Semi-analytical solution to a fractured well in an asymmetric reservoir with a finite conductivity fault

Abstract

The primary scope of this study is to develop a novel compound semi-analytical solution for the general case of a well intersecting a vertical fracture near a finite conductivity fault in an asymmetric reservoir adjoining the fracture/fault model. A number of field cases have highlighted the existence of such complex flow geometries and the importance of developing appropriate solutions for their accurate modelling and performance predictions. In addition, the existence of intersected fractures is commonly observed over the increasing number of image and production logs (hard data), yet, the amount of these data are very limited relative to the field size. Consequently, dynamic data has become a primary tool for the identification, characterisation and modelling of such geological features, and thus, pressure signatures have become gradually more important. Nevertheless, currently there is no analytical solution to interpret such well test data signature(s), and hence, numerical simulation of the flow in such complex geometries is considered, which is cumbersome and often impractical. The method of investigation consists of solving the flow domain of five flow units namely; (i) reservoir Region-1; that defines flow from un-faulted side of the fractured well, (ii) a Fractured-well, which allows fluids to flow into and along the fracture towards the well, (iii) reservoir Region-2; that defines flow between the fractured well and the fault, (iv) a nearby Fault, which allows fluids to flow along, across and towards the fractured well, and (vi) reservoir Region-3; that defines flow in the matrix beyond the fault. It should be noted that the author’s aim is to have a solution to the pressure versus time and space in general and wellbore pressure with time in particular. Laplace and Fourier transformations were applied to the five equations governing the twodimensional flow in this domain. The major divisions of consists of development of semi-analytical solution to the following flow systems: a well intersecting a finite conductivity fracture in a composite reservoir, a well intersecting a finite conductivity fracture near a finite conductivity fault in an asymmetric three-region reservoir and the flux distribution and effective fracture half-length alongside fracture. The reliability of the proposed solution has been demonstrated in a systematic approach by performing a number of sensitivities of varying model parameters and then using a number of synthetic cases and real field examples. Modelling of the flow behaviour at earliest times by performing a number of sensitivities of varying model parameters and then validated the stability and the integrity of the solution, respectively. The calculated flux distribution and the effective fracture half-length reasonably matched the corresponding values input into numerical simulations that generated the synthetic well test signatures. The solution also provided acceptable interpretation of the real field data matching reasonably the corresponding numerical well test exercise routinely performed for such complex geometries. It offers more flexible schemes to easily carry out modelling with larger positive impact on hydrocarbon reservoir management and development decisions.