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Summary Since the introduction of viscous/capillary concepts by Moore and Slobod (1956), several modifications and advancements have been made to the capillary number (Nc) so that it could have a better correlation with residual oil saturation (Sor) during enhanced oil recovery (EOR). In subsequent years, laboratory-scale studies have indicated that the viscoelastic polymers can influence the Sor reduction at relatively higher fluxes and Nc. Although the flux rate of at least 1 ft/D is reported to be needed for viscoelastic polymers to reduce Sor to a noticeable extent, significant Sor reductions were reported to occur only at higher fluxes that are likely to be seen in the reservoir closer to the wellbore. At similar levels of flux and Nc, the polymer solutions with significant elastic properties have shown higher Sor reduction than viscous polymer of similar shear rheology. However, the existing models used for correlating the polymer’s viscoelastic effect on Sor reduction relies on either core-scale Nc and/or the oscillatory Deborah number (De). De also has limitations in quantifying the polymer’s viscoelastic effects at different salinities. In this paper, a modified capillary number called an extensional capillary number (Nce) is developed using the localized pore-scale extensional viscosity. For viscoelastic polymer solutions, pore-scale apparent viscosity dominated by localized extensional viscosity is calculated to be significantly higher than core-scale apparent viscosity. We provide rheological insights using the variable-strain-rate concept to explain why and when the pore-scale apparent viscosity could become significantly higher, even at a flux of approximately 1 to 4 ft/D, and why it will not be reflected on the core-scale apparent viscosity or pressure drop. An exponential correlation was developed between Nce and Sor using the extensive coreflood experimental data sets extracted from various literature. Performance of Nce for predicting the viscoelastic polymer’s residual oil recovery is compared with conventional Nc, De, and a recent correlation. The results show that newly developed Nce can predict the Sor during polymer flooding for a wide range of operational and petrophysical conditions, including brine-salinity effects.

Summary In deep oil-sands deposits using the steam-assisted-gravity-drainage (SAGD) recovery process, real-time optimization (RTO) involves controlling optimum subcool to ensure steam conformance. Contemporary workflows use linear model predictive control (MPC) with oversimplified models that are inadequate to represent highly complex, spatially distributed, and nonlinear reservoir dynamics. In this research, two novel workflows using nonlinear MPC (NMPC) are proposed. The first workflow reduces an NMPC problem to linear MPC by estimating an equivalent linear model of a nonlinear black-box model in a mean-square-error sense. Another approach is to use nonlinear dynamic models explicitly for accurate prediction of the plant states and/or outputs. The resulting nonconvex, nonlinear cost optimization problem is solved using an interior-point algorithm at each control interval. Proposed workflows are tested using the history-matched, field-scale model of a SAGD reservoir located in northern Alberta, Canada. Qualitative and quantitative analysis of the results reveals that nonlinear black-box models based on system identification theory can successfully capture the nonlinearity of the SAGD process. Also, both workflows can control the subcool above the desired set-point while ensuring stable well operations. More than a 24% increment is achieved in net present value (NPV) using proposed NMPC workflows compared with the field operations with no closed-loop control. Overall, NMPC can successfully be used for improved RTO, energy efficiency, and greenhouse gas emissions while considering available surface facilities and well configurations.

Summary Several studies have tried to relate polymers’ enhanced oil recovery (EOR) potential to their viscoelastic characteristics such as onset, rheo thickening, extensional viscosity, and Deborah number (De). Contradictions prevail when it comes to reduction in residual oil saturation (Sor) during polymer flooding and the role of extensional properties. De calculated using the oscillatory relaxation time fails to explain the different pressure profiles exhibited by the viscous and viscoelastic polymers. Extensional viscosity has been ignored in many studies as the reason for additional Sor reduction based on the core-scale apparent viscosity and core-scale capillary number (Nc). In recent studies, a significant oil mobilization was shown by the viscoelastic polymers even before the critical Nc, which indicates that the capillary theory breaks out under specific conditions during polymer flooding. Moreover, the additional residual oil recovery caused by the high-salinity polymer solutions cannot be explained by the oscillatory De. In this paper, we compile and examine many such unresolved challenges from various literature with rheological and petrophysical insights. The uniaxial bulk extensional rheology is performed on the relevant polymers using a capillary breakup extensional rheometer to measure the extensional relaxation time, maximum extensional viscosity at the critical De, and strain hardening index. A detailed analysis signifies the role of extensional rheology on the viscoelastic onset, rheo thickening, and Sor reduction even under varying salinity conditions. The results also highlight the advantages of extensional rheology over oscillatory rheology and validate the capillary theory using modified capillary number.

Summary For heavy-oil-recovery applications, mobility control is more important than interfacial-tension reduction, and therefore importance should be given to the recovery of remaining mobile oil by enhanced sweep efficiency. Although the relative roles of polymer viscosity and elasticity in capillary-trapped residual light-oil recovery have been studied extensively, their roles in sweeping mobile viscous oil have not been explored. Injectivity is vital for heavy-oil-recovery applications, and polymer selection is performed solely using criteria that is based on shear rheology. In this paper, the influence of viscous (shear) resistance and elastic (extensional) resistance of viscoelastic polymer on mobile-heavy-oil recovery and injectivity is investigated through the combination of bulk shear/extensional rheology and single-phase and multiphase coreflood experiments at a typical reservoir-flooding rate of 1 ft/D. Two polymer solutions with different concentrations and salinities are selected such that a polymer with low molecular weight (MW) [hydrolyzed polyacrylamide (HPAM) 3130] provides higher shear resistance than a high-MW polymer (HPAM 3630). Extensional characterization of these two polymer solutions performed using a capillary breakup extensional rheometer revealed that HPAM 3630 provided higher extensional viscosity than HPAM 3130. The results show that the behaviors of polymers in extension and shear are completely different. Two multiphase and two single-phase experiments are conducted at low flux rate to investigate the roles of extensional viscosity on mobile-heavy-oil recovery and high flux rates on injectivity. After 1 pore volume (PV) of polymer injections, higher-concentration and lower-MW HPAM 3130 contributes to approximately 17% higher incremental recovery factor vs. lower-concentration and higher-MW HPAM 3630. The core-scale pressure drop generated by HPAM 3130 is more than twice the pressure drop generated by HPAM 3630. Under low-flux-rate conditions at the core scale, shear forces dominate, and displacing fluid with higher shear viscosity contributes to better sweep. HPAM 3630 exhibits a shear-thickening phenomenon and possesses the apparent viscosity of approximately 90 cp at the flux rate of approximately 90 ft/D. In contrast, HPAM 3130 continued showing shear thinning and has the apparent viscosity of approximately 70 cp at approximately 90 ft/D. This signifies the role of extension rheology on the injectivity at higher flux rates. Results revealed that while the extensional rheological role toward sweeping the mobile heavy-oil recovery at low flux is lesser compared with the shear role, its negative role on the polymer injectivity is very significant. Polymer-selection criteria for heavy-oil-recovery applications should incorporate extensional rheological parameters.

Summary Steam-assisted gravity drainage (SAGD) is a thermal-recovery process to produce bitumen from deep oil-sands deposits. The efficiency of the SAGD operation depends on developing a uniform steam chamber and maintaining an optimal subcool (difference in saturation and actual temperature) along the length of the horizontal well pair. Heterogeneity in reservoir properties might lead to suboptimal subcool levels without the application of closed-loop control. Recently, model-predictive control (MPC) has been proposed for real-time feedback control of SAGD well pairs based on real-time production, temperature, and pressure data along with other well and surface constraint information; however, reservoir dynamics has been represented using extremely simplified and unrealistic models. Because SAGD is a complex, spatially distributed, nonlinear process, an MPC framework with models that account for nonlinearity over an extended control period is required to achieve optimized subcool and steam conformance. In this research, two novel work flows are proposed to handle nonlinear reservoir dynamics in MPC. The first approach is adaptive MPC, and includes continuous re-estimation of the model at each control interval. This allows the evolution of the coefficients of a fixed-model structure such that the updated system-identification model in the MPC controller reflects current reservoir dynamics adequately. Another approach, gain-scheduled MPC, decomposes the subcool-control problem in a parallel manner, and uses a bank of multiple controllers rather than only one controller. This ensures effective control of the nonlinear reservoir system even in adverse control situations by using appropriate variations in input parameters based on the operating region. The work flows are implemented using a history-matched numerical model of a reservoir in northern Alberta. Steam-injection rates and liquid-production rate are considered input variables in MPC, constrained to available surface facilities. The well pair is divided into multiple sections, and the subcool of each section is considered an output variable. Results are compared with actual field data (in which no control algorithm is used), and are analyzed on the basis of two criteria: (1) Do all subcools track the set point while maintaining stability in input variables? and (2) Does the net present value (NPV) of oil improve with adaptive and gain-scheduled MPC? In general, we conclude that both adaptive and gain-scheduled MPC provide superior tracking of subcool set points and, hence, better steam conformance caused by adequate representation of reservoir dynamics by re-estimation of coefficients and multiple controllers, respectively. In addition, the results indicate stability in input parameters and improvement in economic performance. NPV is improved by 23.69 and 10.36% in case of adaptive and gain-scheduled MPC, respectively. The proposed work flows can improve the NPV of an SAGD reservoir by optimizing the well-operational parameters while considering constraints of surface facilities and minimizing environmental footprint.

Fractured reservoirs are highly heterogeneous and can be characterized by the probability distributions of fracture properties in a discrete fracture network model. The relationship between production performance and the fracture parameters is vastly nonlinear, rendering the process of adjusting model parameters to match both the static geological and dynamic production data challenging. This creates a need for a comprehensive history matching workflow for fractured reservoirs, which considers different local as well as global fracture parameters and leads to multiple equally-probable realizations of the discrete fracture network model parameters for uncertainty quantification. This paper presents an integrated approach for the history matching of fractured reservoirs. This new methodology includes generating multiple discrete fracture models, upscaling them for numerical multiphase flow simulation, and updating the fracture properties using dynamic flow responses such as continuous rate and pressure measurements. Available geological and tectonic information such as well-logs, seismic, and structural maps are incorporated into commercially available DFN modeling and simulation software to infer the probability distributions of relevant fracture parameters (including aperture, length, connectivity, and intensity) and to generate multiple discrete fracture network model realizations. The fracture models are further upscaled into an equivalent continuum dual-porosity model in the software using either analytical approaches or dynamic methods. The upscaled models are subjected to the flow simulation, and their production performances are compared to the true recorded responses. An automated history matching algorithm is implemented to reduce the uncertainties of the fracture properties. Components of vectors representing the principal flow directions and average fracture orientations are obtained by means of eigenvector decomposition of the permeability tensor and are optimized in the algorithm. In addition, both global fracture intensity and the local grid based intensity, which highly affect the fluid flow pattern and rate in different regions of the reservoir, are adjusted. A case study with various fracture sets is presented. The initial realizations were generated by means of Monte Carlo simulations, using the observed fractures at the well locations. Fracture intensity, orientation, and conductivity of different fracture sets were the uncertain parameters in our studies. Using the proposed methodology, parameters of different fracture sets were satisfactorily updated. Implementation of this automated history matching approach resulted in multiple equally probable discrete fracture network models and their upscaled flow simulation models that honor the geological information, and at the same time they match the dynamic production history.

Enhanced oil recovery (EOR) from heavy oil reservoirs is challenging. The higher viscosity of oil in such reservoirs, add more challenges and severe the difficulties during any EOR method (i.e. high mobility ratio, inadequate sweep, reservoir heterogeneity) compared to that of EOR from light oil reservoirs. Foam has gained interest as one of the EOR methods especially for challenging and heterogeneous reservoirs containing light oil. However, the foam and especially polymer enhanced foam (PEF) potential for heavy oil recovery is less studied. The current study aims to evaluate the performance of CO2 foam and CO2 PEF during heavy oil recovery from both unconsolidated (i.e. sandpack) and consolidate (rock sample) porous media with the help of fluid flow experiments. The injection pressure profile, oil recovery, and CO2 gas production were monitored and recorded to analyze and compare the performance of CO2 foam and PEF for heavy oil recovery. A visual sandpack made of glass column and a core-flood system capable of measuring the pressure at different sections of the core were used in this study. Homogenous and fractured sandstone core samples, as well as a fractured carbonate core sample, were selected for the core-flood study. Static stability results revealed slower liquid drainage and collapse rates for PEF compared to that of foam even in the presence of heavy crude oil. The addition of polymer significantly improved the performance of CO2 foam flooding during heavy oil recovery in dynamic experiments. This result was inferred from faster propagation rate, higher dynamic stability, and higher oil recovery of CO2 PEF over CO2 foam injection. Moreover, the visual analysis demonstrated more stable frontal displacement and higher sweep efficiency of PEF compared to the conventional foam flooding. In the fractured porous media, additional heavy oil recovery was obtained by liquid diversion into the matrix area rather than gas diversion inferred from pressure profile and gas production data. The results obtained from this study show that CO2 PEF could significantly improve the heavy oil recovery and CO2 sequestration, especially in homogeneous porous media.

Steam injection rate through life cycle optimization (e.g., the constant rate for a long period of time) could lead to the sub-optimal performance of a thermal heavy oil recovery process. On the other hand, finding the optimal steam injection strategy (policy) represents a major challenge due to the complex dynamic of the physical phenomenon, i.e., nonlinear, slow, high order, time-varying, and potentially highly heterogeneous reservoirs. To address this challenge, the problem can be formulated as an optimal control problem that has typically been solved using adjoint state optimization and a model-predictive control (MPC) strategy. In contrast, this work presents a reinforcement learning (RL) approach in which the mathematical model of the dynamic process (SAGD) is assumed unknown. An agent is trained to find the optimal policy only through continuous interactions with the environment (e.g., numerical reservoir simulation model). At each time step, the agent executes an action (e.g., increase steam injection rate), receives a reward (e.g., net present value) and observes the new state (e.g., pressure distribution) of the environment. During this interaction, an action-value function is approximated; this function will offer for a given state of the environment the action that will maximize total future reward. This process continues for multiple simulations (episodes) of the dynamic process until convergence is achieved. In this implementation, the state-action-reward-state-action (SARSA) online policy learning algorithm is employed in which the action-value function is continually estimated after every time step and further used to choose the optimal action. The environment consists of a reservoir simulation model built using data from a reservoir located in northern Alberta. The model consists of one well pair (one injector and one producer) and production horizon of 250 days (one episode) is considered. The state of the environment is defined as cumulative, oil and water production, and water injection and for each time step; three possible actions are considered, i.e., increase, decrease or no change of current steam injection rate; and the reward represents the net present value (NPV). Additionally, stochastic gradient descent is used to approximate the action-value function. Results show that the optimal steam injection policy obtained using RL implementation improves NPV by at least 30% with more than 60% lower computation cost.

The efficiency of a SAGD operation depends on developing a uniform steam chamber and maintaining an optimal subcool along the length of the well pair. Heterogeneity in reservoir properties may lead to suboptimal subcool levels. Recently, Model Predictive Control (MPC) based on the real-time production, temperature, and pressure data along with other well and surface constraint information has been proposed for a real-time feedback control of SAGD well pairs. Reservoir dynamics in MPC is represented using either linear step response model or one-dimensional ordinary differential equation. However, such simplified models are insufficient in MPC since SAGD is more complex and highly nonlinear process. Therefore, MPC framework that represents nonlinear behaviour of SAGD over an extended control period is required to achieve optimized subcool and steam conformance. In this research, two novel workflows are proposed to handle nonlinear reservoir dynamics in MPC. First approach known as Adaptive MPC includes recursive estimations at each control interval based on system identification theory. This allows evolution of the coefficients of a fixed model structure such that the updated system identification model in MPC controller reflects current reservoir dynamics adequately. Another approach, Gain-Scheduled MPC, decomposes the subcool control problem in a parallel manner and uses a bank of multiple controllers rather than only one controller. This ensures effective control of the nonlinear reservoir system even in adverse control situations by employing aggressive variations in input parameters. Suggested workflows are implemented using history-matched numerical model of a reservoir located in northern Alberta. Steam injection rates and liquid production rate are considered as input variables in MPC, constrained to available surface facilities. Well-pair is divided into multiple sections and subcool of each section is considered as an output variable. Optimum set-point for subcool is considered as 20°C. Results are compared with actual field data (in which no control algorithm is used) and analyzed based on two criteria: 1) Do all subcools track optimum set-point while maintaining stability in input variables and 2) Does net present value (NPV) of oil improve in case of Adaptive and Gain-Scheduled MPC? In general, we conclude that both Adaptive and Gain-Scheduled MPC provide superior tracking of subcool set-point and hence better steam conformance due to adequate representation of reservoir dynamics by recursive estimation of coefficients and multiple controllers. In addition, results indicate stability in input parameters and improvement in economic performance. NPV is improved by 23.69% and 10.36% in case of Adaptive and Gain-Scheduled MPC, respectively. Under current economic scenario, proposed workflows can improve the NPV of a SAGD reservoir by optimizing the well operational parameters while considering constraints of surface facilities and minimizing environmental footprints.