Stress-based mathematical model for graded proppant injection in coal bed methane reservoirs

Abstract

A technology called graded proppant (propping agent) injection that consists of the injection of proppant particles, with increasing sizes and decreasing concentrations, into a naturally fractured reservoir results in deeper percolation of the particles into the natural fracture system, and thus expansion of the stimulated reservoir area. The placement of graded proppant particles keeps the fractures open, even after pressure decline due to production. There is, therefore, an enhancement in the well productivity. This proposed technology could be used to improve the productivity of CSG wells and other unconventional resources; for example, in shales, tight gas, and geothermal reservoirs. In this peer-reviewed paper, a mathematical model for well injectivity/productivity was developed for graded particle injection in a vertical well, lying at the centre of a circular drainage area. The model is based on an analytical solution of the quasi 1D problem of coupled axisymmetric fluid flow and geomechanics. Explicit analytical equations were derived for stress, and pressure and permeability distributions, as well as for the well index during injection and production. Results of previous computational fluid dynamic studies were used to determine the hydraulic resistance resulting from proppant plugging in the fractured system. An optimal stimulation radius was identified, which resulted in the highest increment in the productivity index due to the application of graded proppant injection technology. The model was subsequently used for a sensitivity analysis using field data. The results showed that the productivity index increased more than four times by the application of this technology.