed. Figure 10 Open in new tabDownload slide Active calcium oxide in carbonator versus temperature at constant flue gas composition and sorbent flow rate. Figure 10 Open in new tabDownload slide Active calcium oxide in carbonator versus temperature at constant flue gas composition and sorbent flow rate. Figure 11 Open in new tabDownload slide Active calcium oxide versus number of carbonation–calcination cycles at constant temperature (610 °C) and flue gas composition. Figure 11 Open in new tabDownload slide Active calcium oxide versus number of carbonation–calcination cycles at constant temperature (610 °C) and flue gas composition. Neglecting sulphation when designing calcium-looping reactors will therefore lead to over estimation of active calcium oxide in the carbonator and therefore lower amount of carbon dioxide absorbed than expected. In Figure 11, there is a sharp decrease in active calcium oxide in the first 10 cycles and after about 100 cycles, the active calcium particles remain constant. This is caused by the decay in activity of calcium oxide as the number of carbonation–calcination cycles increases [28]. Figure 6b also shows the same effect. There is no appreciable difference in the curves because sulphur dioxide concentration in the flue gas is very low compared to that of carbon dioxide making the amount of active calcium oxide used in the sulphation reaction small. 4.7. Energy balances Figure 12 shows the relationship between amount of energy released during carbonation and number of carbonation–calcination cycles. As number of carbonation–calcination cycles increases, the amount of energy released decreases. This is because as the carbonation–calcination cycles increase the rate of carbonation decreases. Figure 12 Open in new tabDownload slide Energy released in carbonator versus number of carbonation–calcination cycles. Figure 12 Open in new tabDownload slide Energy released in carbonator versus number of carbonation–calcination cycles. As the number of carbonation–calcination cycles increases, the amount of energy absorbed in the calciner decreases (Figure 13). The same reason as in carbonator applies; the rate of calcination also decreases with increase in number of carbonation calcination cycles. The decreases in reaction rates are caused by deactivation of the sorbent (calcium oxide) as number of carbonation–calcination cycles increase. Figure 13 Open in new tabDownload slide Energy absorbed in the calciner versus number of carbonation–calcination cycle. Figure 13 Open in new tabDownload slide Energy absorbed in the calciner versus number of carbonation–calcination cycle. 5. CONCLUSION It has been observed from the analysis of the simulation data that carbonation, sulphation as well as calcination reactions are significantly temperature dependent. As temperature increases, the rate of carbonation decreases while the rate of sulphation increases. Carbonation is an exothermic reaction and increasing the temperature of the system will favour the reverse reaction thus lowering the rate of carbonation. It is therefore necessary to have a low temperature that allows little sulphation, as sulphation reduces the amount of active calcium carbonate for carbonation, and at the same time the temperature should not be too low to suppress the carbonation reaction. Temperatures below 500°C are too low to drive the carbonation reaction [26]. For temperatures below 600°C, the decrease in amount of carbonate formed (carbonation) is less than it is after 600°C. The optimal temperature for carbonation would be approximately 600°C for it is high enough to drive the carbonation reaction and not too high to accelerate the sulphation reaction. Rate of carbonation increases as carbon dioxide concentration in flue gas increases. This is because carbonation is directly proportional to amount of carbon dioxide in the flue gas stream. Increase in the sorbent to carbon dioxide flow ratio leads to an increase in both carbonation and sulphation, as more reactant will be available for reaction with the flue gas stream. High sorbent to carbon dioxide flow ratios also lead to a more concentrated stream of carbon dioxide being removed from the calciner as more carbon dioxide would have been absorbed in the carbonator. A temperature increase in the calciner leads to an increase in rate of calcination. If temperatures become too high (above 900°C for calcium oxide), sintering occurs at an elevated pace [23]. This means that although the rate of calcination increases with an increase in temperature, temperatures above 900°C should be avoided. Increase in carbon dioxide partial pressure in the calciner causes a decrease in calcination reaction. A low carbon dioxide partial pressure is recommended for an increase in calcination. The amount of active calcium oxide particles decreases as the number of carbonation–calcination cycles increase. There is a sharp decrease in the first 10 cycles and after about 100 cycles; the active calcium particles remain constant. It is recommended that the number of carbonation–calcination not exceed 20 after which most (more than 75%) of the sorbent will be inactive. Neglecting the effect of sulphation in the design of the coupled fluidized bed system leads to overestimation of the active fraction of calcium oxide particles that will react with carbon dioxide in the flue gas. Lower amount of carbon dioxide will be absorbed than estimated. Energy adsorbed and released by calcination and carbonation respectively decreases as the number of carbonation–calcination cycles increases due to the decrease in carbonation and calcination reactions as the number of cycles increases. Symbols used Greek symbols |$\rho$| [kg m−3] density α heat transfer coefficient Other symbols |$A$| [m2] cross sectional area C concentration |$c$| heat capacity |$D$| [m2.s] dispersion coefficient |$E$| [J] energy |$e$| [m] thickness of calcium carbonate on the pore wall h enthalpy |${k}_{carb}$| [m4(mol. s)−1] kinetic constant for carbonation |${k}_{calc}$| [mol.m−2.s−1.atm−1] kinetic constant for carbonation |$m$| [kg] mass |$\dot{m}$| [kg/s] mass flow rate |$p$| [Pa] partial pressure |$PM$| [kg] molecular weight |$Q$| [J] reaction enthalpy |${q}_{disp}$| [J/s] energy associated with dispersion between elements |${q}_{chem}$| [J/s] energy associated with chemical reaction |${q}_{ht}$| [J/s] heat transfer |$r$| [kg. s−1] rate |$s$| [m2] surface area |$t$| [s] time |$T$| [oC] temperature |${T}_{NTP}$| [oC] reference temperature of the system |$u$| specific internal enthalpy |$W$| [−] active fraction of calcium particles |$X$| [−] conversion Sub- and superscripts s solid g gas |$i,j$| control volume |$in$| into control volume/element |$out$| out of control volume/element calc calcination carb carbonation References [1] IPCC . 2013 . 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TI - Modelling of a calcium-looping fluidized bed reactor system for carbon dioxide removal from flue gas
JO - International Journal of Low-Carbon Technologies
DO - 10.1093/ijlct/ctaa102
DA - 2021-01-15
UR - https://www.deepdyve.com/lp/oxford-university-press/modelling-of-a-calcium-looping-fluidized-bed-reactor-system-for-carbon-08myV5he1S
SP - 1
EP - 1
VL - Advance Article
IS - 
DP - DeepDyve
ER -