Nonlinear Seepage Theory Of Multistage Fractured Horizontal Wells For Shale Gas Reservoirs

Analysis of lithological properties of shale gas reservoir showed that, the sizes of main nanopores are in a range of5～200nm, and the permeability is in a range of1×10-9～1×10-3μm2. The flow regime in tight shale gas reservoirs, which not only includes seepage, but also diffusion, slippage, desorption and absorption is different from conventional reservoirs obviously. Therefore, it is necessary to establish a new seepage theory to describe the flow law in nanopores and the multi-scale coupled flow in shale gas reservoirs.The flow law was obtained by combining the mechanics of continuous media and molecular kinematics method for shale gas reservoirs with nano/micropores. The continuity assumption is no longer appropriate for the flow in nano-micron pores, In this paper, gas flow formula in nano-micron porous media has been studied. The fluid flow state was judged by Knudsen number, Then the flow state chart was drawn. The different regional flow mechanism and flow state characteristics were illustrated. Based on Beskok-Karniadakis model, the correction coefficient of permeability was improved. The new non-linear seepage model considering the diffusion, slippage and desorption effects was established and simplified. We numerically studied the factors which influence gas flow rate. The steady and transient governing equations were constructed on the basis of the non-linear model. The pressure characteristic analytical solution was then obtained.On basis of the formula, a productivity equation of fractured vertical and horizontal wells is established by method of percolating resistance, which consider of both desorption and diffusion. According to the formula derived and production examples, the influence of well gas productivity from diffusion coefficient, half-length of fractures and fracture conductivity is studied. The steady and transient governing equations were constructed on the basis of the non-linear model. The pressure characteristic analytical solution was then obtained. By introducing moving boundary, the pressure wave boundary equation changing with time was derived. Because of the permeability difference between the fracture network zone and the matrix zone, the composite fracture network system was proposed. We built a two zones coupled composite model to describe the fracture network. I zone indicates fracture network, which contained the major fracture and branch fractures. Ⅱ zone indicates the shale matrix. Then the transient flow model was built and the analytic solution was derived.By numerical simulation, the conclusions were obtained as follows. The free gas contributes85%-90%to the total gas production, so the free gas contributes more than desorbed gas to total gas production. By study on the fracturing network model of horizontal well, the results show that, the formation pressure decreases faster with the increase of production. The moving boundary is at150m when the production increases when the output by a factor of10, the matrix of pressure wave propagation to the net area is150m. When bottom hole flowing pressure of certain circumstances, the production declines rapidly and then gradually stable. The shape of the curve presents’L’style. The model provided a convenient method and strong applicability for the micro scale flow mechanism and engineering application. The model can provide theory basis for shale gas development.