Showing papers by "Steinar Evje published in 2012"

Numerical treatment of two-phase flow in capillary heterogeneous porous media by finite-volume approximations

Abstract: This paper is made available here with permission from the editors. http://www.math.ualberta.ca/ijnam/AIMS.htm

A Mathematical Model for Interpretation of Brine-Dependent Spontaneous Imbibition Experiments

Abstract: In this paper we consider a mathematical model that seeks to explain possible mechanisms for brine-dependent oil recovery in chalk. It is well documented through lab experiments that the brine composition has a strong impact on oil recovery. In particular, the role of the divalent ions (Ca2 , Mg2 and SO24−) present in seawater have been extensively studied. Also the effect of salinity which is mainly controlled by the monovalent ions Na and Cl− has been carefully investigated. It has been observed that chemical reactions occur between rock and brine when seawater or seawater-like brines are injected or diffuse into chalk at high temperature. Different chemical mechanisms are involved like ion exchange, adsorption, and precipitation/dissolution of minerals such as calcite, magnesite and anhydrite. Hence, these experiments suggest that for spontaneous imbibition tests the produced oil is a result of an interplay between capillary forces and the imposed water-rock chemistry. We are interested in formulating a theory for this observed behavior based on a proper combination of geochemical and two-phase model components. The mathematical model we present couples geochemical reactive transport with the capillary forces trapping the oil. When a brine different from the formation brine enters pore space the water-rock chemistry induces changes on the rock surface. It is suggested that this leads to correspond- ing changes of the wetting state as represented by relative permeability and capillary pressure curves. Different hypothesis concerning the possible link between geochemical changes of the rock-surface and changes of wetting state are explored. Specifically, we employ the model to dis- cuss some previously published lab experiments where systematic variations in Ca2 and SO24− in imbibing and initial brine were explored. The model suggests that at 70◦C neither dissolution nor precipitation are the main contributors for wettability alteration. Rather, a conceptual sulfate adsorption mechanism coupled to the surface activity of calcium readily explain how adding more sulfate and calcium to the system would increase oil recovery. Hence, we demonstrate how the model can be used as a tool for systematic investigations aiming at identifying key mechanisms important for mobilization of oil as a function of brine composition.

Two-phase flow in a fissurized-porous media

Abstract: Spontaneous imbibition can be an important drive mechanism in fractured reservoirs. We consider a low-permeable reservoir containing a high-permeable fracture network. This subject is of practical interest as fractured reservoirs represent as much as a third of the reservoirs in the world. In the mathematical description a linear fracture is symmetrically surrounded by porous matrix. Advective flow occurs only along the fracture, while capillary driven flow occurs only along the axis of the matrix. For a given set of relative permeability and capillary pressure curves the behavior of the system is completely determined by the choice of 2 parameters: (i) the ratio of time scales for advective flow in fracture to capillary flow in matrix α = τf/τm; (ii) the ratio of pore volumes in matrix and fracture β = Vm/Vf. A characteristic property of the flow in the coupled fracture-matrix medium is the linear recovery curve (before water breakthrough) followed by a non-linear part where the rate is decreasing. The m...

Dedicated to Professor Constantine M. Dafermos on the occasion of his 70th birthday

Abstract: We are interested in a viscous two-phase gas-liquid mixture model relevant for modeling of well control operations within the petroleum industry. We focus on a simplified mixture model and provide an existence result within an appropriate class of weak solutions. We demonstrate that upper and lower limits can be obtained for the gas and liquid masses which ensure that transition to single-phase regions do not occur. This is used together with appropriate a prior estimates to obtain convergence to a weak solution for a sequence of approximate solutions corresponding to mollified initial data. Moreover, by imposing an additional regularity condition on the initial masses, a uniqueness result is obtained. The framework herein seems useful for further investigations of more realistic versions of the gas-liquid model that take into account different flow regimes.