scholarly journals Hydraulic fracture induced by water injection in weak rock

2021 ◽  
Vol 927 ◽  
Author(s):  
Yue Gao ◽  
Emmanuel Detournay
Keyword(s):  
Porous Media ◽  
Flow Regime ◽  
Hydraulic Fracture ◽  
Large Scale ◽  
Peak Pressure ◽  
Injection Pressure ◽  
Early Time ◽  
Reservoir Rock ◽  
Porous Media Flow ◽  
Late Time

A two-dimensional model of a hydraulic fracture propagating in a weakly consolidated, highly permeable reservoir rock during a waterflooding operation is described in this paper. The model recognizes the essential differences that exist between this class of fractures and conventional hydraulic fracturing treatments of oil and gas wells, namely: (i) the large-scale perturbations of pore pressure and the associated poroelastic effects caused by extended injection time; (ii) the extremely small volume of fluid stored in the fracture compared with the injected volume; and (iii) the leakage of water from both the borehole and the propagating fracture. The model consists of a set of equations encompassing linear elastic fracture mechanics, porous media flow and lubrication theory. Three asymptotic solutions applicable at different time regimes are found theoretically, and numerical results are obtained from the discretized governing equations. The solution reveals that the injection pressure does not evolve monotonically, as it increases with time in the early time radial-flow regime but decreases in the late time fracture-flow regime. Thus, the peak injection pressure does not correspond to a breakdown of the formation, as usually assumed, but rather to a transition between two regimes of porous media flow. However, this problem exhibits an extreme sensitivity of the time scales on a dimensionless injection rate $\mathcal {I}$ . If $\mathcal {I} \lessapprox 1$ , the time to reach the peak pressure could become so large that it cannot be observed in field operations, i.e. the fracture remains hydraulically invisible. Finally, it is found that poroelasticity significantly affects the response of the system, by increasing the injection pressure and delaying the time at which the peak pressure takes place.

Topographic controls on gravity currents in porous media

2013 ◽  
Vol 734 ◽  
pp. 317-337 ◽  
Author(s):  
Samuel S. Pegler ◽  
Herbert E. Huppert ◽  
Jerome A. Neufeld
Keyword(s):  
Porous Media ◽  
Axisymmetric Flow ◽  
Early Time ◽  
Gravity Currents ◽  
Late Time ◽  
Horizontal Distance ◽  
Topographic Controls ◽  
Time Regime ◽  
Flow Transitions ◽  
Theoretical Results

AbstractWe present a theoretical and experimental study of the propagation of gravity currents in porous media with variations in the topography over which they flow, motivated in part by the sequestration of carbon dioxide in saline aquifers. We consider cases where the height of the topography slopes upwards in the direction of the flow and is proportional to the $n\text{th} $ power of the horizontal distance from a line or point source of a constant volumetric flux. In two-dimensional cases with $n\gt 1/ 2$, the current evolves from a self-similar form at early times, when the effects of variations in topography are negligible, towards a late-time regime that has an approximately horizontal upper surface and whose evolution is dictated entirely by the geometry of the topography. For $n\lt 1/ 2$, the transition between these flow regimes is reversed. We compare our theoretical results in the case $n= 1$ with data from a series of laboratory experiments in which viscous glycerine is injected into an inclined Hele-Shaw cell, obtaining good agreement between the theoretical results and the experimental data. In the case of axisymmetric topography, all topographic exponents $n\gt 0$ result in a transition from an early-time similarity solution towards a topographically controlled regime that has an approximately horizontal free surface. We also analyse the evolution over topography that can vary with different curvatures and topographic exponents between the two horizontal dimensions, finding that the flow transitions towards a horizontally topped regime at a rate which depends strongly on the ratio of the curvatures along the principle axes. Finally, we apply our mathematical solutions to the geophysical setting at the Sleipner field, concluding that topographic influence is unlikely to explain the observed non-axisymmetric flow.

Pore-Scale Simulation for Predicting Material Transport Through Porous Media

2002 ◽  
Author(s):  
Goichi Itoh ◽  
Jinya Nakamura ◽  
Koji Kono ◽  
Tadashi Watanabe ◽  
Hirotada Ohashi ◽  
...  
Keyword(s):  
Fluid Dynamics ◽  
Porous Media ◽  
Parallel Computation ◽  
Large Scale ◽  
Message Passing Interface ◽  
Complex Geometry ◽  
Data Communication ◽  
Porous Media Flow ◽  
Pore Scale ◽  
Material Transport

Microscopic models of real-coded lattice gas automata (RLG) method with a special boundary condition and lattice Boltzmann method (LBM) are developed for simulating three-dimensional fluid dynamics in complex geometry. Those models enable us to simulate pore-scale fluid dynamics that is an essential part for predicting material transport in porous media precisely. For large-scale simulation of porous media with high resolution, the RLG and LBM programs are designed for parallel computation. Simulation results of porous media flow by the LBM with different pressure gradient conditions show quantitative agreements with macroscopic relations of Darcy’s law and Kozeny-Carman equation. As for the efficiency of parallel computing, a standard parallel computation by using MPI (Message Passing Interface) is compared with the hybrid parallel computation of MPI-node parallel technique. The benchmark tests conclude that in case of using large number of computing node, the parallel performance declines due to increase of data communication between nodes and the hybrid parallel computation totally shows better performance in comparison with the standard parallel computation.

PLIF flow visualization and measurements of the Richtmyer–Meshkov instability of an air/SF6 interface

2002 ◽  
Vol 464 ◽  
pp. 113-136 ◽  
Author(s):  
B. D. COLLINS ◽  
J. W. JACOBS
Keyword(s):  
Shock Tube ◽  
Large Scale ◽  
Scale Effects ◽  
Nonlinear Models ◽  
Initial Perturbation ◽  
Early Time ◽  
Incident Shock ◽  
Linear Stability Theory ◽  
Diffuse Interface ◽  
Late Time

Investigations of the Richtmyer–Meshkov instability carried out in shock tubes have traditionally used membranes to separate the two gases. The use of membranes, in addition to introducing other experimental difficulties, impedes the use of advanced visualization techniques such as planar laser-induced fluorescence (PLIF). Jones & Jacobs (1997) recently developed a new technique by which a perturbed, membrane-free gas–gas interface can be created in a shock tube. The gases enter the shock tube from opposite ends and exit through two small slots on opposite sides of the test section, forming a stagnation point flow at the interface location. A gentle rocking motion of the shock tube then provides the initial perturbation in the form of a standing wave. The original investigation using this technique utilized dense fog seeding for visualization, which allowed large-scale effects to be observed, but was incapable of resolving smaller-scale features. PLIF visualization is used in the present study to investigate the instability generated by two incident shock strengths (Ms = 1.11 and 1.21), yielding very clear digital images of the flow. Early-time growth rate measurements obtained from these experiments are found to be in excellent agreement with incompressible linear stability theory (appropriately adjusted for a diffuse interface). Very good agreement is also found between the late-time amplitude measurements and the nonlinear models of Zhang & Sohn (1997) and Sadot et al. (1998). Comparison of images from the Ms = 1.11 and 1.21 sequences reveals a significant increase in the amount of turbulent mixing in the higher-Mach-number experiments, suggesting that a mixing transition has occurred.

scholarly journals Slickwater hydraulic fracture propagation: near-tip and radial geometry solutions

2019 ◽  
Vol 880 ◽  
pp. 514-550 ◽  
Author(s):  
Brice Lecampion ◽  
Haseeb Zia
Keyword(s):  
Hydraulic Fracturing ◽  
Turbulent Flow ◽  
Hydraulic Fracture ◽  
Early Time ◽  
High Rate ◽  
Hydraulic Fractures ◽  
Late Time ◽  
Turbulent Regime ◽  
High Molecular Weight Polymer ◽  
Molecular Weight Polymer

We quantify the importance of turbulent flow on the propagation of hydraulic fractures (HF) accounting for the addition of friction reducing agents to the fracturing fluid (slickwater fluid). The addition in small quantities of a high molecular weight polymer to water is sufficient to drastically reduce friction of turbulent flow. The maximum drag reduction (MDR) asymptote is always reached during industrial-like injections. The energy required for pumping is thus drastically reduced, allowing for high volume high rate hydraulic fracturing operations at a reasonable cost. We investigate the propagation of a hydraulic fracture propagating in an elastic impermeable homogeneous solid under a constant (and possibly very high) injection rate accounting for laminar and turbulent flow conditions with or without the addition of friction reducers. We solve the near-tip HF problem and estimate the extent of the laminar boundary layer near the fracture tip as a function of a tip Reynolds number for slickwater. We obtain different propagation scalings and transition time scales. This allows us to easily quantify the growth of a radial HF from the early-time turbulent regime(s) to the late-time laminar regimes. Depending on the material and injection parameters, some propagation regimes may actually be bypassed. We derive both accurate and approximate solutions for the growth of radial HF in the different limiting flow regimes (turbulent smooth, rough, MDR) for the zero fracture toughness limit (corresponding to the early stage of propagation of a radial HF). We also investigate numerically the transition(s) between the early-time MDR regime to the late-time laminar regimes (viscosity and toughness) for slickwater fluid. Our results indicate that the effect of turbulent flow on high rate slickwater HF propagation is limited and matters only at early times (at most during the first minutes for industrial hydraulic fracturing operations).

Toughness-Dominated Hydraulic Fracture in Permeable Rocks

2017 ◽  
Vol 84 (7) ◽  
Author(s):  
Xuelin Dong ◽  
Guangqing Zhang ◽  
Deli Gao ◽  
Zhiyin Duan
Keyword(s):  
Hydraulic Fracture ◽  
Crack Opening ◽  
Fluid Pressure ◽  
Fracture Propagation ◽  
Early Time ◽  
Injection Rate ◽  
Asymptotic Solutions ◽  
Late Time ◽  
Fluid Viscosity ◽  
Propagation Regime

A solution to the problem of a hydraulic fracture driven by an incompressible Newtonian fluid at a constant injection rate in a permeable rock is presented in this paper. A set of governing equations are formed to obtain the fracture half-length, crack opening, and net fluid pressure. The solution is derived under the assumptions of plane strain, zero lag between fluid front and crack tip, followed by negligible fluid viscosity. The last assumption is related to a toughness-dominated fracture propagation regime therefore leading to a uniform fluid pressure along the crack surface. Early-time and late-time asymptotic solutions are obtained, which correspond to both regimes when the fluid contains within the crack and most of the injected fluid infiltrates into the rock, respectively. It is shown that these asymptotic solutions are in a simple form when the fracture propagation is dominated by the material toughness. The transient solution for the evolution from the early time to the late time is also obtained by a numerical method.

scholarly journals Flow Regime Analysis on Pressure Build-up Test Result of Z-01 Well Using Dual Porosity Reservoir Model

2020 ◽  
Vol 2 (3) ◽  
Author(s):  
Anggitya Hafidh ◽  
Muhammad Taufiq Fathaddin
Keyword(s):  
Flow Regime ◽  
Early Time ◽  
Dual Porosity ◽  
Support Pressure ◽  
Finite Conductivity ◽  
Late Time ◽  
Well Test ◽  
Time Flow ◽  
Time Region ◽  
Regime Analysis

<em>Flow regime analysis on the results of pressure build-up Z-01 well test was conducted to determine the type of flow that occurs in each time region section. In the early time stage there is a flow which is dominated by linear flow which is then followed by bilinear flow. At the middle time there is a radial flow where the pressure disturbance has spread towards the reservoir. In the late time flow stage is dominated by steadystate flow where the flow is affected because there is a support pressure caused by the constant pressure boundary. In the analysis of pressure build-up used to determine reservoir parameters can be used in the middle time region. This is used because the plot results between ΔP vs. log HTR (Horner Time Ratio) are straight lines which can be used to calculate reservoir parameter values such as permeability (k), formation damage factor (s). This test was analyzed using the Ecrin software and obtained a dual porosity model with a permeability value of 4.8 md, skin -3.57. From the analyzed model, it is obtained that the well fracture-finite conductivity model means that the Z-01 well has been stimulated to increase production.</em>

Convective mixing in homogeneous porous media flow

2017 ◽  
Vol 2 (1) ◽  
Author(s):  
Jia-Hau Ching ◽  
Peilong Chen ◽  
Peichun Amy Tsai
Keyword(s):  
Porous Media ◽  
Porous Media Flow ◽  
Convective Mixing ◽  
Homogeneous Porous Media
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