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Analytical Modeling of Flow Behavior for Wormholes in Naturally Fractured–Vuggy Porous Media

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Abstract

Acidizing technology has been widely applied when developing naturally fractured–vuggy reservoirs. So testing and evaluating acidizing wells’ pressure behavior become necessary for further improving the wells’ performance. Analyzing transient pressure data can estimate some key reservoir parameters. Generally speaking, carbonate minerals are usually composed of dolomite and calcite which are easy to be dissolved by hydrochloric acid which is often used to react with the rock to create a high conductivity channel, namely wormhole. Pressure transient behavior in fractured–vuggy reservoirs has been studied for many years; however, the models of acidizing wells with wormholes were not reported in previous studies. This article presented an analytical model for wormholes in naturally fractured–vuggy carbonate reservoirs, and wormholes solutions were obtained through point sink integral method. The results were validated accurately by comparing with previous results and numerical simulation. Then in this paper, type curves were established to recognize the flow characteristics, and flow was divided into six flow regimes comprehensively. The calculative results showed that the characteristics of type curves were influenced by inter-porosity flow factor, wormhole number, fluids capacitance coefficient. We also showed that the pressure behavior was affected by the angles between wormholes, and the pressure depletion increased as the angle decreased, because the wormholes were closer, their interaction became stronger. At the end, a reservoir example was showed to demonstrate the methodology of new type curve analysis.

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Abbreviations

\(p_\mathrm{D}\) :

Dimensionless pressure

\(\mathrm{d}p_\mathrm{D}\) :

Dimensionless pressure derivative

\(s\) :

Time variable in Laplace domain, dimensionless

\(\tilde{p}_\mathrm{D}\) :

The dimensionless pressure \(p_\mathrm{D}\) in Laplace domain

\(c_\mathrm{M}\) :

Matrix compressibility (1/psi)

\(c_\mathrm{V}\) :

Vugs compressibility (1/psi)

\(c_\mathrm{f}\) :

Fractures compressibility (1/psi)

\(k_\mathrm{m}\) :

Matrix permeability (mD)

\(k_\mathrm{v}\) :

Vugs permeability (mD)

\(k_\mathrm{f}\) :

Fractures permeability (mD)

\(p_\mathrm{i}\) :

Initial pressure (psi)

\(p_\mathrm{f}\) :

Fractures pressure (psi)

\(p_\mathrm{v}\) :

Vugs pressure (psi)

\(p_\mathrm{m}\) :

Matrix pressure (psi)

\(\mu \) :

Fluid viscosity (cp)

\(h\) :

Formation thickness (ft)

\(\phi _\mathrm{m}\) :

Matrix porosity (fraction)

\(\phi _\mathrm{f}\) :

Fractures porosity (fraction)

\(\phi _\mathrm{v}\) :

Vugs porosity (fraction)

\(r_\mathrm{w}\) :

Wellbore radius (ft)

\(r\) :

The radius for any position in the reservoir (ft)

\(r^{\prime }\) :

The radius for source position in the reservoir (ft)

\(r_\mathrm{e}\) :

Equivalent drainage radius (ft)

\(t\) :

Time variable (h)

\(h\) :

Formation thickness (ft)

\(x_\mathrm{f}\) :

Wormhole length (ft)

\(N\) :

Wormhole number

\(K_{0}(x)\) :

Modified Bessel function (2nd kind, 0 order)

\(D\) :

Dimensionless

\(w\) :

Wellbore property

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Acknowledgments

This article was supported by the National Major Research Program for Science and Technology of China (Grant Nos. 2011ZX05013-002 and 2011ZX05009-004). Key Technologies of horizontal well development in tight sandstone gas reservoir, Sinopec science and technology research project (Contract No. G5800-13-ZS-KJB22). Two anonymous reviewers and the editors are greatly appreciated for their careful reviews and detailed comments.

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Authors and Affiliations

  1. School of Energy Resources, China University of Geosciences, Beijing, 100083, People’s Republic of China

    Lei Wang & Xiaodong Wang

  2. Research Institute of Petroleum Exploration & Development, Beijing, 100083, People’s Republic of China

    Erhui Luo & Junlei Wang

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  1. Lei Wang
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  2. Xiaodong Wang
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  3. Erhui Luo
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  4. Junlei Wang
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Correspondence to Lei Wang.

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Wang, L., Wang, X., Luo, E. et al. Analytical Modeling of Flow Behavior for Wormholes in Naturally Fractured–Vuggy Porous Media. Transp Porous Med 105, 539–558 (2014). https://doi.org/10.1007/s11242-014-0383-7

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