A Study On The Pressure Transient Behavior Of Partially Penetrating Vertical Hydraulic Fractures

Hydraulic fracturing technology has been a common application in the oil and gas industry. More and more attentions were focused on the study of pressure transient behavior of hydraulically fractured wells. In order to evaluate the effect of vertical hydraulic fractured wells availably, it is necessary to study pressure transient behavior of hydraulically fractured wells. In most published literatures, hydraulic fractures were assumed to be fully penetrating the formation. Limited efforts have been made to investigate the effects of partially penetrating fracture height on the performance of wells. In practice, fully penetrating fractures may lead to an early or immediate water or gas breakthrough in a reservoir with bottom water or gas cap in contact, whereas partially penetrating fractures may be the only way to prevent the early breakthrough. Moreover, due to the large thickness and difference of reservoir properties of massive hydrocarbon reservoirs such as volcanic rocks、carbonate rocks, reservoir is impossible to be fractured fully. So the study of this paper has a great practical significance.This paper mainly discusses pressure transient behavior of the hydraulically fractured well which is located in different reservoir model such as circular or box-shaped reservoirs. This paper presents very detailed theoretical derivation process and accurate pressure solution by using analytical method. For circular reservoir, the effects of different outer boundary and fractured parameters on the pressure and pressure derivative are fully investigated. The transient flow of the partially penetrating fracture well is discussed particularly and this paper presents some important research results. The advantage of the analytical solution is easy to incorporate storage coefficient and skin factor. It can also reduce the amount of computation and compute efficiently and quickly. In order to further illustrate the application of the theoretical results, applying well tests method, this paper gives specific expression of every flow period by using asymptotic analysis and explain the method of analysis of well test data and type curve matching analysis by using examples. This study provides the necessary theoretical basis for the actual field research.At present, the actual reservoir is more closed to box-shaped reservoir, so partially penetrating hydraulic fractures in a box-shaped reservoir with closed boundaries is studied. This paper presents a new method to give an analytical solution in Laplace domain directly. The basic building block of the method is to solve diffusivity equation with the integration of Dirac function over the distance that is presented for the first time. Different from the traditional method of using the source solution and Green’s function presented by Gringarten and Ramey, this paper uses Laplace transform and Fourier transform to solve the diffusivity equation and the analytical solution obtained is accurate and simple. By comparison with the results of Kuchuk and Brighan, the method in this study is proved exactly.The study of the pressure transient behavior of partially penetrating fractures can provide theoretical guidance and method of application for reservoir engineering analysis and fractured process design.