Abstract
In this paper, a new rate decline analysis model of horizontal wells with variable conductivity and uneven distribution of multiple fractures is proposed. By Laplace transformation, point source integration, and superposition principle, solutions of multiple infinite conductivity fractures in closed reservoirs are obtained. By coupling Fredholm integral equation of variable conductivity, linear equations of variable conductivity fractures in Laplace space are obtained. Gauss-Newton iteration, Duhamel convolution, and Stehfest numerical inversion method are used to obtain the bottom hole production solution. The accuracy of the results is verified by comparing with Eclipse software simulation. Then, the influence of some important reservoir and fracture parameters on the production is analyzed. The calculative results show that the smaller the fracture spacing is, the earlier the fracture begins to decline, the more the production will decrease; the change of different fracture length with the total fracture length unchanged has almost no effect on the production; the angle between fracture and x -axis has an important effect on the production; the smaller the angle between fracture and x -axis is, the stronger the interference between fractures is, the higher the production; the initial fracture conductivity affects the early production behavior, and the higher the initial fracture conductivity, the higher the production; the larger the fracture declines index, the lower the production, but the decreasing range gradually decreases with the increase of the decline index; the larger the reservoir drainage radius, the later the energy depletion stage, the higher the production. At last, a good fitting effect is obtained by fitting an example of oil field. The model proposed in this paper enriches the model base of rate decline analysis of fractured horizontal wells and lays a theoretical foundation for efficient development and practice of tight reservoirs.
Highlights
Multistage fracturing horizontal well is an important measure for the stimulation of low permeability reservoirs and especially for tight reservoirs
Based on the theory of transient seepage flow, it is of much significance to guiding production practice to establish a productivity decline analysis model and method for multistage fractured horizontal wells and obtain reservoir parameters and well-controlled reserves using the typical curve fitting technology [1]
The transient well test analysis of hydraulic fractures reached the peak in the 1970s and 1980s and laid a theoretical foundation for the subsequent development of models for multistage fractured horizontal wells
Summary
Multistage fracturing horizontal well is an important measure for the stimulation of low permeability reservoirs and especially for tight reservoirs. A point source seepage model for closed reservoirs has been firstly established; an infinite conductivity model with uneven distribution of multiple fractures has been obtained by means of Laplace transformation, point source integration, and superposition principle. By coupling the infinite conductivity multifracture model with the variable conductivity Fredhom integral equation, the system of linear equations of fracture flow rate and horizontal well pressure in Laplace space has been obtained. Assuming that the number of fractures in the multistage fractured horizontal well is N f , the pressure drop of each section of fractures can be obtained as follows by means of point source integration, superposition principle, and coordinate transformation:. The dimensionless bottom hole pressure pwD can be obtained through Stehfest numerical inversion
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