Abstract

Frac-pack treatments are commonly used on highly permeable and unconsolidated (hence, highly productive) formations as a means of preventing the occurrence of sanding while bypassing the damaged zone around the wellbore. These treatments are currently designed using hydraulic fracturing models that assume planar symmetrical geometries, tensile rock failure, and - usually - one-dimensional fluid leak-off schemes. However, it is not uncommon to find that the pressure predictions from these models and the ones measured in the field differ substantially.

This paper addresses the issue of hydraulic fracturing stimulation treatments in poorly consolidated formations without the handicap of using such assumptions. In this study, the discrete element method (DEM) was used and the program was calibrated in order to reproduce the mechanical and hydraulic responses of a selected unconsolidated sandstone . During this process, both its mechanical properties (Young's modulus, Poisson's ratio, stress-strain curve, and compressive strength) as well as its hydraulic characteristics (permeability) were matched.

The modeling effort presented here allows fracture propagation to be a direct consequence of the interaction of shear and tensile microcracks induced in the material during the injection process. Thus, à priori assumptions on the final geometry of the macro-scale fracture are not required.

For the modeled rock, it was found that the nature of fluid leak-off as well as the pumping rate determine the fracture propagation process. The shape of the curves representing the number of induced cracks changed as a function of the fracturing fluid viscosity. The effect of pressure differential was also found to be important during the fracturing process..

A remarkable finding by exercising this model was that, in the particular case of the Antler Sandstone (and possibly for other unconsolidated formations), shear failure seems to be more important than tensile failure during the hydraulic fracturing process. The "normal" planar macro-scale fracture was deemed to be the consequence of microcracks interactions. In addition, a "process" zone was found to exist around the wellbore. This conclusion is in clear contradiction to what has been traditionally accepted in the oil and gas industry, and could explain the difference observed between standard model predictions and the conditions encountered in the field.

Introduction

Traditionally, all hydraulic fracturing modeling has been based on LEFM theory; which was initially developed for stiff, competent rocks. Thus, when standard hydrofrac simulators are run on poorly-consolidated formations; "correction factors" are required in order to fit model predictions to field data. Moreover, the lack of reliable design and prediction tools reduces unconsolidated rock hydrofrac operations to a little more than trial-and-error procedures. The economical consequences of such an approach are enormous; unpredicted pressure requirements, lower-than-expected well productivity and operational problems are of common occurrence.

A discrete element method program, called PFC3D, was utilized to perform several simulations of the hydraulic fracturing process in poorly-consolidated formations. This program allows for the creation of three-dimensional models of granular materials by tracing the motion and interactions of individual rock particles; each of them being modeled as a discrete object with particular geometric and physical state representations. Thus, the whole model evolves over time by tracing characteristics such as shape, size, position, contact forces, and displacements for each of the discrete particles forming the system.

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