Ahmad Ghassemi

Linear chemo-poroelasticity for swelling shales: theory and application

Abstract Optimization of drilling fluid parameters such as mud weight, salt concentration, and temperature is essential to alleviating instability problems when drilling through shale sections. The selection of suitable mud parameters can benefit from analyses that consider significant chemo-mechanical processes involved in shale-drilling–fluid interactions. This paper describes the development of a scientifically robust and practical physicochemical theory for describing shale deformation. The theory considers chemical and poroelastic processes and couples ion transfer in the mud/shale system to formation stresses and pore pressure. The field equations are derived within the framework of a linear, Biot-like isotropic poroelastic theory. These field equations are solved analytically for the problem of a wellbore in shale to yield the solute mass fraction, pore pressure, and the stress distributions around the borehole. The solution is developed using the generalized plane strain approach and is used to study the impact of solute transfer on stress and pore pressure fields. The analyses indicate that solute transfer causes the chemical-osmosis to become time-dependent. As time increases, the transfer of ions leads to osmotic pressure dissipation and re-establishment of a pore pressure regime characteristic of hydraulic flow. Furthermore, it is observed that while the wellbore may be supported by a mud pressure of significant magnitude, the rock can experience a tensile effective radial stress due to the physicochemical interaction between the shale and the drilling mud. Hence, the contribution of the physicochemical processes can significantly impact the stress and pore pressure distributions around a borehole and should be considered when optimizing drilling mud properties.

POROTHERMOELASTICITY FOR SWELLING SHALES

Abstract Optimization of drilling fluid parameters such as mud weight, salt concentration, and temperature is essential to alleviating instability problems when drilling through shale sections, particularly in high-pressure and high-temperature environments. Under these conditions, selection of suitable mud parameters can benefit from analyses that consider significant thermal and chemo–mechanical processes involved in shale–drilling fluid interactions. A non-isothermal poroelastic theory suitable for shales is presented herein. Phenomena related to thermal and chemical osmosis are considered by extending the theory of porothermoelasticity to chemically active rocks. The modified pore pressure and stresses around a borehole in shale are obtained by solving the porothermoelastic field equations in generalized plane strain. Application of the solution to a typical field operational situation has demonstrated that thermal osmosis can significantly impact formation pore pressure, thereby reducing stability. Furthermore, analyses based on the new porothermoelastic formulation for shales suggest that mud temperature should be optimized in order to maximize the efficacy of chemical osmosis in stabilizing the borehole.

Integration of microseismic monitoring data into coupled flow and geomechanical models with ensemble Kalman filter

Hydraulic stimulation of low-permeability rocks in enhanced geothermal systems, shale resources, and CO2 storage aquifers can trigger microseismic events, also known as microearthquakes (MEQs). The distribution of microseismic source locations in the reservoir may reveal important information about the distribution of hydraulic and geomechanical rock properties. In this paper, we present a framework for conditioning heterogeneous rock permeability and geomechanical property distributions on microseismic data. To simulate the multiphysics processes in these systems, we combine a fully coupled flow and geomechanical model with the Mohr-Coulomb type rock failure criterion. The resulting multiphysics simulation constitutes the forecast model that relates microseismic source locations to reservoir rock properties. We adopt this forward model in an ensemble Kalman filter (EnKF) data assimilation framework to jointly estimate reservoir permeability and geomechanical property distributions from injection-induced microseismic response measurements. We show that integration of a large number of spatially correlated microseismic data with practical ensemble sizes can lead to severe underestimation of ensemble spread, and eventually ensemble collapse. To mitigate the variance underestimation issue, two low-rank data representation schemes are presented and discussed. In the first approach, microseismic data are projected onto a low-dimensional subspace defined by the left singular vectors of the perturbed observation matrix. The second method uses a coarser grid for representing the microseismic data. A series of numerical experiments is presented to evaluate the performance of the proposed methods and to illustrate their applicability for assimilating microseismic data into coupled flow and geomechanical forward models to estimate multiphysics rock properties.

Numerical Simulation of Sequential and Simultaneous Hydraulic Fracturing

Hydraulic fracturing of horizontal well hydraulic fracturing technology can help develop unconventional geothermal and petroleum resources. Today, industry uses simultaneous and sequential (also known as zipper) fracturing in horizontal petroleum well stimulations. To achieve successful and desired stimulated rock volumes and fracture networks, one must understand the effect of various rock and fluid properties on stimulation to minimize the risk of unwanted fracture geometries. This paper describes the development of a 2D coupled displacement discontinuity numerical model for simulating fracture propagation in simulta‐ neous and sequential hydraulic fracture operations. The sequential fracturing model consid‐ ers different boundary conditions for the previously created fractures (constant pressure restricting the flow back between stages and proppant-filled). A series of examples are pre‐ sented to study the effect of fracture spacing to show the importance of spacing optimiza‐ tion. The results show the fracture path is not only affected by fracture spacing but also by the boundary conditions on the previously created fractures.

A complete plane strain fictitious stress boundary element method for poroelastic media

A fully coupled generalized plane strain boundary element model for determining the distribution of stress and pore pressure around underground openings in poroelastic media is developed. It is based on the indirect boundary element method of fictitious stress extended to complete plane strain analysis. New fundamental solutions for longitudinal forces were derived for the development of the model which uses elements with a constant variation of fictitious forces and sources in both space and time. As an example, the problem of a borehole drilled in an arbitrary direction in a triaxial stress field is considered. The results indicate that the fictitious stress method is an accurate and suitable means for complete plane strain poroelastic analyses of underground openings.

Benchmark Problems of the Geothermal Technologies Office Code Comparison Study

............................................................................................................................................. iii Summary ............................................................................................................................................. v Acknowledgments ............................................................................................................................. vii Acronyms and Abbreviations ............................................................................................................. ix 1.0 Introduction .............................................................................................................................. 1.1 1.1 Approach ......................................................................................................................... 1.3 1.1.1 Study Objectives .................................................................................................. 1.3 1.1.2 Study History and Structure ................................................................................. 1.3 1.2 Participants and Codes .................................................................................................... 1.5 1.3 Benchmark Problems ...................................................................................................... 1.9 1.3.1 Benchmark Problem 1: Poroelastic Response in a Fault Zone (PermeabilityPressure Feedback) ............................................................................................... 1.9 1.3.2 Benchmark Problem 2: Shear stimulation of randomly oriented fractures aby injection of cold water into a thermo-poro-elastic medium with stress-dependent permeability ........................................................................................................ 1.10 1.3.3 Benchmark Problem 3: Fracture opening and sliding in response to fluid injection .............................................................................................................. 1.11 1.3.4 Benchmark Problem 4: Planar EGS fracture of constant extension, pennyshaped or thermo-elastic aperture in impermeable hot rock .............................. 1.12 1.3.5 Benchmark Problem 5: Amorphous Silica dissolution/precipitation in a fracture zone .................................................................................................................... 1.13 1.3.6 Benchmark Problem 6: Injection into a fault/fracture in thermo-poroelastic rock1.14 1.3.7 Benchmark Problem 7: Surface deformation from a pressurized subsurface fracture ............................................................................................................... 1.15 1.4 Comparison Standard .................................................................................................... 1.16 2.0 Governing and Constitutive Equations .................................................................................... 2.1 2.1 Heat Transfer Modeling .................................................................................................. 2.1 2.2 Fluid Flow Modeling ....................................................................................................... 2.2 2.2.1 Fracture Transmissivity ........................................................................................ 2.2 2.3 Rock Mechanics Modeling .............................................................................................. 2.3 2.3.1 Continuum Geomechanics ................................................................................... 2.4 2.3.2 Discrete Fracture Geomechanics .......................................................................... 2.5 2.3.3 Joint Models ....................................................................................................... 2.10 2.4 Geochemical Reaction Modeling .................................................................................. 2.12 2.4.1 Aqueous Reaction Rates ..................................................................................... 2.14 3.0 Numerical Solution Schemes ................................................................................................... 3.1 3.1 Sequential Schemes ......................................................................................................... 3.1 3.2 Iterative Schemes ............................................................................................................ 3.1

Pore Pressure and Stress Distributions Around a Hydraulic Fracture in Heterogeneous Rock

One of the most significant characteristics of unconventional petroleum bearing formations is their heterogeneity, which affects the stress distribution, hydraulic fracture propagation and also fluid flow. This study focuses on the stress and pore pressure redistributions during hydraulic stimulation in a heterogeneous poroelastic rock. Lognormal random distributions of Young’s modulus and permeability are generated to simulate the heterogeneous distributions of material properties. A 3D fully coupled poroelastic model based on the finite element method is presented utilizing a displacement–pressure formulation. In order to verify the model, numerical results are compared with analytical solutions showing excellent agreements. The effects of heterogeneities on stress and pore pressure distributions around a penny-shaped fracture in poroelastic rock are then analyzed. Results indicate that the stress and pore pressure distributions are more complex in a heterogeneous reservoir than in a homogeneous one. The spatial extent of stress reorientation during hydraulic stimulations is a function of time and is continuously changing due to the diffusion of pore pressure in the heterogeneous system. In contrast to the stress distributions in homogeneous media, irregular distributions of stresses and pore pressure are observed. Due to the change of material properties, shear stresses and nonuniform deformations are generated. The induced shear stresses in heterogeneous rock cause the initial horizontal principal stresses to rotate out of horizontal planes.