A Simple And Rigorous IPR Equation For Vertical And Horizontal Wells Intersecting Long Fractures
Authors: Guo B. , Schechter D.S. 
Published: March 2010

Abstract
A newly developed mathematical model has been used for formation damage analyses of 12 vertical wells in the naturally fractured. reservoirs of the Spraberry Trend Area, West Texas and two hydraulically fractured horizontal wells in the Daqing field, China. The use of the model has captured the characteristics of rapid decline in productivity of the Spraberry vertical wells. Comparisons between the effects of fracture face skin and fracture conductivity indicated that stress-sensitive fracture conductivity is responsible for the productivity loss of these wells. Application of the model to Daqing horizontal wells indicated that these wells should have four to five times higher oil production rates if the formation was not damaged.

Introduction
The Spraberry Trend Area of West Texas was discovered in 1949 and was considered the largest field in the world. The Spraberry Trend Area presents unusual problems for both primary production and waterflooding. After more than 40 years of waterflooding, the current oil recovery is still less than 150/0. A model study of a waterflood pilot in the Spraberry Trend Area indicated a NE-SW trend of the major fractures(1). A contrast of 144/1 was required for the major/minor fracture trend permeability ratio to match the pilot response. This strong anisotropic effective permeability implies the existence of well inter-connected, long natural fractures in the Spraberry reservoir. A characteristic of flow in the long natural fractures is that the pressure variation in the long natural fracture should be significantly higher than that in a hydraulic fracture or a short natural fracture. Unfortunately, no method for analyzing flow behaviour in reservoirs with long fractures is readily available from the literature.
Several analytical solutions have been presented for transient flow in fractured reservoirs(2–8). Numerical models have also been developed for simulating fluid flow in fractured reservoirs(9. 10). However, it is still desirable for reservoir engineers to use steady flow equations for identification of formation damage in the fractured reservoirs. This is not only because the analytical transient flow solutions and numerical simulators are not convenient to use, but also because steady or pseudo-steady flow prevails as the dominating flow mechanism in the lifetime of most oil wells. Therefore, steady flow equations are attractive for formation damage analysis.
This paper demonstrates applications of a newly developed steady-flow mathematical model for formation damage identification. This model is utilized for analyzing performance of twelve vertical wells intersecting natural fractures in the Spraberry Trend Area, West Texas and two horizontal wells with hydraulically induced fractures in the Daqing field, China. The use of the model has captured the characteristics of rapid decline in productivity of Spraberry vertical wells. The results indicate that even though high gas saturation could hinder the productivity of the Spraberry wells, the wells should still have higher oil production rates if the formation was not damaged. Comparison between the effects of fracture face skin and fracture conductivity reduction due to pressure draw down indicates that the stress-sensitive fracture conductivity is responsible for the productivity loss of these wells.