Semi-analytic analysis and optimization of stress-dependent permeability model for the coal bed methane gas reservoir

Abstract

Coal reservoir productions depend entirely on cleat permeability and porosity values. The models used to date to calculate cleat parameters are either stress-dependent or strain-dependent. A study is carried to analyze the individual effects of stress and strain on the reservoir and fluid properties. A one-dimensional cleat for an under saturated low permeable coal bed methane reservoir is semi-analytically solved. Standard stress models, Shi-Durucan and Cui-Bustin, predict a range within which field values lie. A comparative study between strain and stress model behavior is carried out. The strain model considers matrix swell and shrink but ignores stress effects due to them, while a stress model considers them all. The stress-model is dependent on effective horizontal stresses in the reservoir. Stress models are preferred to strain model. Stress-dependent permeability being closer to actual values captures the field in a better manner. Though standard stress models are more accurate than the strain model, yet they cannot determine a specific permeability value at any given point in time. Emphasis is, therefore, laid on developing a new stress-dependent model. An iterative combination study of the standard models provides the new model. An empirical equation to calculate cleat properties, approximate to the field, is developed from the research. The new permeability model is substituted in the fluid production equation to obtain cumulative gas/water produced at any time interval. The results lie in the range predicted by the standard stress models and match the field observations, thus more reliable. The stress model is simple to use and is mathematically easy to formulate. It is flexible and can accommodate reservoir temperature and sorption strain changes.