Simulation of cement clinker process by of microwave heating

Jose Pedro Machado Mendesjose.p.machado.mendes@tecnico.ulisboa.pt

Instituto Superior Tecnico, Universidade de Lisboa, Portugal

June 2017

Abstract

Conventional cement clinker production is a very energy demanding process, that requires up to 3600kJ for a single kilogram of cement clinker. Moreover, since it is one of the most used materials in theworld, its production accounts for up to 6% of the total CO2 emitted by the human activity. Microwaveheating technology has been gaining interest as an alternative for its advantages. It is a clean energywith no direct CO2 emissions, and, unlike conventional heating, microwave heating happens when theelectric field interacts with the material, resulting in a volumetric heating inside the material, returninghigher efficiencies than the conventional counterpart.

This Thesis addresses the subject of microwave heating in the production of cement clinker,specifically in the limestone calcination. The initial goal is to validate capabilities of COMSOL inhandling all the physical phenomena involved. This software has been proven to be a suitable toolto predict chemical processes and the behavior of a microwave induced plasma. Afterwards, a newmethod is proposed and a code developed that can autonomously simulate a limestone processing unitwith overall high efficiency, using microwave energy. The code is capable of making the necessaryadjustments to the input power and resonant state of the microwave system, and was able to achievetotal conversion of limestone, while maintaining high efficiency and avoiding temperature relatedproblems. As such, the presented methodology shows a significant improvement over other availablenumerical models in the literature for microwave heating.Keywords: Microwave heating numerical model, Automatic impedance matching, Input poweroptimization, Cement clinker production, Continuous microwave limestone processing, Autonomoussimulation control

1. IntroductionMicrowave technology for processing materials hasbeen growing, founding use in a wide rangeof applications. Opposing conventional heating,microwave-based applications offer a capability ofgenerating heating in a way that avoids come con-straints related to the first heating technology [1].Whereas in conventional heating, the material isgradually warmed from the outside inwards throughconvection or radiation, in microwave heating, heatis only produced where and when the energy isabsorbed. As microwave can penetrate materialswith ease (except metals), the full volume of thematerial can uniformly absorb its energy leadingto a volumetric heating [2]. This effect translatesinto higher heating rates, increased efficiency andshorter processing times [3]. The application rangeof microwave heating is vast suitable to a wide arrayof heating processes.

Cement is complex mixture of calcareous-, silica-, and alumina-based minerals. It is made trough aprocess consisting on grinding and mixing the feed-stock and then heating it to temperatures around

1450◦C giving origin to a granular clinker. Thismixture forms a well known man-made construc-tion material used widely around the world, beingthe second most used material in the world, onlysurpassed by water [4]. The main issues regardingthe cement industry are the energy required andthe CO2 emissions resultant from its processes. Asingle kilogram of Portland cement requires a theo-retical energy value between 1674 and 1799 kJ, how-ever in the reality of a conventional cement produc-tion, it arises to values around 3100 to 3600 kJ. Onthe other hand, to the CO2 produced by the flame,add the CO2 emitted during the cement formation,namely during the calcination process, where lime-stone (CaCO3) turns into lime (CaO) and CO2.Consider finally the huge amount of cement pro-duced worldwide, and then, taking everything intoaccount, results in a cement industry responsiblefor 5 − 6% of the carbon dioxide greenhouse gasesgenerated by human activities [5].

Since the early 70’s [6] several numerical stud-ies have been conducted regarding the conventionalway of producing cement. In [6] a 1-D differen-

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tial model of a rotary kiln with simplified chemicalprocess is proposed composing on only five equa-tions for the cement clinker formation. Meanwhileother efforts focused on developing better mod-els for the limestone calcination [7], a key step inclinker formation. Incorporating those efforts, in-creasingly complex computational models were de-veloped, from a 1-D [8] to 3-D CFD fully coupledmodels [9] of conventional rotary cement kilns, val-idated with experimental data. Studies were alsocarried aiming at optimizing energy consumptionof those apparatus [10].

As it is impossible to change the cement chem-istry, it might more feasible to tackle the heatsource. Hence, and although scarce, published ex-perimental works are available concerning cementclinker formation using microwave energy. [11] and[12] were able to form clinker mixes through mi-crowaves obtaining similar composition as their con-ventional counterpart. Microwave heating technol-ogy is a clean heating process that do not produceany secondary waste and thus, reduces CO2 emis-sions. Moreover, this heating method is particularlyeffective when a dielectric material is being heated.Cement clinker components happen to exhibit ex-cellent dielectric properties, therefore, they are ableto absorb microwave energy with high efficiencies[3], resulting in a more efficient heating process.

Despite the clear advantages of using microwaveradiation over conventional heating in thermal pro-cesses, some issues may appear due to the use of thisheating technology. Some of the materials have theparticularity to have an imaginary part of the per-mittivity that increases with temperature, cementis a good example of such a material [13]. Thiscreates a sort of loop mechanism where the tem-perature cause the increase of this characteristic,which in its turn, ables the material to absorb moreenergy, increasing the temperature. This can leadto high thermal gradients within the material asin certain areas temperature will increase abruptly.The phenomena depicted is known as thermal run-away [14] and it can be catastrophic for a material’sstructure when it occurs, thus presenting a majorchallenge to the development of microwave heating[13].

When working with cement, other problem mayarise. Due to the CO2 emission during the calcina-tion process, a plasma can be formed when the gasis bombarded with microwave radiation [11]. Theformation of the plasma may, due to its dielectricproperties, divert the energy from the targeted ce-ment leading to low efficiencies. It also poses athreat to the process apparatus as the concentratedenergy can propagate and damage it. Regardingthe literature, extensive experimental and numeri-cal work has been done on CO2 induced plasma due

to it being greenhouse gas [15], but none addressit trough a simple multidimensional computationalmodel. So far, published work resorted to Argonas a gas for developing multidimensional numeri-cal models, as this gas possesses a much simplerchemical model. Models have been created usingnumerical softwares, like COMSOL with promisingresults [16].

From an operational standpoint, the use of mi-crowave heating technology pose some obstacles in-herent to the physical phenomena. The electric fielddistribution in a microwave cavity is very sensitiveto the to the changes happening to the dielectricand thermal field of a material. Moreover, the ge-ometry of the cavity itself will impact the heatingcapacity of the whole system [17]. On top of that,many industrial used materials only have an highloss factor for high temperatures (e.g. cement).With the just presented particular characteristicsof microwave heating, it is easy to see how appeal-ing the use of numerical tools starts to be. Nu-merical simulations present themselves as powerfultools to predict the electromagnetic field distribu-tion and anticipate the heating behavior of a samplematerial [17]. Mathematical models were developedto investigate the effect of dielectric properties ofsome liquids in the heating process [18]. In [17]COMSOL was used to simulate heating of biomasssamples using a sort of microwave oven. The de-veloped model showed to be capable of reproducingexperimental studies and enable the evaluation ofthe biomass sample size that optimized the elec-tromagnetic absorption. In another work, a COM-SOL model was developed to process glass meltingit with microwave radiation [19]. It used a MAT-LAB code to control the 3D transient simulation,adjusting power input and plunger position, in or-der to maximize the glass power absorption whileusing as little power as possible. The conductedstudy was a proven success, giving an insight intothe impact of power and cavity geometry in the ef-ficiency of the whole microwave heating system.

The objective of the present work is to addressthe process of cement clinker using microwave en-ergy as a heating source. Initially, COMSOL willbe used to model the chemical process of the clinkerformation, benchmarking the obtained results withthe available data. Then, the processing of lime-stone in a microwave heating model will be ad-dressed. The purpose of this task is to develop acomputational method capable of maximizing mi-crowave absorption efficiency and power usage. Themain objective is to understand the heating behav-ior of the system and evaluate it form an energystandpoint.

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2. Background2.1. Maxwell’s equationMaxwell’s equations depict the interactions betweenthe electric and magnetic field at a microscopicallevel and consists on four equations presented be-low. The Faraday’s law, Ampere’s law and the elec-tric and magnetic Gauss’ law.

∇× ~E = −∂~B

∂t(1)

∇× ~H =∂ ~D

∂t+ ~J (2)

∇ · ~D = ρ (3)

∇ · ~B = 0 (4)

Where:~E is the electric field, (V/m);~B is the magnetic flux density,(Wb/m2);~H is the magnetic field, (A/m);~D is the electric flux density, (Coul/m2);~J is the electric current density, (A/m2);ρ is the electric charge density, (Coul/m3);t is time, in seconds (s).

Through some algebraic manipulation it is possi-ble to deduce another relation from Maxwell’s equa-tions. Knowing that ∇ · (∇× ~H) = 0 one can sub-stitute equation 2 into it. Combine it then withequation 3 the continuity equation of energy can bederived:

∇ · J +∂ρ

∂t= 0 (5)

Relations can be established between the vec-tor entities seen in the above Maxwell’s equations.These equations are called constitutive equations(equations 6 to 8) and depict the macroscopic prop-erties of the material medium where the electromag-netic field exists.

~D = ε ~E (6)

~B = µ ~H (7)

~J = σ ~E (8)

When the fields are harmonic time dependent, itis very convenient to work with them in a phasornotation. Assuming all field quantities to be com-plex vectors. It is possible to rewrite the Maxwell’sequations as follows [20].

∇× ~E = −jω ~B (9)

∇× ~H = ~J + jω ~D (10)

∇ · ~D = ρ (11)

∇ · ~B = 0 (12)

where ω is the angular frequency (rad/s), f the fre-quency (Hz) and j the imaginary number.

2.2. Complex PermittivityThe microscopic behavior of a material subjected toan external field is generally dependent on the field’sfrequency. This response gives arise to a phase shiftdifference the polarization (~P , in (C/m2)) and the

electric field ( ~E). This behavior can be analyticallyrepresented by means of a complex permittivity, ε,as follows:

ε = ε′ − jε′′ = ε0(ε′r − jε′′r ) (13)

Where ε0 = 8.85 × 10−12 (F/m) is the free spacepermittivity. There are two ways for the electricfield to interact with the permittivity. Either stor-ing energy or dissipating energy in the material [21].The real part of the permittivity (ε′r), the dielectricconstant, is responsible for phase shift of the electricfield and storing its energy. While the capability ofthe material to dissipate energy, one of the mostimportant properties for microwave heating, is rep-resented by the imaginary part of the same equation(ε′′r ) which is called the loss factor and is responsiblefor the electric energy losses that are transformedinto heat.

2.3. Heat Transport EquationThe following equation describes the heat transferphenomenon. Its solution will give the temperaturefield.

ρcp∂T

∂t+ ρcp~u · ∇T = ∇ · κ∇T +Q (14)

where ρ is the density (kg/m3), cp is the specificheat capacity (J/(kg ·K)), u is the velocity vector(m/s), κ is the thermal conductivity (W/(m ·K)),T is the temperature (K) and Q (W/m3) is theheat generation term (W/m3). In microwave heat-ing alone this last term Q represents coupling ofMaxwell’s equations with the heat equation and isthe sum of the power dissipated by joule effect andthe dissipation of the electromagnetic power andcan be represented by the following equations re-spectively:

Qj = σ|E|2 (15)

Qdiss = ε0ε′′rω|E|2 (16)

In the case of this Thesis, as chemical processes areincluded, their heat sources have to be added aswell, and is presented below:

Qreact = ∆H Rreact (17)

In equation (17), ∆H is the enthalpy change for agiven reaction and Rreact is the reaction rate for agiven reaction.

2.4. CouplingIt is possible to obtain a equation that is able tocompute the electromagnetic field using harmonic

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sources. This equations results form manipulationof the Maxwell’s equations and is known as theHelmholtz equation [16].

∇× (µ−1r ∇× ~E)− k20(εr −

j~σ

ωε0

)~E = 0 (18)

The electromagnetic field is obtained through theHelmholtz equation, and so, the heat source pro-vided by microwave dissipated power can be cal-culated and the heat equation solved. The tem-perature field can then be computed as well as alltemperature dependent properties, which will affectthe electromagnetic field.

As temperature change, the complex permittiv-ity, ε′′ may increase abruptly and will enhance themicrowave energy absorption on hotter areas, lead-ing to very rapid heating which can result in theoccurrence of an unwanted phenomenon known asthermal runaway [14]

The thermal field will trigger the chemical mech-anisms, in its turn, a heat source will be generatedthat will affect the thermal field. Thus the couplebetween all physics is complete.

2.5. Mass transport EquationThe mass transport equation for an individualspecies, part of a mixture with i species, can beformulated in the following way assuming no diffu-sion:

ρ∂

∂t(ωi) + ρ(~u · ∇)ωi = ~Ri (19)

where, ρ stands for the density of the mixture(Kg/m3), ωi represents the mass fraction of speciesi (non dimensional), ~u is the average velocity (m/s)

and finally, the last term, ~Ri is the rate expres-sion and depicts the production or consumption ofa species i. With this relation i − 1 of the speciesare independent and possible to solve. The massfraction of the remaining species can be computedknowing that the sum of all mass fractions must beone.

For many chemical reactions, the rate expressioncan be expressed as the product between a temper-ature dependent term and a composition dependentterm [22]. For the majority of reactions, the reac-tion rate constant is well represented by the Arrhe-nius’ equation:

k = k0e−Ea/RT (20)

Where k0 is the frequency factor (or pre-exponentialfactor), Ea is the a activation energy (J/mole), Ris the universal gas constant (J/(K ·mol)) and T isthe temperature (K).

3. Verification and ValidationIn this section, a verification and validation proce-dure is done to the cement clinker chemical model

using the numerical software COMSOL. The studyconducted by [8] is chosen as benchmark, as it de-scribes a very consistent kinetics model among thestudies found in the literature.

The chemical model and kinetics used are pre-sented in table 1 [8].

3.1. Numerical model

The approach to the problem consisted on buildinga three dimensional model (figure 1) of the first in-dustrial kiln presented in [8]. In order to simplifythe problem, and keep it in the scope of this The-sis, the temperature profile obtained in the bench-marked study was assumed as an input of the chem-ical interface. Hence this will be the only physicinvolved, leaving the other aside.

Figure 1: Graphical representation of the rotarykiln.

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The solids inlet flow and the mixture density,38.88Kg/s and 1200Kg/m3 respectively. The in-let mass fractions and the respective molar mass ofthe participant species are presented in table (2).The molar mass will be used to compute the reac-tion rates. The inlet mass fraction for each specieswill be set as a boundary condition at the entranceof the bed. Furthermore, those mass fraction wereassumed as an initial condition in the bed domain.An outflow condition was set to the opposite end ofthe kiln

The transport equation (19) was used to describethe movement of the chemical species along the kiln.The Arrhenius law was used to calculate the reac-tion rates, and those were computed for each chem-ical species. Finally, a steady state study was con-ducted in COMSOL to compute the necessary re-sults.

3.2. Verification and Validation

The table 3 presents a comparison between thenumerical data obtained from [8], the experimen-tal data presented in the same study and the re-sults obtained from the numerical studied carriedin COMSOL. Regarding the data itself, it showsthe mass fraction of product species, namely: CaO,C2S, C3S, C3A, C4AF. The obtained numericaldata shows to be reasonably close to the ones [8]except for the two last species which fall apart, how-ever their mass fraction is rather small across all thestudies when compared to the others, and so, little

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Reaction k0 Ea (KJ/mol) ∆H (KJ/mol)1. CaCO3 → CaO + CO2 4.07× 106(s−1) 185 179.42. 2CaO + SiO2 → C2S 1.0× 107(m3 kg−1 s−1) 240 −127.63. C2S + CaO → C3S 1.0× 109(m3 kg−1 s−1) 420 16.04. 3CaO +Al2O3 → C3A 1.0× 108(m3 kg−1 s−1) 310 21.85. 4CaO +Al2O3 + Fe2O4 → C4AF 1.0× 108(m6 kg−1 s−1) 330 −41.3

Table 1: Reactions, kinetics and heat of reaction.

Species Molar mass (Kg/mol) mass fractionCaCO3 0.1 0.340CaO 0.056 0.396SiO2 0.06 0.179Al2O3 0.1 0.0425Fe2O4 0.16 0.0425CO2 0.044 −C2S 0.172 −C3S 0.228 −C3A 0.27 −C4AF 0.486 −

Table 2: Species’ molar mass and inlet mass frac-tions

disturbances in the numerical study may caused thedifferences in their values.

In figures 2 and 3 the mass fractions of the keyspecies along the kiln are presented. The first fromthe benchmark study, the second from the numer-ical one. It is possible to observe similar behaviorof the mass fraction along the kiln except again forthe two last species as already reported.

Figure 2: Mass fractions evolution along the kilnfrom [8]

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Figure 3: Mass fractions evolution along the kilnfrom COMSOL.

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4. Microwave Limestone Processing

In this section a model for a limestone processingunit using microwave energy at 2.45 GHz is pre-sented.

4.1. Model description

The 3D model is represented in 2D in figure 4. Itconsists on a WR340 waveguide with a quartz tubecutting through it. Limestone flows in the orangematerial domain as indicated. The chemical modeland kinetics for limestone processing are presentedin table 1, its thermal properties are presented intable 4 and its dielectric properties were taken from[23].

Three different phenomena are involved in thismodel: microwave, heat transfer and chemical con-version. The correspondent interfaces are assignedto the whole domain, except for the chemical onewhich is just set in the bed domain.

A TE10 mode is applied at the port with a fre-quency of 2.45 GHz. The initial temperature is setto 293 K except for the bed domain, in which 900K was set. The mass flow is axially set to 0.25 kg/hwith a 40 % fill rate, and a limestone mass fractionof one was set at the inlet at 293 K. The walls ofthe model are assumed to be isothermal with anaverage heat convection coefficient for each one.

4.2. Computational procedure

With the objective to find an high efficient con-verged solution the following methodology seen in

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Species Experimental data [8] Numerical data [10] Numerical data from COMSOLCaO 0.084 0.075 0.0771C3S 0.483 0.503 0.5262C2S 0.239 0.222 0.2159C3A 0.051 0.051 0.0829C4AF 0.143 0.149 0.0988

Table 3: Numerical and experimental results of the mass fraction at kiln’s exit.

Figure 4: Domains of the numerical model.

Property Valueρ 1680 [kgm−3]Cp 800 [J kg−1K−1]κ 0.69 [W m−1K−1]

Table 4: Limestone thermal properties from [8].

figure 5 was executed. It comprises all the stepsrequired to meet the proposed goals, with four ma-jor steps: define initial plunger position, computeinitial input power, develop a MATLAB code toautomatically adjust the previous parameters andfinally run the transient simulation.

4.2.1 Optimum plunger position

To find the initial plunger position, a frequency do-main study was carried with a parametric studyover the total wavelength range, where the plungerposition was varied. Assuming an initial tempera-ture profile and using equation (21) to compute theefficiency.

η = 1− |S11|2 (21)

From the results obtained the plunger was set at144 mm from the quarts tube center. During thesimulation a frequency domain study is carried at acertain time interval to compute a new position.

4.2.2 Microwave power input

Defining a suitable power input is key for the suc-cess of the whole process. During the simulation,this parameter is computed by performing an en-ergy balance to the model as in equation (22).

Pinput =Pchem +mflowCp(Texit − Tin) + Plosses

ηparam(22)

Where Pchem is the theoretical power to convertlimestone, mflow is the mass flow of limestone, Texitand Tin are the mean outlet and inlet temperatures,Plosses portray the convective losses and ηparametric

is the maximum computed efficiency of the para-metric study.

The initial microwave input power is computedconsidering only the first term of equation (22).

4.2.3 MATLAB routine

The following algorithm was coded into MATLABin order to adjust all the key parametric variablesduring the course of the simulation, without anyuser intervention.

1. Define initial variables: mass flow, initial powerinput, simulation time, inlet material temper-ature and plunger position;

2. Load the COMSOL model;

3. Start Loop 1: Run the transient simulation;

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Figure 5: Flow diagram of the computational algorithm.

(a) Set input variables in the model;

(b) Run the first transient simulation;

(c) Save the model and extract all the data;

(d) Carry a frequency domain parametricstudy. For the current plunger positionand for its adjacent ones;

(e) Read the computed efficiencies for thethree plunger positions;

(f) Start loop 2: Finding new plunger posi-tion;

i. If the maximum efficiency is found forthe current position leave loop 2;

ii. If not, run a new frequency domainsimulation for the plunger positionthat returned the highest efficiencyand for the its two neighboring po-sitions;

(g) Compute the new power input requiredfrom the data extracted at (c) using equa-tion (22);

(h) If transient term of the energy balanceequation and the average percentage of re-actant at the quartz tube exit are ≤ 1 and< 1.5% respectively, leave loop 1;

(i) If the new power input is greater thanthe power input at the end of the pre-vious simulation, then the new power islinearly increased during the course of thenew transient simulation;

(j) if the new power input is lower than theprevious one, then the new power inputis established in its full magnitude at thebeginning of the new transient simulation;

4. End of the MATLAB code and the last solutionis the converged one for the set of parametersof velocity and inlet temperature.

4.3. Resutls of Limestone processing

In this section the aim is to analyze the results ob-tained from the transient simulation carried out us-ing the described model. From figures 6 to 9 anevolution of several parameters during the courseof the simulation is presented to give an insight onthe behavior of the model and the controller.

In figure 6 it is possible how the power input canaffect the remaining variables. Initially, due to thelack of it, a great decline in efficiency is observed.This happened because temperature dropped as fig-ure 7, point (a) attests. This reduced the loss fac-tor, cripples the capacity of the material to absorbmicrowave energy, and thus, reduces efficiency. Asthe model is losing energy the stored heat rate isnegative.

Figure 6: Stored heat, power input, microwave ef-ficiency and plunger position evolution during thesimulation time.

In the second time interval, there is a change inthe plunger position and an linear increase in power.As a result, and given the favorable change in theoperational parameters, the efficiency starts to re-

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cover, and the model starts to gain energy (verifiedlooking at the stored heat). At the end of this timeinterval, there is a sudden increase in efficiency andtemperature (point (c) of figure 7). However, duethe lower input power in the subsequent time inter-val, any temperature related problem is mitigated.For the rest of the time intervals, little changesare made, and temperature steady state is achievedwhen the stored heat reaches zero.

Figure 7: Bed power absorption, maximum bedtemperature and outlet bed temperature versussimulation time.

Figure 7 displays the strong coupling between thethermal and the electromagnetic interface. It canbe clearly seen how the feedback mechanism worksbetween this two variables, resulting in a steeperevolution of both the temperature and the absorbedmicrowave energy. For an increase in the microwavepower absorption, a higher maximum temperatureis obtained. Then, as a consequence, the dielectricloss factor increases, allowing for a better microwavepower absorption.

Figure 8 serves the purpose of presenting theinterconnection between the temperature and thechemical processes, through the analysis of thechemical heat source. As can be seen, while tem-peratures are low, no chemical process is occurring.However, once the temperature increases, it triggersthe chemical reaction, and its heat source starts tomanifest itself. The evolution from mid to the endsimulation can be explained by the mass fractionof limestone. Although the temperature remainshigh, the chemical conversion starts to lose pace.This happens because the reaction rate is tied tothe mass fraction, when the second reduces, the firstwill also decrease. At steady state, the value foundfor the chemical heat source is the one required tototally convert the mass flow of limestone travelingalong the tube.

In figure 9, the evolution of the energy consump-

Figure 8: Limestone mass fraction, maximum bedtemperature and reaction heat source versus simu-lation time.

Figure 9: Bed power absorption and powerlosses/usage versus simulation time.

Figure 10: Energy balance of the limestone process-ing unit at steady state for a mass flow of 0.25 kg/hconsidering the Pheat as useful power.

tion and losses are presented. Energy consumptionhappens through the heating of the material to thereaction temperature and through the chemical re-

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Figure 11: Limestone processing steady state distributions (top view).

action itself. Part of the energy spent on heatingexit’s with material at the outlet, the other is lost,through convection. In this figure, it is possibleto notice that the difference between the sum ofpower usage and losses, and the absorbed power re-turns the stored heat. That is why, at steady state,the difference is negligible, stored heat is close tozero, and the input energy matches the power us-age and lost. Figure 10 presents the energy balanceat steady state where the heating enthalpy was in-cluded by considering a temperature of reaction of1073 K. The presented percentages give the amountof power in relation to the total power input atsteady state of 356 W. It can be seen that a lit-tle less than half of the power input is actually usedto convert limestone. The thermal efficiency is ofroughly 55.1 % and finally the total efficiency ofthe system returns 46.61% which is not high, butthen again the, the mass flow is also small and nothermal isolation was considered.

Through figure 11 it is possible to visualize theelectric field distribution (a), loss factor (b) and mi-crowave power deposition (c) from a top perspective(by defining a horizontal planar cut at roughly halfbed height normal to the xx axis). By analyzingthe three images it is possible to notice the influ-ence of the electric field and the loss factor, two keyvariables of the Helmholtz equation (18), on themicrowave power deposition. It can be noticed howthe power deposition manifests itself, in the bothpresence of a significant high electric field and highthe loss factor, as expected. Hence, it is possible toattest that the microwave power dissipation field re-sults from the intersection of the electric field peakswith the loss factor ones (meaning high tempera-tures). Although the electric field plays an impor-tant role in triggering the microwave heat source, itis the loss factor that is the most crucial factor, sinceits only peak is localized in a small zone. Further

downstream the power deposition starts do decaydue to the absence of a strong electric field.

5. Conclusions

This thesis is divided into two parts and presentsan insight into the use of microwave energy as aheating source in the formation of cement clinker.

In the first part the chemical mechanism was ad-dressed. The chemical model was able to predictthe evolution of the complete cement clinker chemi-cal process with reasonable results, being validatedwith the available data in the literature.

On the second part, a 3D microwave heatingmodel was developed for converting a key compo-nent in cement clinker, limestone. By controllingthe cavity geometry, and hence, the resonance ofthe electromagnetic field, and controlling the mi-crowave power input, the model was able to attain asteady state with an optimized microwave efficiencyand power usage.

Considering all the carried simulations it is quitesafe to conclude that COMSOL is a suitable toolto tackle a variety of multiphysics problems. TheMATLAB controller was a proven success, as itconducted the transient simulation with the nec-essary adjustments without any user intervention.Enabling to achieve an optimized and efficient mi-crowave limestone processing unit, while avoidingtemperature related problems, by adjusting opera-tional parameters such as the plunger position andthe microwave power input. Moreover, and unlikeother published models, the proposed controller isalso able to guarantee total conversion of the chem-ical reactant. Finally, it was showed that the de-veloped controller could be applied outside of thenumerical simulation, as all the data used by it canbe also be measured in an experimental apparatus.

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