Upscaling of fractured oil reservoirs using homogenization including non-equilibrium capillary pressure and relative permeability

Abstract

Recovery from incompletely water-wet fractured reservoirs can be extremely low. A reason for the low recovery is related to wetting issues, whereas the reason for slow recovery can be the non-equilibrium behavior of capillary pressure. One of the non-equilibrium theories is developed by Barenblatt et al. and it modifies both capillary pressure and relative permeabilities. The other theory is developed by Hassanizadeh et al. and it only deals with non-equilibrium effects for capillary pressure. To incorporate non-equilibrium in larger-scale problems, we apply homogenization to derive an upscaled model for fractured reservoirs in which the nonequilibrium effects are included. We formulate a fully implicit three-dimensional upscaled numerical model. Furthermore, we develop a computationally efficient numerical approach to solve the upscaled model. We use simulations to determine the range of delay times and capillary-damping coefficients for which discernable effects occur in terms of oil recovery. It is shown that at low Peclet numbers, i.e., when the residence time of the fluids in the fracture is long with respect to the imbibition time, incorporation of delay times of the order of few months have no significant effect on the oil recovery. However, when the Peclet number is large, the delay times reduce the rate of oil recovery. We discuss for which values of the delay time (Barenblatt) and capillary-damping coefficient (Hassanizadeh), significant delays in oil production occur.

Dynamic capillarity during displacement process in fractured tight reservoirs with multiple fluid viscosities

“…44 Thus, we only consider the dynamic capillary pressure, the dynamic coefficient, and the dynamic contact angle in the matrix in this work. The dynamic effect in fractures can be neglected due to the high permeability and low capillary pressure of fractures.…”

“…The dynamic effect in fractures can be neglected due to the high permeability and low capillary pressure of fractures. 44 Thus, we only consider the dynamic capillary pressure, the dynamic coefficient, and the dynamic contact angle in the matrix in this work. The time derivative of water saturation and the relative permeability are measured for the whole core sample.…”

The Global Kondaurov Double Porosity Model

“…We observe that the physical and mathematical models presented in the existing literature are, in fact, the equilibrium ones. However, the experimental studies [4] and the engineering applications of the two-phase flow models [13] show that these models are not sufficient to describe the two-phase flow process in porous media in a proper manner. For example, as it is underlined in [4], the reason for a slow oil recovery can be a non-equilibrium behavior of the capillary pressure.…”

“…However, we observe that only in a few papers the authors start with a locally non-equilibrium model. This is done in [2,13], where the homogenization of Barenblatts and Hassanizadehs flow models (see [3]) and in [10,11], where the homogenization of Kondaurov's model is considered. Notice that the Barenblatt, Hassanizadeh, and Kondaurov flow models are discussed in details in the papers [9,10].…”

Homogenized Model of Two-Phase Flow with Local Nonequilibrium in Double Porosity Media

“…The two-phase flow in double porosity medium with local nonequilibrium has been studied in [12] where upscaling was performed numerically.…”