Effect of Non-Darcy Flow on the Interpretation of Transient Pressure Responses of Hydraulically Fractured Wells

2000 ◽  
Author(s):  
S. Umnuayponwiwat ◽  
E. Ozkan ◽  
C.M. Pearson ◽  
M. Vincent
Keyword(s):  
Darcy Flow ◽  
Transient Pressure

A Semianalytical Model for Predicting Transient Pressure Behavior of a Hydraulically Fractured Horizontal Well in a Naturally Fractured Reservoir With Non-Darcy Flow and Stress-Sensitive Permeability Effects

SPE Journal ◽  
2019 ◽  
Vol 24 (03) ◽  
pp. 1322-1341 ◽  
Author(s):  
Liwu Jiang ◽  
Tongjing Liu ◽  
Daoyong Yang
Keyword(s):  
Mathematical Models ◽  
Horizontal Well ◽  
Flow Behavior ◽  
Stress Sensitivity ◽  
Darcy Flow ◽  
Combined Effects ◽  
Fractured Reservoir ◽  
Transient Pressure ◽  
Linear Flow ◽  
Fractured Horizontal Well

Summary Non-Darcy flow and the stress-sensitivity effect are two fundamental issues that have been widely investigated in transient pressure analysis for fractured wells. The main object of this work is to establish a semianalytical solution to quantify the combined effects of non-Darcy flow and stress sensitivity on the transient pressure behavior for a fractured horizontal well in a naturally fractured reservoir. More specifically, the Barree-Conway model is used to quantify the non-Darcy flow behavior in the hydraulic fractures (HFs), while the permeability modulus is incorporated into mathematical models to take into account the stress-sensitivity effect. In this way, the resulting nonlinearity of the mathematical models is weakened by using Pedrosa's transform formulation. Then a semianalytical method is applied to solve the coupled nonlinear mathematical models by discretizing each HF into small segments. Furthermore, the pressure response and its corresponding derivative type curve are generated to examine the combined effects of non-Darcy flow and stress sensitivity. In particular, stress sensitivity in HF and natural-fracture (NF) subsystems can be respectively analyzed, while the assumption of an equal stress-sensitivity coefficient in the two subsystems is no longer required. It is found that non-Darcy flow mainly affects the early stage bilinear and linear flow regime, leading to an increase in pressure drop and pressure derivative. The stress-sensitivity effect is found to play a significant role in those flow regimes beyond the compound-linear flow regime. The existence of non-Darcy flow makes the effect of stress sensitivity more remarkable, especially for the low-conductivity cases, while the stress sensitivity in fractures has a negligible influence on the early time period, which is dominated by non-Darcy flow behavior. Other parameters such as storage ratio and crossflow coefficient are also analyzed and discussed. It is found from field applications that the coupled model tends to obtain the most-reasonable matching results, and for that model there is an excellent agreement between the measured and simulated pressure response.

scholarly journals Revising Transient-Pressure Solution for Vertical Well Intersected by a Partially Penetrating Fracture with Non-Darcy Flow Effect

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Shuheng Cui ◽  
Jie Kong ◽  
Hongwei Yu ◽  
Cheng Chen ◽  
Junlei Wang
Keyword(s):  
Flow Regime ◽  
Flow Regimes ◽  
Pressure Response ◽  
Darcy Flow ◽  
Transient Pressure ◽  
Fracture Conductivity ◽  
Flow Effect ◽  
Vertical Fracture ◽  
Dimensional Flow ◽  
Penetration Ratio

The principle purpose of this work is to formulate an accurate mathematical model to evaluate the transient pressure behavior of a well intercepted by a partially penetrating vertical fracture (PPVF) with non-Darcy flow effect. Fracture conductivity is taken into account by coupling the three-dimensional flow in reservoir and the two-dimensional flow within fracture; the Barree-Conway model is incorporated into the model to analyze non-Darcy flow behavior in fracture, which leads to the nonlinearity of the governing equations. A high-effective iterative algorithm using a combined technique of fracture-panel discretization and dimension transform is developed to render the nonlinear equations amenable to analytical linear treatment. On the basis of the solutions, the pressure response and its derivative type curves were generated to identify the evolution of flow regimes with time. Furthermore, the influences of fracture conductivity, penetration ratio, and non-Darcy characteristic parameters on pressure response are investigated. The results show that PPVF exhibits five typical flow regimes, and analytical solutions for each flow regime are similar to that for a fully penetrating vertical fracture (FPVF) that can be correlated with the penetration ratio and apparent conductivity. The non-Darcy flow effect is found to have more significant effect on the low and moderate conductivity, especially in early-stage flow regimes. When the penetration ratio is smaller than 0.5, the pressure behavior exhibit a more remarkable variation with penetration ratio. This study provides a better insight into understanding the influence of non-Darcy flow on flow regime identification.

A Semianalytical Solution of a Vertical Fractured Well With Varying Conductivity Under Non-Darcy-Flow Condition

SPE Journal ◽  
2015 ◽  
Vol 20 (05) ◽  
pp. 1028-1040 ◽  
Author(s):  
Luo Wanjing ◽  
Tang Changfu
Keyword(s):  
Flow Condition ◽  
Effective Conductivity ◽  
Early Time ◽  
Flow Equation ◽  
Darcy Flow ◽  
Pressure Curve ◽  
Well Test ◽  
Transient Pressure ◽  
Fracture Conductivity ◽  
Fractured Well

Summary Fracture distributions (simple or complex fractures), fracture-conductivity heterogeneity (uniform or varying conductivity along the fracture), and flow regimes inside the fracture (Darcy or non-Darcy flow) are the three main issues that have been widely investigated for transient-pressure analysis of vertical fracture systems. In this study, we focus on the latter two issues by proposing a semianalytical solution to discuss the transient-pressure behaviors of a varying-conductivity fracture under non-Darcy-flow condition. First, a general fracture-flow equation is established for the uniform-/varying-conductivity fracture under Darcy/non-Darcy flow. Second, for the case of a varying-conductivity fracture, a dimension transformation and an unequal-length-discretization model are proposed to obtain the pressure solution. Then, the transient-pressure response for the case of non-Darcy flow in the fracture can be also obtained by use of an iterative procedure in each timestep in the Laplace domain. It is shown that results from our solutions agree very well with those reported in the literature (Guppy et al. 1982; Poe et al. 1992). Third, the transient-pressure behaviors of the varying-conductivity fracture under Darcy- and non-Darcy-flow condition are discussed in detail. Results show that non-Darcy flow in the fracture mainly reduces the effective conductivity and the transient-pressure curve follows the curve of an equivalently constant conductivity except for the case of extremely small conductivities. The pressure behaviors of varying-conductivity fractures depend on the value of average conductivity, the distribution of conductivity along the fracture, and the maximum-minimum-conductivity ratio. The presence of the varying conductivity not only affects the effective conductivity in the early and late times, but also changes the shape of the pressure curve, especially for the high-conductivity fracture in the early time. It is very difficult to accurately estimate the fracture parameters by well test for most of the cases of varying conductivities under non-Darcy flow in the fracture.

Numerical Investigation of liquefaction in earth dams: A Comparison of Darcy and Non-Darcy flow models

2019 ◽  
Vol 116 ◽  
pp. 103182 ◽  
Author(s):  
Farideh Hosseinejad ◽  
Farhoud Kalateh ◽  
Alireza Mojtahedi
Keyword(s):  
Numerical Investigation ◽  
Darcy Flow ◽  
Earth Dams ◽  
Flow Models

scholarly journals Semi-Analytical Solution to Assess CO2 Leakage in the Subsurface through Abandoned Wells

Energies ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2452
Author(s):  
Tian Qiao ◽  
Hussein Hoteit ◽  
Marwan Fahs
Keyword(s):  
Analytical Solution ◽  
Storage Site ◽  
Co2 Leakage ◽  
Transient Pressure ◽  
Flow Paths ◽  
Abandoned Wells ◽  
Diffusivity Equation ◽  
Carbon Dioxide Co2 ◽  
Good Agreement

Geological carbon storage is an effective method capable of reducing carbon dioxide (CO2) emissions at significant scales. Subsurface reservoirs with sealing caprocks can provide long-term containment for the injected fluid. Nevertheless, CO2 leakage is a major concern. The presence of abandoned wells penetrating the reservoir caprock may cause leakage flow-paths for CO2 to the overburden. Assessment of time-varying leaky wells is a need. In this paper, we propose a new semi-analytical approach based on pressure-transient analysis to model the behavior of CO2 leakage and corresponding pressure distribution within the storage site and the overburden. Current methods assume instantaneous leakage of CO2 occurring with injection, which is not realistic. In this work, we employ the superposition in time and space to solve the diffusivity equation in 2D radial flow to approximate the transient pressure in the reservoirs. Fluid and rock compressibilities are taken into consideration, which allow calculating the breakthrough time and the leakage rate of CO2 to the overburden accurately. We use numerical simulations to verify the proposed time-dependent semi-analytical solution. The results show good agreement in both pressure and leakage rates. Sensitivity analysis is then conducted to assess different CO2 leakage scenarios to the overburden. The developed semi-analytical solution provides a new simple and practical approach to assess the potential of CO2 leakage outside the storage site. This approach is an alternative to numerical methods when detailed simulations are not feasible. Furthermore, the proposed solution can also be used to verify numerical codes, which often exhibit numerical artifacts.

scholarly journals The Lagrangian kinematics of three-dimensional Darcy flow

2021 ◽  
Vol 918 ◽  
Author(s):  
Daniel R. Lester ◽  
Marco Dentz ◽  
Aditya Bandopadhyay ◽  
Tanguy Le Borgne
Keyword(s):  
Three Dimensional ◽  
Darcy Flow

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