Time-dependent closure and permeability of a hydraulic fracture under constant normal stress

Author(s):  
K. Matsuki ◽  
Erqi Wang ◽  
K. Sakaguchi ◽  
K. Okumura
2001 ◽  
Vol 117 (2) ◽  
pp. 101-108
Author(s):  
Erqi WANG ◽  
Kiyotoshi SAKAGUCHI ◽  
Kiyohiko OKUMURA ◽  
Koji MATSUKI

Energies ◽  
2020 ◽  
Vol 13 (24) ◽  
pp. 6474
Author(s):  
Tri Pham ◽  
Ruud Weijermars

The Time-Stepped Linear Superposition Method (TLSM) has been used previously to model and analyze the propagation of multiple competitive hydraulic fractures with constant internal pressure loads. This paper extends the TLSM methodology, by including a time-dependent injection schedule using pressure data from a typical diagnostic fracture injection test (DFIT). In addition, the effect of poro-elasticity in reservoir rocks is accounted for in the TLSM models presented here. The propagation of multiple hydraulic fractures using TLSM-based codes preserves infinite resolution by side-stepping grid refinement. First, the TLSM methodology is briefly outlined, together with the modifications required to account for variable time-dependent pressure and poro-elasticity in reservoir rock. Next, real world DFIT data are used in TLSM to model the propagation of multiple dynamic fractures and study the effect of time-dependent pressure and poro-elasticity on the development of hydraulic fracture networks. TLSM-based codes can quantify and visualize the effects of time-dependent pressure, and poro-elasticity can be effectively analyzed, using DFIT data, supported by dynamic visualizations of the changes in spatial stress concentrations during the fracture propagation process. The results from this study may help develop fracture treatment solutions with improved control of the fracture network created while avoiding the occurrence of fracture hits.


2017 ◽  
Vol 23 (7) ◽  
pp. 1049-1060
Author(s):  
Xu Wang

We examine the time-dependent deformations around a nanosized rigid spherical inclusion in an infinite elastic matrix under uniaxial tension at infinity. The elastic matrix is first endowed with separate Gurtin–Murdoch surface elasticity. Furthermore, interfacial diffusion and sliding both occur on the inclusion–matrix interface. Closed-form expressions of the time-dependent displacements and stresses in the matrix are derived by using Papkovich–Neuber displacement potentials. A concise and elegant expression of the steady-state normal stress on the surface of the inclusion is also obtained. It is seen that the displacements and stresses in the matrix evolve with two relaxation times which are reliant on three size-dependent parameters, one from surface elasticity and the other two from interfacial diffusion and sliding. Numerical results are presented to demonstrate the influence of surface elasticity on the relaxation times and on the stress distribution near the inclusion. It is observed that the surface elasticity can alter the nature of the steady state normal stress on the surface of the inclusion from tension to compression. When the radius of the inclusion is not greater than the ratio of residual surface tension to remote tension, the steady state normal stress on the surface of the inclusion is always compressive. The related problem of a nanosized rigid spherical inclusion with a spring-type imperfect interface is also solved. We find that it is feasible to design a neutral spherical inclusion that does not disturb a prescribed uniform uniaxial stress field or even any uniform stress field outside the inclusion through a judicious choice of the four imperfect interface parameters.


2015 ◽  
Vol 82 (7) ◽  
Author(s):  
James R. Rice ◽  
Victor C. Tsai ◽  
Matheus C. Fernandes ◽  
John D. Platt

A 2008 report by Das et al. documented the rapid drainage during summer 2006 of a supraglacial lake, of approximately 44×106 m3, into the Greenland ice sheet over a time scale moderately longer than 1 hr. The lake had been instrumented to record the time-dependent fall of water level and the uplift of the ice nearby. Liquid water, denser than ice, was presumed to have descended through the sheet along a crevasse system and spread along the bed as a hydraulic facture. The event led two of the present authors to initiate modeling studies on such natural hydraulic fractures. Building on results of those studies, we attempt to better explain the time evolution of such a drainage event. We find that the estimated time has a strong dependence on how much a pre-existing crack/crevasse system, acting as a feeder channel to the bed, has opened by slow creep prior to the time at which a basal hydraulic fracture nucleates. We quantify the process and identify appropriate parameter ranges, particularly of the average temperature of the ice beneath the lake (important for the slow creep opening of the crevasse). We show that average ice temperatures 5–7  °C below melting allow such rapid drainage on a time scale which agrees well with the 2006 observations.


1981 ◽  
Vol 21 (01) ◽  
pp. 21-29 ◽  
Author(s):  
Gordon D. Anderson

Abstract Small-scale laboratory experiments were performed to study the growth of hydraulically driven fractures in the vicinity of an unbonded interface in rocks. The purpose was to evaluate under which conditions the hydraulic fractures would cross the interface. The materials used in these studies were Nugget sandstone from Utah (3 to 6% porosity) and Indiana limestone (12 to 15% porosity). The fracturing fluid was oil (viscosity appx. 300 cp) injected into the rock through high-pressure steel tubing. Prismatic blocks of the rock materials to be studied were held adjacent to one another in a hydraulic press so that a normal stress was set up across their mutual interface. Lubricants and surface roughening were used to vary the frictional properties of the interfaces. It was found that as the interface surface friction coefficient was decreased, the normal stress had to be increased for a hydraulic fracture to cross the interface. The frictional shear stress that the interface can support without slippage appears to be critical in determining fracture growth across the interface. Additional experiments were performed to evaluate the coefficient of friction for the different interface surface preparations used. These experiments demonstrated that a variation in the frictional properties along an interfacial surface in the vicinity of hydraulic fracture growth can alter the path of the fracture. The experiments also demonstrated that cracks, which intersect the interface from the side opposite the approaching hydraulic fracture, can impede fracture growth across the interface. Introduction Hydraulic fracturing and a variant - massive hydraulic fracturing (MHF) - are primary candidates for stimulating production from the tight-gas reservoirs in the U.S. Hydraulic fracturing has been used widely as a well completion technique for about 30 years. MHF is a more recent application that differs from hydraulic fracturing in that larger quantities of fluid and proppant are pumped to create more extensive fractures in the reservoirs. Application of MHF to increase production from the tight reservoirs has provided mixed and, in many cases, disappointing results, especially in lenticular reservoirs. For MHF to be successful in enhancing the production of gas from tight reservoirs, it is important that the fractures be emplaced in productive reservoir rock providing large drainage surfaces in the low-permeability material and conductive channels back to the wellbore. We then are faced with the problem of containing fractures in a given formation.Under the U.S. DOE'S Unconventional Gas Recovery program, Lawrence Livermore Natl. Laboratory is conducting a research program to study the hydraulic fracture process. The general goal of this research is to determine if and to what extent the reservoir parameters control the geometry of the created fractures. These reservoir parameters include (1) the mechanical properties of the rock (i.e., elastic moduli, mechanical strength, etc.), (2) the physical state of the rock (i.e., presence of pre-existing cracks or faults, porosity, pore fluid, etc.), (3) presence of layering or interfaces between different rock strata, and (4) stress field on the rock. In addition to reservoir parameters, the growth of a hydraulically driven crack will be influenced by (1) the manner in which the driving fluid is injected into the rock, (2) the characteristics of the fracturing fluid (i.e., viscosity, presence of proppant, etc.), and (3) any chemical reaction between the fluid and rock. Previous work has shown that crack orientation is controlled primarily by the in-situ or applied stress field, with crack growth oriented perpendicular to the least principal stress. SPEJ P. 21^


2020 ◽  
Vol 125 (3) ◽  
Author(s):  
Guanyi Lu ◽  
Elizaveta Gordeliy ◽  
Romain Prioul ◽  
Gallyam Aidagulov ◽  
Efosa C. Uwaifo ◽  
...  

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