Summary
The mechanical strength of a reservoir formation is the most crucial information required for predicting sand production and recommending sand control completion. So far, the only reliable technique to obtain the formation strength quantitatively is to perform laboratory tests on core samples. The laboratory tests require substantial volumes of cores, which in most cases are not available. In this study, we present a new method to avoid this restriction. The significance of this approach is in its simplicity and efficiency in constructing a reliable mechanical failure envelope. The key results of this study, based on measurements on a variety of sandstones, are the following.A single normalized failure envelope characterizes sandstone formations. This universal curve makes it possible to construct the failure envelope for a sandstone formation from the knowledge of critical pressure.There exists a correlation between the critical pressure and the compressional wave velocity (at equivalent depths of burial).The failure envelope for a sandstone formation can then be constructed simply from compressional wave velocities. These velocities are generally accessible from conventional logging data.
Introduction
A major problem encountered during hydrocarbon production is the influx of sand, or sand production.1 It can cause severe damage to both production equipment and the producing formation. Furthermore, remediation processes after sanding are extremely difficult, costly or often impossible. Although significant research has been conducted on sand production, we are still at an embryonic stage in predicting sand influx.
Several factors determine sand production. The most critical factors are (1) formation strength; (2) in-situ stress; and (3) production rate. The hydrocarbon production process is associated with reservoir depletion, which results in a decrease of reservoir pore pressure. Consequently, the effective overburden pressure, defined as total overburden pressure minus pore pressure, increases. Formation collapse is most likely if the effective stress exceeds the formation strength. In addition, production rate increase, which is associated with large fluid pressure gradients near the borehole, tends to draw the sand into the wellbore. Generally, one can estimate the in-situ stress. For example, the horizontal minimum stress can be measured from hydraulic fracture testing,2-4 and the overburden pressure from overburden density data. The production rate is a controllable parameter. The parameter of concern is the formation strength, which is the focus of this study.
The most reliable technique for obtaining mechanical strength data is triaxial testing of core samples in the laboratory. With appropriate arrangements of applied stresses one can determine a failure envelope in stress space. Such a failure envelope quantifies the stress conditions under which the material fails. Although the laboratory test can provide dependable mechanical strength data, it is not followed routinely simply because it is time-consuming and costly. Moreover, in most cases, a sufficient amount of core is not available. Traditionally the mechanical strength, or Mohr-Coulomb failure criterion, is estimated from P- and S-wave velocities and density log data5-8 based on the correlation of Deere and Miller.9 This approach estimates uniaxial compressive strength, and assumes a constant frictional angle.
In this study, we seek an alternative method of estimating overall nonlinear mechanical strength in a three-dimensional stress space.
Basic Concept of Failure Envelope
Formation collapse is an indication that the in-situ stress is beyond the failure limit of the formation material. This failure stress limit is a quantitative parameter that defines the formation mechanical strength.
For a one-dimensional state of stress, the mechanical strength can be simply quantified with a single parameter: the uniaxial compressive strength. However, because the in-situ formation stress is three dimensional and anisotropic, a more complicated mathematical expression involving all the stresses is required to quantify the mechanical strength. This quantitative expression of mechanical strength is known as the failure envelope or failure criterion.
Numerical simulations of sand production in oil wells using the CFD-DEM-IBM approach