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Abstract

A solution and results of the skin effect of deviated wells presented here suggest that the previous assumption of isotropy would greatly overestimate the absolute magnitude of the skin, in commonly found anisotropies of normal depositional formations and, especially, in laminated reservoirs where the vertical permeability is much smaller. Graphs and correlations of the skin due to slant as a function of the reservoir thickness, index of anisotropy, and well deviation are provided. The performance of a highly deviated well (e.g. 850) can be approximated by a vertical well productivity relationship, augmented by such skin effect, and the results should be practically indistinguishable from those derived from well known horizontal well productivity equations, using equal well production lengths.

Introduction

Previous work has presented the effects of well deviation from the vertical by means of a negative mechanical skin. An often overlooked implication is that a well test in a highly deviated well should result in such negative skin, otherwise the well is likely to be damaged. Well known solutions of the problem have presumed vertical-to-horizontal permeability isotropy but the recent emergence of horizontal wells has brought an awareness of the importance and frequency of an isotropy.

Deviated wells, connecting thin permeable layers that are separated by impermeable streaks, may actually be more attractive than horizontal wells, for reasonable individual layer vertical permeabilities. Studies examining this issue are included in this paper.

It is well known that fully completed deviated holes are generally more attractive than vertical wells by virtue of the larger reservoir-to-well exposure. Quantification of this issue has been provided in the literature by Cinco-Ley et al. through the introduction of a mechanical skin effect accounting for this slant.

Unfortunately, this work has dealt with permeability-isotropic reservoirs, i.e., for the case where the vertical permeability is equal to the horizontal. This is a highly unrealistic assumption and the industry has become far more aware of the concept of anisotropy after the proliferation of horizontal wells.

Once horizontal wells are drilled, the traditional one-permeability perception of a reservoir has to be abandoned. Three permeabilities are thus necessary: two horizontal and one vertical.

A very common method of depiction of the vertical-to-horizontal anisotropy is through the index of anisotropy given by the variable Iani:

(1)

where the horizontal permeability, kH, is itself equal to kxky, the two horizontal components. A typical value of this index of anisotropy for a sandstone reservoir is 3, suggesting a 10:1 ratio between the horizontal and vertical permeabilities.

Several publications and reported field cases have shown that this permeability anisotropy is crucial to the success and relative attractiveness of horizontal wells compared to vertical wells in the same reservoir. For thick formations (e.g. h >100 ft) the impact of anisotropy is decisive; for thinner formations (e.g. h < 40 ft) its impact becomes much less pronounced and often forgiving.

A comprehensive productivity index model has been presented by Economides et al. In their work they introduced a semi-analytical and highly flexible solution procedure capable of accounting for the effects of anisotropy and thickness on any well configuration. This model is used in this work.

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