Modeling Ithaca ’ s natural hydraulic fractures

Joints within the Catskill Delta complex are believed to be natural hydraulic fractures and abundant indirect evidence supports this claim. The indirect evidence is based on many observations of joint surface morphology and joint spacing among other features. The Alleghanian orogeny left a unique imprint on the joint surfaces also, indicating a rotating horizontal compressive stress field. Numerical simulations illustrate that the formation and propagation of the joints can be described by hydraulic fracturing mechanisms. The numerical simulations include hydraulic fracture propagation from sedimentary structures at layer interfaces and fracture twisting in response to the reorientation of the remote stress field after initial joint propagation. Cracks tend to start at points of higher stress concentration (McConaughy & Engelder 2000). In the case of sedimentary beds, the largest stress concentrations are in the form of concretions, fossils, ripples, groove casts, and similar features. Figure 1 shows a joint surface in the Ithaca Formation siltstone that starts at a groove cast, a location where the siltstone penetrates the shale layer, formed during erosion of the muddy substrate and deposition of the silt. The figure also shows the plumose surface morphology of the joint surface. The plumose structures and the related arrest lines are well described by Bahat & Engelder (1984). Barbs, the darkened lines in Figure 1, radiate from the plume axis and indicate the direction of fracture growth. Arrest lines mark the termination of crack propagation increments. Natural hydraulic fractures do not have a steady supply of fluid (Lacazette & Engelder 1992). As the crack propagates, the pressure decays and the crack arrests until the pressure builds up again. Figure 1. Plumose joint surface starting from a groove cast. It can also be seen in Figure 1 that the fracture initially stays within the siltstone layer. It has been found that in sedimentary basins where the horizontal stress is less than the vertical, the shale layers have a higher horizontal stress than the siltstones (Evans et al. 1989, Warpinski 1989). Assuming that the pore pressure is the same in both the shale and siltstone layers, then the fractures would form in the siltstones first. This will be more evident in the next figure. The difference in horizontal stress leads to jointing in the siltstones followed by jointing in the shale. Joints in the shale beds usually start at the edges of existing joints in the siltstone; the joints act as conduits for the pore fluid. If there is no rotation of the principal horizontal stresses, joints will develop in the shale in plane with those in the sandstone. However, if the horizontal stress does rotate, then enechelon or fringe cracks will develop (Pollard et al. 1982). Figure 2 shows a set of fringe cracks that start at the interface between the siltstone and shale. These fractures propagate downward. The numerous small cracks at the immediate interface reduce to a few large cracks as propagation continues. Figure 2. Multiple en-echelon cracks propagate down from the siltstone-shale interface and are rotated from the parent joint. There are many more features of the joints that offer indirect evidence of natural hydraulic fractures, including joint spacing, slip on open joints, crosscutting and abutting relationships, and evidence of a pressure seal that could have led to overpressurization of the formation. However, it is beyond the scope of this paper to discuss all of this evidence. Instead, numerical simulations are used to illustrate that natural hydraulic fracturing processes can explain some of the features described herein. 3 HYDRAULIC FRACTURING SOFTWARE The 3D numerical simulations that are described in the following sections are performed using HYFRANC3D and accompanying software (Carter et al. 2000a,b). In addition, ANSYS (ANSYS 2000) and FRANC2D (CFG 2000) are used for some 2D analyses. The 3D software consists of OSM, FRANC3D, HYFRANC3D, and BES. OSM is used to create the initial geometric models. FRANC3D is a fracture analysis code with preand post-processing capabilities. HYFRANC3D builds upon FRANC3D by adding a fluid flow module that couples the elastic structural response with fluid flowing in the fracture. BES is a linear elastic boundary element program. BES provides an elastic influence matrix that relates the set of unit pressures (p) at the nodes on the crack surface to the elastic displacements (w). The fluid flow formulation is based on the elasticity, lubrication and continuity equations. For a Newtonian fluid, the stress ahead of the crack front has a 1/3 singularity, as does the fluid pressure inside the crack (Carter et al. 2000b). Physically, the fluid pressure cannot be singular, thus, a fluid lag must develop at the crack front (Figure 3). The finite element formulation in HYFRANC3D combines an analytical solution for the pressure and crack opening displacement at the crack front with a standard finite element formulation of the lubrication equation for the bulk of the fracture. The analytical solution at the crack front provides an elegant way to overcome the singular behavior and limits the required number of elements at the crack front. Hydraulic fracture simulation proceeds as a series of crack advance increments, requiring an elastic solution and coupled flow analysis at each step.