A new method of systematic analysis of production data for evaluating the desorption ability of adsorbed gas in coal beds

In consideration of the key influential factor of the unsteady desorption of the absorbed gas in the develop- ment process of coalbed methane,a linear radial seepage flow model for a vertical production well of coalbed methane is constructed through the definition of a pseudo pressure of gas. The numerical solution for the seepage flow model with constant production rate at the inner boundary and no flow at the outer boundary is obtained by a fully implicit fi- nite difference method. Through the analysis of numerical results,it mainly indicates that the unsteady desorption coefficient can make the log-log type curve of the dimensionless transient wellbore pressure and the dimensionless wellbore pressure derivative at the pseudo-steady flow stage,which is dominated by the outer boundary at the late period,and have a falling trend. The two curves become distant and do not both upturn steeply to converge to one straight line yet. The reason is that the desorption of the adsorbed gas can supply the gas sources for the gas reservoir in time,which can slow down the formation pressure drop. However,the coefficient of wellbore storage does not affect the type curve at the pseudo-steady stage,which is dominated by the closed outer boundary and is also affected by the desorption function of absorbed gas. The skin factor affects the transient change of the dimensionless wellbore pressure at the pseudo-steady flow stage,but has little effect on the dimensionless wellbore pressure derivative at the pseudo-steady flow stage. The linear seepage flow model still satisfies the Duhamel principle,and thus the deconvolution technique as a tool can be used in the production data analysis,which can transform the linearized production data according to the definition of pseudo pressure under variable production rate into the transient pseudo wellbore pressure data under the constant unit production rate. Then based on both the aforementioned numerical solutions of the constructed seepage flow model and the analysis results for the sensitivity effects of the main parameters,the normalized production data through the decon- volution treatment can be analyzed through the type curve fitting method for the transient wellbore pressure. As a re- sult,some significant parameters such as the unsteady desorption coefficient representing the desorption ability of the adsorbed gas in coal beds,the permeability of coal beds,the skin factor and the radius of the outer boundary can be in- terpreted. Therefore,a systematic method for the production data analysis for a vertical production well of coalbed methane is presented. Finally,the validity and practicability of the type curve analysis method for the production data for a vertical production well of coalbed methane are verified through the analysis for the actual production data from a vertical well of coalbed methane. Furthermore,the model computation is performed by using the data of the interpreted parameters,and then the transient change principle of the contribution of the desorption function of the adsorbed gas to the wellbore production rate of coalbed methane can be analyzed. It is also demonstrated through the formula deduction that when the seepage flow in the coalbed comes to the stable state,the desorption rate of the absorbed gas in the whole coalbed will be equal to the production rate of the coalbed methane well.