Finite Element Simulation of Ultrasonic and Borehole Acoustic Measurements of Fractured and Anisotropic Reservoirs

Abstract

Unconventional shale rocks are characterized by low porosity and low permeability that impacts the flow of fluids and the production of gas form these reservoirs. The presence of natural fractures in shale formations enhances the reservoir conditions for developing large‐scale fracture networks during hydraulic fracturing, which represents a key factor for shale gas development. Therefore, accurate identification of natural fractures in shale reservoirs improves reservoir stimulation and production.

The estimation of fractures density is usually obtained by first measuring the elastic properties of reservoir rocks using ultrasonic measurements on cores (small scale). When the number of cores is limited or cores are not available, the elastic properties are obtained using borehole acoustic measurements (sonic well logs) which are available continuously in a well (large scale). The measured elastic properties of the rock are then used to estimate the crack (fracture) density using effective medium theories (EMT).

The aim of this thesis is to determine the range of applicability of different EMT models to estimate the elastic properties of fractured shale formations using the finite element method (FEM). The Barnet shale formation properties are used in the modeling. The shale rock includes equidistant horizontal fractures modeled as ellipsoids and approximated as octahedrons. The fractures are either dry or filled with a calcite or a weak material, have an aspect ratio of 0.1 and a volume concentration that varies from 1% to 8% equivalent to a crack density up to 30%. The elastic properties of the rock are calculated using ultrasonic measurements and are compared with three effective medium models: the Hudson 1st and 2nd orders, the self-consistent approximation (SCA) and the differential effective medium theory (DEM).

Ultrasonic results show that octahedrons can be used to approximate the ellipsoids with a relative error below 4% and that using octahedrons enhances the performance of FEM simulations by 40%. The comparison of the elastic properties of the Barnet shale measured using the FEM and calculated using the EMT show that the difference increases as the volumetric concentration of cracks increases. Moreover, the calculated elastic properties of the Barnet shale with cracks filled with calcite are better approximated by the SCA and DEM models compared to the Hudson model while the dry or weak cracks are better approximated by the Hudson and SCA models.

In the last chapter, we describe a model to obtain sonic logs of a fractured formation measured by an acoustic tool in a fluid filled borehole, which can be used to correlate ultrasonic and borehole measurements.