A Multiply-Fractured Horizontal Well in a Rectangular Drainage Region

Abstract

We examine the productivity of a multiply-fractured well in a reservoir that is in the form ofa rectangle. The properties of the individual fractures (length, conductivity, skin, etc.) are entirely arbitrary. The fractures are assumed to be parallel to one of the sides of the rectangle and maybe either parallel or perpendicular to the horizontal well. The primary objective of this work is to outline a computationally-efficient scheme to compute well productivity. This objective yields a simple method to incorporate this completion scheme in reservoir-simulation models. It should permit an engineer to understand interactions between the fractures in the presence of boundaries. The model also permits us to compute pressure distributions under depletion conditions for single-phase oil and gas reservoirs. Further, it provides for a realistic design of this completion scheme.It is to be emphasized that the problem we consider is a nontrivial one in that flow to a single vertical fracture of fmite conductivity in a rectangular drainage area is yet to be modeled successfully. IntroductionThe Ozkan-Raghavan solution! for a point source in a rectangular parallelepiped is used to derive expressions for pressure distributions caused by a multiply-fractured horizontal well in a rectangular drainage region. The central result in the algorithm discussed here is an outline of a scheme that permits us to incorporate the transitional period from infmiteacting to boundary-dominated flow without recourse to approximations. We do not resort to the use of image wells. This is particularly important because this well configuration may result in the aspect ratio of the drainage area becoming rather severe, and, under such circumstances, the image-well concept is a dubious proposition. (Even for the simple case of a single vertical fracture at the center of a square drainage region, no simple method exists to determine the number of image wells a priori should the length of the fracture be comparable with the length of the drainage boundary.)At this time, we envisage four potential uses for the model proposed here: (i) to design of fracture-treatment programs (for example, determination of the number of fractures), (ii) to evaluate the efficacy of this completion scheme; for example as a screening tool, (iii) to analyze pres-

Development of an Efficient Embedded Discrete Fracture Model for 3D Compositional Reservoir Simulation in Fractured Reservoirs

“…We consider flow of a slightly-compressible liquid in a homogenous porous medium. Analytical solutions are from Chen and Raghavan (1997) presented in dimensionless forms. The dimensionless bottom-hole pressure ( ), dimensionless rate ( ), and dimensionless time ( ) are For the EDFM simulation in the first scenario, we used an 11×45×1 matrix grid.…”

Integration of microseismic and other post-fracture surveillance with production analysis: A tight gas study

“…Support for using a vertical well approach for analyzing multi-fractured horizontal wells comes from the work of Raghavan et al (1997) and Chen and Raghavan (1997), which was later summarized by Ozkan et al (2009). Prior to hydraulic fracture interference in a multifractured horizontal well completed in a tight (unconventional) reservoir, flow is mainly perpendicular to the surfaces of the hydraulic fractures and according to Ozkan et al (2009) "the longterm performance of a fractured-horizontal-well/reservoir system can be represented by that of a single hydraulic fracture".…”

Pressure transient analysis of multistage fracturing horizontal wells with finite fracture conductivity in shale gas reservoirs

“…Therefore, the governing equation of every media can be derived; however, the interference among hydraulic fractures is ignored. Some scholars, including Nashawi (2006), Hegre (1991, 1994), Guo and Evans (1993), Horne and Temeng (1995), Chen and Rajagopal (1997), presented some transient analytical solutions in Laplace domain for the fracturing horizontal well with multiple finite conductivity by using sink-source integral. Some other scholars, including Al-Kobaisi and Ozkan (2004), Valk and Amini (2007), Brown et al (2011), coped with this issue using numerical difference method.…”