Numerical Inversion of Laplace Transforms in the Solution of Transient Flow Problems With Discontinuities

Al-Ajmi, Nab Mahdi; Ahmadi, Mahmood; Özkan, Erdal; Kazemi, Hossein

doi:10.2118/116255-ms

Cited by 16 publications

(11 citation statements)

References 24 publications

(32 reference statements)

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“…A deconvolution procedure filtered out variations of flow rate and provided an equivalent constant rate pumping response of the reservoir (i.e., normalized response to a unit rate), which improved the interpretation (Gringarten, 2008). Among the different available algorithms (e.g., von Schroeter et al, 2004;Levitan, 2005;Al-Ajmi et al, 2008;Pimonov et al, 2009;Ahmadi et al, 2012), the deconvolution procedure in Laplace space proposed by Al-Ajmi et al (2008) was used for convenience. In Laplace domain, the deconvolution of two functions becomes the division of their transforms, and therefore the deconvolution of the pressure response, p r (p), to the variable flow rate, q(p), is simply (Bourgeois and Horne, 1993;Al-Ajmi et al, 2008;Ahmadi et al, 2012):…”

Section: Data Processingmentioning

confidence: 99%

Flow-bearing structures of fractured rocks: Insights from hydraulic property scalings revealed by a pumping test

Guihéneuf

Dausse

Dreuzy

et al. 2021

Journal of Hydrology

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Section: Data Processingmentioning

confidence: 99%

Flow-bearing structures of fractured rocks: Insights from hydraulic property scalings revealed by a pumping test

Guihéneuf

Dausse

Dreuzy

et al. 2021

Journal of Hydrology

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“…The Solutions of the Mathematical Models. The solutions of the mathematical models [23,24] at various outer boundary conditions can be obtained by applying source function and integral transform and taking the Laplace transform to with respect to . For gas reservoir with closed outer boundary in vertical direction and infinite outer boundary in horizontal direction, according to (1), (2), (3), (4), and (7), the dimensionless bottomhole pseudopressure of horizontal gas well in the Laplace space can be obtained.…”

Section: The Mathematical Model With Considering the Effect Ofmentioning

confidence: 99%

Characteristic Value Method of Well Test Analysis for Horizontal Gas Well

Yan

Tan

2014

Mathematical Problems in Engineering

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This paper presents a study of characteristic value method of well test analysis for horizontal gas well. Owing to the complicated seepage flow mechanism in horizontal gas well and the difficulty in the analysis of transient pressure test data, this paper establishes the mathematical models of well test analysis for horizontal gas well with different inner and outer boundary conditions. On the basis of obtaining the solutions of the mathematical models, several type curves are plotted with Stehfest inversion algorithm. For gas reservoir with closed outer boundary in vertical direction and infinite outer boundary in horizontal direction, while considering the effect of wellbore storage and skin effect, the pseudopressure behavior of the horizontal gas well can manifest four characteristic periods: pure wellbore storage period, early vertical radial flow period, early linear flow period, and late horizontal pseudoradial flow period. For gas reservoir with closed outer boundary both in vertical and horizontal directions, the pseudopressure behavior of the horizontal gas well adds the pseudosteady state flow period which appears after the boundary response. For gas reservoir with closed outer boundary in vertical direction and constant pressure outer boundary in horizontal direction, the pseudopressure behavior of the horizontal gas well adds the steady state flow period which appears after the boundary response. According to the characteristic lines which are manifested by pseudopressure derivative curve of each flow period, formulas are developed to obtain horizontal permeability, vertical permeability, skin factor, reservoir pressure, and pore volume of the gas reservoir, and thus the characteristic value method of well test analysis for horizontal gas well is established. Finally, the example study verifies that the new method is reliable. Characteristic value method of well test analysis for horizontal gas well makes the well test analysis process more simple and the results more accurate.

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“…For these cases, we suggest the use of the algorithm proposed by Roumboutsos and Stewart (1983) to obtain the Laplace transform of the sampled data and the numerical Laplace inversion algorithm proposed by Iseger (2006) for discontinuous functions. Al-Ajmi et al (2008) provides a discussion of the numerical inversion of discontinuous functions resulting from step-rate changes.…”

Section: Production Conditionsmentioning

confidence: 99%

Semianalytical Representation of Wells and Near-Well Flow Convergence in Numerical Reservoir Simulation

et al. 2008

Self Cite

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This paper presents a new approach to compute wellbore pressures and near-well flow convergence in numerical reservoir simulation. In this semi-analytical approach, the solution of the flow problem in porous media is related to the boundaryelement formulations. To account for reservoir heterogeneity, solution domain is subdivided into internally homogeneous reservoir blocks, which may include wells, and the solutions are coupled with the requirement of flux and pressure continuity at the block boundaries. Knowing the boundary values of the solution domain, this formulation solves for the flux at the block boundaries and flux and pressure on wells. Knowing the flux boundary condition, this formulation also enables the solution of pressure at any point within the reservoir blocks. This feature of the solution serves the purposes of multiscale simulation of flow and transport in porous media. Although the solution can be applied on field scale, this paper focuses on the applications to near-well flow convergence region. When the solution is used for the near-well flow-convergence region, the required boundary values of the solution domain can be obtained from any standard solution techniques, including finitedifference simulation, by accounting for wells as source terms.

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Numerical Inversion of Laplace Transforms in the Solution of Transient Flow Problems With Discontinuities

Cited by 16 publications

References 24 publications

Flow-bearing structures of fractured rocks: Insights from hydraulic property scalings revealed by a pumping test

Flow-bearing structures of fractured rocks: Insights from hydraulic property scalings revealed by a pumping test

Characteristic Value Method of Well Test Analysis for Horizontal Gas Well

Semianalytical Representation of Wells and Near-Well Flow Convergence in Numerical Reservoir Simulation

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