laws:hmic
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laws:hmic [2023/11/24 12:00] gilles |
laws:hmic [2023/12/12 16:03] (current) gilles [Description] |
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| ===== Description ===== | ===== Description ===== | ||
| 2D hydraulic microscopic law for solid elements.\\ | 2D hydraulic microscopic law for solid elements.\\ | ||
| - | Can be parallelised in ELEMB (at the macro-scale) or in the perturbation loop (at the micro-scale). | + | Can be parallelised in ELEMB (at the macro-scale) or in the perturbation loop (at the micro-scale).\\ \\ |
| + | |||
| + | The law definition and typical values of parameters for clays can be found in Corman (2024)((Corman, G. (2024). Hydro-mechanical modelling of gas transport processes in clay host rocks in the context of a nuclear waste repository. PhD thesis, University of Liège. https://hdl.handle.net/2268/307996)). | ||
| Line 48: | Line 50: | ||
| From Darcy's law, the advective component of the liquid water flow respectively reads for a fracture and a tube: | From Darcy's law, the advective component of the liquid water flow respectively reads for a fracture and a tube: | ||
| \[ | \[ | ||
| - | \vec{q_l} = - \frac{k_{r_w}}{\mu_w}\frac{1}{A}\kappa\left[ \vec{grad}(p_w) + g \rho_w \vec{grad}(y)\right]\] | + | \vec{q_g} = - \frac{k_{r_g}}{\mu_g}\frac{1}{A}\kappa\left[ \vec{grad}(p_g) + g \rho_g \vec{grad}(y)\right]\] |
| where\\ | where\\ | ||
| \[ | \[ | ||
| Line 59: | Line 61: | ||
| \] | \] | ||
| \[ | \[ | ||
| - | k_{r_w} | + | k_{r_g} |
| = | = | ||
| \begin{cases} | \begin{cases} | ||
| - | \frac{S_{r}^{*^2}}{2}(3-S_{r}^{*}), fracture\\ | + | (1-S_{r}^*)^3, fracture\\ |
| - | S_{r}^{*^2}, tube | + | (1-S_{r}^*)^2, tube |
| \end{cases} | \end{cases} | ||
| \] | \] | ||
| - | + | From Fick's law, the diffusive component of the dissolved air flow respectively reads for a fracture and a tube: | |
| - | La vitesse de diffusion de l'air sec est liée à un gradient de la masse volumique de l'air. En utilisant la théorie de la diffusion adaptée au cas des milieux poreux, nous pouvons écrire : | + | |
| \[ | \[ | ||
| - | \vec{i}_a = - n S_{r,g} \tau D \rho_g \vec{grad} \omega_a = -\vec{I}_v | + | \vec{i}_a = - n S_{r,g} \tau D \rho_g \vec{grad} (\omega_a) |
| \] | \] | ||
| - | Où $\omega_a = \rho_a/\rho_g$ est la teneur massique d’air sec dans le mélange gazeux. | ||
| - | === Equation d’état de l’air sec === | ||
| - | - Viscosité dynamique $\mu_a$ : dépendance avec la température \[\mu_a (T) = \mu_{a,0} - \alpha_a^T \mu_{a0}(T-T_0)\] | + | where $\omega_a = \rho_a/\rho_g$. |
| - | - Masse volumique $\rho_a$ :\\ //Hypothèse// : L’air est considéré comme un gaz parfait. \[\rho_a (T, p_a) = \rho_{a,0}\frac{p_a}{p_{a,0}}\frac{T_0}{T} \] | + | |
| - | - Perméabilité intrinsèque $k_g$: \\ Dépendance avec le degré de saturation $S_g$ : $k_{r,g} = f(S_g)$ avec $k_{g,effectif} = k_{g, intrinsic}k_{a,w}$ | + | |
| - | - Degré de saturation en liquide $S_g$: \\ Dépendance avec la succion $s = p_g - p_w$ \\ $S_g = 1-S_w$ d’où voir partie liquide | + | |
| - | === Conservation en volume de la chaleur === | + | === Dry gas state equations === |
| - | \[\dot{S_T} + \dot{E}_{H_2O}^{w\rightarrow v}L + div(\vec{V}_T) - Q_T = 0\] | + | |
| - | Où $S_T$ représente la quantité de chaleur emmagasinée, $L$ la chaleur latente de vaporisation, $\vec{V}_T$ le flux de chaleur et $Q_T$ une source de chaleur en volume.\\ | + | |
| - | Cette dernière équation peut être transformée en utilisant l'équation de bilan de la vapeur d'eau: | + | - Density $\rho_a$ :\\ //Assumption of classical ideal gas equation of state: \[\rho_a (T, p_a) = \rho_{a,0}\frac{p_a}{p_{a,0}}\frac{T_0}{T} \]// |
| - | \[ | + | - Perméabilité intrinsèque $k_g$: \\ Depending on the saturation degree $S_g$ : $k_{r,g} = f(S_g)$ avec $k_{g,effectif} = k_{g, intrinsic}k_{a,w}$ |
| - | \dot{S_T} + \dot{S}_vL + div(\vec{V}_T) + div(\vec{V}_v) L - Q_T = 0 | + | - Gaseous saturation degree $S_g$: \\ Depending on suction $s = p_g - p_w$ \\ $S_g = 1-S_w$ |
| - | \] | + | |
| - | + | ||
| - | === Quantité de chaleur emmagasinée par unité de volume === | + | |
| - | La quantité d'enthalpie du système est définie comme la somme des contributions de chaque espèce du système: | + | |
| - | \[ | + | |
| - | S_T = H_m = \sum_i H_i = \sum_i \theta_i \rho_i c_{p,i} (T-T_0) | + | |
| - | \] | + | |
| - | Les contributions de chaque composante à l’enthalpie du système s'exprime selon : | + | |
| - | \[ | + | |
| - | \begin{array}{l} | + | |
| - | H_w = n.S_{r,w} \rho_w c_{p,w} (T-T_0) \\ | + | |
| - | H_a = n(1-S_{r,g})\rho_ac_{p,a} (T-T_0)\\ | + | |
| - | H_s = (1-n)\rho_s c_{p,s} (T-T_0)\\ | + | |
| - | H_v = n(1-S_{r,g})\rho_v c_{p,v} (T-T_0) | + | |
| - | \end{array} | + | |
| - | \] | + | |
| - | Un dernier terme, lié à la vaporisation de l’eau, contribue également à l'emmagasinement de chaleur et dépend de la quantité de vapeur et la chaleur latente de vaporisation. | + | |
| - | \[ | + | |
| - | H_{Lat} = nS_{r,g} \rho_{v} L | + | |
| - | \] | + | |
| - | + | ||
| - | === Transfert de la chaleur par unité de volume === | + | |
| - | \[ | + | |
| - | \vec{V_T} + \vec{V_v}L = \underbrace{- \Gamma_m \vec{\nabla}T}_{conduction} + \underbrace{\left[c_{p,w}\rho_w \vec{q}_l + c_{p,a}(\vec{i}_a + \rho_a \vec{q}_g) + c_{pv}(\vec{i}_v+\rho_v\vec{q}_g)\right](T-T_0)}_{convection} + \underbrace{\left[\vec{i}_v + \rho_v \vec{q}_g\right] L}_{Latente} | + | |
| - | \] | + | |
| - | + | ||
| - | === Equations d’état === | + | |
| - | - $\rho_w, \vec{f_w}, S_w$: Voir partie eau | ||
| - | - $\rho_a, \vec{f_a}, S_a$ : Voir partie air | ||
| - | - Les conductivités thermiques $\Gamma_w,\Gamma_a$ et $\Gamma_s$ : \[\begin{array}{l}\Gamma_w(T) = \Gamma_{w,0} + \Gamma_{w,0} \gamma_w^T (T-T_0)\\ \Gamma_a(T) = \Gamma_{a,0} + \Gamma_{a,0} \gamma_a^T (T-T_0)\\ \Gamma_s(T) = \Gamma_{s,0} + \Gamma_{s,0} \gamma_s^T (T-T_0) \end{array}\] | ||
| - | - Les chaleurs spécifiques $c_{p,w},c_{p,a}$ et $c_{p,s}$ :\[\begin{array}{l} c_{p,w}(T) = c_{p,w0} + c_{p,w0} H_w^T (T-T_0) \\ c_{p,a}(T) = c_{p,a0} + c_{p,a0} H_a^T (T-T_0)\\ c_{p,s}(T) = c_{p,s0} + c_{p,s0} H_s^T (T-T_0)\end{array}\] | ||
| ==== Files ==== | ==== Files ==== | ||
| - | Prepro: LWAVAT.F \\ | + | Prepro: LHMIC.F & EHMICA.F \\ |
| + | Lagamine: HMIC.F & EHMICB.F \\ | ||
| ===== Availability ===== | ===== Availability ===== | ||
| |Plane stress state| NO | | |Plane stress state| NO | | ||
| Line 134: | Line 98: | ||
| ^ Line 1 (2I5, 60A1)^^ | ^ Line 1 (2I5, 60A1)^^ | ||
| |IL|Law number| | |IL|Law number| | ||
| - | |ITYPE| 171 (= 174 in LOI2 for 3D state) | | + | |ITYPE| 628 | |
| |COMMENT| Any comment (up to 60 characters) that will be reproduced on the output listing| | |COMMENT| Any comment (up to 60 characters) that will be reproduced on the output listing| | ||
| ==== Integer parameters ==== | ==== Integer parameters ==== | ||
| - | ^ Line 1 (18I5) ^^ | + | ^ Line 1 (4I10) ^^ |
| - | |IANI|= 0, isotropic permeability case| | + | |NLAWFEM2|Number of constitutive laws at the sub-scale| |
| - | |:::| ≠ 0, anisotropic permeability case| | + | |KFLU|Number of DOF: 1=Pw, 2=Pw+Pg| |
| - | |IKW|formulation index for $k_w$| | + | |IGAS|Type of gas: 0=Air, 1=H2, 2=N2, 3=Ar, 4=He, 5=CO2, 6=CH4| |
| - | |IKA|formulation index for $k_a$| | + | |IDIFF|Activation of diffusion mechanism: 0=No, 1=Yes, | |
| - | |ISRW|formulation index for $S_W$| | + | ^ Line 2 (1G10.0) ^^ |
| - | |ITHERM|formulation index for $\Gamma_T$| | + | |FACONV|Units of conversion of the REV (it has a size of 1 [-])| |
| - | |IVAP|= 0 if no vapour diffusion in the problem| | + | |
| - | |:::|= 1 else| | + | |
| - | |IFORM|= 1 tangent formulation \[ \left\{\begin{array}{l}f_{we} = \dot{M}_w = (\dot{\varepsilon}_v S_w + n S_w\frac{\dot{\rho}_w}{\chi_w} + n \dot{S}_w) \rho_w \\ f_{ae} = \dot{M}_a = (\dot{\varepsilon}_V S_a + n S_a\frac{\dot{p}_a}{p_a} + n \dot{S}_a) \rho_a \end{array}\right. \]| | + | |
| - | |:::|= 0 secant formulation \[ \left\{\begin{array}{l} f_{we} = \dot{M}_w = (n^BS_w^B\rho_w^B - n^AS_w^A\rho_w^A)/\Delta t \\ f_{ae} = \dot{M}_a = (n^BS_a^B\rho_a^B - n^AS_a^A\rho_a^A)/\Delta t \end{array}\right. \]| | + | |
| - | |ICONV|= 0 if no convectif term in the heat transport problem| | + | |
| - | |:::|= 1 else| | + | |
| - | |ITEMOIN|= 0 if analytic matrix (can be used only if IVAP = 0 if no vapour diffusion in the problem)| | + | |
| - | |:::|= 1 if semi-analytic matrix (can be used in all the problems)| | + | |
| - | |IKRN|= 1 if Kozeni-Karmann formulation| | + | |
| - | |:::|= 2, GDR Momas relation $K=f(n)$| | + | |
| - | |:::|= 3 Coupling permeability-deformation $K=f(\varepsilon_n)$ (only in 2D)| | + | |
| - | |IGAS|= 0 if gas is air| | + | |
| - | |:::|= 1 if gas is $H_2$| | + | |
| - | |:::|= 2 if gas is $N_2$| | + | |
| - | |:::|= 3 if gas is Ar| | + | |
| - | |:::|= 4 if gas is He| | + | |
| - | |:::|= 5 if gas is $CO_2$| | + | |
| - | |IENTH|= 0 if we define $\rho$ and $C_p$ for each constituent \[\left\{\begin{array}{l}H_w = N.S_{r,w} \rho_w c_{p,w} (T-T_0) \\ H_v = n(1-S_{r,w})\rho_v c_{p,v} (T-T_0)\\ H_a = n(1-S_{r,w})\rho_ac_{p,a} (T-T_0)\\ H_{a-d} = n S_{r,w} H\rho_ac_{p,a} (T-T_0)\\ H_s = (1-n)\rho_s c_{p,s} (T-T_0) \end{array}\right.\]| | + | |
| - | |:::|= 1 if we define $\rho C_p$ equivalent for the medium and constant \[H_m = \rho C_p (T-T_0)\]| | + | |
| - | |:::|= 2 if we define $\rho C_p$ equivalent for the medium depending on temperature: \[\left\{\begin{array}{l} \rho C_p = RHOC1\ \text{if }\ T>T_u \\ \rho C_p = RHOC2\ \text{if }\ T<T_f \\ \rho C_p = \frac{RHOC1-RHOC2}{T_u-T_f}(T-T_u) + RHOC1\ \text{if }\ T_f\leq T \leq T_u\\ \end{array} \right.\] \[T_u = CLT3\] \[T_f = CLT4\]| | + | |
| - | |IANITH|= 0, isotropic conductivity case| | + | |
| - | |:::|= 1, anisotropic conductivity case| | + | |
| - | |IVISCW|= 0, $\mu_w = \mu_{w,0}\left( 1-ALPHW0(T-T_0)) \right)$| | + | |
| - | |:::|= 1, $\mu_w = 0.6612(T-229)^{-1.562}$| | + | |
| - | |IXHIW| = 0, constant water compressibility| | + | |
| - | |:::|= 1, $\chi_w = \chi_w + \frac{H}{p_a}$ ( $p_a$ is partial pressure of air and H is Henry coefficient)| | + | |
| - | |IDIFF|= 0, with diffusion of dissolved air| | + | |
| - | |:::|≠ 0, divisor (integer becomes real) of diffusion coefficient of dissolved air| | + | |
| - | |ISTRUCT|= 0, constant permeability| | + | |
| - | |:::|= 1, permeability depends on microstructure evolution| | + | |
| - | |ICOAL|= 0, solid conductivity: $\Gamma_s = \Gamma_{s,0}(1+GAMS0(T-T_0))$| | + | |
| - | |:::|= 1, solid conductivity: $\Gamma_s = \Gamma_{s,0}GAMS0(T-T_0)^3$| | + | |
| - | + | ||
| - | ==== Real parameters: permeabilities definition ==== | + | |
| - | The permeability $k_f$ is an \underline{intrinsic} permeability ($\left[L^2\right]$) $\boxed{ \begin{array}{l} k_{f, intrinsic} = K_f \frac{\mu_f}{\rho_f g}\\ \left[ L^2 \right] = \left[ LT^{-1} \right] \frac{ \left[ ML^{-1}T^{-1}\right]}{\left[ML^{-3}\right]\left[LT^{-2}\right]} \end{array}}$\\ | + | |
| - | ^If IANI ≠ 0 (4G10.0) - Repeated IANI times^^ | + | |
| - | |PERME(I)|soil anisotropic int. permeability ($k_f$) in the direction I| | + | |
| - | |COSX(I)|director cosinus of the direction I \\ (in 3d state)| | + | |
| - | |COSY(I)|:::| | + | |
| - | |COSZ(I)|:::| | + | |
| - | Permeabilities in different directions can be input ( $I_{max}= 10$ ).The effect of these permeabilities will be summed. | + | |
| - | ^If IANI = 0 (1G10.0)^^ | + | |
| - | |PERME|soil isotropic intrinsic permeability ($k_f$)| | + | |
| ==== Real parameters ==== | ==== Real parameters ==== | ||
| ^ Line 1 (5G10.0) ^^ | ^ Line 1 (5G10.0) ^^ | ||
| - | |POROS|soil porosity $(= n)$| | + | |VISCW0|Liquid dynamic viscosity $(=\mu_{w,0})\ \left[ Pa.s \right]$| |
| - | |TORTU|soil tortuosity $(=\tau )$| | + | |RHOW0|Liquid density $(=\rho_{w,0})\ \left[ kg.m^{-3}\right]$| |
| - | |T0|definition temperature $(=T_0)\ \left[K\right]$| | + | |UXHIW|Liquid compressibility coefficient $(=1/ \chi_{w})\ \left[ Pa^{-1}\right]$| |
| - | |PW0|definition liquid pression $(=p_{w,0})\ \left[Pa\right]$| | + | |PW0|Initial water pressure $\left[ Pa\right]$| |
| - | |PA0|definition gaz pression $(=p_{a,0})\ \left[Pa\right]$| | + | |T0|Initial temperature $\left[ K\right]$| |
| - | ^ Line 2 (7G10.0) ^^ | + | ^ Line 2 (3E10.2,2G10.0) ^^ |
| - | |VISCW0|liquid dynamic viscosity $(=\mu_{w,0}\ \left[ Pa.s \right]$| | + | |VISCA0|Gas dynamic viscosity $(=\mu_{a,0})\ \left[Pa.s \right]$| |
| - | |ALPHW0|liquid dynamic viscosity thermal coefficient $(=\alpha_{w}^T)\ \left[K^{-1}\right]$| | + | |RHOA0|Gaz density $(=\rho_{a,0})\ \left[kg.m^{-3}\right]$| |
| - | |RHOW0|liquid density $(=\rho_{w,0})\ \left[ kg.m^{-3}\right]$ | + | |PMGAS|Gas molar mass $[g/mol]$| |
| - | |UXHIW0|liquid compressibility coefficient $(=1/ \chi_{w})\ \left[ Pa^{-1}\right]$| | + | |PA0|Initial gas pressure $\left[ Pa\right]$| |
| - | |BETAW0|liquid thermal expansion coefficient $(=\beta{w}^T\ \left[K^{-1}\right]$| | + | |PHENRY|Henry coefficient $\left[ -\right]$| |
| - | |CONW0|liquid thermal conductivity $(=\Gamma_{w,0})\ \left[W.m^{-1}.K^{-1}\right]$| | + | |
| - | |GAMW0|liquid thermal conductivity coefficient $(=\gamma_{w}^T\ \left[K^{-1}\right]$| | + | |
| - | ^ Line 3 (3G10.0) ^^ | + | |
| - | |CPW0|liquid specific heat $(=c_{p,w0})\ \left[J.kg^{-1}.K^{-1}\right]$| | + | |
| - | |HEATW0|liquid specific heat coefficient $(=H_{w}^T)\ \left[K^{-1}\right]$| | + | |
| - | |EMMAG|storage coefficient $(=E_s)\ \left[ P_a^{-1}\right]$| | + | |
| - | ^ Line 4 (7G10.0) ^^ | + | |
| - | |VISCA0|gaz dynamic viscosity $(=\mu_{a,0})\ \left[Pa.s \right]$\ | + | |
| - | |ALPHW0|gaz dynamic viscosity thermal coefficient$(=\alpha_{a}^T)\ \left[K^{-1}\right]$| | + | |
| - | |RHOA0|gaz density$(=\rho_{a,0})\ \left[kg.m^{-3}\right]$| | + | |
| - | |CONA0|gaz thermal conductivity $(=\Gamma_{a,0})\ \left[W.m^{-1}.K^{-1}\right]$| | + | |
| - | |GAMA0|gaz thermal conductivity coefficient $(=\gamma_{a}^T)\ \left[K^{-1}\right]$| | + | |
| - | |CPA0|gaz specific heat $(=c_{p,a0})\ \left[J.kg^{-1}.K^{-1}\right]$| | + | |
| - | |HEATA0|gaz specific heat coefficient $(=H_{a}^T)\ \left[K^{-1}\right]$| | + | |
| - | ^ Line 5 (5G10.0) ^^ | + | |
| - | |BETAS0|solid thermal expansion coefficient $(=\beta_{s}^T)\ \left[K^{-1}\right]$| | + | |
| - | |CONS0|solid thermal conduction$(=\Gamma_{s,0})\ \left[W.m^{-1}.K^{-1}\right]$| | + | |
| - | |GAMS0|solid conduction coefficient $(=\gamma_{s}^T)\ \left[K^{-1}\right]$| | + | |
| - | |CPS0|solid specific heat $(=c_{p,s0})\ \left[J.kg^{-1}. K^{-1}\right]$| | + | |
| - | |HEATS0|solid specific heat coefficient $(=H_{s}^T)\ \left[ K^{-1}\right]$| | + | |
| - | ^ Line 6 (3G10.0) ^^ | + | |
| - | |CKW1|1st coefficient of the function $k_{rw}$| | + | |
| - | |CKW2|2nd coefficient of the function $k_{rw}$| | + | |
| - | |CKW3|3rd coefficient of the function $k_{rw}$| | + | |
| - | ^ Line 7 (3G10.0) ^^ | + | |
| - | |CKA1|1st coefficient of the function $k_{ra}$| | + | |
| - | |CKA2|2nd coefficient of the function $k_{ra}$| | + | |
| - | |CSR5|5th coefficient of the function $S_w$| | + | |
| - | ^ Line 8 (7G10.0/) ^^ | + | |
| - | |CSR1|1st coefficient of the function $S_w$| | + | |
| - | |CSR2|2nd coefficient of the function $S_w$| | + | |
| - | |CSR3|3rd coefficient of the function $S_w$| | + | |
| - | |CSR4|4th coefficient of the function $S_w$| | + | |
| - | |SRES|residual saturation degree $(=S_{res})$| | + | |
| - | |SRFIELD|field saturation degree $(=S_{r, field})$| | + | |
| - | |AIREV|air entry value $\left[Pa\right]$| | + | |
| - | ^ Line 9 (7G10.0) ^^ | + | |
| - | |CLT1|1st coefficient of the function $\Gamma_T$| | + | |
| - | |CLT2|2nd coefficient of the function $\Gamma_T$| | + | |
| - | |CLT3|3rd coefficient of the function $\Gamma_T$| | + | |
| - | |CLT4|4th coefficient of the function $\Gamma_T$| | + | |
| - | |RHOC|coefficient for enthalpie $\rho C_p$ (if ienth = 1)| | + | |
| - | |RHOC1|1st coefficient for enthalpie $\rho C_p$ (if ienth = 2)| | + | |
| - | |RHOC2|2nd coefficient for enthalpie $\rho C_p$ (if ienth = 2)| | + | |
| - | ^ Line 10 (4G10.0) ^^ | + | |
| - | |KRMIN|Minimum value of $kr$| | + | |
| - | |HENRY|Henry coefficient| | + | |
| - | |EXPM|for IKRN=1: $m$ Exponent of Kozeni-Karmann formulation| | + | |
| - | |:::|for IKRN=3 : A parameter| | + | |
| - | |EXPN|n Exponent of Kozeni-Karmann formulation| | + | |
| - | ^Line 11 - Only if IANITH ≠ 0 (4G10.0) - Repeat IANITH times^^ | + | |
| - | |CONDUC(I)|soil anisotropic conductivity in the direction I| | + | |
| - | |COSX(I)|director cosinus of the direction I \\ (in 3d state)| | + | |
| - | |COSY(I)|:::| | + | |
| - | |COSZ(I)|:::| | + | |
| - | |Thermal conductivities in different directions can be input (Imax = 10). The effect of these conductivities will be summed. In that case of anisotropic conductivity, conductivities remain constants for each direction: coefficients ITHERM, CLT1, CLT2, CLT3, CT4, CONS0, CONW0, and CONA0 are so not used in that case|| | + | |
| - | ^If IANITH = 0: nothing^^ | + | |
| - | |Isotropic thermal conductivity is already defined by preceding coefficients ITHERM, CLT1, CLT2, CLT3, CT4, CONS0, CONW0, CONA0 …|| | + | |
| - | Following empirical formulations for describing the evolution of the relative permeability, the thermal conductivity and saturation with the suction are possible: see [[appendices:a8|Appendix 8]]. | + | ==== Sub-scale parameters ==== |
| - | For any suction lower than air entry value (AIREV), the saturation is equal to SRFIELD value. \\ | + | To be repeated as many time as NLAWFEM2. |
| - | __Kozeny Karman formulation:__ | + | ^ Line 1 (7I5) ^^ |
| - | \[K = C_0 \frac{n^{EXPN}}{(1-n)^{EXPM}}\] | + | |ILAW2|No. of the sub-scale constitutive law (=1:NLAWFEM2)| |
| - | $C_0$ is computed automatically from $C_0 = K_0 \frac{(1-n_0)^{EXPM}}{(n_0)^{EXPn}}$ \\ | + | |ITYPE2|Type of sub-scale law: 1=Fracture (manual), 2=Fracture (automatic), 3=Tube (manual), 4=Tube (automatic), 5=Bridge (manual), 6=Bridge (automatic)| |
| - | __GDR Momas formulation:__ | + | |ISR|Retention curve: 1=Brooks-Corey for fracture, 2=Brooks-Corey for tube, 3=van Genuchten for fracture, 4=van Genuchten for tube| |
| - | \[ | + | |IKW|Water relative permeability curve | |
| - | \frac{k}{k_0} = 1+EXPM\left[ \phi - \phi_0\right]^{EXPN}\ \text{où}\ EXPM = 2.10^{12}\ \text{et}\ EXPN = 3 | + | |IKA|Gas relative permeability curve| |
| - | \] | + | |INUMEL2|Number of micro-elements with this law| |
| + | |ICONST|Constant element opening: 0=No, 1=Yes| | ||
| + | ^ Line 2 - Retention curve coefficients (4G10.0) ^^ | ||
| + | |PE0|Initial air entry pressure of the micro-element| | ||
| + | |CDF|Exponent parameter| | ||
| + | |SRES|Residual saturation degree $(=S_{res})$| | ||
| + | |SRG0|Initial gas saturation| | ||
| + | |AKRMIN|Minimum value of relative permeability| | ||
| + | |SRFIELD|Field saturation degree $(=S_{r, field})$| | ||
| + | |CDF2|Exponent parameter| | ||
| + | |CSR8|8th parameter of ISR| | ||
| + | ^ Line 3 - Fracture law coefficients (4G10.0) ^^ | ||
| + | |AKP|Stiffness parameter of the material| | ||
| + | |GAMMA|Exponent parameter| | ||
| + | |DINI|Initial aperture| | ||
| + | |DMAX|Maximum aperture| | ||
| + | ^ Line 3 - Tube law coefficients (3G10.0) ^^ | ||
| + | |DINI|Initial aperture| | ||
| + | |DMAX|Maximum aperture| | ||
| + | |TORT|Tortuosity| | ||
| - | __Coupling permeability-deformation formulation:__ (only in 2D) | ||
| - | \[ | ||
| - | K_{ij} = \sum_n K_n^0 (1+A\varepsilon_n^T)^3\beta_{ij} (\alpha_n) | ||
| - | \] | ||
| - | $\varepsilon_n^T$ tensile deformation \\ | ||
| - | $\alpha_n$ crack orientation with horizontal \\ | ||
| - | $A$ parameter of the crack | ||
| ===== Stresses ===== | ===== Stresses ===== | ||
| ==== Number of stresses ==== | ==== Number of stresses ==== | ||
| - | 24 | + | 28 |
| ==== Meaning ==== | ==== Meaning ==== | ||
| __In 2D state :__ | __In 2D state :__ | ||
| - | |SIG(1)|liquid velocity in the X direction $(=f_{wx})$|| | + | |SIG(1)|$\sigma_x$ (unused)| |
| - | |SIG(2)|liquid velocity in the Y direction $(=f_{wy})$|| | + | |SIG(2)|$\sigma_y$ (unused)| |
| - | |SIG(3)|liquid velocity stored $(=f_{we})$|| | + | |SIG(3)|$\sigma_{xy}$ (unused)| |
| - | |SIG(4)|none|| | + | |SIG(4)|$\sigma_z$ (unused)| |
| - | |SIG(5)|gas total velocity in the X direction $(=f_{ax})$|gas advection + \\ gas diffusion + \\ dissolved gas advection + \\ dissolved gas diffusion| | + | |SIG(5)|Homogenised liquid flow along $x$ $(=f_{wx})$| |
| - | |SIG(6)|gas total velocity in the Y direction $(=f_{ay})$|:::| | + | |SIG(6)|Homogenised liquid flow along $y$ $(=f_{wy})$| |
| - | |SIG(7)|gas total velocity stored $(=f_{ae})$|:::| | + | |SIG(7)|Homogenised liquid flow stored $(=f_{we})$| |
| - | |SIG(8)|none|:::| | + | |SIG(8)|Homogenised gas flow along $x$ $(=f_{ax})$|gas advection + \\ gas diffusion + \\ dissolved gas advection + \\ dissolved gas diffusion| |
| - | |SIG(9)|conductive heat flow in the X direction $(=f_{tx})$|| | + | |SIG(9)|Homogenised gas flow along $y$ $(=f_{ay})$|:::| |
| - | |SIG(10)|conductive heat flow in the Y direction $(=f_{ty})$|| | + | |SIG(10)|Homogenised gas flow stored $(=f_{ae})$|:::| |
| - | |SIG(11)|energy accumulated by heat capacity $(=f_{te})$|| | + | |SIG(11)|Advection dissolved gas flow along $x$ $(=f_{ad,x})$| |
| - | |SIG(12)|none|| | + | |SIG(12)|Advection dissolved gas flow along $y$ $(=f_{ad,y})$| |
| - | |SIG(13)|Water vapour velocity in the X direction $(=f_{vx})$|| | + | |SIG(13)|Diffusion dissolved gas flow along $x$ $(=f_{add,x})$| |
| - | |SIG(14)|Water vapour velocity in the Y direction $(=f_{vy})$|| | + | |SIG(14)|Diffusion dissolved gas flow along $y$ $(=f_{add,y})$| |
| - | |SIG(15)|Water vapour stored $(=f_{ve})$|| | + | |SIG(15)|Advection gaseous gas flux along $x$ $(=f_{ag,x})$| |
| - | |SIG(16)|none|| | + | |SIG(16)|Advection gaseous gas flux along $y$ $(=f_{ag,y})$| |
| - | |SIG(17)|dissolved gas advection and diffusion velocity in the X direction|| | + | |SIG(18)|Unused| |
| - | |SIG(18)|dissolved gas advection and diffusion velocity in the Y direction|| | + | |SIG(18)|Unused| |
| - | |SIG(19)|dissolved gas advection and diffusion velocity stored|| | + | |SIG(19)|Unused| |
| - | |SIG(20)|none|| | + | |SIG(20)|Unused| |
| - | |SIG(21)|dissolved gas diffusion velocity in the X direction|| | + | |SIG(21)|Unused| |
| - | |SIG(22)|dissolved gas diffusion velocity in the Y direction|| | + | |SIG(22)|Unused| |
| - | |SIG(23)|dissolved gas and diffusion velocity stored|| | + | |SIG(23)|Unused| |
| - | |SIG(24)| none|| | + | |SIG(24)|Unused| |
| - | __In 3D state :__ | + | |SIG(25)|Unused| |
| - | |SIG(1)|liquid velocity in the X direction $(=f_{wx})$|| | + | |SIG(26)|Unused| |
| - | |SIG(2)|liquid velocity in the Y direction $(=f_{wy})$|| | + | |SIG(27)|Unused| |
| - | |SIG(3)|liquid velocity in the Z direction $(=f_{wz})$|| | + | |SIG(28)|Unused| |
| - | |SIG(4)|liquid velocity stored $(=f_{we})$|| | + | |
| - | |SIG(5)|gas total velocity in the X direction $(=f_{ax})$|gas advection + \\ gas diffusion + \\ dissolved gas advection + \\ dissolved gas diffusion| | + | |
| - | |SIG(6)|gas total velocity in the Y direction $(=f_{ay})$|:::| | + | |
| - | |SIG(7)|gas total velocity in the Z direction $(=f_{az})$|:::| | + | |
| - | |SIG(8)|gas total velocity stored $(=f_{az})$|:::| | + | |
| - | |SIG(9)|conductive heat flow in the X direction $(=f_{tx})$|| | + | |
| - | |SIG(10)|conductive heat flow in the Y direction $(=f_{ty})$|| | + | |
| - | |SIG(11)|conductive heat flow in the Z direction $(=f_{tz})$|| | + | |
| - | |SIG(12)|energy accumulated by heat capacity $(=f_{te})$|| | + | |
| - | |SIG(13)|Water vapour velocity in the X direction $(=f_{yx})$|| | + | |
| - | |SIG(14)|Water vapour velocity in the Y direction $(=f_{yy})$|| | + | |
| - | |SIG(15)|Water vapour velocity in the Z direction $(=f_{yz})$|| | + | |
| - | |SIG(16)|Water vapour stored $(=f_{ye})$|| | + | |
| - | |SIG(17)|dissolved gas advection and diffusion velocity in the X direction || | + | |
| - | |SIG(18)|dissolved gas advection and diffusion velocity in the Y direction || | + | |
| - | |SIG(19)|dissolved gas advection and diffusion velocity in the Z direction || | + | |
| - | |SIG(20)|dissolved gas advection and diffusion velocity stored || | + | |
| - | |SIG(21)|dissolved gas diffusion velocity in the X direction || | + | |
| - | |SIG(22)|dissolved gas diffusion velocity in the Y direction || | + | |
| - | |SIG(23)|dissolved gas diffusion velocity in the Z direction || | + | |
| - | |SIG(24)|dissolved gas and diffusion velocity stored|| | + | |
| ===== State variables ===== | ===== State variables ===== | ||
| ==== Number of state variables ==== | ==== Number of state variables ==== | ||
| - | = 26 in 2D cases \\ | + | =6 in 2D cases |
| - | = 16 in 3D cases | + | |
| ==== List of state variables ==== | ==== List of state variables ==== | ||
| - | |Q(1)|water relative permeability $(=k_{rw})$ | | + | |Q(1)|Unused| |
| - | |Q(2)|air relative permeability $(=k_{ra})$ | | + | |Q(2)|Unused| |
| - | |Q(3)|Soil porosity (= n) | | + | |Q(3)|Homogenised macro-scale porosity| |
| - | |Q(4)|Soil saturation degree $(=S_w)$ | | + | |Q(4)|Homogenised macro-scale saturation| |
| - | |Q(5)|Suction $(=p_c = p_a-p_w)$ | | + | |Q(5)|Water storage| |
| - | |Q(6)|water specific mass $(=\rho_w)$ | | + | |Q(6)|Gas storage| |
| - | |Q(7)|air specific mass $(=\rho_a)$ | | + | |Q(7)|Saved fracture aperture of the current step (from 7 to 7+nico)| |
| - | |Q(8)|"Pe number" = convective effect / conductive effect \[= \frac{\rho_f . c_f . T . \vec{q}}{\Gamma_{av} . \vec{grad} (T)}\]| | + | |Q(8)|Unused| |
| - | |Q(9)|Water content (=w) | | + | |Q(9)|Unused| |
| - | |Q(10)|Vapour specific mass $(=\rho_v)$ | | + | |Q(10)|Unused| |
| - | |Q(11)|Vapour pressure $(=p_v)$ | | + | |Q(11)|Unused| |
| - | |Q(12)|Relative humidity $(=H_r)$ | | + | |Q(12)|Unused| |
| - | |Q(13)|Liquid water mass per unit soil volume | | + | |
| - | |Q(14)|Dry air mass per unit soil volume | | + | |
| - | |Q(15)|Vapour mass per unit soil volume | | + | |
| - | |Q(16)|Intrinsic permeability | | + | |
| - | |Q(17)|Gas soil saturation degree $(=S_g)$ | | + | |
| - | |Q(18)|$\alpha (H_2, N_2, …)$ partial pressure $(=p_a^g = p^g - p_{H_2O}^g = \text{gas pressure-vapour pressure})$ | | + | |
| - | |Q(19)|Area associated to one integration point | | + | |
| - | |Q(20)|Dissolved air concentration $=\frac{\rho_{a-d}}{\rho_w + \rho_{a-d}} = \frac{H_a \rho_a}{\rho_w + H_a \rho_a}$| | + | |
| - | |Q(21)|$K_{xx}$ (or zero if IANI = 0) | | + | |
| - | |Q(22)|$K_{yy}$ (or zero if IANI = 0) | | + | |
| - | |Q(23)|$K_{xy}$ (or zero if IANI = 0) | | + | |
| - | |Q(24)|$\varepsilon_1$ | | + | |
| - | |Q(25)|$\varepsilon_2$ | | + | |
| - | |Q(26)|$\alpha$ (= angle between principal stress and horizontal) | | + | |
laws/hmic.1700823633.txt.gz · Last modified: 2023/11/24 12:00 by gilles
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