Modelling of Flow during Fracture Growth Driven by Multiple Fluid Stages Using High-Performance Parallel Computing Algorithms.

The present work addresses a particular problem in Hydraulic Fracturing, i.e., characterization of gravity -driven motion of multiple stages of immiscible fluids, with various rheologies, within a narrow fracture cavity. The following capabilities were developed to address the present problem: (1) An analytical algorithm to predict the size and characteristics of encapsulated multiple fluid layers; (2) A semi-analytical algorithm to predict effects on in -plane fluid motion due to finite end-boundaries (e.g., the fracture perimeter), and wedging (crack-width variation) for a two-stage flow; (3) A suite of numerical algorithms, named PARFES (acronym for PARallel Finite Element Solvers) --designed specially to take advantage of highly parallel computer environments--based on an Euler-Lagrangian approach (e.g., nodes delineating the injection region are constrained while other nodes are free to move, according to the coupling of flow field variables with the elastic stress field). PARFES is composed of three modules: (3.1) PARFES1 - tracks the interface motion and mesh nodal distribution of a given fluid stage; (3.2) PARFESAX - models the axisymmetrical multiple stage flow problem; (3.3) PARFES2 - a modified nonlinear Newton-Raphson algorithm to determine non-symmetrical motions. (4) An experimental apparatus, named TARG-DECH (acronym for Test Apparatus for Response to Gravity-Driven Effects in Convective Hydraulics) designed to study the gravity-driven flow regimes at low Reynolds number. TARG -DECH is also used to experimentally verify the results from algorithms (1) and (2) above. In addition, a number of experimental measurements were conducted to characterize properties (e.g., viscosity, density, surface/interfacial tension, wettability and spreading) of the fluids and apparatus used. Based on results of the above projects, it is established that the following two phenomena dominate the placement of fluids and solids (proppant) in uncontained fractures; (I) Convective motion, due to gravity-driven forces, predominate over particle-settling forces and (often) even over pumping-pressure-driven flows. (II) The tendency of higher viscosity fluids to migrate to regions of lower shear rates (and vice-versa) may dramatically alter the (wetting) conditions at the fracture walls, often giving rise to a transverse instability termed encapsulation, in addition to in-plane instabilities, usually referred to as fingering. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617 -253-5668; Fax 617-253-1690.) (Abstract shortened by UMI.).