Petroleum Reservoir Simulation Coupling Flow and Deformation

The paper presents a discussion on the issues related to the interaction between geomechanics and reservoir simulation in deformable hydrocarbon reservoirs. Geomechanics is important in order to account for rock deformations due to pore pressure and temperature changes resulting from production and fluid injection. Rock deformation can affect the permeability and pore compressibility of the rock. In turn, the pore pressures will be vary due to changes in the pore volume. Geomechanics is also required in order to account for the effect of the non-pay rock surrounding the reservoir on the overall reservoir compressibility and the loads transmitted to the reservoir by the weight of the overburden rock. The paper gives the formulation and finite element discretization of Biot's equations for multi-phase fluid flow in deformable porous media. Based on this formulation, it is argued that geomechanical response and multi-phase fluid flow are fully-coupled processes in that pore pressure changes affect rock mechanical response and vice-versa, and that the two processes occur simultaneously. By contrasting Biot's equations and its discretization to the corresponding multiphase fluid flow equations used in reservoir simulations, it is shown that reservoir simulators neglect or simplify important geomechanical aspects that can have impact on reservoir productivity. This is attributed to the fact that the only rock mechanical parameter involved in reservoir simulations is pore compressibility. This parameter is not sufficient in representing aspects of rock behaviour such as stress path dependency and dilatancy, which require a full constitutive relation. Furthermore, the pore pressure changes due to the applied loads from the non-pay rock cannot be accounted for by simply adjusting the pore compressibility. Example problems are shown in order to illustrate the value of coupling geomechanics to reservoir simulators. Finally, the practical benefits of using coupled geomechanics and reservoir simulations are discussed. P. 439

In this research study, we conducted a coupled thermal-stress-fluid flow numerical model on the UTF Phase A SAGD project in order to investigate the fundamental geomechanical behaviour involved in the SAGD process, and to gain insight into the reservoir response to temperature and pore pressure changes. The numerical simulation is carried out by using a self-developed coupled finite element model which incorporates our proposed strain-induced permeability model. The obtained simulation results were compared with the measured data. Introduction Thermal recovery processes involve coupling between heat transfer, multiphase flow and stress/deformation, which has become an increasingly important subject in the petroleum field(1). Particularly, the coupling is crucial in problems such as borehole stability, hydraulic fracturing and injection/production induced deformation of the ground surface during the thermal recovery process in heavy oil or oil sand reservoirs. Numerical modelling of the coupled processes is historically carried out in the areas of geomechanics modelling and reservoir simulation. The former is to compute the stress-strain behaviour; therefore, the deformation. The latter is to essentially model the multiphase flow and heat transfer in porous media. Each of these disciplines simplifies the part of the problem that is not of primary interest. These approaches are unacceptable in situations where the coupling is strong and the changes of porosity and permeability cannot be accounted for by rock compressibility alone. Gutierrez and Lewis(2) extend Biot's theory to multiphase fluid flow in deformable porous media. Based on their formulation, they conclude that the coupling between the geomechanics and the multiphase flow occurs simultaneously. Thus, fully coupled system equations of deformations, multiphase flow and heat transfer should be solved simultaneously. Development of such kinds of fully coupled geomechanics-multiphase flow-heat transfer simulators needs tremendous effort, since the existing FEM geomechanics codes and FDM reservoir simulators cannot be used. Settari and Mourits(3) present an approach to couple the stress-strain behaviour to multiphase flow-heat transfer using porosity as a coupling parameter. The geomechanics module and the thermal reservoir simulator are used in a staggered manner. Pore pressure and temperature changes are calculated from the thermal reservoir simulator and transferred to the geomechanics module. The stress and the displacement changes are then calculated in the geomechanics simulation. An iterative algorithm is used to ensure that the porosity calculated from the geomechanics module is the same as that from the thermal reservoir simulator. The staggered technique employed to solve the coupled system equations allows for the use of the existing geomechanics codes in conjunction with a standard reservoir simulator. Currently, most of the commercial coupled geomechanics-multiphase flow-heat transfer simulators are developed in this way. The disadvantage of these kinds of coupled simulators is that the thermal reservoir module, usually developed using the finite difference method (FDM), cannot accommodate the full permeability tensor, since they adopt the standard discretization scheme, such as 5-spot for 2D problems and 7-spot for 3D problems. In this paper, the development of a coupled geomechanics-multiphase flow-heat transfer simulator using the finite element method (FEM) is described with the use of Galerkin's least squares (GLS) technique(4) to stabilize the saturation equation.

In this research study, we conducted a coupled thermalstress-fluid flow numerical modeling on the UTF Phase A SAGD project in order to investigate the fundamental geomechanical behavior involved in the SAGD process and to gain insight into the reservoir response to temperature and pore pressure changes. The numerical simulation is carried out using a self-developed coupled finite element model which incorporates our proposed strain-induced permeability model. The obtained simulation results were compared with the measured data. Introduction Thermal recovery processes involve coupling between heat transfer, multiphase flow and stress/deformation, which has become an increasingly important subject in the petroleum field(1). Particularly, the coupling is crucial in problems such as borehole stability, hydraulic fracturing and injection/production induced deformation of the ground surface during the thermal recovery processes in the heavy oil or oil sand reservoirs. Numerical modeling of the coupled processes is historically carried out in the areas of geomechanics modeling and the reservoir simulation. The former is to compute the stress-strain behavior, therefore the deformation; the latter is to essentially model the multiphase flow and heat transfer in porous media. Each of these disciplines simplifies the part of the problem that is not of primary interest. These approaches are unacceptable in situations where the coupling is strong and the changes of porosity and permeability cannot be accounted by rock compressibility alone. Gutierrez and Lewis(2) extend Biot's theory to multiphase fluid flow in deformable porous media. Based on their formulation, they conclude that the coupling between the geomechanics and the multiphase flow occurs simultaneously. Thus, fully coupled system equations of deformations, multiphase flow and heat transfer should be solved simultaneously. Development of such kinds of fully coupled geomechanics-multiphase flow-heat transfer simulators needs tremendous effort, since the existing FEM geomechanics codes and the FDM reservoir simulators cannot be used. Settari and Mourits(3) present an approach to couple the stress-strain behavior to multiphase flow, heat transfer using porosity as a coupling parameter. The geomechanics module and the thermal reservoir simulator are used in a staggered manner. Pore pressure and temperature changes are calculated from the thermal reservoir simulator and transferred to the geomechanics module. The stress and the displacement changes are then calculated in the geomechanics simulation. An iterative algorithm is used to ensure that the porosity calculated from the geomechanics module is the same as that from the thermal reservoir simulator. The staggered technique employed to solve the coupled system equations allows for the use of the existing geomechanics codes in conjunction with a standard reservoir simulator. Currently, most of the commercial coupled geomechanics-multiphase flow-heat transfer simulators are developed in this way. The disadvantage of these kinds of coupled simulators is that the thermal reservoir module, usually developed using finite difference method (FDM), cannot accommodate the full permeability tensor, since they adopt the standard discretization scheme such as 5-spot for 2-D problems and 7-spot for 3-D problems. In this paper, the development of a coupled geomechanicsmultiphase flow-heat transfer simulator using finite element method (FEM) is described with the use of the Galerkin's least squares (GLS) technique(4) to stabilized the saturation equation.

Reliable data input into the reservoir simulator of production-induced changes in matrix and fault permeabilities is essential for the successful planning and management of oil and gas reservoirs. Withdrawing and injecting fluid from/to the reservoir causes a change in pore pressure, which in turn, changes the three dimensional effective stress state. The stress path followed by the reservoir controls the evolution of the effective stress state, and with it the changes in deviatoric stresses which cause reservoir rock deformation and permeability changes. In order to allow for these effects, a new type of reservoir simulator – the stress-sensitive simulator – is required. This paper presents the results of a stress-sensitive simulation using a nonlinear finite element geomechanics model coupled to a finite difference fluid flow simulator, applied to a typical North Sea reservoir. This reveals the effects of dynamic changes in permeability and the reactivation of faults on the reservoir performance. In the 3D coupled field-sized reservoir model, the permeability of intact rock is stress sensitive; faults are represented by joint elements with a permeability which is strain sensitive. The stress path is recorded and the hysteresis effect is considered in an interface program to modify the permeability according to the current and previous stress states. The results show that the evolution of the stress state, captured as a stress path, significantly affects the oil production profile. The pressure recovery caused by injection may also be diminished by hysteresis. The results also show the spatial and temporal changes in stress state, which are useful data for the analysis and exploitation of production induced anisotropy in permeability, with particular reference to the location of by-passed oil.

Mobil plots normalized rates of penetration in real-time using its Drilling Data Center. Field results indicate that this technique reveals changes in lithology and pore pressure. It illustrates one way that the Drilling Data Center integrates computer based drilling technology into field operations. This technique differs from those previously reported in that: (1) A departmental computer collects, calculates, and displays real-time drilling information; (2) Normalized rate of penetration is correlated with conductivity for pore pressure prediction. Prudent use of this tool directly reduces cost per foot. Confidence that pore pressure changes will be quickly noticed encourges the operator to drill near-balance, which yields faster rates of penetration. This tool also provides the geologist with an excellent correlation tool when wireline logs are not run. This paper: (1) reviews normalized rate of penetration theory and its application with field results; (2) illustrates how the plot is obtained; (3) discusses predictions of lithology and pore pressure; and (4) discusses development plans.

How pore pressure changes affect stress and strain in fault zones with complex internal structure – Insights from hydromechanical modelling

The capability to monitor the enhanced oil recovery processes in heavy oil reservoirs by active or passive seismic methods provides valuable tools for the reservoir engineer to manage the recovery process. The seismic wave velocities (compressional and shear wave) in reservoir formations are strongly dependent on the formation's mechanical and thermal characteristics which are influenced by changes in temperature, pore pressure and stress slate. In order to analyze and understand lhe field seismic data, the influence of temperature, pore pressure and compressional and shear deformations on the seismic wave velocities must be known. A state-of-the-art laboratory testing system to determine these influences on seismic wave velocities has been developed and is described in this paper. The calibration oi the equipment and typical calibration results determined during the development of the apparatus are presented. Introduction Enhanced oil recovery (EOR) processes are used to extract bitumen and heavy oil from deeply buried heavy oil reservoirs by water or steam flooding, cyclic steam stimulation or fire flooding. The capability to monitor EOR processes by active or passive seismic methods provides new tools for the reservoir engineer to monitor the recovery development. Such monitoring allows the reservoir engineer to know when the recovery process should be altered and to modify the processes promptly. The strong dependence of seismic wave velocities in oil sand and heavy oil reservoir formations on the formation's mechanical and thermal characteristics make it possible to apply in situ seismic methods to track the progress of temperature fronts, flooded zones and fractures; and to assess the effectiveness of the thermally enhanced oil recovery processes. However, to allow these seismic monitoring methods to be used in situ, the influence of temperature, pore pressure, effective stress, compressional and shear deformations on the seismic wave velocities must be known. A comprehensive laboratory study is underway at the University of Alberta in geomechanics engineering to identify the effects of temperature, pore pressure, effective stress, porosity, volumetric changes, shearing, gas and liquid saturation on the seismic velocities. This research will provided important data to assist in the interpretation of field seismic survey results. The objective of this paper is to describe the development of laboratory equipment for the measurement of seismic velocities under controlled conditions of confining stress, shear stress and temperature. The calibration of the equipment and typical calibration results determined during the development of the apparatus are presented. Material Changes Affecting Seismic Wave Velocities Research by Tosaya et al. (1988); Wang (1989); Wang and Nur (1987, 1988, 1989, 1990) show that seismic wave velocities in oil sand and heavy oil bearing materials decrease significantly as the temperature increases. Other research by Agar (1984); Agar, Morgenstern and Scott (1989); Kosar (1989); Scott, Adhikary and Proskin (1991) show that during the recovery processes, stresses and deformations occur in the reservoir and adjacent strata which are caused by changes in pore pressures and temperature. These changes cause shearing and compressive deformations which can affect formation permeability and hydraulic fracturing.

The focus of the underlying research work is on the macroscopic modeling of unstable multiphase fluid flow in deformable porous media, where a lower‐viscous fluid is displaced by a more viscous fluid. This process leads to the formation of channel‐like networks, called viscous fingering. The instability effect is involved in a wide range of different fields in engineering. Some of the most common applications include carbon sequestration to store carbon dioxide (CO2) in underground reservoirs, contaminant transport in geostructures, in industrial processes, such as filtration, catalytic reactions, and in the operation of polymer electrolyte membrane fuel cells with multiphase flow in the gas diffusion layers. In this work, ideal miscible water–glycerin fluids are considered. It is assumed that the interacting fluids in the deformable porous media are incompressible. In addition, a dispersion–diffusion law is applied to capture the fluid–fluid interactions. The presence of a deformable porous material adds additional effects to the problem of the multiphase flow in porous media. The stresses in the porous solid matrix lead to changes in the porosity and influence the flow velocity of the fluids. To couple the deformable porous media with the multiphase flow, a macroscopic approach is used that relies on the theory of porous media. For the porous solid matrix, a linear elastic material model within small strains assumption is applied. The influence of the deformation‐dependent porosity on the instability is studied for 2D simulations, such as a multilayered geometry with different elastic parameters. The presented coupled nonlinear system of differential equations is simulated with the finite element method. Furthermore, a stabilization technique based on the quasi‐compressibility method is used.

<p><b>Increases in rainfall-induced landsliding following large earthquake are well documented but the time frames over which this heightened hazard persists in the land scape remains poorly understood. Whilst it is well known that the presence of failed and partially slopes after earthquakes significantly reduces the rainfall thresholds required to activate slope movement, their failure susceptibility during specific storms and how this changes through time remains poorly studied. To improve knowledge in this field requires well documented slope failures following earthquakes and a detailed understanding of their potential failure mechanisms when pore pressures are elevated in the slope. The 2016 Mw 7.8 Kaikōura earthquake provides a unique opportunity to study how rainfall events following the earthquake may impact the timing and mechanisms of landslide reactivation. </b></p><p>This study conducted a suite of specialist triaxial cell experiments, designed to replicate varying rainfall scenarios on remoulded samples collected from two sites where numerous earthquake-induced landslides were recorded in similar Late Cretaceous to Neogene sediments with similar physical properties (the Leader Dam Landslides (LDL) and the Limestone Hill landslide (LHL)). In each experiment rainfall events were simulated using a series of different pore pressure scenarios (increases and decreases in mean effective stress) at representative field stress conditions whilst monitoring material deformation behaviour. </p><p>The results demonstrate that both the deformation behaviour and pore pressure required to generate failure were influenced by the previous changes in pore pressure. Samples subjected to stepped increases in pore pressure were subject to greater pre-failure deformation (dilation) and subsequently failed at lower pore pressures (higher mean effective stress) when compared to samples subjected to linear increases in pore pressure. In addition, increases in the rate of pore pressure also increased the amount of pre-failure deformation allowing failure to occur when pore pressures were lower. In contrast a sample subjected to both increases and decreases in pore pressure underwent pre-failure densification and subsequently required a larger increase in pore pressure to fail. The results demonstrate that landslide reactivation is influenced by a number of factors including the amount and rate of previous changes in pore pressure and the slope drainage history. </p><p>The results provide new insights into why landslide susceptibility may remain elevated for prolonged periods of time (e.g. decades) in the landscape as well as why the rainfall thresholds for site specific failures during storms may be difficult to predict. </p>

Summary Accounting for poro-mechanical effects in full-field reservoir simulation studies and uncertainty quantification workflows is still limited, mainly because of their high computational cost. We introduce a new approach that couples hydrodynamics and poro-mechanics with dual-porosity flow diagnostics to analyze how poro-mechanics could affect reservoir dynamics in naturally fractured reservoirs without significantly increasing computational overhead. Our new poro-mechanically informed dual-porosity flow diagnostics account for steady-state and single-phase flow conditions in the fractured medium while the fracture-matrix fluid exchange is approximated using a physics-based transfer rate coefficient, which models two-phase flow using an analytical solution for spontaneous imbibition or gravity drainage. The deformation of the system is described by the dual-porosity poro-elastic theory, which is based on mixture theory and micromechanics to compute the effective stresses and strains of the rock matrix and fractures. The solutions to the fluid flow and rock deformation equations are coupled sequentially. The governing equations for fluid flow are discretized using a finite-volume method with two-point flux-approximation while the governing equations for poro-mechanics are discretized using the virtual element method. The solution of the coupled system considers stress-dependent permeabilities for fractures and matrix. Our framework is implemented in the open-source MATLAB Reservoir Simulation Toolbox (MRST). We present a case study using a fractured carbonate reservoir analog to illustrate the integration of poro-mechanics within the dual-porosity flow diagnostics framework. The extended flow diagnostics calculations enable us to quickly screen how the dynamics in fractured reservoirs (e.g., reservoir connectivity, sweep efficiency, and fracture-matrix transfer rates) are affected by the complex interactions between poro-mechanics and fluid flow where changes in pore pressure and effective stress modify petrophysical properties and hence affect reservoir dynamics. Because of the steady-state nature of the calculations and the effective coupling strategy, these calculations do not incur significant computational overheads. They provide an efficient complement to traditional reservoir simulation and uncertainty quantification workflows because they enable us to assess a broader range of reservoir uncertainties (e.g., geological, petrophysical, and hydromechanical uncertainties). The capability of studying a much broader range of uncertainties allows the comparison and ranking from a large ensemble of reservoir models and select individual candidates for more detailed full-physics reservoir simulation studies without compromising on assessing the range of uncertainties inherent to fractured reservoirs.

Injecting fluids in the crust, or their extraction, changes pore pressure and poroelastic stresses. Both pressure and stress changes can promote seismicity and, hence, the seismic events are called induced earthquakes. The filling of reservoirs on Earth’s surface can also induce earthquakes from some combination of surface loading and pore pressure changes. Attribution of any given earthquake to human activities, however, is not always straightforward. There remains debate about what controls the magnitude of induced earthquakes, the relative importance of pore pressure changes and poroelastic stresses, and how to best manage injection and extraction to minimize seismicity. As the scale and distribution of subsurface engineering expand globally, we should expect more and larger induced earthquakes in the future.

Understanding the risk associated with anthropogenic earthquakes is essential in the development and management of engineering processes and hydraulic infrastructure that may alter pore pressures and stresses at depth. The possibility of earthquakes triggered by reservoir impoundment, ocean tides, and hydrological events at the Earth surface (hydro-seismicity) has been extensively debated. The link between induced seismicity and hydrological events is currently based on statistical correlations rather than on physical mechanisms. Here, we explore the geomechanical conditions that could allow for small pore pressure changes due to reservoir management and sea level changes to propagate to depths that are compatible with earthquake triggering at critically-stressed faults (several kilometers). We consider a damaged fault zone that is embedded in a poroelastic rock matrix, and conduct fully coupled hydromechanical simulations of pressure diffusion and rock deformation. We characterize the hydraulic and geomechanical properties of fault zones that could allow for small pressure and loading changes at the ground surface (in the order of tens or hundreds of kPa) to propagate with relatively small attenuation to seismogenic depths (up to 10 km). We find that pressure diffusion to such depths is only possible for highly permeable fault zones and/or strong poroelastic coupling.

Pore pressures in the sediment were measured at two locations in the East Bay area of the Mississippi delta. These measurements showed the sediment to be highly under-consolidated with the effective stress approaching zero even at significant depths below the mudline. During storms the pore pressures exhibited cyclic response to the wave-induced bottom pressures. In at least two instances the pore pressures increased significantly during storms, which is probably indicative of major sub-bottom movements. Several different piezometers systems were utilized to make the pore pressure measurements. Each system is described in detail and the advantages and shortcomings of the systems with respect to measurements of pore pressures in the marine environment are presented. Analysis of the data leads to the conclusion that pore gas, rather than pore water, pressure was measured in most instances even though in one set of experiments high air entry stones were utilized to exclude gas from-the measuring system. Introduction The two projects known as SEASWAB I and SEASWAB II were aimed at studying sediment behavior in the Mississippi delta under the action of storm waves. Details of the projects have been discussed elsewhere1,2 and will not be repeated here. During both SEASWAB projects, pore pressures in the sediment were measured. These measurements were made to help determine the degree of consolidation in the sediments, and to detect gross subsurface movements. The rationale for the latter was that any significant subsurface slides or sediment collapse would be accompanied by a marked change in pore pressures. Further, it was anticipated that the pore pressures would exhibit a cyclic response to the wave-induced bottom pressures which have been hypothesized as a cause for sub-bottom movements in soft sediments3,4. The primary purpose of this paper is to describe the pore pressure measuring systems that have been used to accomplish these functions, to discuss the suitability of the various systems, and to present a preliminary analysis of the pore pressure results. Detailed analysis of the pore pressure data is still underway. Seaswab I SEASWAB I was initiated in September 1975 when several sensors were implanted in South Pass Block 28 in East Bay. Among the sensors installed were an accelerometer to measure mudline motions, a wave staff, and a bottom pressure transducer. However, the two systems of primary interest to this paper were probes for measuring pore pressures which were developed at Lehigh University and at the Atlantic Oceanographic and Marine Laboratory of NOAA in Miami, Florida. Devices used to measure pore pressures in soils are termed piezometers. They may range from a simple open stand pipe with a well point at the tip to the more sophisticated closed system utilizing an electronic pressure transducer. Closed system piezometers can be remotely read and if a hard system is utilized the response times to changes in pore pressures are very rapid.

Understanding the influence of CO2 injection on rock stress is one of the key elements to analyze CO2 Enhanced gas recovery and long-term CO2-storage in tight sand gas reservoirs. Producing natural gas from a reservoir and injecting CO2 to the tight reservoir causes a change in pore pressure, which in turn, changes the three-dimensional effective stress state that can result in reservoir rock deformation and permeability changes. In order to depict these effects, a new experiment and modeling method for CO2 flooding, considering the interaction between CO2 and rock is required. This paper presents a series of stress-sensitive experiments during CO2 flooding. A total of twenty sandstone rock samples, which include sandstones with natural fractures, shear fractures and artificial sanding crack fractures, were selected to study stress-sensitivity during gas production and CO2 flooding. Core flooding experiments were conducted using the following flow regime: depletion followed by CO2 injection. numerical simulations coupled with nonlinear geo-mechanic model with fluid flow were performed using the experimental data. The simulation results give a detailed understanding of the experimental geo-mechanic system. It is concluded that the experimental and simulation methods can be used in combination to evaluate the potential for stress changes during CO2 flooding in tight gas reservoirs. The results show that the evolution of the stress state, captured as a stress path, significantly affects the gas production profile and CO2 storage capability.

When implementing CO2 WAG EOR, fluid distribution and pore pressure in the reservoir vary. The interpretation of seismic reservoir monitoring for WAG-EOR often includes uncertainty in the changes obtained by time-lapse seismic surveys because these changes are the integration of effects by several factors. The objective of this study is to estimate the impact of each factor on elastic property and investigate a dominant factor through a rock physics study at a CO2 WAG site in Abu Dhabi. To estimate the effect of pore-pressure change on elastic velocity, an empirical relation between elastic velocity and confining pressure was used. Sonic velocity using core plug samples of the reservoir was measured under multiple confining pressures to construct empirical relations. As for the effect of fluid saturation changes on elastic velocity, we estimated it through Gassmann's equation. Realistic changes in pore pressure and saturations during the WAG operations were based on reservoir simulation results. Finally, based on the input petrophysical data and the relations from rock physics analyses, elastic property changes in WAG-EOR are estimated. Density and P-wave velocity (Vp) changes caused by the fluid substitution from oil to water are more significant than those by the substitution from oil to CO2. Pore pressure changes have less of an impact on Vp variations than does fluid substitution. Based on the estimation of elastic property changes associated with WAG operations, density changes are affected mainly by the increase in water saturation because of the density difference between water, oil and CO2. Vp changes seem to be consistent with the increase of gas (CO2) saturation. Even in the upper zone of the reservoir where oil is swept by both injected water and CO2, the effect of CO2 is prominent as well-known low gas saturation effects. Vp is significantly affected by the small amount of CO2 which was observed in the comparison of Vp with and without 10% of CO2 saturation in the rock. P-impedance changes are consistent with Vp changes because of the larger changes of Vp than the density changes. From these observations, the changes obtained by seismic reservoir monitoring would mainly represent the effect of CO2 saturation changes. We quantitatively looked into the impact that changes in pore pressure and saturation had changes on elastic properties such as density and elastic velocity. Furthermore, it was determined which elements predominately control changes in elastic properties when these changes occur simultaneously in WAG-EOR operations. These findings play an important role in the interpretation of seismic reservoir monitoring for WAG-EOR in Abu Dhabi.