Productivity of Selectively Perforated Vertical Wells
- Turhan Yildiz (U. of Tulsa)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- June 2002
- Document Type
- Journal Paper
- 158 - 169
- 2002. Society of Petroleum Engineers
- 2.7.1 Completion Fluids, 4.1.2 Separation and Treating, 2.4.3 Sand/Solids Control, 5.3.2 Multiphase Flow, 5.6.8 Well Performance Monitoring, Inflow Performance, 3.2.5 Produced Sand / Solids Management and Control, 2.2.2 Perforating, 2.4.5 Gravel pack design & evaluation, 2 Well Completion, 4.3.4 Scale, 3.3.1 Production Logging, 1.8 Formation Damage, 5.3.4 Integration of geomechanics in models
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This study presents analytical models to predict the productivity of selectively perforated vertical wells. The models consider arbitrary phasing angle, nonuniform perforation size and length, and formation damage around perforations. The accuracy of the models was verified against the results from the experimental studies, the semianalytical correlation, and the numerical models all available in the literature. Unique applications of the models are presented. A comprehensive sensitivity study showing the impact of different perforation schemes on well productivity is documented.
Since its invention in the 1930s, perforating has been one of the most commonly used well completion techniques in oil and gas wells. Wells are often cased to prevent sand production and wellbore collapse and to delay gas/water coning. The main objective in perforating is to create flow tunnels across the casing for formation fluid entry. In many cases, oil and gas wells are selectively perforated at multiple intervals.
The fluid flow into perforated completions is three-dimensional (3D) and has a convergent flow geometry. The nature of this complex flow pattern makes the flow modeling considerably more difficult compared to that for an openhole completion.
The objectives of this study are:
To develop general productivity models accounting for 3D nature of flow into perforations and nonuniform perforation properties.
To verify the models.
To investigate the impact of different perforation strategies on well productivity.
The influences of the reservoir, well, and perforation parameters on the productivity of perforated wells have been the subject of many investigations. A great number of publications have concentrated on the flow efficiency of perforated vertical wells. Some of these studies are summarized below to acknowledge their previous contribution. For convenience, the previous models on well performance are divided into three categories: electrolytic models, semi-analytical and empirical models, and numerical models.
The earliest models of flow into perforations relied upon the experimental results from electrolytic analog apparatus. 1-3 McDowell and Muskat1 measured the effect of perforation length and diameter and phasing angle on well productivity. They concluded that if the perforations are long enough, the productivity of a perforated well might be even higher than that of an open hole. In an independent study, Howard and Watson2,3 conducted similar experiments and reported similar results. Most recently, Pan and Tang4 conducted a comprehensive set of experiments on a scaled electrolytic apparatus and developed empirical equations for perforation flow efficiency.
Mathematical models based on finite-difference and finite-element methods have been proposed in many studies.5-13 The studies relying on the numerical solution techniques reported significantly different productivities. An important drawback for the numerical solutions is the extensive computational time and effort.
Harris5 investigated the productivity of perforated completions considering a wedge-shaped perforation by a finite difference model. Hong6 worked with a similar model and reported the impact of the formation damage and perforation pattern on well productivity. It was recommended that the perforation density should be at least 12 shots per foot (spf) to establish reasonable flow efficiency in damaged formations.
It was later noted that the geometrical irregularities involved in perforated completions couldn't be easily built into the finite difference models. Therefore, it became apparent that the finite difference models were not appropriate to simulate the flow into irregular perforations. It was realized that the finite element methods would be more convenient to represent the irregular perforation geometry.
Klotz et al.7 used a 2D finite element model and investigated the impact of a crushed zone and formation damage around the perforations on the well productivity. To come with more realistic perforation geometries and to account for spiral perforation distributions, Locke8 made use of a 3D finite element model. He also presented a nomograph to predict the pseudoskin factor in perforated wells. Tariq9 investigated the influence of nondarcy flow on the flow efficiency of perforated completions. He remarked that Locke's numerical model, and thus his nomograph, overestimated the perforated well productivity owing to insufficient grid size. In a later study, Tariq et al.10 investigated flow into perforations under the influence of formation anisotropy, shale laminations, and natural fractures. They concluded that perforated completion efficiency is strongly affected by near-wellbore heterogeneities, and high shot densities are required in anisotropic and laminated formations. Recently, Tang et al.11 reported results from a similar finite element model.
Behie and Settari12 and Dogulu13 proposed the use of hybrid grids and local grid refinement to overcome the shortcomings of finite difference models. Both studies reported that the results from their model do not agree with those from Tariq's work when nondarcy flow regime is considered.
Semi-Analytical and Empirical Models.
The semi-analytical models proposed by McLeod,14 Karakas and Tariq,15 and Bell et al.16 are extensively used because of the simplicity of the proposed equations. However, the simple radial flow model proposed by McLeod14 only accounts for the flow across the crushed and damaged zones around perforation and assumes that all the perforations are equivalent.
By integrating the results of the finite element simulations with the analytical solutions for hydraulically fractured and horizontal wells, Karakas and Tariq15 constructed a semi-analytical model and presented empirical equations to compute the perforation pseudoskin. To estimate the productivity index of a partially perforated well, Bell et al.16 combined a pseudoskin equation for a partially penetrating well with the semi-analytical equation of Karakas and Tariq.15 However, the proposed method is limited to only one perforated interval.
Ahmed et al.17 developed a 3D analytical solution and compared their model with electrolytic tank model of McDowell and Muskat.1 Their analytical model was in reasonable agreement with the electrolytic model. However, the computation of the analytical model presented in Ref. 17 is very cumbersome.
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