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Similar Constructing Method and Gaver-Stehfest Numerical Inversion Equation for Solving the Composite Reservoir Models Under Three Outer Boundary Conditions

  • Research Article-Petroleum Engineering
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Abstract

This article studies composite reservoir models under infinite, constant pressure and closed outer boundary conditions, which considers the impact of wellbore storage, skin factor and effective wellbore radius. The dimensionless reservoir transient pressure inner and outer areas and dimensionless bottom-hole transient pressure of composite reservoir models under infinite, constant pressure and closed outer boundary conditions in the real space are obtained by using the similar constructing method and Gaver-Stehfest numerical inversion (SCM-GSNI). Then, we conduct numerical experiments, where the characteristic curves of bottom-hole transient pressure and its derivative are analyzed and the sensitivities of the relevant parameters are discussed. This research provides a new method for engineers to solve composite reservoir models.

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Abbreviations

\(B\) :

Crude volume coefficient (dimensionless)

\(C\) :

Wellbore storage coefficient (\({{{\text{m}}^{3} } \mathord{\left/ {\vphantom {{{\text{m}}^{3} } {{\text{MPa}}}}} \right. \kern-\nulldelimiterspace} {{\text{MPa}}}}\))

\(p_{w}\) :

Bottom-hole pressure (\({\text{MPa}}\))

\(r_{w}\) :

Effective wellbore radius (m)

\(p_{0}\) :

Initial reservoir pressure (MPa)

\(R\) :

The radius of outer boundary (m)

\(h\) :

The thickness of reservoir (m)

\(\eta _{i}\) :

Pressure transmitting coefficient (\(\mu {\text{m}}^{2} \cdot {\text{MPa}}\))

\(z\) :

Laplace space variable (dimensionless)

\(C_{t}\) :

Compressibility (\({\text{MPa}}^{{ - 1}}\))

\(k_{i}\) :

Permeability (\(\mu {\text{m}}^{2}\))

\(p_{i}\) :

Reservoir pressure in \(i\)th area (\({\text{MPa}}\))

\(r\) :

Wellbore radius (m)

\(S\) :

Skin factor (dimensionless)

\(\mu _{i}\) :

Viscosity (\({\text{MPa}} \cdot {\text{s}}\))

\(\phi _{i}\) :

Porosity (dimensionless)

\(t\) :

Time (h)

\(q\) :

Production rate (\({{{\text{m}}^{3} } \mathord{\left/ {\vphantom {{{\text{m}}^{3} } {\text{d}}}} \right. \kern-\nulldelimiterspace} {\text{d}}}\))

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Authors and Affiliations

  1. School of Sciences, Xihua University, Chengdu, 610039, China

    Xiaoxu Dong & Shunchu Li

  2. School of Sciences, Southwest Petroleum University, Chengdu, 610500, China

    Zhibin Liu & Hehua Wang

  3. Chengdu North Petroleum Exploration and Development Technology Company Limited, Chengdu, 610051, China

    Hehua Wang

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  1. Xiaoxu Dong
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  2. Shunchu Li
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Correspondence to Xiaoxu Dong.

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Project supported by Talent introduction project of Xihua University (Z202068) and the Major Program of Sichuan Province (No. 20QYCX0030).

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Dong, X., Li, S., Liu, Z. et al. Similar Constructing Method and Gaver-Stehfest Numerical Inversion Equation for Solving the Composite Reservoir Models Under Three Outer Boundary Conditions. Arab J Sci Eng 47, 11239–11253 (2022). https://doi.org/10.1007/s13369-021-05896-x

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