Research Papers: Petroleum Engineering

Effects of Non-Darcy Flow and Penetrating Ratio on Performance of Horizontal Wells With Multiple Fractures in a Tight Formation

[+] Author and Article Information
Feng Zhang

Petroleum Systems Engineering,
Faculty of Engineering and Applied Science,
University of Regina,
Regina, SK S4S 0A2, Canada

Daoyong Yang

Petroleum Systems Engineering,
Faculty of Engineering and Applied Science,
University of Regina,
Regina, SK S4S 0A2, Canada
e-mail: tony.yang@uregina.ca

1Present address: Computer Modelling Group Ltd., Calgary, AB T2L 2M1, Canada.

2Corresponding author.

Contributed by the Petroleum Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received July 17, 2017; final manuscript received August 18, 2017; published online September 28, 2017. Editor: Hameed Metghalchi.

J. Energy Resour. Technol 140(3), 032903 (Sep 28, 2017) (11 pages) Paper No: JERT-17-1366; doi: 10.1115/1.4037903 History: Received July 17, 2017; Revised August 18, 2017

A novel slab source function has been formulated and successfully applied to examine effects of non-Darcy flow and penetrating ratio on performance of a horizontal well with multiple fractures in a tight formation. The Barree–Conway model is incorporated in the mathematical model to analyze non-Darcy flow behavior in the hydraulic fractures, while the pressure response under non-Darcy flow is determined by two dimensionless numbers (i.e., relative minimum permeability (kmr) and non-Darcy number (FND)). A semi-analytical method is then applied to solve the newly formulated mathematical model by discretizing the fracture into small segments. The newly developed function has been validated with numerical solution obtained from a reservoir simulator. Non-Darcy effect becomes more evident at a smaller relative minimum permeability (kmr < 0.05) and a larger non-Darcy number (FND > 10). The non-Darcy number is found to be more sensitive than the relative minimum permeability, resulting in a larger pressure drop even at a larger kmr. In addition, the non-Darcy flow is found to impose a significant impact on the early-stage bilinear/linear flow regime, resulting in an additional pressure drop that is similar to lowering the fracture conductivity. The pressure response can be classified into two categories by a penetrating ratio of 0.5. When the penetrating ratio is decreased, the early bilinear/linear flow regime occurs, followed by an early radial flow regime.

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Fig. 1

Schematic of a horizontal well with multi-stage fractures in a box-shaped reservoir

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Fig. 2

Schematic of a slab source model

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Fig. 3

Discretization of one fracture in the global fracture system

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Fig. 4

Flowchart of solving the nonlinear system

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Fig. 5

The coefficient matrix for solving the matrix-hydraulic fracture system

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Fig. 6

(a) Top view of the 3D grid system and (b) cross section of the 3D grid system

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Fig. 7

Pressure drop obtained from this study and CMG simulation as a function of time

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Fig. 8

Effect of non-Darcy number FND at (a) kmr = 0.01 and (b) kmr = 0.10

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Fig. 9

Effect of relative minimum permeability kmr at (a) FND = 1000 and (b) FND = 10

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Fig. 10

Effect of non-Darcy flow on flow distribution at (a) tD = 1.0 × 10−6 and (b) tD = 1.0 × 103

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Fig. 11

Effect of partially penetrating ratio of three stages at (a) α > 0.5 and (b) α < 0.5

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Fig. 12

(a) Flow regime interpretation for the pressure buildup response and (b) type curve matching of pressure buildup data



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