An Equation for the Bulk Modulus of Composites Derived From the Effective Medium Theory

Abstract

Bulk modulus has wide applications in well engineering, seismic exploration, waste reinjection, and predicting pore pressure in carbonate reservoirs. However, there is no easy way to obtain accurate values for the effective bulk modulus of rocks. Practically, researchers use rigorous, costly, and time-consuming experiments on core samples. But, stress release and changing rock’s environment have affected the accuracy of results. Also, it is impossible to get accurate values of the effective bulk modulus from theory without accounting for the deformation of microcracks in the rock. Existing models do not consider the presence of microcracks because of the inability to define the positions of cracks relative to one another. Thus, earlier studies introduced approximations to define the upper and lower bounds of values. This study aims to overcome this limitation by accounting for the fluids in the microcracks, apart from those in stiff pores. From the product of the surface area and thickness of the fluid in the microcracks, the authors generated proportionality between the volume of fluid and that of the grain and obtained expression for the crack porosity. Then analytical and numerical techniques were applied to obtain models for the effective bulk modulus. The results show that the presence and magnitude of inclusions reduce the effective bulk modulus significantly. This was validated by a finite element analysis (FEA) using the FEATool run in matlab. In addition, higher volume of fluids in the microcracks makes the rate of change of the bulk modulus with the porosity to be higher.