Semi-analytical Productivity Model Research Of Multi-Fractured Horizontal Well In Tight Gas Reservoirs

Multi-stage Fracturing Horizontal Wells(MFHW)are widely used in the development of tight gas reservoirs and shale gas reservoirs.In order to further improve the productivity of fracturing horizontal wells,it is necessary to carry out the capacity testing and capacity evaluation for horizontal wells.For tight sandstone gas reservoirs,the permeability stress sensitivity coupled by linear effective stress is not applicable and the permeability calculated based on nonlinear effective stress is more reasonable,thus,we can get a more accurate productivity prediction model.The contents and conclusions of this paper are as follows:(1)According to the definition of effective stress,we choose the basic mathematical relationship between permeability and effective stress and derive a more reasonable mathematical relationship between permeability and nonlinear effective stress,the accuracy of the relation is verified by conventional stress-sensitive experimental.Then we get the permeability values under different confining pressures and pore fluid pressures by special stress-sensitivity experiment.Using the key parameters,nonlinear effective stress coefficient a,obtained by permeability data of experiment and response surface method,we establish the relationship between the nonlinear effective stress and the pressure,finally,we can obtain the relationship between the permeability and the pressure.(2)Based on the complex seepage mechanism of fractured gas reservoirs,a mathematical model of permeability stress sensitivity considering nonlinear effective stress in porous media has been built with seepage equation and different initial and boundary conditions.We establish the single-fracture vertical well productivity prediction model with two different mathematical models(flow from the reservoir to fractures and flow inside the fractures).Based on vertical well model,the multi-stage fracturing horizontal well productivity prediction model has been built by adding other two mathematical models(flow from the reservoir to horizontal wellbore and flow inside horizontal wellbore).The models can be finally solved in Laplace space with the dimension and Laplace transform.(3)Permeability stress sensitivity-permeability changed with pressure under nonlinear effective stress theory will lead to partial nonlinear equations with strong nonlinear characteristics.At this time,semi-analytic method is more reasonable and effective:in the time and space domain,the nonlinear term k in the grid takes the average value in each grid,and,then we can obtain the solution of the single grid mathematical model by combining the mathematical methods such as Laplace transform to solve the linearized partial differential equation,finally,we get the pressure and flow distribution on the Visual Studio 2012 programming platform with pressure and flow continuous conditions(4)Based on the productivity prediction model and case calculation,while verifying the rationality of the model and method,the flow states are divided by drawing the pressure and pressure derivative curves,the flow distribution at different locations of the fractures and horizontal wellbore is obtained,the influence of stress sensitivity and fracture parameters on productivity are also analyzed.Through theoretical research and case calculation,this paper forms a semi-analytical solution method to solve PDE equations in finite-flow fracturing vertical well and horizontal well productivity prediction model considering permeability stress sensitivity with nonlinear effective stress.These jobs deepen the understanding of characteristics of flow distribution and productivity in unstable gas reservoirs.It provides a theoretical basis for optimizing the fracture parameters,arranging production system rationally,and achieving cost-effective development in tight gas reservoirs.