Fracturing Gas Reservoir Of Non-steady Flow Model And Its Solution Method Study

In order to gain the well stimulation, the oil and gas wells should be implemented by the fracturing technology, and the flow in the artificial fracture, fracture geometry and the influence of the flow intensity of fracture on the strata should also be taken into consideration in the oil and gas field development. However, generally speaking, the flow intensity of fracture in the strata is not easily measured but acquired by calculation.In this paper, the initial boundary value of the partial differential equation of the non-steady and mobile gas in the strata is established by combining the filtration mechanics theory of gas reservoir with the reality of strata and by considering the two-dimensional and rectangular-domain bounded stratum, as well as the motion equation, state equation and the continuity equation of simultaneous gas. Considering the flow of fracture, the non-steady infiltrating mathematical model is established to describe the artificial fracture reservoir. When the flux function is known, the accurate expression about the strata pressure and fracture pressure could be obtained by using orthogonal transformation method to solve the model. But in fact, the flow intensity of fracture is unknown and difficult to measure. Therefore, the inverse problem of partial differential equations is proposed.In order to improve accuracy, the strata and the fracture should be considered as a whole. When the flow function is unknown, the relational expression among strata pressure, fracture pressure and flow function could be established, as well as the accurate solution expression of simultaneous strata pressure and fracture pressure could be established by the infinitesimal analysis method so that the boundary value function of the non-steady flow model of strata gas or the inverse problem of free items of non-steady flow model could be attained. After these problems have been handled with the local discretization, the linear algebraic equations about the flow function node value are obtained. Then through the calculation by using Matlab programming and with specific examples, the approximate value of the flow function node could be acquired. According to the accurate expression, the well bottom pressure value which changes with time can be obtained. Finally, the test analysis of the well bottom pressure and the various factors influencing the model testing curve is carried out with the fact that the results are suitable for the production requirements.The model established in this paper can be used in the situations in which there are a number of parallel fractures or in other more complex situations in which the shape of the fracture is curve. And the infiltrating model of the two-dimensional and rectangular-domain partial differential equations can be extended to the initial boundary value problems of other boundary conditions and the semi-infinite or unbounded domains.Moreover, the three-dimensional or high dimensional problems also can be treated similarly.