A simple recipe for solid substitution at low frequencies and application to heavy oil rocks
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Solid substitution is important for characterisation of rocks saturated with heavy oil or bitumen, rock matrix dissolution and related problems. The dependency of the elastic moduli of the rock on the shear modulus of the pore fill may be much larger than the variation of the solid shear modulus itself. This effect can be caused by uneven distribution of stress within the pore fiill due to the presence of stiff and soft pores. To take these effects into account, we present a simple recipe for solid substitution based on the concept of dual porosity. The main idea of the model is to modify the Mavko-Jizba model for rocks with hydraulically isolated cracks by replacing the bulk modulus of the crack infill with its Young's modulus. The use of Young's modulus implies that the pressure on the edges of the crack is zero. This is an a boundary condition corresponding to a relaxed infill, and thus is suitable for low frequencies (as opposed to the Mavko-Jizba model, which is designed for ultrasonic frequencies). The model is applied to heavy oil data measured by the Center of Rock Abuse as the Colorado School of Mines and produces a reasonable fit.
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