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Summary

An algorithm has been developed for computing the pressure response for a well with constant wellbore storage and non-Darcy skin factor across the completion. The algorithm has been used to generate type curves for drawdown and buildup tests. The buildup-pressure-derivative response for a well with non-Darcy flow across the completion exhibits a much steeper slope during the transition out of wellbore storage than that of a well with constant skin.

No reservoir model with constant wellbore storage and skin can reproduce this steep derivative. Thus, if it is present in a buildup test, the well is experiencing either decreasing wellbore storage or decreasing skin factor, or both.

With the new type curves, under favorable conditions, both Darcy and non-Darcy skin components may be estimated from a single buildup test following constant-rate production. The new algorithm also may be used to model a test sequence comprising multiple flow and buildup periods.

Introduction

Nodal production-system analysis¹ is one of the primary tools for optimizing production and predicting well performance. In nodal analysis, reservoir performance is described through the inflow-performance-relationship (IPR) curve. To construct accurate IPR curves for gas wells, both Darcy and non-Darcy skin components must be known.

The non-Darcy skin is traditionally estimated by performing a multirate test. The effective skin factor is then graphed as a function of flow rate, allowing the Darcy and non-Darcy components to be determined from a straight-line fit through the data.

When multirate tests are not available, the non-Darcy flow coefficient may be estimated from correlations. However, the resulting values may be in error by as much as 100%.²

The behavior of a pressure-transient test with infinite-acting radial flow with constant wellbore storage and skin factor is well known.^3,4 Other authors have considered the case of variable wellbore storage with constant skin factor.^5,6

This paper examines the behavior of a well with constant wellbore storage and rate-dependent skin factor for drawdown and buildup tests. Buildup tests with non-Darcy skin factor exhibit a much steeper pressure derivative during the transition out of wellbore storage than those with Darcy skin factor, as seen in Fig 1.

The new type curves provide three significant contributions to the industry: (1) they allow the test analyst to recognize non-Darcy flow from a log-log diagnostic plot of pressure change and pressure derivative; (2) they provide estimates of both Darcy and non-Darcy components of skin factor from a single buildup test, allowing construction of IPR curves based on well performance instead of correlations; and (3) they help identify the cause of high skin factors.

High-rate wells with high skin factors represent excellent candidates for stimulation.^7,8 However, because of the risks involved in any workover, there often is a reluctance to stimulate such a well. Given that high-rate wells are the ones most likely to exhibit non-Darcy skin, the new type curves will contribute to informed decisions regarding whether to stimulate one of these wells.

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