Research Papers: Petroleum Engineering

Insight Into the Heel–Toe Effect of a Long Horizontal Wellbore Based on a Hybrid Numerical Method

[+] Author and Article Information
Pranab N. Jha

Department of Mechanical Engineering,
University of Houston,
Houston, TX 77004
e-mail: pjha2@uh.edu

Chuck Smith

Apache Corporation,
Houston, TX 77056
e-mail: csapache1@gmail.com

Ralph W. Metcalfe

Department of Mechanical Engineering,
Mathematics and Biomedical Engineering,
University of Houston,
Houston, TX 77004
e-mail: metcalfe@uh.edu

1Present address: Occidental Oil and Gas Corporation, 5 Greenway Plaza, Suite 110, Houston, TX 77046.

2Corresponding author.

Contributed by the Petroleum Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received February 2, 2015; final manuscript received August 26, 2015; published online September 23, 2015. Assoc. Editor: Egidio Marotta.

J. Energy Resour. Technol 138(1), 012905 (Sep 23, 2015) (8 pages) Paper No: JERT-15-1045; doi: 10.1115/1.4031509 History: Received February 02, 2015; Revised August 26, 2015

Numerical simulation of flow inside a horizontal wellbore with multiple completion stages is presented. Using a hybrid method combining computational fluid dynamics and a lumped parameter model, blocking effect on the toe-end stages observed in long horizontal wells (heel–toe effect) under simplified conditions is explained. A two-dimensional channel geometry was used to model the wellbore, with side inlets representing completion stages. First, using a five-stage well with steady state flow conditions, the existence of three basic flow regimes—trickle flow, partially blocked flow and fully blocked flow—was established. Using these results, the phenomenon of blocking of upstream inlets near the toe by the downstream ones near the heel is explained. The existence of these flow regimes is consistent with well-log data obtained from a horizontal shale gas well with 31 completion stages at two different times during production. Further, to study the dynamic behavior of the completion stages when reservoir fluid flows into the wellbore, a basic reservoir depletion model was created using a pressure boundary condition at the side inlets, varying in time. A lumped-parameter model was used to account for the pressure drop between two inlets separated by large axial distance. Different characteristic time scales, related to the depletion of the reservoirs, were identified. By varying initial conditions, the dynamic behavior of the system with multiple inlets was observed and analyzed. The transition of flow regimes with depletion of reservoirs is consistent with the observed behavior of the horizontal shale gas well.

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Fig. 2

Representation of a two-dimensional channel with five side inlets

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Fig. 1

(a) Cumulative production curves for a horizontal shale gas well at two different times from start of production. (b) Variation of Re and Ma along the wellbore with time.

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Fig. 6

(a) Inlet pressure and (b) flow rate. Here, h’ = 1.0 and initial Re ≈ 12,100.

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Fig. 3

Effect of inlet size on flow regimes. Total pressure on each inlet is 50 mPa.

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Fig. 5

(a) Pressure and (b) flow rate history showing equilibration time Te. Here, h’ = 1.0 was used to get blocking effect initially.

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Fig. 4

Effect of pressure on flow blocking shown, h’ = 0.2

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Fig. 7

Regime change from blocked flow at t = 5 s to trickle flow at t = 60 s. Flow rate is added starting from I1 near the heel going toward I5 near the toe.

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Fig. 8

(a) Comparison of turbulence models for a channel flow. (b) Determination of development length for turbulent cross-flow. One side inlet (I5) flows into the domain, locations correspond to downstream from I5. h’ = 0.1.

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Fig. 9

(a) Friction factor comparison between SA model and experimental data from Ref. [3]; (b) contours of velocity magnitude near pipe junction at the center z = 0 plane, Re = 9190



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