Abstract
An artificial neural network (ANN) is presented for computing a parameter of dynamic two-phase flow in porous media with water as wetting phase, namely, dynamic coefficient (τ), by considering micro-heterogeneity in porous media as a key parameter. τ quantifies the dependence of time derivative of water saturation on the capillary pressures and indicates the rates at which a two-phase flow system may reach flow equilibrium. Therefore, τ is of importance in the study of dynamic two-phase flow in porous media. An attempt has been made in this work to reduce computational and experimental effort by developing and applying an ANN which can predict the dynamic coefficient through the learning from available data. The data employed for testing and training the ANN have been obtained from computational flow physics-based studies. Six input parameters have been used for the training, performance testing and validation of the ANN which include water saturation, intensity of heterogeneity, average permeability depending on this intensity, fluid density ratio, fluid viscosity ratio and temperature. It is found that a 15 neuron, single hidden layer ANN can characterize the relationship between media heterogeneity and dynamic coefficient and it ensures a reliable prediction of the dynamic coefficient as a function of water saturation.
Highlights
Mathematical models of two-phase flow in porous medium require equations for conservation of fluids’ mass and momentum in conjunction with appropriate constitutive equations for capillary pressure (Pc)-saturation (Sw)-relative permeability (Kr) relationships (Ataie-Ashtiani et al 2003; Das and Mirzaei 2013)
Similar to Hanspal et al (2013), we argue that the effects of any other system parameters that are not explicitly accounted for in the artificial neural network (ANN) structure are lumped in the values of the saturation and dynamic coefficient
The best linear fit is described by a slope (M) = 1, y-intercept (B) = 0 and a mean square error (MSE) = 1
Summary
Mathematical models of two-phase (e.g., oil-water) flow in porous medium require equations for conservation of fluids’ mass and momentum in conjunction with appropriate constitutive equations for capillary pressure (Pc)-saturation (Sw)-relative permeability (Kr) relationships (Ataie-Ashtiani et al 2003; Das and Mirzaei 2013). Recent studies have established that while the experiments for measuring the dynamic coefficient is a time consuming process lasting from many days to weeks (Das and Mirzaei 2013; Mirzaei and Das 2013), the mathematical and computer simulation tools based on flow physics are complex or computationally resource/time intensive (Manthey et al 2005; Mirzaei and Das 2007; Hanspal and Das 2012) This issue becomes important in the case of experiments involving heterogeneous domain where controlling the distribution and intensity of heterogeneity (defined as the ratio of the volume of heterogeneity to the total sample volume). The results in this paper seem to suggest that an ANN structure with 6 input and 1 output variables can incorporate the salient features of the dependence of dynamic coefficient on the intensity of micro-heterogeneity in porous media
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