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A new formulation for non-equilibrium capillarity effect using multi-gene genetic programming (MGGP): accounting for fluid and porous media properties

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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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