laws:rchim
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laws:rchim [2024/04/19 13:55] arthur |
laws:rchim [2024/04/22 16:59] (current) arthur |
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| 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.\\ | 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 time. It is obtained from the reaction rate $\tau_{O_2}$: | + | Because of the rate of the reaction, a sub-incrementation is performed with respect to the time. It is obtained from the reaction rate $\tau_{O_2}$: |
| \[\tau_{O_2}= \frac{1089}{26 * 32}\left[C_{coal}*AK0*\exp{\left(\frac{-EDR}{TEMP}\right)}\right]^{-1}\] | \[\tau_{O_2}= \frac{1089}{26 * 32}\left[C_{coal}*AK0*\exp{\left(\frac{-EDR}{TEMP}\right)}\right]^{-1}\] | ||
| - | The new chemical time step is then $\Delta T_{ch} = 0.1*\tau_{O_2}$. The following calculations are then performed until reaching $\Delta T$: | + | The new chemical time step is then $\Delta t_{ch} = 0.1*\tau_{O_2}$. The following calculations are then performed until reaching $\Delta t$: |
| \[AQF = C_{COAL} * C_{O_2} * AK0 * \exp{\left(\frac{-EDR}{TEMP}\right)}\] | \[AQF = C_{COAL} * C_{O_2} * AK0 * \exp{\left(\frac{-EDR}{TEMP}\right)}\] | ||
| - | \[C_{COAL} = C_{COAL}- AQF * \Delta T_{ch}\] | + | \[C_{COAL} = C_{COAL}- AQF * \Delta t_{ch}\] |
| - | \[C_{O_2} = C_{O_2}- AQF * \Delta T_{ch}* \left(\frac{26*32}{1089}\right) \frac{1}{CPORO}\] with $CPORO=0.4$.\\ | + | \[C_{O_2} = C_{O_2}- AQF * \Delta t_{ch}* \left(\frac{26*32}{1089}\right) \frac{1}{CPORO}\] with $CPORO=0.4$.\\ |
| - | Finally, the increment of $CO_2$ concentration ($\Delta T_{CO_2}= C_{CO_2,ini} - C_{CO_2}$) is calculated and the parameters of interest are updated only if that increment is inferior to 1E-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: |
| - | \[\Delta T_{C_{coal}}= C_{coal,ini} - C_{coal}\] | + | \[\Delta C_{coal}= C_{coal,ini} - C_{coal}\] |
| - | \[FL_{coal} = -\Delta H * \frac{\Delta T_{C_{coal}}}{\Delta T}\] | + | \[FL_{coal} = -\Delta H * \frac{\Delta C_{coal}}{\Delta t}\] |
| - | \[CEG = CEG + \Delta T_{C_{coal}}* \left(\frac{47*305E-1}{1089}\right)\frac{1}{CPORO}\] | + | \[CEG = CEG + \Delta C_{coal}* \left(\frac{47*305E-1}{1089}\right)\frac{1}{CPORO}\] |
| - | \[CSP = CSP + \Delta T_{C_{coal}}* \left(\frac{1*489}{1089}\right)\] | + | \[CSP = CSP + \Delta C_{coal}* \left(\frac{1*489}{1089}\right)\] |
| Otherwise, $FL_{coal}$ is set to zero and all the parameters are set equal to their initial values. | Otherwise, $FL_{coal}$ is set to zero and all the parameters are set equal to their initial values. | ||
| Line 27: | Line 27: | ||
| === IF ICOAL = 2: === | === IF ICOAL = 2: === | ||
| - | The sixth degree of freedom is the concentration in $CO_2$.\\ | + | 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 $CO_2$.\\ |
| - | \[A=1E7, E0 = 0.044*E0, TEMP = 293 and R = 8.31\]\\ | + | Several parameters are defined beforehand: $A=1E7$, $E_0 = 0.044*E0$, $TEMP = 293$ and $R = 8.31$.\\ |
| - | \[TAUCO2 = \frac{76}{44}\left[ \frac{ALPHA1*FH*CCO2}{GMAX}*\left(1-(\frac{CACO3}{CMAX})\right)*A*\exp\left(\frac{-E0}{(R*TEMP)}\right)\right]^{-1}\] | + | Then, a reaction rate $\tau_{CO_2}$ is calculated: |
| - | \[DELTATCH = 0.1*TAUCO2\] | + | \[\tau_{CO_2}= \frac{76}{44}\left[ \frac{\alpha_1*FH*C_{CO2}}{G_{max}}*\left(1-\left(\frac{C_{CaCO_3}}{C_{max}}\right)\right)*A*\exp\left(\frac{-E_0}{(R*TEMP)}\right)\right]^{-1}\] |
| - | \[NSTEP = \frac{DELTAT}{DELTATCH}\]\\ | + | |
| - | \[AQF = \frac{ALPHA1*FH*CCO2}{GMAX}*\left(1-(\frac{CACO3}{CMAX})\right)*A*\exp\left(\frac{-E0}{(R*TEMP)}\right)\] | + | The new chemical time step is then $\Delta t_{ch} = 0.1*\tau_{CO_2}$. The following calculations are then performed until reaching $\Delta t$: |
| - | \[CAOH2 = CAOH2-AQF*DELTATCH\] | + | \[AQF = \frac{\alpha_1*FH*C_{CO_2}}{G_{max}}*\left(1-\left(\frac{C_{CaCO_3}}{C_{ma}}\right)\right)*A*\exp\left(\frac{-E_0}{(R*TEMP)}\right)\] |
| - | \[CACO3 = 0\] | + | \[C_{Ca(OH)_2} = C_{Ca(OH)_2}-AQF*\Delta t_{ch}\] |
| - | \[CCO2 = CCO2 - AQF*DELTATCH*\frac{44}{76}\] | + | \[C_{CaCO_3}= 0\] |
| + | \[C_{CO_2} = C_{CO_2}- AQF*\Delta t_{ch}*\frac{44}{76}\] | ||
| - | \[DELTATF = DELTAT - (NSTEP-1)*DELTACH\] | + | 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: |
| - | \[AQF =\frac{ALPHA1*FH*CCO2}{GMAX}*\left(1-(\frac{CACO3}{CMAX})\right)*A*\exp\left(\frac{-E0}{(R*TEMP)}\right)\] | + | \[\Delta C_{Ca(OH)_2} = C_{Ca(OH)_2,ini} - C_{Ca(OH)_2}\] |
| - | \[CAOH2= CAOH2- AQF*DELTATF\] | + | \[FL_{coal} = \frac{\Delta C_{CO_2}}{\Delta t}\] |
| - | \[CACO3 = 0\] | + | Otherwise, $FL_{coal}$ is set to zero and all the parameters are set equal to their initial values. |
| - | \[CCO2 = CCO2 - AQF * DELTATF* \left(\frac{44}{76}\right) \frac{1}{CPORO}\] | + | |
| - | + | ||
| - | \[DELTATCCO2 = CCO2_INI- CCO2\] | + | |
| - | \[DELTATCAOH2 = QA(1) - CAOH2\] | + | |
| - | IF $DELTATCCO2<1E-10$: | + | |
| - | \[FLCOAL = -DELTATCCO2 * DELTATCCO2/DELTAT\] | + | |
| - | ELSE: | + | |
| - | \[FLCOAL = 0\] | + | |
| - | \[CAOH2= QA(1)\] | + | |
| === IF ICOAL = 3: === | === IF ICOAL = 3: === | ||
| Line 128: | Line 119: | ||
| ==== Integer parameters ==== | ==== Integer parameters ==== | ||
| ^ Line 1 (1I5) ^^ | ^ 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 | | |:::|= 3 to use the biochemical degradation of the organic matter | | ||
| + | |:::|=4 to use the carbonation of cementitious materials| | ||
| ^ Line 2 (2G10.0) ^^ | ^ Line 2 (2G10.0) ^^ | ||
| |FLUXF|| | |FLUXF|| | ||
| Line 176: | Line 168: | ||
| |CM|initial condition on methanogen biomass concentration| | |CM|initial condition on methanogen biomass concentration| | ||
| |ORG|initial condition on organic matter content| | |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 ===== | ===== Stresses ===== | ||
| ==== Number of stresses ==== | ==== Number of stresses ==== | ||
| Line 207: | Line 223: | ||
| |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)|/ | | ||
laws/rchim.1713527716.txt.gz · Last modified: 2024/04/19 13:55 by arthur
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