Modeling Capillary Pressure and Relative Permeability for Systems with Heterogeneous Wettability

by
Sonia Mariette Embid Droz, Ph.D.

University of Texas at Austin, 1997
Supervisors: Larry W. Lake
Kamy Sepehrnoori

Relative permeability is one of the most important parameters in reservoir simulation. Because of the complexity of representing multiphase flow in a permeable medium, most relative permeability models are empirical. Also these empirical correlations are mainly for water-wet systems while it is now well known that most reservoirs have mixed wettability.

The purpose of this study is to develop a relative permeability model that takes into account hysteresis and can be used for media with mixed wettability. To achieve this objective, we follow two approaches. The first is based on modifying empirical correlations, originally developed for water-wet systems, to mixed wet systems. We present an extension of the Brooks and Corey correlation that includes the contact angle and the pore size distributions. This approach gives an integral expression that must be solved numerically for relative permeability and capillary pressure. In this first approach, we also include correlations using neural networks to determine relative permeability and capillary pressure for water-, oil-, and mixed wet systems.

In the second approach, we modified the Carman-Kozeny equation to obtain an analytical model to calculate the capillary pressure and relative permeability for systems with heterogeneous wettability. To extend the Carman-Kozeny equation to multiphase systems, we assumed that each phases behaves as if it were alone. The final expression is a function of the surface areas and phase and residual saturations.

To validate those approaches we designed a new experimental apparatus to measure relative permeability and capillary pressure simultaneously. This equipment was based on alternating oil-wet and water-wet ceramic rings placed along a core holder in which steady-state flow was carried out to determine relative permeability. The difference in the pressures measured at the oil-wet and water-wet ceramic rings gave the capillary pressure.

A sensitivity analysis using the integral model shows that wettability, initial saturations and pore-sized distribution control the values and shape of the capillary pressure and relative permeability curves. The correlation obtained with the neural networks can reproduce the experimental capillary pressure data with an error smaller than the analytical model based on the Carman-Kozeny equation (sum-squared error less than 0.02 and 1.3 respectively). On the other hand, the analytical model provides a better understanding of the wettability phenomena than the empirical models.

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