Abstract
Dynamic coefficient as an important parameter in determination of the dynamic behavior of capillary pressure is considered as a function of various fluid and porous media properties. In this study, a new and general formulation for predicting the dynamic coefficient was proposed and developed through which the key fluid and porous media properties are accounted for. For expressing new formulation, multi-gene genetic programming (MGGP) was employed. Efficiency and robustness of the proposed model were investigated through experimental data and statistical measures of performance. A parametric study was designed to evaluate the impact of different parameters on the dynamic coefficient. Results show that the developed model is valid for a wide range of the conditions of two-phase flow in porous media. The model is a prerequisite for the accurate design, modeling, and application of dynamic capillarity effect in various fields of fluid flow in porous media. Furthermore, a new dimensionless number, the so-called dynamic effect number, was proposed and formulated which quantifies dynamic capillary force to viscous force ratio. Such a number would be useful and practical for the upscaling process and quantification of dominant forces in two-phase flow in porous media where limited experimental data are present.
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Abbreviations
- K (Darcy):
-
Intrinsic permeability
- k rnw (-):
-
Non-wetting phase relative permeability
- k rw (-):
-
Wetting phase relative permeability
- L d (cm):
-
Domain scale
- N Dy (-):
-
Dynamic effect number
- P c e (kPa):
-
Capillary pressure at equilibrium condition
- P d (kPa):
-
Entry pressure (Brooks–Corey parameter)
- P nw :
-
Non-wetting phase pressure
- P w :
-
Wetting phase pressure
- S w (Fraction):
-
Wetting phase saturation
- t :
-
Time
- τ (kPa S):
-
Dynamic coefficient
- λ (–):
-
Pore size distribution coefficient (Brooks–Corey parameter)
- λ nw :
-
Non-wetting phase mobility
- λ w :
-
Wetting phase mobility
- λ e :
-
Effective mobility
- μ nw (cP):
-
Non-wetting phase viscosity
- μ w (cP):
-
Wetting phase viscosity
- μ e (cP):
-
Effective viscosity
- Ø (Fraction):
-
Porosity
- MAE:
-
Mean absolute error
- MAPE:
-
Mean absolute percentage error
- MGGP:
-
Multi-gene genetic programming
- R 2 :
-
Coefficient of determination
- RMSE:
-
Root mean squared error
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Sakhaei, Z., Nikooee, E. & Riazi, M. A new formulation for non-equilibrium capillarity effect using multi-gene genetic programming (MGGP): accounting for fluid and porous media properties. Engineering with Computers 38, 1697–1709 (2022). https://doi.org/10.1007/s00366-020-01109-5
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DOI: https://doi.org/10.1007/s00366-020-01109-5