Semianalytical Productivity Models for Perforated Completions

Abstract

Summary. This paper discusses the effects of various perforation and reservoir parameters on the productivity (or injectivity) of perforated completions. Because of the Complex, 3D flow into a spiral perforated completions. Because of the Complex, 3D flow into a spiral system of perforations, productivity analysis of perforated completions is not easily amenable to analytical treatment. This paper presents a semianalytical solution for the estimation of skin in presents a semianalytical solution for the estimation of skin in perfo-rated completions. Results are presented for two separate cases: to perfo-rated completions. Results are presented for two separate cases: to 2D-plane-flow problem, which is essentially valid at small dimensionless perforation spacings (large perforation penetrations or high perforation perforation spacings (large perforation penetrations or high perforation shot densities) and the general 3D problem. where the vertical convergent flow into perforations is significant. In these analyses, the wellbore and vertical-flow effects are quantified in terms of pseudoskins obtained by accurate finite-element simulations. The effects of pseudoskins obtained by accurate finite-element simulations. The effects of perforation damage and formation anisotropy are also included. perforation damage and formation anisotropy are also included. The results provide a better understanding of the relative role of various perforation parameters in affecting well productivity. Because perforation parameters in affecting well productivity. Because they are based on theoretical considerations, the correlations allow reliable estimates of the skin in perforated completions. New relations are provided for estimating productivity of perforated completions with formation permeability damage. Results indicate the importance of angular phasing, in addition to perforation penetration, in overcoming the effects of formation damage on well productivity. Introduction Well productivity (or injectivity) is an important consideration in any reservoir development program. While the near-wellbore heterogeneities and the cleanup flow conditions during perforating strongly influence the final outcome, the selection of proper perforating hardware (perforator and gun type) is essential for perforating hardware (perforator and gun type) is essential for optimizing productivity in perforated completions. A theoretical analysis of productivity under idealized reservoir conditions can provide some general guidelines for achieving this objective. Such studies also shed considerable light into the perforation-flow problem. Fur-thermore, accurate productivity estimates are generally require for flow predictions and for completion evaluation. A comparison of the observed well productivity (or skin from well test) with the expected productivity is a useful check on the completion efficiency. Although gun perforating has been used widely to control production or injection of fluids in oil and gas reservoirs, the effects production or injection of fluids in oil and gas reservoirs, the effects of various perforation and reservoir parameters on the productivity of perforated completions are not yet fully understood. productivity of perforated completions are not yet fully understood. Productivity analysis of perforated completions, because of the 3D nature Productivity analysis of perforated completions, because of the 3D nature of the flow, is significantly more complex than that of openhole completions. The major difficulty arises from two important con-siderations: the spiral distribution of the perforations in the vertical direction and the presence of the wellbore, which is a barrier to flow into perforations. This study shows that the wellbore effect, which is generally neglected in the productivity analysis of vertically fractured wells, can be important for perforated completions. Because an analytical treatment is extremely difficult even with simplifying assumptions, various numerical techniques frequently have been used to study the steady-state flow into perforated completions. While they provide useful insight into the productivity problem, numerical models do not readily reveal the functional productivity problem, numerical models do not readily reveal the functional relationship between various perforation and reservoir parameters. Because the large number of system parameters affecting well productivity can assume values over a wide range, a large number productivity can assume values over a wide range, a large number of numerical experiments are required to generalize the dependency of well productivity (or perforation skin) on these parameters. Consequently, the reliability of any empirical correlations for estimating skin in perforated completions can be a serious concern. In this paper, we first consider the simpler 2D steady-state-flow problem, which is essentially valid at small dimensionless problem, which is essentially valid at small dimensionless perforation spacings (high perforation densities or large perforation perforation spacings (high perforation densities or large perforation penetra-tions). Using an accurate 2D finite-element model (FEM), we penetra-tions). Using an accurate 2D finite-element model (FEM), we establish the dependency of perforation skin on the angular perforation phasing, the perforation penetration, and the well radius. The perforation phasing, the perforation penetration, and the well radius. The wellbore effect on well productivity is formulated in terms of a well-bore pseudoskin. For the general case of 3D flow, we decouple the convergent flow effects from wellbore effects. The vertical flow effects are quantified in terms of a vertical pseudoskin, which is obtained through 3D finite-element simulations. We later extend these results to include the effects of permeability reduction in the crushed zone and formation anisotropy. Finally, we examine the combined effect of formation damage and perforations on well productivity. As verified, these semianalytical productivity models productivity. As verified, these semianalytical productivity models provide a good estimate of skin in perforated completions for a wide provide a good estimate of skin in perforated completions for a wide range of perforation parameters. Background The effects of perforating parameters on the well flow efficiency are well documented. In Muskat's first analytical treatment of the problem, perforations were represented by mathematical sinks problem, perforations were represented by mathematical sinks distributed spirally around the wellbore and did not extend into the formation. Later, McDowell and Muskat, using electrolytic tank experiments, reported productivity results for perforations extending beyond the well casing. Harris first used a finite-difference modeling technique to examine the productivity aspects of perforated completions. He also presented a dimensionless analysis of the problem and provided presented a dimensionless analysis of the problem and provided skinfactor curves as a function of dimensionless parameters. While this analysis provided useful insight into the problem, Harris' results were restricted to wedge-shaped in-plane perforations because of limitations of the finite-difference model. Klotz et al. examined the crushed- and damaged-zone effectusing a 2D FEM. Hong extended Harris' model to include the effects of drilling damage and various staggered perforation patterns. He also presented his correlations in two separate nomograms for formations with or without a damaged zone. Hong did not verify these correlations. Later, Locke applied the FEM to model the full 3D problem of flow into perforations by properly taking into account the actual perforation geometry and the spiral nature of their distributions perforation geometry and the spiral nature of their distributions around the wellbore, which is commonly used in real perforating guns. Locke also presented a nomograph for estimating the skin in perforated completions but did not discuss the development of the nomograph or the verification of results. Using a similar, but more refined, FEM than Locke's, Tariq examined the non-Darcy flow effects in perforated completions and confirmed Locke's productivity results. Tariq pointed out, however, that Locke's productivity estimates were slightly optimistic, mainly because of insufficient grid size in Locke's FEM. Tariq's model, which is used here for the 3D productivity simulations, is also in close agreement with McDowell and Muskat's electrolytic tank experiments. Problem Statement Problem Statement In this work, we assume cylindrical perforations surrounded by a crushed zone of reduced permeability. As Fig. 1 shows, the perforations are distributed spirally around the wellbore. perforations are distributed spirally around the wellbore. SPEPE P. 73