Improve Mechanical Earth Model Calibration Using Statistical Concepts

Abstract

ABSTRACT: Mechanical Earth Model (MEM) has a broad impact on drilling, completion, production, and reservoir management decisions. For example, wellbore stability calculated using a MEM can provide safe mud windows for drilling, thereby reducing wellbore instability related non-productive time and drilling costs. A MEM can also provide safe injection limits for CO2 storage, enhanced oil recovery, and wastewater injection. The process of building and calibrating a MEM often involves collecting and analyzing offset well drilling observations, such as leak-off tests (LOT), diagnostic fracture injection test (DFIT), breakouts (BKOUT), and drilling induced tensile fractures (DITF) along with mud weights used. This process can be time-consuming and challenging because of the large number of wells available for review within a field and the difficulty of finding a single solution that provide best matches for all observations. This process requires multiple iterations and is based on minimizing the error between the model and data. The process can also be subjective due to the lack of sufficient information. This paper demonstrates how statistical tools can be leveraged to streamline and reduce subjectivity of the calibration process. 1. INTRODUCTION The process and procedure for building a MEM are well documented (Goodman & Connolly, 2007; Plumb et al., 2003; Ray et al., 2007). One of the key components in building a one-dimensional mechanical earth model (1DMEM) is to estimate the magnitudes of horizontal stresses. The horizontal stresses for an isotropic formation are commonly calculated using the following equations: (equation) (equation) Where: σ h = minimum horizontal stress. σ H = maximum horizontal stress. σv = vertical stress (overburden). ν = Poisson's ratio. E = Young's modulus. α = Biot's coefficient. Pp = pore pressure. εh = tectonic strain in the minimum horizontal stress direction. εH = tectonic strain in the maximum horizontal stress direction. To solve Eq. (1) & (2), the tectonic strains in both (minimum and maximum) horizontal directions is required, however, these parameters cannot be measured directly. Generally, tectonic strains are estimated from stress measurements, such as leak-off tests (LOT) or diagnostic fracture injection tests (DFIT), however these tests only measure the minimum horizontal stress. Consequently, there are infinite possible combinations of minimum and maximum tectonic strains that can fit the LOT and DFIT measurements. Figure 1 illustrates five MEMs with different combinations of minimum and maximum tectonic strains that all match the DFIT measurement yet produce different tectonic stress regimes. Models 1 and 2 are characterized by an extensional stress regime, Models 3 and 4 by a mix of extensional and strike-slip stress regimes, and model 5 by a strike-slip stress regime.