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Research Papers: Petroleum Engineering

Production Forecasting for Shale Gas Reservoirs With Fast Marching-Succession of Steady States Method

[+] Author and Article Information
Bailu Teng

School of Mining and Petroleum Engineering,
Faculty of Engineering,
University of Alberta,
Edmonton, AB T6G 1H9, Canada
e-mail: bailu@ualberta.ca

Linsong Cheng

School of Petroleum Engineering,
China University of Petroleum (Beijing),
Beijing 102249, China
e-mail: lscheng@cup.edu.cn

Shijun Huang

School of Petroleum Engineering,
China University of Petroleum (Beijing),
Beijing 102249, China
e-mail: fengyun7407@163.com

Huazhou Andy Li

School of Mining and Petroleum Engineering,
Faculty of Engineering,
University of Alberta,
Edmonton, AB T6G 1H9, Canada
e-mail: huazhou@ualberta.ca

1Corresponding author.

Contributed by the Petroleum Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received November 28, 2016; final manuscript received October 9, 2017; published online January 22, 2018. Assoc. Editor: Daoyong (Tony) Yang.

J. Energy Resour. Technol 140(3), 032913 (Jan 22, 2018) (14 pages) Paper No: JERT-16-1482; doi: 10.1115/1.4038781 History: Received November 28, 2016; Revised October 09, 2017

In this paper, we introduce fast marching-succession of steady-states (FM-SSS) method to predict gas production from shale gas formations. The solutions of fast marching method (FMM) will describe the dynamic drainage boundary, and the succession of steady-state (SSS) method is applied to predict the gas production within the drainage boundary. As only the grids within drainage need to be taken into calculation at each time-step, this approach works much more efficiently than the implicit finite difference method, especially, at the early stage of production when the drainage is relatively small.We combine FMM with SSS to conduct reservoir simulation and predict gas production in shale gas reservoirs. The pressure profiles of transient flow are approximated with the pressure profiles of steady-state flow in our approach. The difference between the proposed method and the conventional SSS method is that we provide an efficient method to characterize the boundary conditions. In the conventional SSS method, the boundary pressure has to be measured, which is inconvenient for simulation purposes, whereas FM-SSS method takes the dynamic drainage as a changing boundary and approximates the drainage boundary pressure with initial reservoir pressure, such that the boundary condition can be numerically characterized. A major advantage of our approach is that it is unconditionally stable and more efficient than the implicit finite difference method because much smaller-scale linear equations need to be solved at each time-step.

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Figures

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Fig. 1

Pressure profiles of transient flow and steady-state flow

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Fig. 2

The concept of moving boundary in FMM method. As time elapses, the dynamic boundary propagates forward.

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Fig. 3

Schematic showing the evolution of FMM computations. The numerical values used here are only for demonstrations purposes.

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Fig. 4

Tracking dynamic drainage boundary with FMM for an anisotropic and heterogeneous reservoir: (a) permeability (mD) in X direction, (b) permeability (mD) in Y direction, and (c) drainage boundary at different DTOFs (d)

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Fig. 5

Production rates and pressure drops of the homogeneous/isotropic reservoir as a function of time calculated by the Eclipse and FM-SSS method, respectively

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Fig. 6

Pressure fields (MPa) calculated at the 1000th day in the homogeneous and isotropic reservoir model: (a) pressure field (MPa) calculated by Eclipse for the constant-bottomhole-pressure case, (b) pressure field (MPa) calculated by Eclipse for the constant-production-rate case, (c) pressure field (MPa) calculated by FM-SSS for the constant-bottomhole-pressure case, (d) pressure field (MPa) calculated by FM-SSS for the constant-production-rate case, (e) relative difference (%) in pressures calculated by Eclipse and FM-SSS for the constant-bottomhole-pressure case, and (f) relative difference (%) in pressure calculated by Eclipse and FM-SSS for the constant-production-rate case

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Fig. 7

Production rates and pressure drops of the homogeneous/isotropic reservoir under variable-bottomhole-pressure constraint and variable-production-rate constraint as a function of time calculated by the Eclipse and FM-SSS method, respectively

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Fig. 8

Pressure fields (MPa) calculated at the 1000th day in the homogeneous and isotropic reservoir model under variable-bottomhole-pressure constraint and variable-production-rate constraint: (a) pressure field (MPa) calculated by Eclipse for the variable-bottomhole-pressure case, (b) pressure field (MPa) calculated by Eclipse for the variable-production-rate case, (c) pressure field (MPa) calculated by FM-SSS for the variable-bottomhole-pressure case, (d) pressure field (MPa) calculated by FM-SSS for the variable-production-rate case, (e) relative difference (%) in pressures calculated by Eclipse and FM-SSS for the variable-bottomhole-pressure case, and (f) relative difference (%) in pressure calculated by Eclipse and FM-SSS for the variable-production-rate case

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Fig. 9

Production rates and pressure drops of the heterogeneous/anisotropic reservoir as a function of time calculated by the Eclipse and FM-SSS method, respectively

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Fig. 10

Pressure fields (MPa) calculated at the 1000th day in the heterogeneous and anisotropic reservoir model: (a) pressure field (MPa) calculated by Eclipse for the constant-bottomhole-pressure case, (b) pressure field (MPa) calculated by Eclipse for the constant-production-rate case, (c) pressure field (MPa) calculated by FM-SSS for the constant-bottomhole-pressure case, (d) pressure field (MPa) calculated by FM-SSS for the constant-production-rate case, (e) relative difference (%) in pressures calculated by Eclipse and FM-SSS for the constant-bottomhole-pressure case, and (f) relative difference (%) in pressure calculated by Eclipse and FM-SSS for the constant-production-rate case

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Fig. 11

Production rates and pressure drops of the fractured reservoir as a function of time calculated by the Eclipse and FM-SSS method, respectively

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Fig. 12

Pressure fields (MPa) calculated at the 1000th day in the fractured reservoir model: (a) pressure field (MPa) calculated by Eclipse for the constant-bottomhole-pressure case, (b) pressure field (MPa) calculated by Eclipse for the constant-production-rate case, (c) pressure field (MPa) calculated by FM-SSS for the constant-bottomhole-pressure case, (d) pressure field (MPa) calculated by FM-SSS for the constant-production-rate case, (e) relative difference (%) in pressures calculated by Eclipse and FM-SSS for the constant-bottomhole-pressure case, and (f) relative difference (%) in pressure calculated by Eclipse and FM-SSS for the constant-production-rate case

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Fig. 13

A shale-gas reservoir model containing seven hydraulic fractures intersecting with natural fractures

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Fig. 14

Ratio of desorption compressibility to matrix total compressibility under different pressures for the fractured network model

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Fig. 15

Pseudopressure response curves under different production rates for the fracture-network model

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Fig. 16

Pseudopressure derivative curves under different production rates for the fracture-network model

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Fig. 17

Contribution of desorption under different production rates for the fracture-network model

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Fig. 18

Rate decline curves at different bottomhole pressure constraints for the fracture-network model

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Fig. 19

Contribution of desorption at different bottomhole pressure constraints for the fracture-network model

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