Pressure Calculation And Analysis Of Multi-fractured Horizontal Well

During the exploration of shale gas and other low permeability oilfields, due to the low natural productivity of the reservoirs, reservoir reform must be carried out to reach the standard of commercial oil and gas flow. As a powerful means for exploring tight oil and gas reservoir, horizontal well, together with its staged fracturing, can effectively enlarge the contact area of oil and gas, and then increase the productivity of oil and gas. Therefore, it develops rapidly and is widely applied to low permeability oilfields in recent years. It’s difficult and expensive to reform the fracturing due to the tightness of low permeability oilfields. Hence, optimization design on the construction scheme for fracturing has become an important and key issue; for instance, carrying out well spacing for the horizontal wells based on the characteristics of the reservoir, and optimizing the number of fracturing stages and the half-length of the fracture of the horizontal wells. Based on this consideration, this paper researched the aforesaid optimization issues from two respects of analytical solution and numerical solution. The research is as follows:Firstly, an equation was built for the oil well of multistage fractured horizontal well. The analytical solutions to the single fracture of vertical well and horizontal well were acquired by using Newman method. To promote the single fracture to multistage fractured well, a two-dimensional model was built. The flow of each fracture was assumed to be not equal to its length ratio, and an equation for multistage fractured horizontal well was built to solve the flow of each fracture as well as the change of bottom hole pressure with time. The result shows that the fracture length is basically in direction proportion to its flow at the early flowing stage. Therefore, in the early stage, the flow at the fracture can be assumed as being in direction proportion to its length. However, in the late stage, the flow at the fracture is unrelated to the length. Under this condition, the positions of facture affect the flow at the fracture. Therefore, this paper proposes that fracturing of horizontal wells should be consistent with the fracture length as far as possible, and the factures should be distributed uniformly.Secondly, this paper took into account real gas state equation to describe the state of shale gas, and described the adsorption and dissociative adsorption of shale gas by using Langmuir adoption. Moreover, the pressure-sensitive effect of gas was considered, and the standard pressure of shale gas was defined. Finally, the analytical solution to the multistage fractured horizontal well of shale gas was acquired. GPU computation accelerating technology was adopted to accelerate computation speed amid computation. After obtaining the bottom hole pressure of shale gas as well as the change of its derivative with time, the researchers discussed the influence from the parameters such as adsorption coefficient and storage ratio, etc. on the bottom hole pressure of shale gas amid exploration.Thirdly, to overcome the limits in the aforesaid analytical method as well as the limit that the rectangular boundaries must be parallel with well and boundaries in numerical method, the researchers proposed the method for partitioning PEBI network and the effective fracture half-length of multistage fracturing of horizontal wells in complicated oil and gas reservoir. Based on this, the finite volume discretization of seepage equation was realized. In view of the discretized system of linear equations which was featured by sparsity, irregularity, large-scale and asymmetry, it was solved by using preprocessed GMRES, and corresponding numerical simulation program was researched and developed. The correctness of the analytical solution was verified by comparing with the numerical solution. Finally, the conclusion in this paper was applied to an oilfield. The result shows that multistage fractured horizontal well can approximate to negative skin disposal under the condition of longer horizontal wells with more fractures. Simulation was carried out on this example under different fracture half-lengths and angles, and specific optimization suggestions were provided.