Abstract

Thermal recovery processes such as cyclic steam stimulation and steam assisted gravity drainage induce significant shear dilation in oil sand formation. Shear dilation deformation results in an increase in pore volume, thereby enhancing permeability. In previous studies, it is assumed that the change in absolute permeability is a function of porosity or volume strain, which is in turn a function of mean or minimum effective stress. In such conventional semi-empirical correlations (e.g., 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 shear dilation of oil sand. This model is based on a granular interaction approach. The fundamental approach accounts for how pore throat area along flow channels and grains contacts changes 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 experiment data is presented to show the validity of the proposed model.

Introduction

Conventional numerical modeling of thermal recovery process has been historically carried out in the area of reservoir simulation, which concentrates on modeling multiphase flow and heat transfer in porous media. However, awareness of geotechnical aspects of reservoir engineering problem is growing, particularly for uncemented deformable oil sand1–2. Oil sand has an interlocked granular structure and displays a large degree of dilation when loaded to failure3. During steam assisted gravity drainage (SAGD) process, the oil sand formation will encounter 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 process4–5. In the literature5–7, the permeability change of oil sand subjected to deformation (or stress) changes is usually determined as a function of a state variable, which relates to average volumetric behavior, such as void ratio (or porosity). The concept of Kozeny-Carman equation8 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 behavior of permeability changes. Sometimes, the permeability functions for horizontal and vertical permeability have to be adjusted to different terms to achieve a good history-matching simulation of field production data. Theoretical and laboratory work is required to model the permeability change in three dimensions. The objective of this paper is to develop a model for oil sand, which quantifies the changes of permeability when the material experiences volumetric dilation. First, deformation-permeability relationships are derived analytically for ideal packing of uniform spheres. Then these analytical relationships are extended to interpret laboratory measurements in oil sand.

1. DEFORMATION-PERMEABILITY RELATIONSHIPS OF AN IDEALIZED GRANULAR ASSEMBELY

Consider the fluid flow through an idealized granular assembly as shown in Figure 1.

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