Constraining the Spatial Distribution of Fracture Networks in Naturally Fractured Reservoirs Using Fracture Mechanics and Core Measurements

Observations of natural fractures in core or image logs typically give limited information on orientation, aperture and intensity. Because of the sparseness of wellbore intersections of fractures, data analysis results in incomplete statistical characterization of the fracture population, leaving interwell characterization almost impossible. Using basic fracture mechanics models and a novel core-testing technique, we propose that the fundamental shape of fracture parameter distributions can be predicted, and that there is a characteristic, quantifiable relationship between fracture length, spacing and aperture. We have performed subcritical fracture growth tests on numerous core samples, using credit card sized specimens, demonstrating the ability to characterize fracture mechanics properties of rock on a bed by bed basis. Using the subcritical index, a parameter that quantifies the relationship between natural fracture propagation velocity and tip loading conditions, we can predict the degree of fracture spacing regularity or clustering for a given reservoir bed. This subcritical parameter, along with information on the number of initial natural flaws in a given rock type, allows us to quantify the expected length distribution of the fractures. Under many conditions, as verified from outcrop data, fracture length is theoretically expected to follow an exponential distribution. Since natural fracture length is typically unobservable in subsurface data, we derive relationships that relate fracture length to aperture and spacing, both more readily measurable quantities. With this information, matrix block size and fracture drainage continuity can be estimated for the purpose of flow simulation in a fractured reservoir. Introduction Direct characterization of fracture network attributes such as length, spacing, aperture, orientation and intensity from core or image logs is often difficult. Fractures are infrequently intersected by wells, and if fractures do intersect the wellbore they are rarely abundant enough to give a good representation of the fracture geometry. Due to sparseness of these data sets, various predictive schemes, based on geostatistics or geomechanical models, are used to estimate subsurface fracture attributes. There are two types of statistical approaches in modeling fracture network geometry. The first approach addresses each fracture characteristic separately. Data for each attribute are gathered, and distributions are fit to the data. If not enough data are available, distributions published in literature are used (Table 1). This type of modeling is particularly useful to estimate the upper and lower bounds on reservoir response. However, lack of reservoir data often makes selecting a correct distribution difficult, thus leading to the use of outcrop data rather than wellbore data, which can sometimes be misleading. Recent advances in using microcracks as proxies for larger scale fractures have improved the capability of getting pertinent subsurface data, circumventing some of the problems associated with data sparseness. The second statistical approach takes the statistical data for individual fracture attributes and also specifies their interdependence, describing the 3D fracture network as a whole. The simplest model often used in petroleum applications is a network of three unbounded, mutually orthogonal fractures. However, there are many fracture characteristics and a seemingly limitless number of correlations between those parameters, although Dershowitz and Einstein argue that nature restricts the number of applicable models and only a few predominant models need to be defined. Choosing among the possible models may require more fracture data than is available, and it may be difficult to determine a priori whether, for example, a fracture network is clustering or more uniformly distributed spatially. An alternative to geostatistical characterization is a geomechanics-based approach, where a physical understanding of the fracturing process is combined with measurements of mechanical properties of rock to predict fracture network characteristics. This process-oriented SPE 71342 Constraining the Spatial Distribution of Fracture Networks in Naturally Fractured Reservoirs Using Fracture Mechanics and Core Measurements Jon E. Olson, Yuan Qiu, Jon Holder and Peggy Rijken, The University of Texas at Austin 2 J. E. OLSON, Y. QIU, J. HOLDER AND P. RIJKEN SPE 71342 approach can also provide a theoretical basis for deciding what types of fracture attribute distributions are physically reasonable, and how attributes such as length, spacing and aperture are inter-related. The combined prediction of all fracture attributes is possible using geomechanics, and the mechanistic approach as postulated in this paper requires less direct fracture sampling than typical statistical methods. The subcritical fracture index, a rock parameter that can be measured from core samples, can be used to constrain the distributions of aperture, spacing and length. Additional geological information, such as the strain, pore pressure and diagenetic history of the reservoir can provide further constraint on fracture network predictions. Fracture Mechanics Constraints on Fracture Network Properties Linear elastic fracture mechanics has been successfully applied to many geologic fracture problems. The parameters of particular interest for fractured reservoirs are fracture length, spacing, aperture and connectivity. Each of these parameters can be addressed using mechanical analyses based on geologically-inferred or measured boundary conditions and rock properties. We find that fracture length and spacing are both tied to the same mechanical property, the subcritical crack index, and that further analysis can relate fracture aperture to fracture length. Fracture Length. The analysis of mode I (opening mode), en echelon fracture arrays has shown that mechanical fracture interaction will influence a fracture’s stress intensity factor, KI. The stress intensity factor for a uniformly loaded, isolated crack of length 2a is defined as a K I I π σ ∆ = ............................................................ (1) The mode I driving stress, I σ ∆ ,is defined as ) ( n p I P σ σ − = ∆ ......................................................... (2) where Pp is the pore pressure in the rock, and n σ is the in situ stress resolved perpendicular to the crack. The stress intensity factor is compared to the fracture toughness of a material, KIc, to determine crack propagation. For critical crack propagation, Ic I K K ≥ , but fractures in rock can also propagate subcritically ( Ic I K K < ). Fig. 1 shows the normalized stress intensity factor for the right (inner) tip of the left member of a two crack, en echelon array, as a function of overlap as the two cracks grow toward one another. An overlap of –0.5 corresponds to zero length for the echelon segments, an overlap of 0 corresponds to each segment having a length of 1⁄2 the total array length, and an overlap of 0.5 corresponds to each segment side by side with a length equal to the total array length. The stress intensity factor for the en echelon crack is normalized by the stress intensity factor of an isolated crack of the same length with the same driving stress (Eq. 1). As parallel, en echelon fractures approach one another and have just begun to overlap (overlap between -0.1 and 0.02 in Fig. 1), mechanical interaction increases the stress intensity at the inner tips. When the fracture tips pass one another and the overlap increases, the stress intensity is reduced at the inner tips, hindering propagation. However, the outer tips experience a stress intensity increase (propagation enhancement), such that the outer tips are expected to grow while the inner tips arrest. These interaction effects diminish as the fracture spacing increases relative to the fracture height, such that when spacing is equal to fracture height, the peak perturbation of the stress intensity factor is less than 20%. Based on the mechanical interaction behavior of nearby cracks, we developed a fracture length model for larger opening mode fractures (main cracks) propagating through a material with randomly distributed, parallel flaws (field cracks). If the propagating main crack passes within a critical spacing distance of a smaller field crack, the main crack propagation is arrested or captured at its overlapping inner tip, and propagation is transferred to the outer tip of the field crack. Simulation results indicate that the critical spacing for main crack capture is approximately equal to 1⁄2 the field crack length. The probability that a propagating main crack will be captured by a smaller field crack corresponds to the probability that a propagating crack will reach a particular length. The more field cracks present in a rock, the less likely fractures are to achieve great length. We have quantified this fracture capture probability, and thus quantified the expected frequency distribution of fracture length. The probability that a main crack with length 2a will be captured is equal to the probability that at least one field crack of length 2b will lie within its capture zone (Fig. 2). The capture zone is a rectangular region around the main crack with dimensions of crack length by 2 times the critical spacing (because the capture zone lies on both sides of the main crack), or 2a x 2b. Assuming N field cracks are uniformly randomly distributed in a total area A, the probability, P’, that at least one field crack will lie within the capture zone of a propagating main crack of length 2a is equal to 1 minus the probability that no cracks reside in the capture zone, or