Fractured Well Productivity Calculation Method

Hydraulic fracture technology is a promising stimulation method in a variety of aspects, mainly based on the evaluation of hydraulic fractured wells. Unsteady porous flow in horizontal wells with single or multiple fractures is a complicated study of mechanics through porous media. Especially for the fractures which are not perforated the formation, the flow process in this system is a coupling flow about reservoir and fractures. Because of the complexity of porous flow model and restriction of different reservoirboundaries, to solving this problem is a difficult process.The history of hydraulic fracture technology is reviewed and the developing character and character of field is summarized firstly, then the increasing production mechanism and main influencing factors of hydraulic fracture technology is expatiated, in the following part,then according to the oil gas store seeping mechanics theory and energy conversation law,for infinite stratum , rectangle region boundary close stratum of the double medium ,we think over the ellipse crack,triangle crack,rectangle crack to constitute the accounting model that is hydraulic fracture level well stratum noncertain seep and the level well stream coupling.The paper mainly apply rectangle crack because of the crack actual instance and material calculating question,then present the solving method of the model. The mathematical model of the infinite stratum is the differential equation rthetorical question that partial differential equation rthetorical solve boundary item. In the course of thesolution,in the case ofμ(x_D,t_D) known, we mainly uses the theory of laplace transformation to solve the hydraulic fracture pressure p_f1D and the oil store crude crack pressure p_f2D. We may disperse the unknown function. With the relation of the stratumand crack,we use the numerical value calculation to solveμ(x_D,T_D). We useμ(x_D,T_D) toconfirm the pressure of the stratum and the crack,and detrude the productive calculated formula of the fractured well. In the rectangle double medium oil store ,we consititute the mathematical model of the many cracks system nonsteady seepage ,and solve the long and short advance solution ,then use the model to carry through actual calculation.The essay mainly contains the following conclusions:1. According to the subatance balanceable equation and Darcy law, we research the seepage question of the single-phase decline compress liquid about the double medium by the numbers , then we gain the seepage equation group of the single-phase decline compress liquid about the double medium.2. In the infinite crude crack oil store, we suppose basal rock is comminutedby orthogonal crack reseau. According to the subatance balanceable equation and Darcy law, we can found the bottom of a well stream depressive basic differential equation of the decline compress liquid ,and make use of the laplace transformation to deduce the analytic solvtion according to the cuticle domino offect. We protract the graph about output, from the basic configuration of the output descendant graph, we can make out that the process approximately is divided into three phases: inchoate output descend rapidly; transition assume sidestep shape; terminal segent go to placidity then change according to the same speed.3. In the infinite double medium oil store, we analyse from the hydraulic fracture crack system and oil store system respectively, and construct the seepage equation to solve, then protract corresponding output graph. From the graph we knowωis comparative small,the distance of the early and terminal segment is comparative big, and the altitude of the transition is comparative big. Butλis comparative big, the time of transition is comparative early,and the output of transition hold the line basically.4. In the rectangle double medium oil store ,we consititute the mathematical model of the many cracks system nonsteady seepage ,use the orthogonal transforma,laplacetransformation,numerical value evolve in reverse to solve for the based model ,and protract the output graph, Comparison of calculated result with the real production of a hydraulically fractured gas well in a certain field shows an excellent agreement.