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--- laws:rchim [2024/04/19 10:53]
arthur [The model]
+++ laws:rchim [2024/04/22 16:59] (current)
arthur
@@ Line 5: / Line 5: @@
 ==== The model ====
-=== **__IF ICOAL = 3:__** ===
+=== IF ICOAL = 1: ===
+If ICOAL=1, the reaction modelled is the burning of coal. Several chemical species are of interest: the $O_2$ content required for the reaction to take place and the $CO_2$ produced. The concentration of solid product (CSP) and the concentration of exhausted gas (CEG) are also measured. In this case, the 6th DOF is the $O_2$ content.\\
+Because of the rate of the reaction, a sub-incrementation is performed with respect to the time. It is obtained from the reaction rate $\tau_{O_2}$:
+\[\tau_{O_2}= \frac{1089}{26 * 32}\left[C_{coal}*AK0*\exp{\left(\frac{-EDR}{TEMP}\right)}\right]^{-1}\]
+The new chemical time step is then $\Delta t_{ch} = 0.1*\tau_{O_2}$. The following calculations are then performed until reaching $\Delta t$:
+\[AQF = C_{COAL} * C_{O_2} * AK0 * \exp{\left(\frac{-EDR}{TEMP}\right)}\]
+\[C_{COAL} = C_{COAL}- AQF * \Delta t_{ch}\]
+\[C_{O_2} = C_{O_2}- AQF * \Delta t_{ch}* \left(\frac{26*32}{1089}\right) \frac{1}{CPORO}\] with $CPORO=0.4$.\\
+Finally, the increment of $O_2$ concentration ($\Delta C_{O_2}= C_{O_2,ini} - C_{O_2}$) is calculated and the parameters of interest are updated only if that increment is inferior to 1E-4:
+\[\Delta C_{coal}= C_{coal,ini} - C_{coal}\]
+\[FL_{coal} = -\Delta H * \frac{\Delta C_{coal}}{\Delta t}\]
+\[CEG = CEG + \Delta C_{coal}* \left(\frac{47*305E-1}{1089}\right)\frac{1}{CPORO}\]
+\[CSP = CSP + \Delta C_{coal}* \left(\frac{1*489}{1089}\right)\]
+Otherwise, $FL_{coal}$ is set to zero and all the parameters are set equal to their initial values.
+=== IF ICOAL = 2: ===
+If ICOAL = 2, then the reaction modelled is the one between $CO_2$ and $Ca(OH)_2$ to form $CaCO_3$. The sixth degree of freedom is then the concentration in $CO_2$.\\
+Several parameters are defined beforehand: $A=1E7$, $E_0 = 0.044*E0$, $TEMP = 293$ and $R = 8.31$.\\
+Then, a reaction rate $\tau_{CO_2}$ is calculated:
+\[\tau_{CO_2}= \frac{76}{44}\left[ \frac{\alpha_1*FH*C_{CO2}}{G_{max}}*\left(1-\left(\frac{C_{CaCO_3}}{C_{max}}\right)\right)*A*\exp\left(\frac{-E_0}{(R*TEMP)}\right)\right]^{-1}\]
+The new chemical time step is then $\Delta t_{ch} = 0.1*\tau_{CO_2}$. The following calculations are then performed until reaching $\Delta t$:
+\[AQF = \frac{\alpha_1*FH*C_{CO_2}}{G_{max}}*\left(1-\left(\frac{C_{CaCO_3}}{C_{ma}}\right)\right)*A*\exp\left(\frac{-E_0}{(R*TEMP)}\right)\]
+\[C_{Ca(OH)_2} = C_{Ca(OH)_2}-AQF*\Delta t_{ch}\]
+\[C_{CaCO_3}= 0\]
+\[C_{CO_2} = C_{CO_2}- AQF*\Delta t_{ch}*\frac{44}{76}\]
+Finally, the increment of $CO_2$ concentration ($\Delta C_{CO_2}= C_{CO_2,ini} - C_{CO_2}$) is calculated and the parameters of interest are updated only if that increment is inferior to 1E-10:
+\[\Delta C_{Ca(OH)_2} = C_{Ca(OH)_2,ini} - C_{Ca(OH)_2}\]
+\[FL_{coal} = \frac{\Delta C_{CO_2}}{\Delta t}\]
+Otherwise, $FL_{coal}$ is set to zero and all the parameters are set equal to their initial values.
+=== IF ICOAL = 3: ===
 This constitutive law is used to take into account the degradation of organic matter and the following production of Volatil Fatty Acid (VFA). Those VFA are then consumed to produce methanogen biomass. \\ This law is based on McDougall’s model.
@@ Line 79: / Line 119: @@
 ==== Integer parameters ====
 ^ Line 1 (1I5) ^^
-|ICOAL|= 1 |
+|ICOAL|= 1 for the combustion of coal (?)|
-|:::|= 2 |
+|:::|= 2 for a reaction of carbonation (?)|
 |:::|= 3 to use the biochemical degradation of the organic matter  |
+|:::|=4 to use the carbonation of cementitious materials|
 ^ Line 2 (2G10.0) ^^
 |FLUXF||
@@ Line 89: / Line 130: @@
 __If ICOAL = 1__
 ^ Line 1 (5G10.0) ^^
-|DELTAH|Heat produced/consumed by the chemical reaction ?|
+|DELTAH|Heat produced/consumed by the chemical reaction|
 |CF0|Initial coal content|
 |CO2|Oxygen content|
-|CO2||
 |AK0||
 |EDR||
@@ Line 98: / Line 138: @@
 __If ICOAL = 2__
 ^ Line 1 (7G10.0) ^^
-|Hfh||
+|FH||
-|Hgmax||
+|GMAX||
-|Hcmax||
+|CMAX||
 |Alpha1||
 |Alpha4||
-|CAOH2|Ca(OH)_2 content|
+|CAOH2|$Ca(OH)_2$ content|
 |E0|Activation energy|
@@ Line 128: / Line 168: @@
 |CM|initial condition on methanogen biomass concentration|
 |ORG|initial condition on organic matter content|
+__If ICOAL = 4__
+^ Line 1 (7G10.0) ^^
+|hmin|Minimal pore relative humidity|
+|ALPHA|Material parameter|
+|GMAX|Maximum CO2 content|
+|z|Cement content of the mix|
+|C|Ca(OH)2 content of the mix|
+|CAOH2|Ca(OH)2 content of the mix|
+|CACO3|CaCO3 content of the mix|
+^ Line 2 (7G10.0) ^^
+|ISR|Index for the water retention curve|
+|CSR1|Parameter 1 of the WRC|
+|CSR2|Parameter 2 of the WRC|
+|CSR3|Parameter 3 of the WRC|
+|CSR4|Parameter 4 of the WRC|
+|CSR5|Parameter 5 of the WRC|
+|NSUBH|Number of sub-increment for the hysteresis (if ISR=53)|
+^Line 3 (4G10.0) ^^
+|SRW|Initial saturation degree of the porous medium|
+|SRES|Minimal Srw|
+|SRFIELD|Maximal Srw|
+|POROS|Porosity|
 ===== Stresses =====
 ==== Number of stresses ====
@@ Line 143: / Line 207: @@
 __IF ICOAL = 1:__
-|Q(1)|CF0|
+|Q(1)|CCOAL: Coal concentration|
-|Q(2)|CO2|
+|Q(2)|NSTEP|
-|Q(3)|/|
+|Q(3)|CSP: Concentration of solid product|
-|Q(4)|/|
+|Q(4)|CEG: Concentration of exhausted gas|
 __IF ICOAL = 2:__
-|Q(1)|CAOH2|
+|Q(1)|$Ca(OH)_2$ concentration|
-|Q(2)|/|
+|Q(2)|$CaCO_3$ concentration|
 |Q(3)|/|
 |Q(4)|/|
 __IF ICOAL = 3 :__
-|Q(1)|ORG: organic matter content  |
+|Q(1)|Organic matter content  |
-|Q(2)|CM: methanogen biomass concentration  |
+|Q(2)|Methanogen biomass concentration  |
-|Q(3)|/: modified enzymatic hydrolysis rate (VFA accumulation rate) |
+|Q(3)|Modified enzymatic hydrolysis rate (VFA accumulation rate) |
-|Q(4)|/: VFA depletion rate |
+|Q(4)|VFA depletion rate |
+__IF ICOAL = 4 :__
+|Q(1)|Ca(OH)2 content  |
+|Q(2)|CACO3 content  |
+|Q(3)|SRW |
+|Q(4)|/ |

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