As shale gas reservoirs have different change pattern of porosity with conventional gas reservoirs and their effective stress tending to lower porosity and matrix shrinkage tending to enlarge porosity have coupling effect

these two factors must be considered comprehensively when establishing the material balance equation for shale gas reservoir.Based on the material balance principle

Bangham solid deformation theory and Langmuir isotherm adsorption model are used to establish shale gas reservoir material balance equation with correction rock compressibility.The equation is linearized to a straight line equation only containing original free gas and absorbed gas.Actual production data are substituted in the equation to obtain the data points of the linear equation.These data points are fitted to obtain a fitting equation

the slop of which is the content of free gas and theintercept is original absorption content of gas.The sum of these two is original geological reserves of shale gas reservoir.Case analysis shows that considering the matrix shrinkage effect makes compressibility factor decrease at the beginning and stablize at the later.The lowering of shale gas reservoir porosity caused by the change of compressibility factor is slower than that of conventional gas reservoir.The correction of the rock compressibility of shale gas reservoirs and linear fitting the actual production data lead to the increase of the calculated amount of absorbed gas and the decrease of estimated content of free gas

so the estimated geological reserves increase and are more close to actual reserves.