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WPRO
Description
Constitutive law for well limit condition for element WEPRO
Implemented by: F. Collin, 2001
The model
This constitutive law is used for non-linear flow analysis of solids and allows to model fluids exchanges between a well and the reservoir.
The retention curve allows to compute the relative permeabilities and to see which fluids is mobile.
Files
Prepro: LWPRO.F
Lagamine: WPRO.F
Availability
| Plane stress state | NO |
| Plane strain state | YES |
| Axisymmetric state | YES |
| 3D state | NO |
| Generalized plane state | NO |
Input file
Parameters defining the type of constitutive law
| Line 1 (2I5, 60A1) | |
|---|---|
| IL | Law number |
| ITYPE | 197 |
| COMMENT | Any comment (up to 60 characters) that will be reproduced on the output listing |
Integer parameters
| Line 1 (4I5) | |
|---|---|
| ISR | Formulation index for $S_w$ (see Appendix 8) |
| IKW | Formulation index for $k_{r,w}$ (see Appendix 8) |
| IKP | Formulation index for $k_{r,p}$ (see Appendix 8) |
| IINJ | Index to specify the type of well |
| = 0 : production well | |
| = 1 : injection well | |
Real parameters
| Line 1 (1G10.0) | |
|---|---|
| TFACT | Soil geometric factor |
| Line 2 (4G10.0) | |
| VISCW | Water dynamic viscosity |
| RHOW | Water density |
| VISCP | Oil dynamic viscosity |
| RHOP | Oil density |
| Line 3 (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 [Pa] |
| Line 4 (3G10.0) | |
| CKW1 | 1st coefficient of the function $k_{r,w}$ |
| CKW2 | 2nd coefficient of the function $k_{r,w}$ |
| CKW3 | 3rd coefficient of the function $k_{r,w}$ |
| Line 5 (2G10.0) | |
| CKP1 | 1st coefficient of the function $k_{r,p}$ |
| CKP2 | 2nd coefficient of the function $k_{r,p}$ |
| Line 6 (1G10.0) | |
| KRMIN | Minimum value of $k_r$ |
Stresses
Number of stresses
2
Meaning
| SIG(1) | Current value of water flow |
| SIG(2) | Current value of oil flow |
State variables
Number of state variables
5
List of state variables
| Q(1) | none |
| Q(2) | Water saturation degree |
| Q(3) | Element jacobian |
| Q(4) | Well pressure at the integration point |
| Q(5) | Generalised reservoir pressure at the integration point |
Comments
For IINJ = 0 (production well), the fluid flow has the following expression : \[SIG(1) = f_w=T^{well}.\frac{k_{rw}}{\mu_w}(p_w-p_{well})\]\[SIG(2) = f_o=T^{well}.\frac{k_{ro}}{\mu_o}(p_o-p_{well})\]
For IINJ = 1 (injection well), the water injection flow has the following expression : \[SIG(1) = f_w = T^{well}.\left(\frac{k_{rw}}{\mu_w}+\frac{k_{ro}}{\mu_o}\right).(p_w-p_{well})\]\[SIG(2)=0\]
