Differences

This shows you the differences between two versions of the page.

--- laws:rchim [2024/04/19 10:59]
arthur [The model]
+++ laws:rchim [2024/04/22 16:59] (current)
arthur
@@ Line 7: / Line 7: @@
 === IF ICOAL = 1: ===
-The 6th DOF is the $CO_2$ content.
+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: ===
@@ Line 85: / 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 95: / 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 104: / 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 134: / 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 149: / Line 207: @@
 __IF ICOAL = 1:__
-|Q(1)|Coal concentration|
+|Q(1)|CCOAL: Coal concentration|
-|Q(2)|Oxygen concentration|
+|Q(2)|NSTEP|
-|Q(3)|Concentration of solid product|
+|Q(3)|CSP: Concentration of solid product|
-|Q(4)|Concentration of exhausted gas|
+|Q(4)|CEG: Concentration of exhausted gas|
 __IF ICOAL = 2:__
-|Q(1)|Ca(OH)_2 concentration|
+|Q(1)|$Ca(OH)_2$ concentration|
-|Q(2)|CaCO_3 concentration|
+|Q(2)|$CaCO_3$ concentration|
 |Q(3)|/|
 |Q(4)|/|
@@ Line 165: / Line 223: @@
 |Q(3)|Modified enzymatic hydrolysis rate (VFA accumulation rate) |
 |Q(4)|VFA depletion rate |
+__IF ICOAL = 4 :__
+|Q(1)|Ca(OH)2 content  |
+|Q(2)|CACO3 content  |
+|Q(3)|SRW |
+|Q(4)|/ |

Lagamine

User Tools

Site Tools

Differences

Page Tools