Mathematical Model For Productivity Prediction In CN-WY Shale Gas Reservoir

Shale gas productivity prediction is an important gas reservoir engineering method for shale gas reservoir optimization design and planning decision,and the productivity prediction model based on the complex flow mechanisms is the key to predict productivity accurately.Shale reservoirs are very dense,and developed by horizontal wells with large scale staged fracturing technology.Meanwhile,there are many complex mechanisms,which contains adsorption and desorption,mass transfer diffusion,fracture deformation,matrix and fracture seepage.However,the present shale gas productivity prediction models based on the regular seepage theory don't consider above mechanisms.Therefore,it is necessary to establish a productivity prediction model to guide the development of shale gas reservoirs.In this paper,the flow mechanisms are studied and the mathematical models are deduced based on theoretical analysis and laboratory experiments.And then,the fluid-solid coupling productivity prediction model for fracturing horizontal well is established innovatively.The model is applied to the main influencing factors analysis and the productivity prediction in the CN-WY block,and good results are obtained.The innovative achievements and understandings have been achieved in terms of supercritical shale gas phase state characteristics,adsorption and desorption mechanism,mass transfer and diffusion mechanism,productivity prediction model.The main results are as follows:Firstly,the supercritical shale gas density characteristics are clarified.When the temperature is at 30?~90?,and the pressure is at 4.6MPa~38MPa,the density isothermy curves are "first concave and then convex",which indicates that the density increases with the pressure increase,and the amplification increases sharply first and then tends to slow.The isobaric density decreases with the temperature increase.At high pressure,the density is affected by temperature greatly.Secondly,the reliable isothermal adsorption mathematical model of shale gas is established based on the microporous filling theory,and the adsorption mechanism has been revealed.The correction methods for absolute adsorption and saturated vapor pressure are proposed given the supercritical properties of shale gas.This model reliability is verified by the isothermal adsorption test and the field test data.The physical properties characteristics of shale gas adsorption are clarified based on this model.Shale gas adsorption is a physical adsorption process in shale micropores.The maximum adsorption of micropores decreases and the adsorbed gas density increases with the emperature increase.The characteristic adsorption energy is stable.Thirdly,the reliable mass and diffusion mathematical model for shale gas is established,and the related mechanisms are revealed.The mass transfer and diffusion mechanism of adsorbed gas and free gas is clarified.And then,the mathematical model is established based on surface diffusion and mass transfer diffusion.This mass transfer and diffusion model reliability is verified by the mass transfer diffusion test.It is revealed that the contribution rate of surface diffusion,slippage effect and Darcy seepage to diffusive flux is different under different pressure gradients.Fourthly,the reliable productivity prediction model for shale gas is established,and the affecting production factors are analyzed.The numerical model baesed on this productivity prediction model is established by using the finite difference method.It is clear that shale gas reservoir with high adsorbed gas is favorable for gas reservoir development.When shale gas reservoirs are developed with horizontal well segmented fracturing,the number of fracturing sections and the fractures length should be increased.During the dynamic prediction production,the mass transfer diffusion mechanism,including surface diffusion,slippage effect and Darcy seepage,should be considered comprehensively,otherwise the well production capacity will be underestimated.Finally,the verification and application of shale gas productivity prediction model has been completed.The reliability for productivity prediction model has been confirmed by using the actual geological data and production data coming from four wells in CN-WY shale gas reservoir.And then the production fitting and prediction in six wells and the distribution analysis in two typical wells have been completed by this model.