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Research Papers: Oil/Gas Reservoirs

Analytical Solutions for a Quad-Linear Flow Model Derived for Multistage Fractured Horizontal Wells in Tight Oil Reservoirs

[+] Author and Article Information
Wendong Wang, Yuliang Su

School of Petroleum Engineering,
China University of Petroleum (East),
No. 66, Changjiang West Road, Huangdao District,
Qingdao 266580, China

Mohammad Shahvali

Reservoir Engineering Consultant iReservoir,
1490 W. Canal Court, Suite 2000,
Littleton, CO 80120
e-mail: mshahvali@ireservoir.com

1Corresponding author.

2Present address: iReservoir.com, Inc., 1490 W Canal Court, Suite 2000, Littleton, CO 80120

Contributed by the Petroleum Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received December 7, 2015; final manuscript received June 2, 2016; published online July 12, 2016. Assoc. Editor: Daoyong (Tony) Yang.

J. Energy Resour. Technol 139(1), 012905 (Jul 12, 2016) (9 pages) Paper No: JERT-15-1463; doi: 10.1115/1.4033860 History: Received December 07, 2015; Revised June 02, 2016

Analysis of microseismic field data shows that the stimulated reservoir volume (SRV) in unconventional reservoirs partially covers the area between hydraulic fracture stages. Consequently, we are often faced with an effective fracture network area (EFNA) rather than a full SRV in such reservoirs. In this paper, we develop a new semi-analytical solution for pressure of hydraulically fractured horizontal wells in tight oil reservoirs with various SRV sizes. Our model is based on four linear flow regions including the hydraulic fracture, the stimulated reservoir, the unstimulated reservoir, and the outer reservoir region. Flow in each region is represented by a set of governing equations and boundary conditions that are coupled to those of other regions. The dual-porosity formulation represents the SRV, while single-porosity formulation is used for other flow regions. We transform the coupled system of equations into Laplace domain, solve for wellbore pressure, and invert the solutions back to time domain numerically. We validate the semi-analytical solutions by comparing them to other semi-analytical solutions in the literature for the special case of trilinear flow. We further validate the quad-linear flow solutions using numerical simulation. Based on the semi-analytical solutions, we generate logarithmic plots of wellbore pressure and pressure derivative. Moreover, we perform sensitivity studies to present the degree to which the solutions vary as size and other properties of the SRV change.

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References

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Figures

Grahic Jump Location
Fig. 1

Schematic of the quad-linear flow model representing four linear flow regions for a fractured horizontal well. ye is the distance from the no-flow boundary to the middle of the hydraulic fracture, ld is half-width of the stimulated reservoir region, xf represents half-length of the hydraulic fracture, and xe denotes the distance from the outer boundary to the wellbore.

Grahic Jump Location
Fig. 6

Effect of width of the SRV, ld, on dimensionless wellbore pressure and pressure derivative solutions of the quad-linear flow model

Grahic Jump Location
Fig. 7

Effect of the interporosity flow coefficient of the SRV, λ, on dimensionless wellbore pressure and pressure derivative solutions of the quad-linear flow model

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Fig. 8

Effect of the storativity ratio of the SRV, ω, on dimensionless wellbore pressure and pressure derivative solutions of the quad-linear flow model

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Fig. 2

Comparison between dimensionless wellbore pressure and pressure derivative solutions obtained from the proposed quad-linear flow model and trilinear flow model (Ref. 18), for the special case of ld = ye

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Fig. 3

Microseismic fracture mapping data related to hydraulic fracture stages of several horizontal wells in tight oil field in China. Several FCI values are displayed for reference.

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Fig. 4

Reservoir simulation model (Eclipse) with fractured horizontal well and dual-porosity SRV, used for validation of the quad-linear flow model solutions

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Fig. 5

Comparison between dimensionless wellbore pressure solutions obtained from the semi-analytical quad-linear flow model and numerical simulation (Eclipse). No wellbore storage or skin is considered. The input data are presented in Table 1.

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