Development of a Simpler but Accurate Free Gas Deviation Factor for Fractured (Dual-Porosity) Volumetric Gas Reservoir Fluid

Abstract

Gas compressibility factor, also known as gas deviation factor or Z-factor, is a thermodynamic correction factor which describes the deviation of a real gas from ideal gas behaviour. The, free gas Z-factor in the Material Balance Equation (MBE) of single-porosity gas reservoirs with insignificant rock (matrix) compaction (after pressure depletion) does not reflect cases in low-permeability gas reservoirs having remarkable rock compaction. Through gas MBE modifications, previous researchers developed Z-factors for dual-porosity (fractured) low permeability gas reservoirs by incorporating gas desorption; however, their approaches create complexity for routine calculations. Therefore this study was designed with the purpose of deriving a free gas Z-factor for single-porosity low-permeability gas reservoirs and further modifying it for more simplicity and accuracy in a dual-porosity scenario. The free gas Z-factor derived for single-porosity low-permeability gas reservoirs is expressed as:  where , , , ,  and  are single-porosity Z-factor without rock compaction at pressure , water compressibility, initial water saturation, matrix compressibility, initial gas saturation and pressure depletion, respectively. However, the developed dual porosity free gas Z-factor model incorporates ratio of dual porosity to initial matrix porosity, and it is expressed as:    where  and  are initial matrix porosity and fracture porosity, respectively. The Z-factor model was graphically and statistically correlated with an existing free gas Z-factor model for dual porosity reservoirs. For all the hydraulically fractured shale gas formations considered, the correlations yield R2 values of 1.000.