A Novel Semi-Analytical Solution for Transient Pressure Data Interpretation of a Fractured Well in an Asymmetric Reservoir
Authors: Al-Thawad Faisal Mohammed , Jamiol Ahmady Mahmoud 
Published: March 2015

Abstract
The presence of fractures and faults play a significant role in recovery and performance of tight reservoirs exploited with hydraulically fractured wells. Faulting may result in asymmetric reservoirs, i.e. different quality reservoirs across the fault plane, due to the displacement of reservoir blocks along the fault plane. Typically, numerical well-test packages are used to match the pressure responses of such complex geology and well geometry. The limitations of such approaches in terms of ease of use and wide range of possible solutions plead for more attractive approach. Hence, here a semi-analytical approach has been followed to develop a new practically efficient flow solution for a well intersecting a finite conductivity vertical fracture in an asymmetric reservoir. The solution is characterised mainly by the bilinear flow resulting from formation and fracture linear flows. The pressure derivative curve exhibits a distinctive feature of an early fracture linear flow regime at a very early time reflecting the first fluid flow into the well from the fracture only. The shape of the derivative plot also suggests the characteristics of a bilinear flow, quarter slope, uttering the fracture characteristics, followed by a radial flow, zero slope, articulating the quality of the two reservoirs. Type curves of dimensionless time and pressure are presented along with field cases for vertical wells intersecting natural fractures or exploited by hydraulically fractures. The results of this paper enable reservoir engineers to carry out modelling of such complex reservoir/well scenarios with increasing certainty and long-term benefits and greater additional and favourable business impacts.

Introduction
Ramey (1976) and Raghavan (1977) have previously presented a review of the work done on flow along and toward fractures. They highlighted that intersecting fractures will strongly affect transient flow behavior of the well. Houze et al. (1984) described a well intersecting an infinite conductivity fracture in a naturally fractured reservoir simulated using a double-porosity model. Cinco-Ley and Samaniego (1978) presented a semi-analytical solution for the analysis of the transient pressure data of analysis for fractured wells in symmetric reservoirs, which is most likely to occur in the case of small fractures or strike-slip faults. Yet, in the case of reverse or normal faulting with large throw (Juxtaposing), different quality reservoirs could adjoin the fault plan. That is, faulting may result in a sudden displacement of rock along the fault plane that possibly yields, a large-scale slippage resulting in different quality fault blocks on both sides of the fault. Many production logs have shown two different fault-blocks resulting from a reverse fault that offset two zones sequence. Figure 1 illustrates a good example of faulting that juxtaposes different geology across the fault plane, whereby; two different quality zones are aligned through the fault plane. Here a semi-analytical solution for such a scenario is presented.