The DSC analyses of coal gangue CG compared to the pure coal PC are presented by in Figure 2; the heating rate was 10 °C/min under air.

The DSC analysis of coal gangue shows an endothermic region occurring between 100°C-150°C attributed to the evaporation of free water. Additionally, two dehydration processes, specifically from gypsum to plaster and then to anhydrite:

and 2 C a S O 4 + H 2 O g = 2 C a S O 4 . 1 2 H 2 O : Δ r G ° 2 ( T , k J / m o l ) = - 62.20 + 0.1491 T

They are theoretically expected to occur at 106°C and 153°C, respectively: Comparing these theoretical values to those reported in literature (20), the temperature for the first dehydration aligns closely, with literature reporting 105°C. However, for the second dehydration, the literature reports a slightly higher temperature of 175°C.

At 580°C, the coal gangue (CG) undergoes a polymorphic transformation of quartz: SiO_2α → SiO_2β.

At 580°C, we have the polymorphic transformation of quartz: SiO_2α → SiO_2β. Then, in the range, an exothermal effect is observed, mainly attributed to the combustion of coal.

Using the DSC characterization (10°C/min, in air) for CG, we obtain the combustion enthalpy of CG is H_CG = - 63.74 J.g^-1; this value is used in the thermochemical balance calculations for the cementitious mixture LG. It's important to note that this value represents a minimum estimate, as the observed exothermic effect persists across multiple heating and cooling cycles, indicating incomplete combustion. This persistence is demonstrated in Figure 2(b), where the PC sample exhibits the observable exothermic effect even after five cycles of heating and cooling.

Characterizations of materials LG and CG was done using thermogravimetric TGA and thermo-differential TDA analyses. The graphical representations of these analyses are illustrated in Figure 3.

In the temperature interval of 300-600°C, we observe the presence of the exothermic effect due, mainly, to the combustion of coal in the coal gangue, this effect is also noticeable in the limestone-gangue cementitious mixture LG. At about 850°C (P=1bar), we observe a main endothermic peak attributed to the calcination of the limestone, in the LG mixture:

At this temperature the standard free enthalpy of this equilibrium verifies the condition ∆_ca G° (T_ca) =0: ∆_ca G° (T) = 178.2-0.1601.T (kJ.mol^-1), T_ca=1113K(840°C).

Similarly, the temperature at which dolomite decomposes is determined, considering a hypothetical single-stage decomposition:

The standard free enthalpy of this equilibrium is:

This reaction occurs at T_do~=831K (558°C). Adopting a two-step decomposition, as reported in some literatures (21); the process involves the initial formation of MgO, CO₂, and calcite at the temperature of 750°C, followed by the subsequent decarbonation of calcite around 900°C.

A DSC characterization has been done under argon atmosphere for the mixtures LG and RR; therefore, the thermal effects excluding combustions can be seen; thus, we will consider that the combustion phenomenon, in the LG mixture, is predominant in front of other reactions taking place in the interval 300-600°C. The comparative results are reported in Figure 4.

The thermal behavior of the two mixtures, LG and RR, exhibits notable similarities. Two endothermic phenomena are observed:

It's important to note that limestone typically contains dolomite (calcium magnesium carbonate), which undergoes calcination around 500°C. Additionally, around 550°C, the decomposition of clays initiates through dehydrations, dehydroxylations, and decompositions (22). These reactions continue until approximately 900°C.

The main thermochemical events involve the heating of all substances, and the main reactions are: decomposition of calcite and dolomite, combustion of coal residues, decomposition of clays and formation of the four phases of clinker. In addition to these primary events, there are, also, minor thermal occurrences like the alpha-beta transition of silica and dehydration of gypsum, and polymorphism in phases of clinker. In the literature, these main physicochemical phenomena take place in temperature intervals (23). Due to the complexity of these physicochemical phenomena, detailed studies are challenging, and approximations become necessary. To facilitate analysis, relevant temperatures T_r=1,2… are introduced, corresponding to the key reactions. For instance, the combustion phenomena of coal begins at 727K as showed in thermal characterization and in literature (24); the αβ transformation of quartz occurs at 848K. T₀=298K is the initial temperature and T₇=1723K is the final temperature of clinkerization.

We study mass and energy balances during the production of LG* and RR* clinkers, from raw materials. These balances are examined for different stages as presented in the Table 5:

Stage I: the first stage of decomposition.

Stage II: the second stage of clinkerization.

Overall balance:

In the energy balance analysis, the focus is on the algebraic determination of energies required to produce 1 kg of clinkers denoted LG* and RR*. We are interested in the difference of the energies Δ E = E L G − E R R , in this way we will reduce the impact of approximations done. Moreover, since the limestone LR is the same for both raw feeds, certain terms in the balance are inherently similar.

We present the balance involving the main thermochemical transformations. These include the heating energies for the main compounds in the temperature intervals considered (Formula F1), as well as the enthalpies of the chemical reactions listed in Table 5 (Formulas F2 and F3). The heats of change of physical state or of polymorphism are included with those of the reactions presented in Table 5.

Where Δ E r i , I o r I I , Δ E h s , I o r I I , Δ E h l , I o r I I and Δ E h g , I o r I I , and are respectively the differences in energies of: reactions and heating of solids s, liquids l and gases g in stages I and II.

The terms of heating are of the form: ∫ T j T k ∑ i Δ m i . C p i ( T ) . d T in general, for a given substance i, the massic heat capacity is:

The data on the specific heat capacity C_p,i shown in Table 5 is given in literature, mainly from the NASA/TP-2002-211556 report (25) and other sources (26-36). The specific heat capacity of coal is reported based on the work of Lesniak et al and Eisermann et al (28, 29), it is formed by two contributions of fixed carbon FC (fraction m_C, C_pC) and volatile matter (fraction 1- m_C, C_pV). In our case, for anthracite, the value is FC=93 and VM =5 (37).

Using formula (F₁ ), we calculate the heating of all solids, liquids and gases; the gases CO₂, H₂O, SO₂, O₂, and N₂ are involved in the reactions of calcinations of calcite and dolomite, dehydrations of gypsum, decomposition of clays and combustion of coal.

The coal gangue consists of various compounds, including quartz, illite, muscovite, clinochlore, gypsum, ferric oxide (F), and sulfur dioxide (SO₂). These compounds are derived, in part, from pyrite, which makes up approximately 2-5% of the coal (38). In the analysis of coal gangue (CG), adjustments are made to align the total amount of oxides ‘CSAMKS’ given by XRD (94.51%), to that given by XRF (79.24%). The experimental percentage of coal in the gangue is estimated using the loss on ignition L.O.I, which is formed by dehydration of the three water-bound in clays and gypsum (2.39 %). This estimation suggests a maximum coal content approaching 11.85%, consistent with previous estimates. For different samples of gangue, the losses on ignition varied between 10.6 and 14.22, corresponding to a coal content between 8.8 and 11.8%. For the mass balance, the study uses the conservative assumption of 11.85 % coal in GC.

The gases released during combustion include water vapor, carbon dioxide, and sulfur dioxide. In this study, we use the experimental amounts of CO₂ and SO₂ estimated by Taha et al: 0.243 kg CO₂ and 0.00628 kg SO₂ per kg of gangue and we obtain the amount of water vapor released from an approximate ‘formula’ of the anthracite. Coal can be modeled by the formula ‘C_xH_yO_zS_tN_u’. Jerada's anthracite analysis indicates volatile matter (VM) at about 5%, fixed carbon (FC) at approximately 93%, and ash (ASH) at 5.5

A model proposed by Shen et al. (39) and reported in Lawal et al’s study (40) provides an approximate formula (‘C₁H _1.158O _0.418 N_uS_t’). This model predicts that the combustion of 1 ton of CG produces 62.1 kg H₂O and 263 kg CO₂. The optimal limestone-gangue mixture retained has a composition of 17.1% coal gangue. The massic composition of coal gangue is given in Table 7.

We complete the determination of the mass fractions of the main compounds forming the LR and RR materials. The total amount of carbon dioxide from calcite and dolomite, and from the XRD analysis we obtain the ratios of calcite to dolomite and to quartz: 6.58 and 11.9 respectively. For the LR material, the total 96.089% in CMC given by XRD is adjusted to 74.865% given by XRF; and for the RR material the total of L.O.I is composed of carbon dioxide and water of clay, maintaining the same ratio, 6.58, of CC to CMC. All the results are reported in Table 7 and used to determine the energies involved in the comparative energy balance of the two cement mixtures LG, and RR.

The masses of the gases I: CO₂, H₂O, SO₂, O₂ and N₂ concerned by this phase I are respectively: 66.14, 16.81, 1.682, 55.04, 192.7 gram for 1 kg of clinker. For the energy balance, the solids in this phase are denotes solids I.

During the clinkering phase, the oxide compositions (XRF) of the two mixtures are used to calculate the saturation factor lime moduli LSF=100C/ (2.8S+1.65A+0.35F), the ratio SR=S/ (A+F) as well as the four phases of the clinker and possibly, the percentage of free lime Cf. In order to calculate compositions of the four phases, we use the Taylor’s matrix (41) leading to the system of equations:

After calculating the total mass of the four phases (solids II1), we assumed that the difference with the mass of the C-S-A-F oxides was that of the free lime, in order to adjust the total mass. The theoritical percentage of free lime can be approximated using Fundal’s empirical equation :% CaO_(free)=0.31 (LSF-100)+2.18 (SR-1.8)+(0.73 Q₄₅ + 0.33 C₁₂₅ + 0.34 Aq). The total amount of C₂S formed at 1173K will be distributed between the final masses of C₂S and that of C₃S which will form at 1573 K; these two masses are obtained by the Taylor model above.

In Table 8, we give the massic composition of these four phases, anhydrite, minor oxides and the gases. All the results are used to determine the energies involved in the comparative energy balance of the two cement mixtures LG and RR.

Finally, in Table 9, we present the energy balance of the reactions and the heating, then we deduce the overall balance; these results are generated by the program Python.