Estimating Non-Darcy Flow Coefficient From Buildup-Test Data With Wellbore Storage

Abstract

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 builduppressure-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. IntroductionNodal production-system analysis 1 is one of the primary tools for optimizing production and predicting well performance. In nodal analysis, reservoir performance is described through the inflowperformance-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...

Semianalytical Model for Reservoirs With Forchheimer's Non-Darcy Flow

“…To validate the results of non-Darcy flow in the reservoir (F ND,R 0), we compare the results of this work with the numerical results reported by Spivey et al (2004) at C D ‫,1ס‬ 10, and 100. Shown in Fig.…”

“…When near-wellbore non-Darcy skin factor is considered (s ND,W 0 and F ND,R ‫,)0ס‬ comparison of the results of this work with those of Spivey et al (2004) is presented in Fig. 3 for both drawdown (DD curves) and buildup tests (BU curves).…”

“…Instead of treating the rate-dependent skin factor as Dq sc , Kim and Kang (1994) and Spivey et al (2004) treated the ratedependent skin factor as being proportional to sandface flow rate (i.e., Dq sf ). Their studies on the buildup test with wellbore storage and non-Darcy flow revealed the unique pressure-derivative feature between wellbore storage and radial-flow regions, which made it possible to estimate the non-Darcy coefficient, D, from a single buildup test.…”

“…Near-wellbore non-Darcy flow may be different from non-Darcy flow in the reservoir because of perforation or formation damage/stimulation. Spivey et al (2004) found that in a cased hole with a gravel-pack completion, 90% of the pressure drop caused by non-Darcy flow occurs within a range of 0.5 ft from the wellbore, so they applied Eq. 2 to represent the non-Darcy flow across perforations, called "non-Darcy flow across the completion."…”

Non-Darcy displacement by a non-Newtonian fluid in porous media according to the Barree-Conway model

“…However, the relationship between pressure (or potential) gradient and flow velocity at high flow rates cannot be modelled by Darcys law any more (Bear, 2013;Spivey et al, 2004). There is more evidence that the non-Darcy flow at high flow rates occurs in many subsurface, engineering porous and biological porous flow systems (Schfer and Lohnert, 2006;Vafai, 2010;Wu et al, 2011).…”