Abstract

This paper presents an efficient global sensitivity approach based on the Analysis of Variance (ANOVA) and the FM-DDM to assess the uncertainty of geomechanical reservoir parameters. The proposed approach was evaluated in the context of the global sensitivity analysis in a large-scale NFR subjected to injection and production operations. The geomechanical parameters were selected as the rock mechanical properties (shear modulus, Poisson ratio and normal joint stiffness), and minimum far-field stresses, and the performance measures were chosen as fluid pressures in the injector and producer wells. The results show the effectiveness and efficiency of the proposed approach since it allows establishing the relative contribution associated with the uncertainty of the geomechanical properties (main factors and interactions) in the variability of well performance metrics using a computationally expensive fluid flow-geomechanics numerical reservoir simulations.

1. INTRODUCTION

Unconventional petroleum reservoirs contain vast resources to supply the energy demand in the United States. However due to their ultra-low matrix permeability, the development of such reservoirs depends mainly on the ability to transport the underground fluid to the surface through extensive natural fracture networks subjected to geoemachanical deformation of the rock and fractures. Fluid injection and extraction operations are usually carried out in Naturally Fractured Reservoirs (NFR). The performance of this recovery process strongly depends on the flow properties of the fracture network and then controlled by geomechanical reservoir parameters, which are usually defined under uncertainty.

A important step for the design and control of injection and production operations in those reservoirs is to find the relative contributions of the geomechanical parameters (e.g., material properties and far-field stresses) in the variability of given performance measures (e.g., bottomhole pressure) under large-scale situations.

Previous works have determined the effects of geomehcanical parameters in reservoirs performing a local sensitivity analysis [1-4]. On this parametric study, the individual effect of each input parameter on the output response is determined in a one-byone basis by keeping constant the values of the remaining parameters. Mathematically, it can be seen as the partial derivative of that function with respect to its variables. However, the accuracy and usefulness of this approach is limited because the interaction effects when two or more parameters are changing at the same time are ignored.The expansion of a circular cavity, such as a production well in rock, has been of considerable interest for decades. However, some aspects of fracturing have not been fully addressed. For example, in the interpretation of the critical (breakdown) pressure for hydraulic fracturing, the peak of the recorded pressure data is often assumed to be associated with tensile fracture initiation. The significant non linearity in the variation of the borehole diameter with breakdown pressure suggests fracturing prior to peak [1].

In this study, using a particle tracking technique named digital image correlation (DIC), a displacement discontinuity at the cavity boundary was identified. It was noticed that a fracture (process zone) develops prior to peak pressure. Another important issue in the problem of borehole expansion is the discrepancy between theoretical predictions and lab/field measurements regarding a size (and rate) effect. Many previous studies demonstrate that a rate effect strongly exists and that the faster the loading, the higher the breakdown pressure [2- 6]. Size effect on the critical load required to initiate a tensile (mode I) fracture in a quasi-brittle material is well known [7], and therefore, understanding the mechanism associated with mode I fracture initiation from a wellbore is important. Previous studies have confirmed that with increase in size, the critical pressure decreases [2, 8]. A recent study [9] demonstrated that the size effect is governed by the ratio between a material length scale and a structural length scale. The material length is defined as the square of the ratio of the fracture toughness to its tensile strength, while the structural length scale is the wellbore radius.

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