Multi-stage Fracturing Horizontal Gas Well Productivity Based On Nonlinear Medium Coupling

Evaluating productivity of Multi-staged Fractured Horizontal Wells(MFHW),which are always used in the exploitation of tight gas reservoir,accurately is of great significance.Some researchers use the linear media coupling mechanism to describe influence of stress-sensitivity for permeability when they study on productivity of MFHW.However,the media coupling mechanism of tight sandstone reservoirs is certified to be nonlinear,leading to inaccuracy of productivity.Thus,it is necessary to study on productivity of MFHW based on non-linear media coupling.Effective stress experiments and changing-confining pressure experiments of tight sandstones with micro fractures or artificial fractures are carried out.Relationships between permeability and effective stress are calculated based on the latter,while non-linear media coupling mechanisms are recognized based on combining the former with response surface method.With foundation of the two consequences above and non-linear effective stress equation,results of changing-confining pressure experiments are able to transformed into relationships between permeability and pore pressure,which are contrast to results of changing-pore pressure experiments.Besides,for non-linear media coupling,partial differential equations of production models tend to be non-linear,which bring in great difficulty in solution by analytical method.Then semi-analytical method more applicable is needed.Based on different coupling mechanisms,mathematical models,in which non-linear terms of all dispersed gridding are averaged,of MFHW in rectangular reservoir are established.Production distributions are calculated based on Newman methodology and continuity conditions between adjacent gridding in Laplace domain.Finally,based on locale data,influence factors are analyzed.Through theoretical study,the method,using the non-linear media coupling mechanism to describe influence of stress-sensitivity for permeability,and a whole set of methods for productivity prediction and analyzation are established,which further deepens the knowledge of flow mechanism in tight reservoir and dynamic characteristics under unstable state,and provides theoretical basis for using effective stress correctly and determining the rational working system and structure optimization strategies of MFHWs.