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SUMMARYResearch investigations on three-dimensional (3-D) rectangular hydraulic fracture configurations with varying degrees of fluid lag are reported. This paper demonstrates that a 3-D fracture model coupled with fluid lag (a small region of reduced pressure) at the fracture tip can predict very large excess pressure measurements for hydraulic fracture processes. Predictions of fracture propagation based on critical stress intensity factors are extremely sensitive to the pressure profile at the tip of a propagating fracture. This strong sensitivity to the pressure profile at the tip of a hydraulic fracture is more strongly pronounced in 3-D models versus 2-D models because 3-D fractures are clamped at the top and bottom, and pressures in the 3-D fractures that are far removed from the fracture tip have little effect on the stress intensity factor at the fracture tip. This rationale for the excess pressure mechanism is in marked contrast to the crack tip process damage zone assumptions and attendant high rock fracture toughness value hypotheses advanced in the literature. A comparison with field data is presented to illustrate the proposed fracture fluid pressure sensitivity phenomenon. This paper does not attempt to calculate the length of the fluid lag region in a propagating fracture but instead attempts to show that the pressure profile at the tip of the propagating fracture plays a major role in fracture propagation, and this role is magnified in 3-D models.

Cyclic loading-induced consolidation behavior of soft soil is of great interest for the analysis of offshore and onshore structures. In this study, an analytical solution for one-dimensional (1D) nonlinear consolidation of saturated double-layered soil under various types of cyclic loadings such as trapezoidal cyclic loading, rectangular cyclic loading, and triangular cyclic loading was derived. The proposed solution was subsequently degenerated into solutions for special cases and compared to the existing solutions. The degenerate solutions show good agreement with the existing results, which proves that the proposed solutions are more general ones for 1D nonlinear consolidation of saturated soils under time-dependent loading. Finally, a comprehensive parametric study was conducted to investigate the influences of different layer parameters, drainage conditions, and loading parameters on nonlinear consolidation of saturated double-layered soil under cyclic loadings.

A three-dimensional hydraulic fracture simulator (HYFFIX) is reformulated using finite element methodology and a newly adapted fixed grid. The numerical procedures for the coupled equations governing the fracture width, fluid pressure, and evolution of equilibrium planar crack in layered media are summarized. Fixed grid mesh control algorithms for the efficient tracking of the moving crack/fracture fluid front are detailed. The introduction of these novel algorithms in the simulator makes it numerically efficient and stable, in comparison to previously reported models which utilize migrating mesh techniques. Due to the enhanced numerical efficiency and compactness of the refined code, the model can also be readily implemented on a workstation or microcomputer.

Research investigations on three-dimensional (3-D) rectangular hydraulic fracture configurations with varying degrees of fluid lag are reported. The interpretations deduced from the computed stress intensity factors for a wide spectrum of fracture slenderness ratios and effective minimum in situ stresses are dramatically different from those derived from plane-strain crack simulations. In particular, this paper demonstrates that a 3-D fracture model coupled with fluid lag at the fracture tip can predict very large excess pressure measurements for hydraulic fracture processes. In addition, this paper demonstrates that 3-D predictions of fracture propagation based upon critical stress intensity factors are extremely sensitive to the pressure profile at the tip of a propagation fracture and that plane-strain models of fracture propagation will underestimate the fracture pressures required for propagation. This rationale for the excess pressure mechanism is in marked contrast to the crack tip process damage zone assumptions and attendant high rock fracture toughness value hypotheses advanced in the literature. Selected model result comparisons with experimental data are presented to provide additional validation of the proposed 3-D rectangular geometry and fluid lag-fracture fluid pressure sensitivity phenomenon.