March  2008, 3(1): 149-183. doi: 10.3934/nhm.2008.3.149

Modelling of wettability alteration processes in carbonate oil reservoirs


University of Stavanger, NO-4036 Stavanger, Norway, Norway, Norway, Norway


International Research Institute of Stavanger (IRIS), Prof. Olav Hanssensvei 15, NO-4068 Stavanger, Norway, Norway

Received  September 2007 Revised  November 2007 Published  January 2008

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.
Citation: Liping Yu, Hans Kleppe, Terje Kaarstad, Svein M. Skjaeveland, Steinar Evje, Ingebret Fjelde. Modelling of wettability alteration processes in carbonate oil reservoirs. Networks & Heterogeneous Media, 2008, 3 (1) : 149-183. doi: 10.3934/nhm.2008.3.149

Qiang Du, Zhan Huang, Richard B. Lehoucq. Nonlocal convection-diffusion volume-constrained problems and jump processes. Discrete & Continuous Dynamical Systems - B, 2014, 19 (2) : 373-389. doi: 10.3934/dcdsb.2014.19.373


Walter Allegretto, Yanping Lin, Zhiyong Zhang. Convergence to convection-diffusion waves for solutions to dissipative nonlinear evolution equations. Conference Publications, 2009, 2009 (Special) : 11-23. doi: 10.3934/proc.2009.2009.11


Youngmok Jeon, Eun-Jae Park. Cell boundary element methods for convection-diffusion equations. Communications on Pure & Applied Analysis, 2006, 5 (2) : 309-319. doi: 10.3934/cpaa.2006.5.309


Iryna Pankratova, Andrey Piatnitski. Homogenization of convection-diffusion equation in infinite cylinder. Networks & Heterogeneous Media, 2011, 6 (1) : 111-126. doi: 10.3934/nhm.2011.6.111


Iryna Pankratova, Andrey Piatnitski. On the behaviour at infinity of solutions to stationary convection-diffusion equation in a cylinder. Discrete & Continuous Dynamical Systems - B, 2009, 11 (4) : 935-970. doi: 10.3934/dcdsb.2009.11.935


Suman Kumar Sahoo, Manmohan Vashisth. A partial data inverse problem for the convection-diffusion equation. Inverse Problems & Imaging, 2020, 14 (1) : 53-75. doi: 10.3934/ipi.2019063


M. González, J. Jansson, S. Korotov. A posteriori error analysis of a stabilized mixed FEM for convection-diffusion problems. Conference Publications, 2015, 2015 (special) : 525-532. doi: 10.3934/proc.2015.0525


Holger Heumann, Ralf Hiptmair. Eulerian and semi-Lagrangian methods for convection-diffusion for differential forms. Discrete & Continuous Dynamical Systems - A, 2011, 29 (4) : 1471-1495. doi: 10.3934/dcds.2011.29.1471


Runchang Lin. A robust finite element method for singularly perturbed convection-diffusion problems. Conference Publications, 2009, 2009 (Special) : 496-505. doi: 10.3934/proc.2009.2009.496


Chunpeng Wang, Yanan Zhou, Runmei Du, Qiang Liu. Carleman estimate for solutions to a degenerate convection-diffusion equation. Discrete & Continuous Dynamical Systems - B, 2018, 23 (10) : 4207-4222. doi: 10.3934/dcdsb.2018133


Lili Ju, Wensong Wu, Weidong Zhao. Adaptive finite volume methods for steady convection-diffusion equations with mesh optimization. Discrete & Continuous Dynamical Systems - B, 2009, 11 (3) : 669-690. doi: 10.3934/dcdsb.2009.11.669


Markus Gahn. Multi-scale modeling of processes in porous media - coupling reaction-diffusion processes in the solid and the fluid phase and on the separating interfaces. Discrete & Continuous Dynamical Systems - B, 2019, 24 (12) : 6511-6531. doi: 10.3934/dcdsb.2019151


Huan-Zhen Chen, Zhao-Jie Zhou, Hong Wang, Hong-Ying Man. An optimal-order error estimate for a family of characteristic-mixed methods to transient convection-diffusion problems. Discrete & Continuous Dynamical Systems - B, 2011, 15 (2) : 325-341. doi: 10.3934/dcdsb.2011.15.325


Antti Lipponen, Aku Seppänen, Jari Hämäläinen, Jari P. Kaipio. Nonstationary inversion of convection-diffusion problems - recovery from unknown nonstationary velocity fields. Inverse Problems & Imaging, 2010, 4 (3) : 463-483. doi: 10.3934/ipi.2010.4.463


Catherine Choquet, Marie-Christine Néel. From particles scale to anomalous or classical convection-diffusion models with path integrals. Discrete & Continuous Dynamical Systems - S, 2014, 7 (2) : 207-238. doi: 10.3934/dcdss.2014.7.207


Huiqing Zhu, Runchang Lin. $L^\infty$ estimation of the LDG method for 1-d singularly perturbed convection-diffusion problems. Discrete & Continuous Dynamical Systems - B, 2013, 18 (5) : 1493-1505. doi: 10.3934/dcdsb.2013.18.1493


Ivan Gentil, Bogusław Zegarlinski. Asymptotic behaviour of reversible chemical reaction-diffusion equations. Kinetic & Related Models, 2010, 3 (3) : 427-444. doi: 10.3934/krm.2010.3.427


Esther S. Daus, Josipa-Pina Milišić, Nicola Zamponi. Global existence for a two-phase flow model with cross-diffusion. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 957-979. doi: 10.3934/dcdsb.2019198


Yachun Tong, Inkyung Ahn, Zhigui Lin. Effect of diffusion in a spatial SIS epidemic model with spontaneous infection. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020273


Hideki Murakawa. A relation between cross-diffusion and reaction-diffusion. Discrete & Continuous Dynamical Systems - S, 2012, 5 (1) : 147-158. doi: 10.3934/dcdss.2012.5.147

2019 Impact Factor: 1.053


  • PDF downloads (22)
  • HTML views (0)
  • Cited by (4)

[Back to Top]