Modelling of wettability alteration processes in carbonate oil reservoirs

Previous studies have shown that seawater may alter the wettability in the direction of more water-wet conditions in carbonate reservoirs. The reason for this is that ions from the salt (sulphat, magnesium, calsium, etc) can create a wettability alteration toward more water-wet conditions as salt is absorbed on the rock. In order to initiate a more systematic study of this phenomenon a 1-D mathematical model relevant for spontaneous imbibition is formulated. The model represents a core plug on laboratory scale where a general wettability alteration (WA) agent is included. Relative permeability and capillary pressure curves are obtained via interpolation between two sets of curves corresponding to oil-wet and water-wet conditions. This interpolation depends on the adsorption isotherm in such a way that when no adsorption of the WA agent has taken place, oil-wet conditions prevail. However, as the adsorption of this agent takes place, gradually there is a shift towards more water-wet conditions. Hence, the basic mechanism that adsorption of the WA agent is responsible for the wettability alteration, is naturally captured by the model. Conservation of mass of oil, water, and the WA agent, combined with Darcy's law, yield a 2x2 system of coupled parabolic convection-diffusion equations, one equation for the water phase and another for the concentration of the WA agent. The model describes the interactions between gravity and capillarity when initial oil-wet core experiences a wettability alteration towards more water-wet conditions due to the spreading of the WA agent by molecular diffusion. Basic properties of the model are studied by considering a discrete version. Numerical computations are performed to explore the role of molecular diffusion of the WA agent into the core plug, the balance between gravity and capillary forces, and dynamic wettability alteration versus permanent wetting states. In particular, a new and characteristic oil-bank is observed. This is due to incorporation of dynamic wettability alteration and cannot be seen for case with permanent wetting characteristics. More precisely, the phenomenon is caused by a cross-diffusion term appearing in capillary diffusion term.

[1]  T. Austad,et al.  Wettability and oil recovery from carbonates: Effects of temperature and potential determining ions , 2006 .

[2]  Mark A. J. Chaplain,et al.  Mathematical modelling of cancer invasion of tissue: dynamic heterogeneity , 2006, Networks Heterog. Media.

[3]  T. Austad,et al.  Seawater as IOR Fluid in Fractured Chalk , 2005 .

[4]  Mostafa Bendahmane,et al.  ON A TWO-SIDEDLY DEGENERATE CHEMOTAXIS MODEL WITH VOLUME-FILLING EFFECT , 2007 .

[5]  Hermano Frid,et al.  A Quasi-linear Parabolic System for Three-Phase Capillary Flow in Porous Media , 2003, SIAM J. Math. Anal..

[6]  Gary A. Pope,et al.  The Application of Fractional Flow Theory to Enhanced Oil Recovery , 1980 .

[7]  L. K. Thomas,et al.  Ekofisk Formation Pilot Waterflood , 1988 .

[8]  A. Kjosavik,et al.  Relative Permeability Correlation for Mixed-Wet Reservoirs , 2002 .

[9]  Zhongke Shi,et al.  Application of a fourth-order relaxation scheme to hyperbolic systems of conservation laws , 2006 .

[10]  Y. AMIRAT,et al.  Global Weak Solutions to Equations of Compressible Miscible Flows in Porous Media , 2007, SIAM J. Math. Anal..

[11]  Thormod Johansen,et al.  The Riemann problem for multicomponent polymer flooding , 1989 .

[12]  T. Austad,et al.  Wettability alteration of carbonates—Effects of potential determining ions (Ca2+ and SO42−) and temperature , 2006 .

[13]  A. Kjosavik,et al.  Capillary Pressure Correlation for Mixed-Wet Reservoirs , 2000 .

[14]  Z. Xin,et al.  The relaxation schemes for systems of conservation laws in arbitrary space dimensions , 1995 .

[15]  S. Evje,et al.  Relaxation schemes for the calculation of two-phase flow in pipes , 2002 .

[16]  A. Ziani,et al.  Global weak solutions for a parabolic system modeling a one-dimensional miscible flow in porous media , 1998 .

[17]  E. Tadmor,et al.  New High-Resolution Central Schemes for Nonlinear Conservation Laws and Convection—Diffusion Equations , 2000 .

[18]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[19]  Béatrice Rivière,et al.  Computational methods for multiphase flows in porous media , 2007, Math. Comput..

[20]  Pavel Bedrikovetsky,et al.  Mathematical Theory of Oil and Gas Recovery , 1993 .

[21]  Raimund Bürger,et al.  Strongly Degenerate Parabolic-Hyperbolic Systems Modeling Polydisperse Sedimentation with Compression , 2003, SIAM J. Appl. Math..

[22]  B. Perthame.  Transport Equations in Biology , 2006 .

[23]  Ragnar Winther,et al.  The Solution of the Riemann Problem for a Hyperbolic System of Conservation Laws Modeling Polymer Flooding , 1988 .

[24]  D. Standnes,et al.  Wettability alteration in chalk 1. Preparation of core material and oil properties , 2000 .

[25]  D. Standnes,et al.  Spontaneous Imbibition of Aqueous Surfactant Solutions into Neutral to Oil-Wet Carbonate Cores: Effects of Brine Salinity and Composition , 2003 .

[26]  Eduardo Abreu,et al.  Three-phase immiscible displacement in heterogeneous petroleum reservoirs , 2006, Math. Comput. Simul..

[27]  Dung Le,et al.  Global existence for a class of strongly coupled parabolic systems , 2006, 2105.08615.

[28]  Hermano Frid,et al.  Initial Boundary Value Problems for a Quasi-linear Parabolic System in Three-Phase Capillary Flow in Porous Media , 2005, SIAM J. Math. Anal..

[29]  T. Austad,et al.  Wettability alteration and improved oil recovery by spontaneous imbibition of seawater into chalk: Impact of the potential determining ions Ca2+, Mg2+, and SO42− , 2007 .

[30]  Yuanle Ma,et al.  Computational methods for multiphase flows in porous media , 2007, Math. Comput..

[31]  D. Le,et al.  Persistence for a Class of Triangular Cross Diffusion Parabolic Systems , 2005 .

[32]  D. Standnes,et al.  Wettability alteration in carbonates , 2003 .

[33]  H. Joachim Schroll.  Relaxed High Resolution Schemes for Hyperbolic Conservation Laws , 2004, J. Sci. Comput..

[34]  Dag Chun Standnes,et al.  Wettability alteration in chalk 2. Mechanism for wettability alteration from oil-wet to water-wet using surfactants , 2000 .