Geomechanics of Fluid Injection in Geological Reservoirs

Numerous petroleum engineering, mining, and enhanced geothermal energy operations involve cyclic ‎injection of fluids into geological formations. Geomechanics of injection operations in weakly ‎consolidated or unconsolidated reservoirs is complex, and means for analyzing the involved physical ‎processes are limited. The key feature that must be considered is parting of the formation during ‎injection, which occurs at near zero effective stresses when strength and stiffness of the medium ‎become effectively zero. Even if peculiarities of the granular media behavior at near zero effective ‎stresses are disregarded and a highly idealized Mohr-Coulomb behavior coupled with constant ‎permeability Darcy flow is assumed, the injection problem is still highly challenging. This type of ‎poroplastic formulation remains analytically intractable even for simplest geometries. Numerical ‎computations are highly challenging as well, due to high fluid-solid matrix stiffness contrast. ‎ Much effort has been devoted thus far to understand soil-fluid interactions in geological reservoirs ‎triggered by borehole excavation and production operations. With regards to injection operations ‎however, practically no comprehensive study has been performed to access the fundamental ‎geomechanical processes involved. Previous attempts to evaluate injection operations mainly ‎concentrate on describing fracture growth in hard brittle formations. In principle, the geomechanical ‎processes prior to fracture initiation are particularly complicated in weakly consolidated strata. This ‎dissertation presents analytical solutions and numerical models to examine geomechanics of high ‎pressure fluid injection in conditions when flow rates are high enough to induce plasticity yet not ‎parting of the formation. The study considers injection through a fully-penetrating vertical wellbore ‎into an isotropic, homogeneous unconsolidated geological layer confined between impermeable seal ‎rock layers. Axisymmetric conditions are assumed. The main objective is to evaluate the time ‎dependent geomechanical response of the unconsolidated reservoir in such conditions focusing on ‎failure mechanisms and permanent changes in stress conditions around the injection area. Results of ‎this research makes it possible to address the issue of integrity of confining strata, facilitate assessments ‎of potential leakage areas, and offer aid for optimization of injection operations as well as in ‎formulating monitoring strategies.‎ First, rock-fluid interactions are evaluated prior to the state where limiting shear resistance is ‎reached during injection. Unlike previous studies, impacts of vertical confinement governed by the ‎stiffness of the overburden layer are incorporated. The Winkler spring model approximation is ‎implemented to describe the response of the confining strata in the plane perpendicular to the reservoir. ‎New poroelastic analytical solutions are derived to describe evolution of stress and strain components in ‎time as a function of induced pore pressures. Solutions are verified against fully-coupled numerical ‎models designed in this study. Next, novel insights into the geomechanics of parting in various stress ‎regimes is offered via a comprehensive assessment of stress perturbations surrounding vertical injection ‎wellbores. A thorough sensitivity analysis is conducted to examine the effect of vertical confinement ‎and rock-fluid characteristic parameters on the reservoir response in the wellbore vicinity. Results ‎demonstrate a notable impact of seal rock stiffness on the near wellbore rock behavior in formations ‎with high intrinsic permeability (typically exceeding 0.05 Darcy). The study shows that the key ‎parameter controlling the injection process in the poroelastic regime is the ratio of the overburden ‎Winkler stiffness to the reservoir’s bulk modulus, with the Winkler parameter reflecting the seal rock ‎stiffness. When this ratio approaches unity, practically no shear stress is induced in the reservoir while ‎for ratios exceeding unity, deviatoric stresses gradually increase. In situations when the stiffness ratio is ‎below unity, the porous formations can behave in a rather complicated manner depending on the initial ‎stress regime where redirection of the minimal principal stress occurs from a horizontal to a vertical ‎plane. Sensitivity analyses reveal that at the same injection rate rock failure occur more rapidly in ‎conditions of higher stress anisotropy, higher elastic moduli, lower permeability, higher degree of rock-‎fluid coupling, and a higher vertical confinement.‎ Next, rock-fluid interactions are evaluated in an unconsolidated reservoir formation confined ‎between two stiff seal rock layers subjected to injection pressures high enough to induce plasticity yet ‎not parting of the formation. The injection process is first examined numerically by constructing a ‎fluid-coupled poro-elasto-plastic model in which propagation of the significant influence zone ‎surrounding the injection borehole is quantified by the extent of the plastic domain. A comprehensive ‎assessment of stresses, pore pressures, as well as failure planes is carried out throughout an entire ‎transient state of an injection cycle, at steady state, and also during the shut-in period. The numerical ‎solution describes five distinct zones evolving with time around the injection well and corresponding to ‎different stress states: liquefaction at the wellbore followed by three inner plastic domains where ‎directions of major principal stress changes from vertical to radial and failure planes change accordingly. ‎The plastic domains are followed by a region where stress states remain in the elastic range. Failure ‎mechanisms at the wellbore is found to be in shear initially, followed by development of a state of zero ‎effective stress, i.e. liquefaction. Next, a novel methodology is proposed based on which new weakly-‎coupled poro-elasto-plastic analytical solutions are derived for the stress/strain components during ‎injection. Unlike previous studies, extension of the plastic zone is obtained as a function of injection ‎pressure, incorporating the plasticity effects around the injection well. The derived loosely-coupled ‎solutions are proven to be good approximations of fully-coupled numerical models. These solutions ‎offer a significant advantage over numerical computations as the run time of a fully-coupled numerical ‎model is exceedingly long (requiring about six months for 661 million time computational steps using ‎FLAC3D 3.0 code on Intel® i7 3.33 GHz CPU).‎ The final part of this dissertation includes a brief chapter on the post-injection behavior of ‎unconsolidated reservoir formations confined with stiff seal rock layers. Pore pressure dissipation, stress ‎variations, and the transition behavior of the plastic domain surrounding the injection wellbore to an ‎elastic state are numerically evaluated. Results offer an original insight into the permanent ‎geomechanical effects of injection operations in such formations.

Monitoring Oil Reservoir Deformations by Measuring Ground Surface Movements

It has long been known that any activity that results in changes in subsurface pressure, such as hydrocarbon production or waste or water reinjection, also causes underground deformations and movement, which can be described in terms of volumetric changes. Such deformations induce surface movement, which has a significant environmental impact. Induced surface deformations are measurable as vertical displacements; horizontal displacements; and tilts, which are the gradient of the surface deformation. The initial component of this study is a numerical model developed in C++ to predict and calculate surface deformations based on assumed subsurface volumetric changes occurring in a reservoir. The model is based on the unidirectional expansion technique using equations from Okada’s theory of dislocations (Okada, 1985). A second numerical model calculates subsurface volumetric changes based on surface deformation measurements, commonly referred to as solving for the inverse case. The inverse case is an ill-posed problem because the input is comprised of measured values that contain error. A regularization technique was therefore developed to help solve the ill-posed problem. A variety of surface deformation data sets were analyzed in order to determine the surface deformation input data that would produce the best solution and the optimum reconstruction of the initial subsurface volumetric changes. Tilt measurements, although very small, were found to be much better input than vertical displacement data for finding the inverse solution. Even in an ideal case with 0 % error, tilts result in a smaller RMSE (about 12 % smaller in the case studied) and thus a better resolution. In realistic cases with error, adding only 0.55 % of the maximum random error in the surface displacement data affects the back-calculated results to a significant extent: the RMSE increased by more than 13 times in the case studied. However, in an identical case using tilt measurements as input, adding 20 % of the maximum surface tilt value as random error increased the RMSE by 7 times, and remodelling the initial distribution of the volumetric changes in the subsurface was still possible. The required area of observation can also be reduced if tilt measurements are used. The optimal input includes tilt measurements in both directions: dz/dx and dz/dy. iv With respect to the number of observation points chosen, when tilts are used with an error of 0 %, very good resolution is obtainable using only 0.4 % of the unknowns as the number of benchmarks. For example, using only 10 observation points for a reservoir with 2500 elements, or unknowns resulted in an acceptable reconstruction. With respect to the sensitivity of the inverse solution to the depth of the reservoir and to the geometry of the observation grid, the deeper the reservoir, the more ill-posed the problem. The geometry of the benchmarks also has a significant effect on the solution of the inverse problem

A Theoretical Model to Predict Both Horizontal Displacement and Vertical Displacement for Electromagnetic Induction-Based Deep Displacement Sensors

Deep displacement observation is one basic means of landslide dynamic study and early warning monitoring and a key part of engineering geological investigation. In our previous work, we proposed a novel electromagnetic induction-based deep displacement sensor (I-type) to predict deep horizontal displacement and a theoretical model called equation-based equivalent loop approach (EELA) to describe its sensing characters. However in many landslide and related geological engineering cases, both horizontal displacement and vertical displacement vary apparently and dynamically so both may require monitoring. In this study, a II-type deep displacement sensor is designed by revising our I-type sensor to simultaneously monitor the deep horizontal displacement and vertical displacement variations at different depths within a sliding mass. Meanwhile, a new theoretical modeling called the numerical integration-based equivalent loop approach (NIELA) has been proposed to quantitatively depict II-type sensors’ mutual inductance properties with respect to predicted horizontal displacements and vertical displacements. After detailed examinations and comparative studies between measured mutual inductance voltage, NIELA-based mutual inductance and EELA-based mutual inductance, NIELA has verified to be an effective and quite accurate analytic model for characterization of II-type sensors. The NIELA model is widely applicable for II-type sensors’ monitoring on all kinds of landslides and other related geohazards with satisfactory estimation accuracy and calculation efficiency

Impact of local thermal non-equilibrium on temporal thermo-hydro-mechanical processes in low permeable porous media

The thermo-hydraulic-mechanical (THM) response of low permeable media is of crucial significance in thermal fracturing for production of unconventional shale oil, enhanced geothermal systems, and waste disposal. During such processes, pore pressures and stresses change in a spatiotemporal manner due to hydraulic and thermal loadings. From the viewpoint of the energy balance equation, the available theoretical studies can be classified as local thermal equilibrium (LTE), and local thermal non-equilibrium (LTNE) models. LTE models consider identical temperature for different phase of the porous system. LTNE models allow different temperature variations in solid and fluid phases of a porous medium. Current LTNE studies are weakly-coupled – not incorporating thermo-osmosis. This paper presents novel coupled LTNE thermo-poroelastic solutions in a transversely isotropic saturated porous medium, incorporating thermo- osmosis effect. Solutions are obtained for permeable and impermeable boundaries. Thermo-osmosis is found to have a very different effect in case of LTNE versus LTE, resulting in a fundamentally different THM response. LTNE effect analysis reveals different THM responses under different heat transfer properties at the solid-fluid interface in low permeable strata

Assessment of Direct Tensile Strength Tests in Rock Through a Multi-laboratory Benchmark Experiment

This study aims to experimentally assess repeatability and reproducibility of direct tensile strength (DTS) tests with deformability measurements on two types of rocks: Blanco Mera granite (Spain) and Cotta sandstone (Germany). The tests were conducted in four rock mechanics laboratories located in different countries (Canada, Germany, Spain and Sweden). A total of 51 tests were performed on cylindrical specimens of the two rocks, using different test equipment and measuring devices. Mean and standard deviation DTS values were determined in the four laboratories for the granite (5.70 ± 0.32, 6.06 ± 0.11, 3.84 ± 0.50 and 6.76 ± 0.10 MPa) and for the sandstone (1.88 ± 0.07, 1.96 ± 0.06, 1.15 ± 0.32 and 1.74 ± 0.19 MPa), together with Young’s moduli and Poisson’s ratios in tension, being statistically analysed to evaluate the variability and compare the main results obtained from the participating laboratories. The findings indicate that the DTS test with deformability measurements on cylindrical rock specimens is operationally feasible. However, certain shortcomings have been identified during the course of the experiments with the existing methodologies, such as the one suggested by the ISRM for DTS tests. The results have also shown to be sensitive to appropriate test and strain measurement configurations. The objective of this study was to shed light on these issues and provide new insights for potential future improvements of the existing testing methods