A Deformation-Dependent Model for Permeability Changes in Oil Sand due to Shear Dilation

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Abstract Thermal recovery processes such as cyclic steam stimulation and steam assisted gravity drainage induce significant shear dilation in oil sand formations. Shear dilation deformation results in an increase in pore volume, thereby enhancing permeability. In previous studies, it was assumed that the change in absolute permeability is a function of porosity or volumetic strain, which is, in turn, a function of mean or minimum effective stress. In such conventional semi-empirical correlations (e.g., the Kozeny- Carman equation), the changes in permeability are equal in all directions even though the changes in strains are different in each direction. This paper proposes a new deformation dependent permeability model for the shear dilation of oil sands. This model is based on a granular interaction approach. The fundamental approach accounts for how pore throat areas along flow channels and grain contacts change with shear dilation. This allows one to quantify the evolution of changes in permeability in one direction under continuous shearing. The model explicitly states that the permeability changes are highly anisotropic, dependent on the induced principal strains. Comparison with experimental data is presented to show the validity of the proposed model. In addition, the proposed model is extended and formulated in a generalized 3D tensor notation so that it can be implemented into existing reservoir or coupled geomechanics-reservoir simulators. Introduction Conventional numerical modelling of thermal recovery processes has been historically carried out in the area of reservoir simulation, which concentrates on modelling multiphase flow and heat transfer in porous media. However, awareness of the geotechnical aspects of reservoir engineering problems is growing, particularly for uncemented deformable oil sands(1, 2). Oil sands have an interlocked granular structure and display a large degree of dilation when loaded to failure(3). During a steam assisted gravity drainage (SAGD) process, the oil sands formation encounters shear dilation, affecting formation absolute permeability. The absolute permeability of the reservoir controls the drainage of fluids from the steam front, and thus the frontal stream advance rate and the bitumen production rate. It is one of the most important parameters governing the performance of the SAGD process(4, 5). In the literature(5-7), the permeability change of oil sands subjected to deformation (or stress) changes is usually determined as a function of a state variable, which relates to average volumetric behaviour, such as void ratio (or porosity). The concept of the Kozeny- Carman equation(8) is commonly used in correlating the change in permeability with the change in porosity. This type of correlation assumes the permeability changes are equal in all directions, and does not reflect the directional behaviour of permeability changes. Sometimes, the permeability functions for horizontal and vertical permeabilities have to be adjusted to different terms to achieve a good history-matching simulation of field production data. Theoretical and laboratory works are required to model the permeability change in three dimensions. The objective of this paper is to develop a model for oil sands, which quantifies the changes of permeability when the material experiences volumetric dilation. First, deformation-permeability relationships are derived analytically for an idealized packing of uniform spheres.