Summary The method of continuous gas lift has been commonly used in the oil industry to enhance production. Existing optimization models consider an approximate performance curve anchored by production test data, often disregarding reservoir uncertainty. We propose a robust optimization model that jointly considers the most recent data and an uncertainty set for the reservoir pressure, a critical parameter that is usually not measured precisely. As a result, we obtain what we call a “bow-tie” uncertainty set for the performance curves, in which the performance uncertainty increases when we move away from the production test’s operational point. We test our model with real data from an offshore oil platform and compare it against a fully deterministic model. We show superior out-of-sample performance for the robust model under different probability distributions of the reservoir pressure.

Summary Modern reservoir simulation must handle complex compositional fluid behavior, orders-of-magnitude variations in rock properties, and large velocity contrasts. We investigate how one can use nonlinear domain-decomposition preconditioning to combine sequential and fully implicit (FI) solution strategies to devise robust and highly efficient nonlinear solvers. A full simulation model can be split into smaller subdomains that each can be solved independently, treating variables in all other subdomains as fixed. In subdomains with weaker coupling between flow and transport, we use a sequential fully implicit (SFI) solution strategy, whereas regions with stronger coupling are solved with an FI method. Convergence to the FI solution is ensured by a global update that efficiently resolves long-range interactions across subdomains. The result is a solution strategy that combines the efficiency of SFI and its ability to use specialized solvers for flow and transport with the robustness and correctness of FI. We demonstrate the efficacy of the proposed method through a range of test cases, including both contrived setups to test nonlinear solver performance and realistic field models with complex geology and fluid physics. For each case, we compare the results with those obtained using standard FI and SFI solvers. This paper is published as part of the 2021 Reservoir Simulation Conference Special Issue.

Summary In this paper, we propose a fully implicit space-time multiscale scheme to improve computational efficiency in solving nonlinear multiphase flow in porous media. Here, error estimators are used for adaptively changing the spatial-temporal mesh. This algorithm applied to the black-oil model is compared to a standard control volume approach using a fine time and spatial mesh. Error estimators are introduced to determine subdomains of the reservoir in which high nonlinearity hinders Newtonian convergence. This is followed by applying local fine timesteps to these marked regions, whereas the remaining regions retain the coarse time scale. Once a temporal discretization is determined for different parts of the reservoir, the spatial mesh is refined for treating saturation fronts. The nonmatching interfaces arising from different temporal and spatial scales are resolved by the enhanced velocity method, which enforces strongly the continuity of fluxes. This whole system is solved monolithically. Results from a three-phaseblack-oil model are described. The multiscale solution is compared to a uniformly fine spatial mesh and fine timestepping solution to confirm accuracy. Solutions from both Gaussian and channelized permeability fields are presented. In the multiscale solution, we observe temporal refinements being applied to the water and gas saturation fronts by reducing the timestep size to guarantee Newtonian convergence. We also observe that the extent of refinements is balanced between the two saturation fronts based on their respective nonlinearity. For Gaussian permeability fields, the algorithm only treats saturation fronts spatially, whereas for channelized permeability fields, the geological features are also considered. Production profiles for the three phases match well between the two solutions under specific refinement criteria. We also investigate the improvement in computational efficiency, as well as the algorithm scalability in regard to increasing problem sizes. We observe a speedup of approximately 10 for solving the linear system, and such speedup increases as the problem size expands. In reservoir simulation, schemes that attempt to decouple the diffusion and advection process become less robust as the physics becomes more complex. Our approach, which is focused on handling the high nonlinearities, can be treated fully implicitly and provide a reduction in simulation costs. This approach can also be applied to model order reduction in providing accurate snapshot solutions. NOTE: This paper is published as part of the 2021 Reservoir Simulation Conference Special Issue.

Summary This work studies 1D steady-state flow of gas from compressible shale matrix subject to water blocking toward a neighboring fracture. Water blocking is a capillary end effect causing wetting phase (e.g., water) to accumulate near the transition from matrix to fracture. Hydraulic fracturing is essential for economical shale gas production. Water is frequently used as fracturing fluid, but its accumulation in the matrix can reduce gas mobility and production rate. Gas transport is considered at a defined pressure drop. The model accounts for apparent permeability (slip), compressibility of gas and shale, permeability reduction, saturation tortuosity (reduced relative permeability upon compaction), and multiphase flow parameters like relative permeability and capillary pressure, which depend on wettability. The behavior of gas flow rate and distributions of gas saturation, pressure, and permeability subject to different conditions and the stated mechanisms is explored. Water blockage reduces gas relative permeability over a large zone and reduces the gas flow rate. Despite gas flowing, strong capillary forces sustain mobile water over the entire system. Reducing drawdown gave lower driving force and higher resistance (by water blockage) for gas flow. The results show that 75% reduction of drawdown made the gas flow rate a couple orders of magnitude lower compared to if there was no blockage. The impact was most severe in more water-wetsystems. The blockage caused most of the pressure drop to occur near the outlet. High pressure in the rest of the system reduced effects from gas decompression, matrix compression, and slip-enhanced permeability, whereas rapid gradients in all these effects occurred near the outlet. Gas decompression resulted in an approximately 10 times higher Darcy velocity and pressure gradient near the outlet compared to inlet, which contributed to removing blockage, but the added resistance reduced the gas production rate. Similarly, higher gas Corey exponent associated gas flow with higher pressure drop. The result was less blockage but lower gas production. Slip increased permeability, especially toward the outlet, and contributed to increase in gas production by 16%. Significant matrix compression was associated with permeability reduction and increased Corey exponent in some examples. These effects reduced production and shifted more of the pressure drop toward the outlet. Upstream pressure was more uniform, and less compression and permeability reduction were seen overall compared to a system without water blockage.

Summary A deep learning framework, called the theory-guided convolutional neural network (TgCNN), is developed for efficient uncertainty quantification and data assimilation of reservoir flow with uncertain model parameters. The performance of the proposed framework in terms of accuracy and computational efficiency is assessed by comparing it to classical approaches in reservoir simulation. The essence of the TgCNN is to take into consideration both the available data and underlying physical/engineering principles. The stochastic parameter fields and time matrix comprise the input of the convolutional neural network (CNN), whereas the output is the quantity of interest (e.g., pressure, saturation, etc.). The TgCNN is trained with available data while being simultaneously guided by theory (e.g., governing equations, other physical constraints, and engineering controls) of the underlying problem. The trained TgCNN serves as a surrogate that can predict the solutions of the reservoir flow problem with new stochastic parameter fields. Such approaches, including the Monte Carlo (MC) method and the iterative ensemble smoother (IES) method, can then be used to perform uncertainty quantification and data assimilation efficiently based on the TgCNN surrogate, respectively. The proposed paradigm is evaluated with dynamic reservoir flow problems. The results demonstrate that the TgCNN surrogate can be built with a relatively small number of training data and even in a label-free manner, which can approximate the relationship between model inputs and outputs with high accuracy. The TgCNN surrogate is then used for uncertainty quantification and data assimilation of reservoir flow problems, which achieves satisfactory accuracy and higher efficiency compared with state-of-the-art approaches. The novelty of the work lies in the ability to incorporate physical laws and domain knowledge into the deep learning process and achieve high accuracy with limited training data. The trained surrogate can significantly improve the efficiency of uncertainty quantification and data assimilation processes. NOTE: This paper is published as part of the 2021 Reservoir Simulation Conference Special Issue.

Summary As the crucial step in closed-loop reservoir management, robust life-cycle production optimization is defined as maximizing/minimizing the expected value of a predefined objective (cost) function over geological uncertainties (i.e., uncertainties in the reservoir permeability, porosity, endpoint relative permeability, etc.). However, with robust optimization, there is no control over downside risk defined as the minimum net present value (NPV) among the individual NPVs of the different reservoir models. Yet, field operators generally wish to keep this minimum NPV reasonably large to try to ensure that the reservoir is commercially viable. In addition, the field operator may desire to maximize the NPV of production over a much shorter time period than the life of the reservoir under the limitation of surface facilities (e.g., field liquid and water production rates). Thus, it is important to consider multiobjective robust production optimization with nonlinear constraints and when geological uncertainties are incorporated. The three objectives considered in this paper are; to maximize the average life-cycle NPV, to maximize the average short-term NPV, and to maximize the minimum NPV of the set of realizations. Generally, these objectives are in conflict; for example, the well controls that give a global maximum for robust life-cycle production optimization do not usually correspond to the controls that maximize the short-term average NPV of production. Moreover, handling the nonlinear state constraints (e.g., field liquid production rates and field water production rates for the bottom-hole pressure controlled producers in the robust production optimization) is also a challenge because those nonlinear constraints should be satisfied at each control steps for each geological realization. To provide potential solutions to the multiobjective robust optimization problem with state constraints, we developed a modified lexicographic method with a minimizing-maximum scheme to attempt to obtain a set of Pareto optimal solutions and to satisfy all nonlinear constraints. We apply the sequential quadratic programming filter with modified stochastic gradients to solve a sequence of optimization problems, where each solution is designed to generate a single point on the Pareto front. In the modified lexicographic method, the objective is always considered to be the primary objective, and the other objectives are considered by specifying bounds on them to convert them to state constraints. The temporal damping and truncation schemes are applied to improve the quality of the stochastic gradient on nonlinear constraints, and the minimizing–maximum procedure is applied to enforce constraints on the normal state constraints. The main advantage that the modified lexicographic method has over the standard lexicographic method is that it allows for the generation of potential Pareto optimal points, which are uniformly spaced in the values of the second and/or third objective that one wishes to improve by multiobjective optimization.

Summary Gas kicks occur frequently in deepwater drilling because of the extremely narrow mud-weight window [minimum 0.01 specific gravity (sg)]. The traditional kick-detection method mainly relies on the driller's analysis of monitored compound comprehensive mud-logging data. However, the traditional method has significant time lag, including missed and false detection, and often leads to severe gas influxes during deepwater drilling. A novel machine-learning (ML) model is presented here using pilot-scale rig data combined with surface-riser-downhole monitoring for gas-kick early detection and risk classification. A series of pilot-scale test-well experiments (a total of 108 tests) are performed to simulate deepwater gas kicks and produce a multisource data set through fusion of comprehensive mud-logging data from surface monitoring, acoustic data from riser-monitoring technologies, and measurement-while-drilling data [e.g., bottomhole pressure (BHP)] from downhole monitoring technologies. During these experiments, the deepwater blowout preventer (BOP) is simulated using a variable cross section of crossover (X/O; equipped with booster-flow pipes); the Coriolis flowmeter is installed in the mud-return pipe to accurately measure flow out; the acoustic wave sensors are installed outside of the riser section (X/O) to monitor gas migration; and the downhole memory pressure gauges are installed to monitor BHP. Next, data preparation and data analysis are performed including raw-data exploration, data cleaning, signal/noise-ratio (SNR) analysis, feature scaling, outlier detection, and feature engineering. Further, a novel and improved data-labeling criterion for gas-kick alarms is proposed, with six levels (displayed using different colors) instead of two-state alarms (“kick” or “no kick”). The proposed gas-kick-alarm classification is in accordance with the actual field practices. Subsequently, four ML algorithms—decision tree (DT), k -nearest neighbors (KNN), support vector machine (SVM), and long short-term memory (LSTM)—are developed through the complete workflow, beginning with the data allocation and followed by building, evaluation, and optimization of each ML model. Because the LSTM recurrent neural network (RNN) algorithm showed the best performance, it is selected and deployed to early detect gas kicks and classify the corresponding kick alarms. The recall for gas-kick levels corresponding to Risk 0, Risk 1, Risk 2, Risk 3, Risk 4, and Risk 5 are 0.92, 0.93, 0.91, 0.91, 0.92 and 0.92, respectively. Because recall for each gas-kick-alarm level is greater than 0.9, it ensures rare false negatives (FNs) during kick detection. The accuracy, precision, recall, and f 1 score of the deployed LSTM model in the testing data set is 91.6%, 0.93, 0.92 and 0.92, respectively. Further, the detection time delay is approximately 2 to 7 seconds only, which provides an improved time margin to take appropriate safety measures, promptly deal with a gas kick through a well-control program, and prevent a potential blowout during deepwater drilling.

Summary We studied the applicability of a gradient-boosting machine-learning (ML) algorithm for forecasting of oil and total liquid production after hydraulic fracturing (HF). A thorough raw data study with data preprocessing algorithms was provided. The data set included 10 oil fields with more than 2,000 HF events. Each event has been characterized by well coordinates, geology, transport and storage properties, depths, and oil/liquid rates before fracturing for target and neighboring wells. Each ML model has been trained to predict monthly production rates right after fracturing and when the flows are stabilized. The gradient-boosting method justified its choice with R 2 being approximately 0.7 to 0.8 on the test set for oil/total liquid production after HF. The developed ML prediction model does not require preliminary numerical simulations of a future HF design. The applied algorithm could be used as a new approach for HF candidate selection based on the real-time state of the field.

Summary A physics-based data-driven model is proposed for forecasting of subsurface energy production. The model fully relies on production data and does not require any in-depth knowledge of reservoir geology or governing physics. In the proposed approach, we use the Delft Advanced Reservoir Terra Simulator (DARTS) as a workhorse for data-driven simulation. DARTS uses an operator-based linearization technique that exploits an abstract interpretation of physics benefiting computational performance. The physics-based data-driven model is trained to fit data increasing the fidelity of the model forecast and reflecting significant changes in reservoir dynamics or physics over its history. The model is examined and validated for both synthetic and real field production data. We demonstrate that the developed approach is capable of providing accurate and reliable production forecast on a daily basis, even if the exact geological information is not available.

Summary Decline curve analysis (DCA) has been the mainstay in unconventional reservoir evaluation. Because of the extremely low matrix permeability, each well is evaluated economically for ultimate recovery as if it were its own reservoir. Classification and normalization of well potential is difficult because of ever-changing stimulation total contact area and a hyperbolic curve fit parameter that is disconnected from any traditional reservoir characterization descriptor. A new discrete fracture model approach allows direct modeling of inflow performance in terms of fracture geometry, drainage volume shape, and matrix permeability. Running such a model with variable geometrical input to match the data in lieu of standard regression techniques allows extraction of a meaningful parameter set for reservoir characterization, an expected outcome from all conventional well testing. Because the entirety of unconventional well operation is in transient mode, the discrete fractured well solution to the diffusivity equation is used to model temporal well performance. The analytical solution to the diffusivity equation for a line source or a 2D fracture operating under constrained bottomhole pressure consists of a sum of terms, each with exponential damping with time. Each of these terms has a relationship with the constant rate, semisteady-state solution for inflow, although the well is not operated with constant rate, nor will this flow regime ever be realized. The new model is compared with known literature models, and sensitivity analyses are presented for variable geometry to illustrate the depiction of different time regimes naturally falling out of the unified diffusivity equation solution for discrete fractures. We demonstrate that apparent hyperbolic character transitioning to exponential decline can be modeled directly with this new methodology without the need to define any crossover point. The mathematical solution to the physical problem captures the rate transient functionality and any and all transitions. Each exponential term in the model is related to the various possible interferences that may develop, each occurring at a different time, thus yielding geometrical information about the drainage pattern or development of fracture interference within the context of ultralow matrix permeability. Previous results analyzed by traditional DCA can be reinterpreted with this model to yield an alternate set of descriptors. The approach can be used to characterize the efficacy of evolving stimulation practices in terms of geometry within the same field and thus contribute to the current type curve analyses subject to binning. It enables the possibility of intermixing of vertical and horizontal well performance information as simply gathering systems of different geometry operating in the same reservoir. The new method will assist in reservoir characterization and evaluation of evolving stimulation technologies in the same field and allow classification of new type curves.

Summary Organic matters in source rocks store oil in significantly larger volume than that based on its pore volume (PV) due to so-called nanoconfinement effects. With pressure depletion and production, however, oil recovery is characteristically low because of the low compressibility of the fluid and amplified interaction with pore surface in the nanoporous material. For the additional recovery, CO 2 injection has been widely adopted in shale gas and tight oil recovery over the last decades. But its supply and corrosion are often pointed out as drawbacks. In this study, we propose ethane injection as an alternative enhanced oil recovery (EOR) strategy for more productive oil production from tight unconventional reservoirs. Monte Carlo (MC) molecular simulation is used to reconstruct molecular configuration in pores under reservoir conditions. Further, molecular dynamics (MD) simulation provides the basis for understanding the recovery mechanism of in-situ fluids. These enable us to estimate thermodynamic recovery and the free energy associated with dissolution of injected gas. Primary oil recovery is typically below 15%, indicating that pressure depletion and fluid expansion are no longer effective recovery mechanisms. Ethane injection shows 5 to 20% higher recovery enhancement than CO 2 injection. The superior performance is more pronounced, especially in nanopores, because oil in the smaller pores is richer in heavy components compared to the bulk fluids, and ethane molecules are more effective in displacing the heavy hydrocarbons. Analysis of the dissolution free energy confirms that introducing ethane into reservoirs is more favored and requires less energy for the enhanced recovery.

Summary The analysis of gas production from fractured ultralow-permeability (ULP) reservoirs is most often accomplished using numerical simulation, which requires large 3D grids, many inputs, and typically long execution times. We propose a new hybrid analytical/numerical method that reduces the 3D equation of gas flow into either a simple ordinary-differential equation (ODE) in time or a 1D partial-differential equation (PDE) in space and time without compromising the strong nonlinearity of the gas-flow relation, thus vastly decreasing the size of the simulation problem and the execution time. We first expand the concept of pseudopressure of Al-Hussainy et al. (1966) to account for the pressure dependence of permeability and Klinkenberg effects, and we also expand the corresponding gas-flow equation to account for Langmuir sorption. In the proposed hybrid partial transformational decomposition method (TDM) (PTDM), successive finite cosine transforms (FCTs) are applied to the expanded, pseudopressure-based 3D diffusivity equation of gas flow, leading to the elimination of the corresponding physical dimensions. For production under a constant- or time-variable rate ( q ) regime, three levels of FCTs yield a first-order ODE in time. For production under a constant- or time-variable pressure ( p wf ) regime, two levels of FCTs lead to a 1D second-order PDE in space and time. The fully implicit numerical solutions for the FCT-based equations in the multitransformed spaces are inverted, providing solutions that are analytical in 2D or 3D and account for the nonlinearity of gas flow. The PTDM solution was coded in a FORTRAN95 program that used the Laplace-transform (LT) analytical solution for the q -problem and a finite-difference method for the p wf problem in their respective multitransformed spaces. Using a 3D stencil (the minimum repeatable element in the horizontal well and hydraulically fractured system), solutions over an extended production time and a substantial pressure drop were obtained for a range of isotropic and anisotropic matrix and fracture properties, constant and time-variable Q and p wf production schemes, combinations of stimulated-reservoir-volume (SRV) and non-SRV subdomains, sorbing and nonsorbing gases of different compositions and at different temperatures, Klinkenberg effects, and the dependence of matrix permeability on porosity. The limits of applicability of PTDM were also explored. The results were compared with the numerical solutions from a widely used, fully implicit 3D simulator that involved a finely discretized (high-definition) 3D domain involving 220,000 elements and show that the PTDM solutions can provide accurate results for long times for large well drawdowns even under challenging conditions. Of the two versions of PTDM, the PTD-1D was by far the better option and its solutions were shown to be in very good agreement with the full numerical solutions, while requiring a fraction of the memory and orders-of-magnitude lower execution times because these solutions require discretization of only the time domain and a single axis (instead of three). The PTD-0D method was slower than PTD-1D (but still much faster than the numerical solution), and although its solutions were accurate for t < 6 months, these solutions deteriorated beyond that point. The PTDM is an entirely new approach to the analysis of gas flow in hydraulically fractured ULP reservoirs. The PTDM solutions preserve the strong nonlinearity of the gas-flow equation and are analytical in 2D or 3D. This being a semianalytical approach, it needs very limited input data and requires computer storage and computational times that are orders-of-magnitude smaller than those in conventional (numerical) simulators because its discretization is limited to time and (possibly) a single spatial dimension.

Summary The steam-assisted gravity drainage (SAGD) recovery process is strongly impacted by the spatial distributions of heterogeneous shale barriers. Though detailed compositional flow simulators are available for SAGD recovery performance evaluation, the simulation process is usually quite computationally demanding, rendering their use over a large number of reservoir models for assessing the impacts of heterogeneity (uncertainties) to be impractical. In recent years, data-driven proxies have been widely proposed to reduce the computational effort; nevertheless, the proxy must be trained using a large data set consisting of many flow simulation cases that are ideally spanning the model parameter spaces. The question remains: is there a more efficient way to screen a large number of heterogeneous SAGD models? Such techniques could help to construct a training data set with less redundancy; they can also be used to quickly identify a subset of heterogeneous models for detailed flow simulation. In this work, we formulated two particular distance measures, flow-based and static-based, to quantify the similarity among a set of 3D heterogeneous SAGD models. First, to formulate the flow-based distance measure, a physics-based particle-tracking model is used: Darcy’s law and energy balance are integrated to mimic the steam chamber expansion process; steam particles that are located at the edge of the chamber would release their energy to the surrounding cold bitumen, while detailed fluid displacements are not explicitly simulated. The steam chamber evolution is modeled, and a flow-based distance between two given reservoir models is defined as the difference in their chamber sizes over time. Second, to formulate the static-based distance, the Hausdorff distance (Hausdorff 1914) is used: it is often used in image processing to compare two images according to their corresponding spatial arrangement and shapes of various objects. A suite of 3D models is constructed using representative petrophysical properties and operating constraints extracted from several pads in Suncor Energy’s Firebag project. The computed distance measures are used to partition the models into different groups. To establish a baseline for comparison, flow simulations are performed on these models to predict the actual chamber evolution and production profiles. The grouping results according to the proposed flow- and static-based distance measures match reasonably well to those obtained from detailed flow simulations. Significant improvement in computational efficiency is achieved with the proposed techniques. They can be used to efficiently screen a large number of reservoir models and facilitate the clustering of these models into groups with distinct shale heterogeneity characteristics. It presents a significant potential to be integrated with other data-driven approaches for reducing the computational load typically associated with detailed flow simulations involving multiple heterogeneous reservoir realizations.

Summary In the next decades, tens of thousands of well plugging and abandonment (P&A) operations are expected to be executed worldwide. Decommissioning activities in the North Sea alone are forecasted to require 2,624 wells to be plugged and abandoned during the 10-year period starting from 2019 ( Oil&Gas_UK 2019 ). This increase in decommissioning activity level and the associated high costs of permanent P&A operations require new, fit-for-purpose, P&A design tools and operational technologies to ensure safe and cost-effective decommissioning of hydrocarbon production wells. This paper introduces a novel modeling framework to support risk-based evaluation of well P&A designs using a fluid-flow simulation methodology combined with probabilistic estimation techniques. The developed well-centric modeling framework covers the full range of North Sea P&A well designs and allows for quantification of the long-term (thousands of years) evolution of hydrocarbon movement in the plugged and abandoned well. The framework is complemented by an in-house visualization tool for identification of the dominant hydrocarbon flow-paths. Monte Carlo methods are used to account for uncertainties in the modeling inputs, allowing for robust comparison of various P&A design options, which can be ranked on the basis of hydrocarbon leakage risks. The proposed framework is able to model transient conditions within the well P&A system, allowing for the development of new key performance indicators (e.g., time until hydrocarbons reach surface and changes in hydrocarbon saturation within the P&A well). Such key performance indicators are not commonly used, because most published work in this area relies on steady-state P&A models. The developed framework was used in the assessment of several P&A design cases. The results obtained, which are presented in this paper, demonstrate its value for supporting risk-based decision-making by allowing for quantitative comparison of the expected performance of multiple P&A design options for given well/reservoir conditions. The framework can be used for identifying cost-effective, fit-for-purpose P&A designs, for example by optimizing the number, location, and length of wellbore barriers and evaluating the effectiveness of annular cement sheath remedial operations. Additionally, this framework can be used as a sensitivity analysis tool to identify the critical parameters that have the greatest impact on the modeled leakage risks, to guide data acquisition plans and model refinement steps aimed at reducing the uncertainties in key model parameters.

Summary Decline curve analysis (DCA) has been widely applied in production forecasting of wells in unconventional hydrocarbon reservoirs. However, traditional curve-fit-based methods fall short of forecast accuracy due to three weaknesses: first, they cannot capture the reservoir signals not modeled by the underlying DCA model formulas; second, when predicting the production of a target well, the production history of other wells in the geologic formation (which is valuable information) is not considered; third, the wells’ geographic, geologic, wellbore, well spacing, and completion properties, which are highly relevant to production capability, are not used. More recent approaches have begun replacing traditional DCA with machine-learning methods [e.g., random forest (RF), support vector regression (SVR), etc.] for production forecast. Nevertheless, these methods are still suboptimal in detecting similar production trends in different wells, leading to large forecast error. A new and simple method called dynamic production rescaling (DPR) is developed to improve the accuracy of machine-learning DCA (ML-DCA). By combining DPR with common ML-DCA methods, we observe that the error mean, deviation, and skewness can be significantly reduced by 15 to 35% compared with ML-DCA without DPR. The error reduction is 30 to 60% compared with automatic curve fit of the traditional modified Arps DCA model. DPR has been tested successfully on monthly production data of over 20,000 unconventional horizontal wells in the Permian and Appalachian basins for both long- and short-term forecasts. The significant error reduction is consistent across different basins and formations. DPR is computationally efficient, so a large number of wells can be analyzed automatically and quickly. Moreover, the effectiveness and efficiency of DPR is independent of the underlying machine-learning algorithm, further demonstrating its robustness.

Summary Because of complex chemical reactions and multiphase flow physics, the displacement front stability for in-situ combustion (ISC) enhanced oil recovery (EOR) processes are not well understood. In this work, theory and numerical simulation validation are presented to establish an analytical frontal stability criterion for ISC processes. First, the four influencing factors for ISC displacement stability are analyzed: viscous force, heat conduction, matrix permeability changes caused by coke deposition, and gravity. A thorough analysis of the different zones and displacement fronts in a typical ISC process is conducted, and the most unstable front with the strongest tendency for gravity override is identified. Second, analytical solutions for judging the frontal stability and gravity override are established. Third, numerical reservoir simulation is performed to study the frontal stability and gravity override to validate the analytical theory. Carefully selected numerical schemes, as well as spatial and temporal discretization, are used to ensure the accuracy of these simulations. The four major zones and three displacement fronts (combustion front, leading edge of steam plateau, and oil bank leading edge) are identified in a typical 1D ISC process. The most unstable front with the largest pressure gradient contrast is the leading edge of the steam plateau. Gravity override also first takes place here with large fluid density differences across the front. By establishing material and energy balances and solving the wavy perturbation of the steam front, an analytical equation for deciding the ISC flood front stability in a 2D horizontal plane is achieved. Furthermore, the analytical solution for ISC gravity override is established. In numerical simulations, we are able to obtain results with sufficient accuracy to capture unstable ISC displacements and show fingering behavior under different conditions. The matrix permeability reduction caused by coke deposition has minimal impact on frontal stability. The simulation results are successfully validated with the analytical work for conditions in which the ISC process is stable or unstable and also for the degree of ISC gravity override. This demonstrates the predictive capability of the analytical method. In summary, a theoretical framework to analyze whether the displacement front of an ISC process is stable or not has been established. Numerical simulations confirm its predictive capability. This serves as a new reservoir engineering tool to aid the implementation and design of practical ISC projects.

Summary Double-porosity/naturally fractured reservoir models have traditionally been used to represent the flow and pressure behavior for highly fractured carbonate reservoirs. Given that unconventional reservoirs such as shale-oil/gas reservoirs might not be considered to be multiporosity media, the use of the traditional/classical “double-porosity” models might not be adequate (or appropriate). The recent development of anomalous diffusion models has opened the possibility of adapting double-porosity models to estimate reservoir (and related) parameters for unconventional reservoirs. The primary objective of this work is to develop and demonstrate analytical reservoir models that provide (possible) physical explanations for the anomalous diffusion phenomenon. The models considering anomalous diffusion in reservoirs with Euclidean shape are developed using a convolved (i.e., time-dependent) version of Darcy's law. The use of these models can yield a power-law (straight-line) behavior for the pressure and/or rate performance, similar to the fractal reservoir models. The main advantage of using anomalous diffusion models compared with models considering fractal geometry is the reduction from two parameters (i.e., the fractal dimension and the conductivity index) to only one parameter (i.e., the anomalous diffusion exponent). However, the anomalous diffusion exponent does not provide information regarding the geometry or spatial distribution of the reservoir properties. To provide an alternative explanation for the anomalous diffusion phenomenon in petroleum reservoirs, we have developed double-porosity models considering matrix blocks with fractal geometry and fracture networks with either radial or fractal fracture networks. The flows inside the matrix blocks and the fractal fracture network assume that Darcy’s law is valid in its space-dependent (fractal) form, whereas the classical version of Darcy’s law is assumed for the radial-fracture-network case. The transient interporosity transfer is modeled using the classical convolution schemes given in the literature. We have defined the matrix blocks to be “infinite-acting” to represent the nano/micropermeability of shale reservoir. For the system defined by a fractal fracture network and infinite-acting fractal matrix blocks, we have investigated the influence of the fractal parameters (both matrix and fracture network) in the pressure- and rate-transient performance behaviors. We have defined the flow periods that can be observed in these sorts of systems and we have developed analytical solutions for pressure-transient analysis. We demonstrate that the use of the convolved version of Darcy’s law results in a model very similar to the diffusivity equation for double-porosity systems (which incorporates transient interporosity flow). In performing this work, we establish the following observations/conclusions derived from our new solutions: We find that the assumption of a well producing at variable rate (time-dependent inner-boundary condition) has a more-significant effect on the pressure (and derivative) functions and obscures the effects of the properties of the reservoir. We demonstrate that the anomalous-diffusion-phenomena model proposed for unconventional reservoirs can be directly related to the multiporosity concept model. Pressure and pressure-derivative responses can be used in the diagnosis of flow periods and in the evaluation/estimation of reservoir parameters in unconventional reservoirs.

Summary To determine the effect on oil recovery and carbon dioxide (CO 2 ) storage, laboratory experiments are run with various fractions of CO 2 injected (FCI): pure CO 2 injection (FCI = 1), water-saturated CO 2 (wsCO 2 ) injection (FCI = 0.993), simultaneous water and gas (SWAG) (CO 2 ) injection (FCI = 0.75), carbonated water injection (CWI) (FCI = 0.007), and water injection (FCI = 0). All experiments are performed on Bentheimer sandstone cores at 70°C and 11.7 MPa (1,700 psia). The oil phase is composed of 65% hexane and 35% decane by molar fraction. Before any fluid is injected, the core is filled with oil and irreducible water. Pressure difference across the core and production rate of gas are measured during the experiment. The collected produced fluids are analyzed in a gas chromatograph to determine their composition. Cumulative oil recovery after injection is found to be 78 to 83% for wsCO 2 , 78% for SWAG, 74% for pure CO 2 , 53% for CWI, and 35% for water. Net CO 2 stored is also found to be the highest for wsCO 2 (59 to 65% of the pore volume), followed by that for CO 2 injection (56%) and that for SWAG (42%). These results suggest that wsCO 2 injection might outperform pure CO 2 injection at both oil recovery and net CO 2 stored.

Summary With the increasing application of distributed temperature sensing (DTS) in downhole monitoring for multifractured horizontal wells (MFHWs), well performance interpretation by inversing DTS data has become a popular topic around the world. However, because of the lack of efficient inversion models, great challenges still exist in interpreting flow rate profiles and fracture parameters for MFHWs in unconventional gas reservoirs from DTS data. In this paper, a robust inversion system is developed to interpret flow rate profiles and fracture parameters for MFHWs in unconventional gas reservoirs by inversion of DTS data. A temperature prediction model serves as a forward model to simulate the temperature behaviors of MFHWs. A new inversion model based on a simulated annealing (SA) algorithm is proposed to find inversion solutions to flow rate profiles and fracture parameters. The simulated results of temperature behaviors indicate that the temperature profile of each MFHW is irregularly serrated, and the temperature drop in each serration is positively correlated with the inflow rate and fracture half-length. These results provide an excellent method to identify and locate effective hydraulic fractures for field MFHWs. Because of the far more significant influence of fracture half-length than conductivity on a temperature profile, fracture half-length was chosen as the inversion target parameter when performing the inversion of DTS data for MFHWs. Then a synthetic inversion task was accomplished using the SA algorithm-based inversion system, and it took only 110 iterations to reach the target inversion accuracy (10 −6 level). Real-time inversion error distributions indicate that this novel inversion system shows great advantages in computational efficiency. Finally, a field application in a shale gas reservoir is presented to validate the reliability of the new inversion model. Based on accurate identification of effective fractures from DTS profiles, satisfactory inversion solutions (the maximum temperature deviation of less than 0.03 K) are obtained. The absolute error of the inversed gas production rate is less than 4 m 3 /d. The SA algorithm‐based inversion system proves reliable to interpret flow rate profiles and fracture parameters, which is a great help to postfracturing evaluation and productivity improvement for MFHWs in unconventional gas reservoirs.

Summary Production optimization led by computing intelligence can greatly improve oilfield economic effectiveness. However, it is confronted with huge computational challenge because of the expensive black-box objective function and the high-dimensional design variables. Many low-fidelity methods based on simplified physical models or data-driven models have been proposed to reduce evaluation costs. These methods can approximate the global fitness landscape to a certain extent, but it is difficult to ensure accuracy and correlation in local areas. Multifidelity methods have been proposed to balance the advantages of the two, but most of the current methods rely on complex computational models. Through a simple but efficient shortcut, our work aims to establish a novel production-optimization framework using genetic transfer learning to accelerate convergence and improve the quality of optimal solution using results from different fidelities. Net present value (NPV) is a widely used standard to comprehensively evaluate the economic value of a strategy in production optimization. On the basis of NPV, we first established a multifidelity optimization model that can synthesize the reference information from high-fidelity tasks and the approximate results from low-fidelity tasks. Then, we introduce the concept of relative fidelity as an indicator for quantifying the dynamic reliability of low-fidelity methods, and further propose a two-mode multifidelity genetic transfer learning framework that balances computing resources for tasks with different fidelity levels. The multitasking mode takes the elite solution as the transfer medium and forms a closed-loop feedback system through the information exchange between low- and high-fidelity tasks in parallel. Sequential transfer mode, a one-way algorithm, transfers the elite solutions archived in the previous mode as the population to high-fidelity domain for further optimization. This framework is suitable for population-based optimization algorithms with variable search direction and step size. The core work of this paper is to realize the framework by means of differential evolution (DE), for which we propose the multifidelity transfer differential evolution (MTDE). Corresponding to multitasking and sequential transfer in the framework, MTDE includes two modes, transfer based on base vector (b-transfer) and transfer based on population (p-transfer). The b-transfer mode incorporates the unique advantages of DE into fidelity switching, whereas the p-transfer mode adaptively conducts population for further high-fidelity local search. Finally, the production-optimization performance of MTDE is validated with the egg model and two real field cases, in which the black-oil and streamline models are used to obtain high- and low-fidelity results, respectively. We also compared the convergence curves and optimization results with the single-fidelity method and the greedy multifidelity method. The results show that the proposed algorithm has a faster convergence rate and a higher-quality well-control strategy. The adaptive capacity of p-transfer is also demonstrated in three distinct cases. At the end of the paper, we discuss the generalization potential of the proposed framework.