Numerical simulation of fracture set formation: A fracture mechanics model consistent with experimental observations

Abstract

A physically based model for the evolution of a single set of planar, parallel fractures subject to a constant remote stress is presented. The model simulates the mechanical interaction between fractures using a recently developed approximation technique for stress analysis in elastic solids with many fractures. A comparison between experimental and numerical results shows that the model can accurately simulate the development of experimentally generated fracture sets. Once the flaw geometry is specified, only one parameter controls the geometric evolution of the fracture set. This parameter, the velocity exponent, relates fracture propagation velocity to stress concentration at the fracture tip. Monte Carlo sensitivity analyses suggest that this parameter also controls the extent to which fracture growth is concentrated within zones or clusters. Similar analyses suggest that the extent of fracture clustering is less sensitive to the flaw density. Pollard, 1983;Thomas and Pollard, 1993].As the critical role that fractures play in controlling fluid flow has become more apparent, many techniques for simulating the geometry of networks have been developed [e.g., Dershowitz and Einstein, 1988; Dverstorp and Andersson, 1989; La Pointe and Hudson, 1985; Lee et al., 1990; Long and Billaux, 1987]. However, counter to the trend in rock fracture mechanics to base models and interpretations on the physics of rock fracture [DeGraff and Aydin, 1987; Delaney et al., 1986; Olson, 1993; Pollard and Aydin, 1988; Rubin and Pollard, 1987], these techniques rely on descriptive statisticsto stochastically generate realizations of fracture networks which are statistically similar to those observed in nature. This approach can be problematic in that many important geometric aspects of natural fracture networks may not be adequately described by the statistics used to generate the stochastic networks. For example, it has been found that flow through a natural fracture network was consistently greater than flow through statistically similar, stochastically generated networks [Odling and Webman, 1991]. The reason for this discrepancy was attributed to the failure of the stochastic While stochastic simulators can be improved by choosing a better set of statistics to describe natural fracture networks, an alternative to the stochastic approach is to attempt to include the physics of fracture formation explicitly within the fracture network simulator. In so doing, the fracture simulator is improved in the two following ways: (1) the number of possible realizations of the network is restricted to those which are physically reasonable; and (2) information about the geologic history of the region, such as boundary conditions and material properties, can be directly put into the model to further restrict the number of possible realizations. Physically based network simulators have the additional advantage that they can be used to understand how fracture network geometries are related to the conditions of their formation.As a first step toward a ...

Advanced Technology for Predicting the Fluid Flow Attributes of Naturally Fractured Reservoirs From Quantitative Geologic Data and Modeling

“…The new, three dimensional simulations presented here more clearly delineate how variation in the subcritical parameter n can determine whether the fracture pattern will exhibit clustered or more regular spacing. We also show, contrary to previous theorizations (Olson, 1993;Renshaw and Pollard, 1994), that fracture pattern development at very high subcritical index values (n > 40) can be materially different than results generated at moderately high subcritical index values (n…”

“…The conceptual framework of the fracture propagation model presented here assumes that the initial starter flaws in a layer already extend across the full thickness of the layer, and the modeled propagation is the addition of fracture length caused by some manner of extensional loading. This model is similar to previous work by Olson (1993) and Renshaw and Pollard (1994) except for the fact that it represents the three-dimensional effects of fracture height contained by bed thickness. …”

“…Two dimensional, plane strain modeling of the development of fracture networks utilizing subcritical crack growth conditions has shown that the value of the subcritical index, n, exerts a strong influence on the spatial arrangement and length distribution of fractures (Segall, 1984;Olson, 1993;Renshaw and Pollard, 1994). Results in Olson (1993) demonstrated how subcritical index controls fracture spacing to bed thickness ratio when modeling vertical fracture propagation across a bed under plane strain conditions.…”

“…Varying subcritical index affects the propagation velocity distribution in a growing fracture network, influencing the final length distribution 12,21,28 as well as spacing and clustering. 12,29 To specifically address the validity of our analytical length distribution equation, we examined the effect of increasing the density of field cracks by running identical simulations in all aspects except the number of initial flaws (analogous to changing N in Eq. 7) and quantifying the final length distributions from the simulations with an exponential curve fit.…”

Connectivity of joint networks with power law length distributions

“…in addition to parameter sensitivity studies, we also discuss appropriate parameter values for jointed rock and compare our results to theoretical and field observations. Finally, our approach is shown to reasonably predict the connectivities of fracture networks simulated using a mechanically based model of fracture growth [Renshaw and Pollard, 1994]. …”