Computer Simulation of Hydraulic Fracturing in Shales-Influences on Primary Migration
Authors: Ozkaya Ismail 
Published: December 2007

Summary
Hydraulic tension fractures in a shale layer during sedimentation are simulated by use of computer techniques. The depth at which fractures form is directly proportional to the hydraulic conductivity and tensile proportional to the hydraulic conductivity and tensile strength, and inversely proportional to the rate of sedimentation and thickness of the shale layer. Hydraulic fractures may form at depths of oil generation to facilitate primary migration. This paper describes an attempt to simulate the process of hydraulic fracturing during burial and compaction of a shale layer by use of an elementary model. One objective is to investigate the role of various factors in hydraulic tension fracturing of shales in a tectonically relaxed area. Another objective is to see whether hydraulic fractures form at depths of oil generation.

Introduction
Hydraulic fracturing of rocks was first investigated by Hubbert and Willis, and subsequently by other investigators. The role played by hydraulic fracturing in the process of primary migration has attracted the attention of several authors. Existing computer simulation experiments of oil generation and migration, however, do not deal with hydraulic fracturing.

Simulation Model
A horizontal shale layer of thickness h, bounded by porous and permeable sand layers, is taken as the basis porous and permeable sand layers, is taken as the basis of the simulation model. The shale is buried progressively at a constant rate of sedimentation. Sands retain progressively at a constant rate of sedimentation. Sands retain hydropressures during sedimentation, whereas shales generally develop abnormally fluid pressures because of compaction and low permeability values. Pore fluids tend to flow from the abnormally pressured shale vertically upward and downward into the hydropressured envelope. The general differential equation governing such a vertical fluid flow from shale is
(1)
Solution of this equation with appropriate boundary conditions gives the value of potential and hence pressure in time across the shale layer. In areas that are tectonically relaxed, the principal stress, Vt, is vertical and given by
(2)
The effective vertical stress, sigma Ve, is
(3)
In such a case, the least stress is horizontal. If no lateral strain is assumed to exist, and if the effect of temperature is neglected, the least horizontal effective stress, sigma He, is related to effective vertical stress, sigma Ve, by
(4)
Hydraulic fracture generation and propagation require an elaborate mathematical treatment taking into account stress-intensity factor, fracture length, height, rate of fluid flow in and out of the fracture, factors controlling such rates, effect of temperature and fracture geometry on tensile strength, etc. In the present model, a simple criterion is used. Fractures propagate if
(5)
Maximum fluid pressure, Pmax, occurs around the center in compacting shales. When Pmax, satisfies Eq. 5, then a fracture is initiated at the point where pore pressure is maximum. The fracture is oriented vertically since the least effective stress is horizontal and principal stress is vertical. Hence, a fracture extends from a high-pore-pressure zone into a low-pore-pressure and low-permeability zone. It is assumed that the rate of fluid flow into the fracture at the origin is high enough to keep Pf at Pmax and to ensure propagation of the crack toward the edge of the shale layer. propagation of the crack toward the edge of the shale layer. Parameters Parameters The parameters and corresponding values used in this simulation experiment are listed in Table 1. Some of these parameters vary with depth and temperature. Nevertheless, constant values are used in a single simulation run to keep the model basic. The variation of parameters such as pw and pb with temperature and parameters such as pw and pb with temperature and depth has only a negligible effect on the final results.
JPT
P. 826