New Semianalytic Technique To Determine Horizontal Well Productivity Index in Fractured Reservoirs

Abstract

Summary Simplified analytical relations derived for homogeneous formations are usually applied to the determination of the productivity of horizontal wells, regardless of the presence of heterogeneities in the reservoir. Furthermore, complex well architectures and the wealth of completion options currently available cannot be taken into account properly because the well trajectory can only be schematized as a single horizontal wellbore. However, the use of numerical reservoir simulators to reliably forecast the productivity of horizontal wells draining heterogeneous reservoirs may be time-prohibitive or not feasible because of a lack of sufficiently detailed information, especially during the appraisal phase or the early stages of production. A new semianalytic technique is proposed in this paper to solve the inflow equations in an approximate yet reliable manner. A solution to 3D problems of single-phase flow into a horizontal well, taking into account friction in the wellbore, is provided for both single-layer reservoirs and reservoirs comprising two interfering layers. The method also has been extended to describe the fluid flow when the well intercepts one or more fractures. The presented technique allows very fast calculation of the well productivity in oil and gas reservoirs, offering great flexibility in the placement and architecture of the wells. The method has been applied to two field cases for which the well productivity under pseudosteady-state conditions was measured. One of these is a 200-m-long horizontal well draining an isotropic carbonatic reservoir and intersected by a natural low-conductivity fracture. The other is a similar well, intercepting a natural high-conductivity fault, but the oil-bearing formation is anisotropic. Good correspondence was found between the actual productivity and the predictions obtained by application of the proposed semianalytic technique. Introduction Horizontal wells are common practice in the present hydrocarbon industry, and smart wells (including multilateral completions and wells with selective access of different zones) are becoming increasingly commonplace. The modeling of such wells is, in many cases, not ideal. Areas in which improvements are welcome are well testing, well models in reservoir simulators, and fast models for quick assessment of many field-development options. Further, the handling of natural or hydraulic fractures is often suboptimal. In reservoir simulation, fine grids need to be selected to properly capture the flow behavior close to the well. Moreover, most reservoir simulators are not equipped with extensive well models, which are required when friction in the well becomes important or when two-phase flow develops in the well. This situation has prompted the development of a number of analytical and semianalytical tools, some of which are intended for implementation in a reservoir simulator. Most of the first models, as well as many of the more recent models, assume either constant influx density along the well or infinite well conductivity in a single homogeneous layer. Dikken introduced the effect of well conductivity for a single horizontal well in a homogeneous formation. He started with the assumption that the flow is mainly perpendicular to the wellbore, which allowed him to reduce the reservoir to a 2D flow domain, coupled to a friction model in the well. Others followed this approach, but 3Dmodels were developed as well. A second kind of extension are the multilayer models. Lee and Milliken and Kuchuk and Habashy used a method of reflection and transmission, while Basquet et al. used a "quadrupole" method relating the pressures between the various layers. The multilayer models are also, however, still limited to constant-influx or infinite-conductivity wells.

Numerical Modeling of Periodic Pumping Tests in Wells Penetrating a Heterogeneous Aquifer

“…Well testing is a valuable source of information on reservoir properties and a lot of work has been done and is being performed in this realm (Kruseman and Ridder, 1990;Horne, 1995;Fetter, 2001;Bourdet, 2002;Gringarten, 2008;Fokker et al, 2005;Beretta et al, 2007;Benetatos and Viberti, 2010;Viberti, 2010;Verga et al, 2011;Cancelliere and Verga, 2012). Two issues remain which need further attention in well test analysis: the inclusion of reservoir heterogeneity and the treatment of rate variations.…”

A Fast Simulation Tool for Evaluation of Novel Well Stimulation Techniques for Tight Gas Reservoirs

“…Thus the effect of water inflow in case of an active aquifer or nearby boundaries cannot be accounted for. Furthermore it does not allow for heterogeneity, although the method can be extended to a layered reservoir with homogeneous layers 4 , 8 . The method in this paper is formulated for a gas reservoir but can straightforwardly be applied to an oil reservoir by considering pressures instead of pseudo pressures.…”

“…5 for the derivation and full expression for the varying influx pressure solution (3). The total, but not yet fully determined, pressure field is obtained by (a) summing up the individual solutions using the linearity of the diffusivity equation (3) and (b) using the method of images 4 , 8 to form a solution that satisfies the no-flow boundaries; the reservoir layer with the line sink is repeatedly mirrored around the no-flow boundary planes. A finite, but sufficiently large, number of images approximate accurately the no-flow boundaries at the top and bottom of the reservoir.…”

Forward and inverse modeling of near-well flow using discrete edge-based vector potentials

“…156-180, 367-386;Joshi 1991, pp. 165-200), although also pseudo-steady flow (Fokker et al 2005) is sometimes considered (Joshi 1991, p. 203). Here we focus on heterogeneity and steady flow.…”