Showing papers in "Spe Journal in 2021"

Physical Simulation of Hydraulic Fracturing of Large-Sized Tight Sandstone Outcrops

Abstract: Hydraulic fracturing is an indispensable technology in developing tight oil and gas resources. However, the development of tight oil and gas is not consistently satisfactory. Further understanding of hydraulic fracturing of tight sandstone is required, which increases the production of tight oil and gas reservoirs, particularly in China. Currently, there are a few true triaxial hydraulic fracturing physical simulations of large tight sandstone outcrops. To weaken the boundary effect, this study performed simulations using large tight sandstone outcrops (500 × 500 × 500 mm and 500 × 500 × 800 mm) in the Shahezi Formation (Fm.), Jilin Province, China. The effect of natural fracture (NF) development degree, in-situ stress conditions, fracturing treatment parameters, and temporary plugging on fracture propagation were investigated. Furthermore, fracture propagation was investigated based on post-fracturing fine reconstruction, high-energy computed tomography (CT) scan, acoustic emission monitoring (AEM), and analysis of a fracturing pressure curve. Finally, suggestions on fracturing treatment were proposed. The results show that the NF is a key factor in determining the hydraulic fracture (HF) morphology in the tight sandstone reservoir. Further, the number, approaching angle, and cementation strength of the preexisting NF affect the HF propagation path; these are the key factors for forming complex fractures. In the tight sandstone reservoir with well-developed NFs, the fracture morphology is dominated by the NF under horizontal differential stress ≤ 9 MPa. A single fracture is more likely to occur under horizontal differential stress ≥ 12 MPa, which is less affected by the NF. In the fracturing at variable injection rates, a low rate facilitates fluid penetration into the NF, while a high rate facilitates deep HF propagation. A low-viscosity fracturing fluid at a high rate facilitates further propagation of the temporary plugging agent (TPA), thus achieving deep temporary plugging and fracture diversion. A high-viscosity fluid does not facilitate accumulation and plugging of particulate TPA. Higher horizontal differential stress leads to a smaller diversion radius of new HF, which is closer to the original HF, leading to poorer stimulation effect. The results provide a reference for the fracturing design of the tight sandstone.

History Matching of Naturally Fractured Reservoirs Using a Deep Sparse Autoencoder

Abstract: Although researchers have applied many methods to history matching, such as Monte Carlo methods, ensemble-based methods, and optimization algorithms, history matching fractured reservoirs is still challenging. The key challenges are effectively representing the fracture network and coping with large amounts of reservoir-model parameters. With increasing numbers of fractures, the dimension becomes larger, resulting in heavy computational work in the inversion of fractures. This paper proposes a new characterization method for the multiscale fracture network, and a powerful dimensionality-reduction method by means of an autoencoder for model parameters. The characterization method of the fracture network is dependent on the length, orientation, and position of fractures, including large-scale and small-scale fractures. To significantly reduce the dimension of parameters, the deep sparse autoencoder (DSAE) transforms the input to the low-dimensional latent variables through encoding and decoding. Integrated with the greedy layer-wise algorithm, we set up a DSAE and then take the latent variables as optimization variables. The performance of the DSAE with fewer activating nodes is excellent because it reduces the redundant information of the input and avoids overfitting. Then, we adopt the ensemble smoother (ES) with multiple data assimilation (ES-MDA) to solve this minimization problem. We test our proposed method in three synthetic reservoir history-matching problems, compared with the no-dimensionality-reduction method and the principal-component analysis (PCA). The numerical results show that the characterization method integrated with the DSAE could simplify the fracture network, preserve the distribution of fractures during the update, and improve the quality of history matching naturally fractured reservoirs.

Data-Driven Niching Differential Evolution with Adaptive Parameters Control for History Matching and Uncertainty Quantification

Abstract: History matching is a typical inverse problem that adjusts the uncertainty parameters of the reservoir numerical model with limited dynamic response data. In most situations, various parameter combinations can result in the same data fit, termed as nonuniqueness of inversion. It is desirable to find as many global or local optima as possible in a single optimization run, which may help to reveal the distribution of the uncertainty parameters in the posterior space, which is particularly important for robust optimization, risk analysis, and decision making in reservoir management. However, many factors, such as the nonlinearity of inversion problems and the time-consuming numerical simulation, limit the performance of most existing inverse algorithms. In this paper, we propose a novel data-driven niching differential evolution algorithm with adaptive parameter control for nonuniqueness of inversion, called DNDE-APC. On the basis of a differential evolution (DE) framework, the proposed algorithm integrates a clustering approach, niching technique, and local surrogate assistant method, which is designed to balance exploration and convergence in solving the multimodal inverse problems. Empirical studies on three benchmark problems demonstrate that the proposed algorithm is able to locate multiple solutions for complex multimodal problems on a limited computational budget. Integrated with convolutional variational autoencoder (CVAE) for parameterization of the high-dimensional uncertainty parameters, a history matching workflow is developed. The effectiveness of the proposed workflow is validated with heterogeneous waterflooding reservoir case studies. By analyzing the fitting and prediction of production data, history-matched realizations, the distribution of inversion parameters, and uncertainty quantization of forecasts, the results indicate that the new method can effectively tackle the nonuniqueness of inversion, and the prediction result is more robust.

Multifidelity Genetic Transfer: An Efficient Framework for Production Optimization

Abstract: 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.

A New Ensemble Machine-Learning Framework for Searching Sweet Spots in Shale Reservoirs

Abstract: Jizhou Tang*, State Key Laboratory of Marine Geology, Tongji University; Bo Fan*, Motorola Solutions; Lizhi Xiao** and Shouceng Tian, State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing; Fengshou Zhang, Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University; and Liyuan Zhang and David Weitz, John A. Paulson School of Engineering and Applied Sciences, Harvard University

Gradient-Enhanced Support Vector Regression for Robust Life-Cycle Production Optimization with Nonlinear-State Constraints

Abstract: In the context of production optimization, we consider the general problem of finding the well controls that maximize the net present value (NPV) of life-cycle production, where the well controls are either the bottomhole pressure (BHP) or a rate (oil, gas, water, or total liquid) at each well on a set of specified control steps (time intervals), with the limitations on surface facility considered as nonlinear-state constraints [e.g., field-liquid-production rates (FLRs), field-water-production rates (FWRs), and/or field-gas-production rates]. If the reservoir simulation used for reservoir management has sufficient adjoint capability to compute gradients of the objective function and all state constraints, we show that one can develop a significantly more computationally efficient procedure by replacing the adjoint-enhanced reservoir simulator by a proxy model and optimizing the proxy. Our methodology achieves computational efficiency by generating a set of output values of the cost and constraint functions and their associated derivative values by running the reservoir simulator for a broad set of input design variables (well controls) and then using the set of input/output data to train a proxy model to replace the reservoir simulator when computing values of cost and constraint functions and their derivatives during iterations of sequential quadratic programming (SQP). The derivation of the equations for computing the proxy-based model that uses both function and gradient information is similar to that of least-squares support vector regression (LS-SVR). However, this method is referred to as gradient-enhanced support vector regression (GE-SVR) because, unlike LS-SVR, the method uses derivative information, not just function values, to train the proxy. Similar to LS-SVR, improved (higher) estimated optimal NPV values can be obtained by using iterative resampling (IR). With IR, after each proxy-based optimization, one evaluates the cost and constraint functions and their derivatives at the estimated optimal controls using reservoir-simulator output, and then adds this new input/output information to the training set to update the proxy models for predicting NPV and constraints. Using the updated proxies, one applies SQP optimization again. IR continues until the simulator and proxy evaluated at the latest estimate of the optimal well controls give the same value of NPV within a specified percentage tolerance and the constraints evaluated by reservoir simulator at the latest optimal well controls are such that the constraints are satisfied within some small specified tolerance. Our results indicate that proxy-based optimization with iterative resampling might require up to an order of magnitude less computational time than pure reservoir-simulator-based optimization. By comparing the results generated with an LS-SVR proxy with the GE-SVR results, we find that GE-SVR is roughly an order of magnitude more computationally efficient than LS-SVR but also provides a better approximation of a complex cost-function surface so that it is possible to locate multiple optima in cases where LS-SVR fails to identify the multiple optima.

Pore-Scale Perspective of Gas/Water Two-Phase Flow in Shale

Abstract: The transport behaviors of both single-phase gas and single-phase water at nanoscale deviate from the predictions of continuum flow theory. The deviation is greater and more complex when both gas and liquid flow simultaneously in a pore or network of pores. We developed a pseudopotential-based lattice Boltzmann (LB) method (LBM) to simulate gas/water two-phase flow at pore scale. A key element of this LBM is the incorporation of fluid/fluid and fluid/solid interactions that successfully capture the microscopic interactions among phases. To calibrate the model, we simulated a series of simple and static nanoscale two-phase systems, including phase separation, a Laplace bubble, contact angle, and a static nanoconfined bubble. In this work, we demonstrate the use of our proposed LBM to model gas/water two-phase flow in systems like a single nanopore, two parallel nanopores, and nanoporous media. Our LBM simulations of static water-film and gas-film scenarios in nanopores agree well with the theory of disjoining pressure and serve as critical steps toward validating this approach. This work highlights the importance of interfacial forces in determining static and dynamic fluid behaviors at the nanoscale. In the Applications section, we determine the water-film thickness and disjoining pressure in a hydrophilic nanopore under the drainage process. Next, we model water imbibition into gas-filled parallel nanopores with different wettability, and simulate gas/water two-phase flow in dual-wettability nanoporous media. The results showed that isolated patches of organic matters (OMs) impede water flow, and the water relative permeability curve cuts off at water saturation [= 1–volumetric total organic carbon (TOC)]. The residual gas saturation is also controlled by the volumetric TOC, ascribed to the isolation of organic patches by the saturating water; therefore, the gas relative permeability curve cuts off at water saturation (= 1–volumetric TOC).

Modeling and Analysis of Carbonate Matrix Acidizing Using a New Two-Scale Continuum Model

Abstract: Matrix acidizing is a common technique for carbonate reservoir stimulation. In this work, a new two-scale continuum model is developed to study the 2D acidizing process. The Navier-Stokes-Darcy equation is used instead of the Darcy’s-law equation to describe fluid flow. The continuity equation is also modified to consider the mass-exchange term between fluid and solid phases. The comparison results show that neglecting the solid-matrix-dissolution source term results in overestimation of pore volume (PV) to breakthrough (PVBT). The Darcy’s-law equation does not well-capture physical behaviors of fluid phase with low acid-injection velocity compared with the Navier-Stokes-Darcy equation. On the basis of this model, we discuss different processes influencing matrix acidizing, including convection, diffusion, and reaction, and different models, including classical and new two-scale continuum models. Besides, a comprehensive parametric study is also conducted to study the effect of parameters with respect to acid and rock physical parameters on the matrix-acidizing process. The typical dissolution patterns and optimal acid-injection rate presented in experimental studies can be well-observed by the new two-scale continuum model. Increasing the acid-injection concentration has a limited effect on the amount of acid mass but substantially reduces the amount of solute required. The acidizing curve is very sensitive to the dispersity coefficient, acid-surface-reaction rate, and porosity/permeability relationship.

Liquid Nitrogen Fracturing in Boreholes under True Triaxial Stresses: Laboratory Investigation on Fractures Initiation and Morphology

Abstract: Multistage hydraulic fracturing is widely used in developing tight reservoirs. However, the economic and environmental burden of freshwater souring, transportation, treatment, and disposal in hydraulic fracturing operations has been a topic of great importance to the energy industry and public alike. Waterless fracturing is one possible method of solving these water-related issues. Liquid nitrogen (LN2) is considered a promising alternate fracturing fluid that can create fractures by coupled hydraulic/thermal loadings and, more importantly, pose no threats to the environment. However, there are few laboratory experiments that use LN2 directly as a fracturing fluid. In this work, we examine the performance of LN2 fracturing based on a newly developed cryogenic-fracturing system under true-triaxial loadings. The breakdown pressure and fracture morphologies are compared with water fracturing. Moreover, fracture-initiation behavior under cryogenic in-situ conditions revealed by cryo-scanning electron microscopy (cryo-SEM) is presented, and the role of thermal stress is quantified by a coupled thermoporoelastic-damage numerical simulation. Finally, the potential application considerations of LN2 fracturing in the field site are discussed. The results demonstrate that LN2 fracturing can lower fracture initiation and propagation pressure and generate higher conductive fractures with numerous thermally induced cracks in the vicinity of the wellbore. Thermal gradient could generate enormously high-tensile hoop stress and bring about extensive rock damage. Fracture-propagation direction is inclined to be influenced by the thermal stress. Furthermore, phase transition during the fracturing process and low fluid viscosity of LN2 can also facilitate the fracture propagation and network generation. The key findings obtained in this work are expected to provide a viable alternative for the sustainable development of tight-reservoir resources in an efficient and environmentally acceptable way.

Field-Scale Numerical Investigation of Proppant Transport among Multicluster Hydraulic Fractures

Abstract: Plug-and-perforation (P-n-P) completion has been widely used in horizontal wells for the development of unconventional reservoirs. In the field, uneven proppant distribution among different fractures within a fracturing stage has been frequently observed in P-n-P treatments, leaving a large portion of reservoir volume understimulated. In this paper, an efficient 3D multiphase particle-in-cell (MP-PIC) method has been used to simulate proppant transport among multiple fractures (fracture near the heel, middle fracture, fracture near the toe) at the field scale. This work studies the fundamental physics of the proppant transport process and reveals the mechanisms of uneven proppant placement, giving strategies to improve the proppant placement. Before applying the MP-PIC method to field-scale problems, we conducted indoor experiments to validate the model. The simulation results show an excellent agreement with the vertical slot experimental results. After model validation, we used the MP-PIC method to directly simulate the field process of proppant transport, involving slurry transport from the wellbore through perforation holes and finally into fractures. A base case with three fractures in a stage was first established to calculate the percentage of proppant mass distribution in each fracture. Then, we performed the sensitivity analysis of both proppant size and injection rate to investigate their effects on proppant placement. The results reveal that all the cases tend to have a heel-biased proppant distribution among three fractures, which agrees with the field observations. There are two reasons for the heel-biased proppant distribution. First, at the very beginning of the injection, more proppants tend to flow toward the toe side because of large momentum. As more and more proppants move to the toe side, the concentration near the toe side gradually increases, which adds flow resistance to the newly injected proppants. Therefore, most newly injected proppants will go to the first fracture. The second reason comes from the fracture geometry. Because the first fracture has the largest fracture width among three fractures, it has the smallest flow resistance for proppant transport. More slurry will flow into the first fracture. Apart from giving explanations for the heel-biased distribution, we also suggest some strategies to improve the proppant distribution. The sensitivity analysis shows that the strong heel-biased proppant distribution can be mitigated by optimizing the proppant size and injection rate. Our study for the first time conducts a field-scale numerical investigation of proppant transport in the wellbore-fracture system during P-n-P treatments. The results can provide us with more insights into the optimization of fracture design in field practice.

Coupled Flow/Geomechanics Modeling of Interfracture Water Injection To Enhance Oil Recovery in Tight Reservoirs

Abstract: Unconventional tight reservoirs that are typically characterized by low permeability and low porosity have contributed significantly to the global hydrocarbon production in recent years. Although hydraulic fracturing, along with horizontal well drilling, enables the economic development of such reservoirs, the production rate often declines sharply and results in low primary hydrocarbon recovery. The application of enhanced-oil-recovery (EOR) techniques in tight reservoirs has received much interest. In this study, the feasibility and efficiency of interfracture water injection to enhance oil recovery in multistage fractured tight oil reservoirs are analyzed through an efficient coupled flow/geomechanics model with an embedded discrete-fracture model (EDFM). A combined finite-volume/finite-element scheme is used to discretize the governing equations for flow and geomechanics, and the coupled problem is solved sequentially using a fixed-stress splitting algorithm. A basic numerical model consisting of a 15-stage fractured horizontal well is constructed using the petrophysical and geomechanical properties of a tight oil formation in Ordos Basin, China. Fractures indexed with even numbers are switched into injecting fractures when the production rate has dropped to less than a certain threshold. The improvement of oil recovery is analyzed by comparing the production profiles with and without water injection. In this coupled model, the fracture closure/opening during production/injection is considered according to the constitutive relations between fracture aperture and effective normal stress acting on the fracture faces. The poromechanical response of matrix is modeled by the Biot (1941) theory. The effects of fracture spacing, injection rate, and the presence of a natural-fracture network on oil-recovery enhancement are discussed through sensitivity analysis. The main mechanisms of interfracture water injection for enhancing oil recovery are waterflooding and reservoir-pressure maintenance. Small fracture spacing tends to reduce the oil recovery because of fracture interference and a limited drainage area; therefore, the primary depletion stage is shortened as the fracture spacing is reduced. The influence of interfracture water injection is more pronounced with smaller fracture spacing because the pressure-transient responses near the producing fractures are more dramatic considering the close proximity between the injecting fracture and the producing fracture. Although a higher injection rate results in higher oil recovery, the injectivity in low-permeability reservoirs limits the maximum-allowable injection rate. When secondary (natural)-fracture networks are considered, neighboring hydraulic fractures can be connected to one another via the secondary fractures, particularly if the interfracture spacing is small. Water can break through in the producing fractures quickly, which could also lead to high water cut and suboptimal oil-recovery performance. This study tests the feasibility and efficiency of interfracture injection to enhance tight oil recovery. The results indicate that interfracture injection can be a promising EOR technique for tight oil reservoirs, which sheds lights on future completion strategies and production design in tight reservoirs.

Enhancing Heavy-Oil-Recovery Efficiency by Combining Low-Salinity-Water and Polymer Flooding

Abstract: Combining low-salinity-water (LSW) and polymer flooding was proposed to unlock the tremendous heavy-oil resources on the Alaska North Slope (ANS). The synergy of LSW and polymer flooding was demonstrated through coreflooding experiments at various conditions. The results indicate that the high-salinity polymer (HSP) (salinity1⁄4 27,500 ppm) requires nearly two-thirds more polymer than the low-salinity polymer (LSP) (salinity1⁄4 2,500 ppm) to achieve the target viscosity at the condition of this study. Additional oil was recovered from LSW flooding after extensive high-salinity-water (HSW) flooding [3 to 9% of original oil in place (OOIP)]. LSW flooding performed in secondary mode achieved higher recovery than that in tertiary mode. Also, the occurrence of water breakthrough can be delayed in the LSW flooding compared with the HSW flooding. Strikingly, after extensive LSW flooding and HSP flooding, incremental oil recovery (approximately 8% of OOIP) was still achieved by LSP flooding with the same viscosity as the HSP. The pH increase of the effluent during LSW/LSP flooding was significantly greater than that during HSW/HSP flooding, indicating the presence of the low-salinity effect (LSE). The residual-oil-saturation (Sor) reduction induced by the LSE in the area unswept during the LSW flooding (mainly smaller pores) would contribute to the increased oil recovery. LSP flooding performed directly after waterflooding recovered more incremental oil (approximately 10% of OOIP) compared with HSP flooding performed in the same scheme. Apart from the improved sweep efficiency by polymer, the low-salinity-induced Sor reduction also would contribute to the increased oil recovery by the LSP. A nearly 2-year pilot test in the Milne Point Field on the ANS has shown impressive success of the proposed hybrid enhanced-oil-recovery (EOR) process: water-cut reduction (70 to less than 15%), increasing oil rate, and no polymer breakthrough so far. This work has demonstrated the remarkable economical and technical benefits of combining LSW and polymer flooding in enhancing heavy-oil recovery.

Mechanism and Effect of Nanoparticles on Controlling Fines Migration in Unconsolidated Sandstone Formations

Abstract: Pore throat blockage due to fines migration during drilling and completion is one of the leading causes of damage to unconsolidated sandstone reservoirs. Therefore, it is necessary to explore an effective control method for fines migration. Five types of nanoparticles in suspension with aqueous NaCl solutions of six different ionic strengths were chosen. Their ability to control the migration of quartz and kaolinite fines in quartz sand as the porous medium is discussed in this work. Results show that nanoparticles can effectively adsorb and fix fines, thus successfully suppressing their migration. Among these nanoparticles, Al2O3 showed the best performance, and nanoparticle suspensions with higher ionic strengths were preferable. A surface element integration method was used to establish a mathematical model for calculating the interaction energy between the formation fines and the rock pore surface with adsorbed nanoparticles. Through atomic force microscopy and zeta potential measurements, the effect of nanoparticle adsorption on the heterogeneity of the pore surface was analyzed in terms of roughness and electrical properties. The interaction energy between the formation fines and the heterogeneous pore surface was calculated; it revealed the microscopic mechanism of how nanoparticles control fines migration. The results indicated that the nanoparticles form an adsorption layer, which enhances the physical and chemical heterogeneities of the pore surface and provides favorable conditions for the adsorption and fixation of fines. As a result, the interaction energy curves of the fines and the pore surface shift downward, and their repulsive barriers decrease or even disappear, exhibiting higher attractive potential energy. These variations promote adsorption and fixation of fines at the pore surface, as confirmed by the experimental results reported in this work, thus successfully preventing formation damage.

Dynamic Contact Angle Reformulates Pore-Scale Fluid-Fluid Displacement at Ultralow Interfacial Tension

Abstract: Surfactant flooding is an effective enhanced oil recovery method in which the oil/water interfacial tension (IFT) is reduced to ultralow values (<0.01 mN/m). The microscopic fluid-fluid displacement has been extensively studied at high IFT (>10 mN/m). However, the microscopic displacement dynamics can be significantly different when the IFT is ultralow because the dynamic contact angle increases with the increase of the capillary number. In this study, surfactant flooding was performed and visualized in micromodels to investigate the dynamics of multiphase displacement at ultralow IFT. Although the micromodels used were strongly water-wet, the displacements of oil by surfactant solutions at ultralow IFT appeared as drainage. Furthermore, a macroscopic oil film was left behind on the surface, which indicates that a contact line instability occurred during displacements. The shape of the oil/water meniscus was determined by the balance between viscous forces and capillary forces. The meniscus can be significantly distorted by viscous forces at ultralow IFT. Therefore, the water-wet micromodel exhibits an oil-wet behavior at ultralow IFT, and the displacements of oil by surfactant solutions at ultralow IFT manifested as drainage rather than imbibition. The flow behavior is further complicated by the spontaneous formation of microemulsion during displacement. The microemulsion is mainly formed from the residual oil. The formation of a microemulsion bank made the surfactant solution discontinuous, with transport in the form of droplets in the microemulsion bank and displacement front. The novelty of this work is to reveal the effects of dynamic contact angle on the ultralow IFT displacement.

Impact of Proppant Pumping Schedule on Well Production for Slickwater Fracturing

Abstract: Slickwater fracturing has become one of the most leveraging completion technologies in unlocking hydrocarbon in unconventional reservoirs. In slickwater treatments, proppant transport becomes a big concern because of the inefficiency of low-viscosity fluids to suspend the particles. Many studies have been devoted to proppant transport experimentally and numerically. However, only a few focused on the proppant pumping schedules in slickwater fracturing. The impact of proppant schedules on well production remains unclear. The goal of our work is to simulate the proppant transport under real pumping schedules (multisize proppants and varying concentration) at the field scale and quantitatively evaluate the effects of proppant schedules on well production for slickwater fracturing. The workflow consists of three steps. First, a validated 3D multiphase particle-in-cell (MP-PIC) model has been used to simulate the proppant transport at real pumping schedules in a field-scale fracture (180-m length, 30-m height). Second, we applied a propped fracture conductivity model to calculate the distribution of propped fracture width, permeability, and fracture conductivity. In the last step, we incorporated the fracture geometry, propped fracture conductivity, and the estimated unpropped fracture conductivity into a reservoir simulation model to predict gas production. Based on the field designs of pumping schedules in slickwater treatments, we have generated four proppant schedules, in which 100-mesh and 40/70-mesh proppants were loaded successively with stair-stepped and incremental stages. The first three were used to study the effects of the mass percentages of the multisize proppants. From Schedules 1 through 3, the mass percentage of 100-mesh proppants is 30, 50, and 70%, respectively. Schedule 4 has the same proppant percentage as Schedule 2 but has a flush stage after slurry injection. The comparison between Schedules 2 and 4 enables us to evaluate the effect of the flush stage on well production. The results indicate that the proppant schedule has a significant influence on treatment performance. The schedule with a higher percentage of 100-mesh proppants has a longer proppant transport distance, a larger propped fracture area, but a lower propped fracture conductivity. Then, the reservoir simulation results show that both the small and large percentages of 100-mesh proppants cannot maximize well production because of the corresponding small propped area and low propped fracture conductivity. Schedule 2, with a median percentage (50%) of 100-mesh proppants, has the highest 1,000-day cumulative gas production. For Schedule 4, the flush stage significantly benefits the gas production by 8.2% because of a longer and more uniform proppant bed along the fracture. In this paper, for the first time, we provide both the qualitative explanation and quantitative evaluation for the impact of proppant pumping schedules on the performance of slickwater treatments at the field scale by using an integrated numerical simulation workflow, providing crucial insights for the design of proppant schedules in the field slickwater treatments.

A Deep-Learning-Based Approach for Reservoir Production Forecast under Uncertainty

Abstract: This paper presents a deep-learning-based proxy modeling approach to efficiently forecast reservoir pressure and fluid saturation in heterogeneous reservoirs during waterflooding. The proxy model is built on a recently developed deep-learning framework, the coupled generative adversarial network (Co-GAN), to learn the joint distribution of multidomain high-dimensional image data. In our formulation, the inputs include reservoir static properties (permeability), injection rates, and forecast time, while the outputs include the reservoir dynamic states (i.e., reservoir pressure and fluid saturation) corresponding to the forecast time. Training data obtained from full-scale numerical reservoir simulations were used to train the Co-GAN proxy model, and then testing data were used to evaluate the accuracy and generalization ability of the trained model. Results indicate that the Co-GAN proxy model can predict the reservoir pressure and fluid saturation with high accuracy, which in turn, enable accurate predictions of well production rates. Moreover, the Co-GAN proxy model also is robust in extrapolating dynamic reservoir states. The deep-learning proxy models developed in this work provide a new and fast alternative to estimating reservoir production in real time.

The Impact of Kerogen Tortuosity on Shale Permeability

Abstract: Shale-matrix-associated transport phenomena exhibit multiple mechanisms including advective-, diffusive-, and adsorptive-driven transport modes, depending on the pore type. Diffusive processes are governed by the shale organic constituents known as kerogens. Kerogens, composed of fine-scale organic microstructures, vary with respect to their petrophysical properties, depending on their origin and maturity level. The extent to which kerogens contribute to the overall transport is governed by their ability to diffuse hydrocarbons contained within. The diffusion coefficient is a crucial parameter used to quantify diffusivity based on the interactions between the host material and the diffusing molecules. Kerogen as a hosting medium allows for diffusion of natural gas at various rates based on several factors. One of these factors, kerogen porosity, is conjectured to significantly influence diffusive transport phenomena. In this paper, taking advantage of the predictive power of molecular dynamics (MD) simulation, we investigate the impact of kerogen porosity on the diffusivity coefficient of natural gas. Starting from a single type II kerogen macromolecule, several kerogen structures for a realistic range of porosity values were created and, subsequently, used for diffusivity calculations of methane molecules. Simulation results suggest a direct link between diffusion and kerogen porosity, allowing for delineation of the diffusion tortuosity factor. Furthermore, the microscale tortuosity–diffusivity relationship in kerogens was investigated at the reservoir scale by means of a shale permeability model. The results substantiate the critical impact of the diffusion process on the shale permeability.

Machine Learning for Deepwater Drilling: Gas-Kick-Alarm Classification Using Pilot-Scale Rig Data with Combined Surface-Riser-Downhole Monitoring

Abstract: 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-scaletest-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 f1 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.

Fracture Hits in Unconventional Reservoirs: A Critical Review

Abstract: “Fracture hit” was initially coined to refer to the phenomenon of an infill-well fracture interacting with an adjacent well during the hydraulic-fracturing process. However, over time, its use has been extended to any type of well interference or interaction in unconventional reservoirs. In this study, an exhaustive literature survey was performed on fracture hits to identify key factors affecting the fracture hits and suggest different strategies to manage fracture hits. The impact of fracture hits is dictated by a complex interplay of petrophysical properties (high-permeability streaks, mineralogy, matrix permeability, natural fractures), geomechanical properties (near-field and far-field stresses, tensile strength, Young’s modulus, Poisson’s ratio), completion parameters (stage length, cluster spacing, pumping rate, fluid and proppant amount), and development decisions (well spacing, well scheduling, fracture sequencing). It is difficult to predict the impact of fracture hits, and they affect both parent and child wells. The impact on the child wells is predominantly negative, whereas the effect on parent wells can be either positive or negative. The “child wells” in this context refer to the wells drilled with pre-existing active/inactive well(s) around. The “parent well” refers to any well drilled without any pre-existing well around. Overall, fracture hits tend to negatively affect both the production and economics of lease development. The optimal approach rests in identifying the reservoir properties and accordingly making field-development decisions that minimize the negative impact of fracture hits. The different strategies proposed to minimize the negative impact of fracture hits are simultaneous lease development, thus avoiding parent/child wells (i.e., rolling-, tank-, and cube-development methods); repressuring or refracturing parent wells; using far-field diverters and high-permeability plugging agents in the child-well fracturing fluid; and optimizing stage and cluster spacing through modeling studies and field tests. Finally, the study concludes with a recommended approach to manage fracture hits. There is no silver bullet, and the problem of fracture hits in each shale play is unique, but by using the available data and published knowledge to understand how fractures propagate downhole, measures can be taken to minimize or even completely avoid fracture hits.

A Recurrent Neural Network–Based Proxy Model for Well-Control Optimization with Nonlinear Output Constraints

Abstract: In well-control optimization problems, the goal is to determine the time-varying well settings that maximize an objective function, which is often the net present value (NPV). Various proxy models have been developed to predict NPV for a set of inputs such as time-varying well bottomhole pressures (BHPs). However, when nonlinear output constraints (e.g., maximum well/field water production rate or minimum well/field oil rate) are specified, the problem is more challenging because well rates as a function of time are required. In this work, we develop a recurrent neural network (RNN)–based proxy model to treat constrained production optimization problems. The network developed here accepts sequences of BHPs as inputs and predicts sequences of oil and water rates for each well. A long-short-term memory (LSTM) cell, which is capable of learning long-term dependencies, is used. The RNN is trained using well-rate results from 256 full-order simulation runs that involve different injection and production-well BHP schedules. After detailed validation against full-order simulation results, the RNN-based proxy is used for 2D and 3D production optimization problems. Optimizations are performed using a particle swarm optimization (PSO) algorithm with a filter-based nonlinear-constraint treatment. The trained proxy is extremely fast, although optimizations that apply the RNN-based proxy at all iterations are found to be suboptimal relative to full simulation-based (standard) optimization. Through use of a few additional simulation-based PSO iterations after proxy-based optimization, we achieve NPVs comparable with those from simulation-based optimization but with speedups of 10 or more (relative to performing five simulation-based optimization runs). It is important to note that because the RNN-based proxy provides full well-rate time sequences, optimization constraint types or limits, as well as economic parameters, can be varied without retraining. NOTE: This paper is published as part of the 2021 Reservoir Simulation Conference Special Issue.

Multicomponent Diffusion Modeling of Cyclic Solvent Injection in Ultratight Reservoirs

Abstract: We present a new semianalytical compositional model designed for primary production of multicomponent oil and cyclic solvent injection in ultratight oil reservoirs that is dependent on diffusion-dominated transport within the matrix (k < 200 nd) coupled to advection-dominated transport in the fractures. The semianalytical model consists of a well-mixed tank model for the fractures coupled to diffusive transport within the matrix. Production of oil, gas, and water from the fractures to the well is proportional to its phase mobility. The matrix allows for differing effective-diffusion coefficients for each component. Because there are no gridblocks within the matrix, the analytical solution is computationally less expensive than numerical simulation while capturing the steep, nonmonotonic compositional changes occurring a short distance into the matrix that result from multiple injection cycles. The Peng-Robinson equation of state (PR EOS) (Robinson and Peng 1978) is used to calculate phase behavior with time within the fractures and to initialize density and mass concentrations within the matrix based on the semianalytical framework. The coupled convective (fracture) and diffusive (matrix) model is validated with several laboratory- and field-scale cases. For primary recovery, the results show that the model correctly reproduces the pressure and oil-recovery declines observed in the field. We show that the hydrocarbon-recovery mechanism for solvent huff ’n’ puff (HnP) is facilitated by greater density reduction and compositional changes. Two solvents are considered in HnP calculations: carbon dioxide (CO2) and methane (CH4). Recovery of heavier components is enhanced with CO2 compared with CH4 within the reservoir (matrix and fractures). Furthermore, the results demonstrate that multiple HnP cycles constrained to surface injection are needed to enhance density and compositional gradients, and therefore oil recovery. Although shorter soaks are better for short-term recovery (i.e., 3 to 5 years), longer soaks maximize recovery over a longer time frame (i.e., 10 to 15 years). This paper provides a limiting case model based on diffusive matrix transport and convective fracture transport to determine the optimal number/duration of cycles and when to start the HnP process after primary recovery.

Flow-Based Characterization of Digital Rock Images Using Deep Learning

Abstract: X-ray imaging of porous media has revolutionized the interpretation of various microscale phenomena in subsurface systems. The volumetric images acquired from this technology, known as digital rocks (DR), make it a suitable candidate for machine learning and computer-vision applications. The current routine DR frameworks involving image processing and modeling are susceptible to user bias and expensive computation requirements, especially for large domains. In comparison, the inference with trained machine-learning models can be significantly cheaper and computationally faster. Here we apply two popular convolutional neural network (ConvNet) architectures [residual network (ResNet) and ResNext] to learn the geometry of the pore space in 3D porous media images in a supervised learning scheme for flow-based characterization. The virtual permeability of the images to train the models is computed through a numerical simulation solver. Multiple ResNet variants are then trained to predict the continuous permeability value (regression). Our findings demonstrate the suitability of such networks to characterize volume images without having to resort to further ad-hoc and complex model adjustments. We show that training with richer representation of pore space improves the overall performance. We also compare the performance of the models statistically based on multiple metrics to assess the accuracy of the regression. The model inference of permeability from an unseen sandstone sample is executed on a standard workstation in less than 120 ms/sample and shows a score of 0.87 using explained variance score (EVS) metric, a mean absolute error (MAE) of 0.040 darcies, and 18.9% relative error in predicting the value of permeability compared to values acquired through simulation. Similar metrics are obtained when training with carbonate rock images. The training wall time and hyperparameters setting of the model are discussed. The findings of this study demonstrate the significant potential of machine learning for accurate DR analysis and rock typing while leveraging automation and scalability.

Enhanced Oil Recovery in the Wolfcamp Shale by Carbon Dioxide or Nitrogen Injection: An Experimental Investigation

Abstract: We present a comprehensive investigation of gas injection for enhanced oil recovery (EOR) in organic-rich shale using 11 coreflooding experiments in sidewall core plugs from the Wolfcamp Shale, and three additional coreflooding experiments using Berea Sandstone. Our work studies the effect of pressure, minimum miscibility pressure (MMP), soak time, injection-gas composition, and rock-transport properties on oil-recovery factor. The injection gases were carbon dioxide (CO2) and nitrogen. The core plugs were resaturated with crude oil in the laboratory, and the experiments were performed at reservoir pressure and temperature using a design that closely replicates gas injection through a hydraulic fracture, minimizes convective flow, and exaggerates the fracture to the reservoir-rock ratio. We accomplished this by surrounding the Wolfcamp reservoir-rock matrix with glass beads. Computed-tomography (CT) scanning enabled the visualization of the compositional changes with time and space during the gas-injection experiments and gas chromatography provided the overall change in composition between the crude oil injected and the oil recovered. As gas surrounds the oil-saturated sample, a peripheral, slow-kinetics vaporization/condensation process is the main production mechanism. Gas flows preferentially through the proppant because of its high permeability, avoiding the formation and displacement of a miscible front along the rock matrix to mobilize the oil. Instead, the gas surrounding the reservoir-core sample vaporizes the light and intermediate components from the crude oil, making recovery a function of the fraction of oil that can be vaporized into the volume of gas in the fracture at the prevailing thermodynamic conditions. The mass transfer between the injected gas and the crude oil is sufficiently fast to result in significant oil production during the first 24 hours, but slow enough to cause the formation of a compositional gradient within the matrix that exists even 6 days after injection has started. The peripheral and the slow-kinetics aspects of the recovery mechanism are a consequence of the low fluid-transport capacity associated with the organic-rich shale that is saturated with liquid hydrocarbons. Our results show CO2 overperforms nitrogen as an EOR injection gas in organic-rich shale, and higher injection pressure leads to higher oil recovery, even beyond the MMP. The gas-injection scheme should allow enough time for the mass transfer to occur between the injected gas and the crude oil; we achieved this in the laboratory with a huff ’n’ puff scheme. Our results advance the understanding of gas injection for EOR in organic-rich shale in a laboratory scale, but additional work is required to rigorously scale up these observations to better design field applications.

Hydraulic-Fracture-Width Inversion Using Low-Frequency Distributed-Acoustic-Sensing Strain Data—Part I: Algorithm and Sensitivity Analysis

Abstract: Low-frequency distributed-acoustic-sensing (LF-DAS) data, which can be treated as linear-scaled strain variations, have been used recently to monitor hydraulic-fracturing treatments. Forward geomechanical modeling has been the subject of recent research efforts to better interpret the observed signatures of field LF-DAS data. To the best of our knowledge, there is no study that attempts to quantitatively characterize fracture geometries by directly inverting the LF-DAS strain data. In this study, we propose an inversion algorithm, in which the strains monitored by LF-DAS along an offset well are related to the fracture widths through a Green function. A 3D displacement-discontinuity method is used to construct the Green function. The least-squares method is first used to solve the linear system of equations. Regularization might be needed to stabilize the underdetermined system. Then, Markov-chain Monte Carlo (MCMC) simulations are conducted to generate fracture-width samples from the target distribution of LF-DAS strain data and to quantify uncertainties associated with the inverted widths. The inversion results obtained by the least-squares method are nonunique, heavily depending on the a priori regularization information. Regardless of the additional constraints imposed on the linear system, the inverted fracture width at the monitor-well location is always consistent with the true value because the LF-DAS data show a dominant sensitivity of fracture width near the monitor well. MCMC simulation results confirm that the LF-DAS strain data can only impose constraints on fracture segments near the monitor well. Moreover, the average value of the inverted widths in the vicinity of the monitor well is usually the same as the width right at the monitor well, except for the very early time after fracture hit when there are sharp width variations near the fracture tip. Therefore, it is efficient to use a single width for each fracture during the inversion process. The presented algorithm is successfully applied to invert the width evolution near the monitor well as a function of injection time. The results of this study demonstrate how much information can be obtained with high confidence from the inversion of LF-DAS strain data, which is beneficial for future use of LF-DAS data. The accurate estimation of fracture width at the monitor well can be used to calibrate hydraulic-fracturing models, improve the design of completion parameters such as proppant size, and provide the possibility of characterizing the whole fracture geometry with additional information or assumptions.

Experimental and Numerical Investigations of the Role of Proppant Embedment on Fracture Conductivity in Narrow Fractures (includes associated Errata)

Abstract: With the advancement of drilling and completion technologies in unconventional reservoirs, more extended reach wells are developed, and narrow-fracture environments are created in these reservoirs. Proppant embedment in monolayer/thin-layer-propped fractures can be significantly different from multilayer-propped fractures. In this study, a comprehensive investigation combining laboratory experiments with numerical simulations was conducted to explore the factors affecting proppant embedment and induced fracture conductivity loss in narrow fractures. The fracture-conductivity experiments were performed using monolayers of sand and ceramic proppant particles sandwiched between Berea Sandstone and Eagle Ford Shale plates under different closure pressures. The experiment study demonstrated that the long-term rock/fluid interaction leads to significant proppant embedment, and the fracture having a rough rock surface has higher fracture conductivity in monolayer-propped fractures. To further quantify the influence of proppant layer number, size, distribution variations, and particle crushing on proppant embedment, a numerical modeling approach that coupled continuum mechanics, discrete element method (DEM), and the lattice Boltzmann (LB) method was developed. In the simulation, the fracture/proppant system was constructed by filling proppant, modeled by DEM, between two fracture surfaces that were modeled by FLAC3D (Itasca Consulting Group 2012); LB simulation was then performed on the changing proppant pack to compute its time-dependent permeability. The numerical model was validated by comparing numerical results with measured fracture conductivities in the laboratory experiment. The simulation results demonstrated a strong correlation between proppant embedment and rock mechanical properties. When the Young’s modulus of the rock plate is less than 5 GPa, large magnitudes of proppant embedment can be expected in fractures supported by monolayers of ceramic proppant particles. Moreover, large-size proppant particles are more sensitive to the variations of Young’s modulus of the rock plate. When the rock formation in a narrow fracture environment has a relatively high Young’s modulus, the proppant diameter distribution has a lesser effect on the fracture conductivity. The outcome of this study will provide insights into the role of reservoir rock characteristics, proppant properties, and closure pressure on proppant embedment in narrow fractures.

Novel Near-Wellbore Fracture Diagnosis for Unconventional Wells Using High-Resolution Distributed Strain Sensing during Production

Abstract: The characteristics of hydraulic fractures in the near-wellbore region contain critical information related to the production performance of unconventional wells. We demonstrate a novel application of a fiber-optic-based distributed strain sensing (DSS) technology to measure and characterize near-wellbore fractures and perforation cluster efficiency during production. Distributed fiber-optic-based strain measurements are made based on the frequency shift of the Rayleigh scatter spectrum, which is linearly dependent on strain and temperature changes of the sensing fiber. Strain changes along the wellbore are continuously measured during the shut-in and reopening operations of a well. After removing temperature effects, extensional strain changes can be observed at locations around the perforation cluster during a shut-in period. We interpret that the observed strain changes are caused by near-wellbore fracture aperture changes caused by pressure increases within the near-wellbore fracture network. The depth locations of the measured strain changes correlate well with distributed acoustic sensing (DAS) acoustic intensity measurements that were measured during the stimulation of the well. The shape and magnitude of the strain changes differ significantly between two completion designs in the same well. Different dependencies between strain and borehole pressure can be observed at most of the perforation clusters between the shut-in and reopening periods. We assess that this new type of distributed fiber-optic measurement method can significantly improve understanding of near-wellbore hydraulic fracture characteristics and the relationships between stimulation and production from unconventional oil and gas wells.

Modeling of Cutting Rock: From PDC Cutter to PDC Bit—Modeling of PDC Cutter

Abstract: The main purpose of this paper is to present our polycrystalline diamond compact (PDC) cutter model and its verification. The PDC cutter model we developed is focused on a PDC cutter cutting a rock in 3D space. The model studies the forces between a cutter and a rock and applies the theory of poroelasticity to calculate the stress state of the rock during the cutting process. Once the stress state of the rock is obtained, the model can then predict rock failure by the modified Lade criterion (Ewy 1999). This work also developed a trial-and-error procedure to predict cutting forces, and the stress state of a rock before cutting process is also considered. A complete verification of the cutter model is conducted. The model results (i.e., predicted cutting forces) are compared with measured cutting forces from cutter tests in multiple published articles. The major influencing factors on cutting forces—backrake angle, side-rake angle, depths of cut, worn depth (or wear flat area), and hydrostatic pressure—are all studied and verified. A good agreement between the model results and cutter test data is found, and the overall mean relative error is approximately 15%. The influence of inhomogeneous precut stress state of a rock is also studied. Overall, the cutter model in this paper is complete and accurate. It is ready to be integrated into a PDC bit model.

Robust Multiobjective Nonlinear Constrained Optimization with Ensemble Stochastic Gradient Sequential Quadratic Programming-Filter Algorithm

Abstract: 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.

Understanding the Plugging Performance of HPAM-Cr (III) Polymer Gel for CO2 Conformance Control

Abstract: With the demand for conformance control in carbon dioxide (CO2) flooding fields, hydrolyzed polyacrylamide-chromium [HPAM-Cr (III)] polymer gel has been applied in fields for CO2 conformance control. However, the field application results are mixed with success and failure. This paper is intended to understand the HPAM-Cr (III) polymer gel plugging performance in CO2 flooding reservoirs through laboratory experiments and numerical analysis. We conducted core flooding tests to understand how the cycles of CO2 and water affect the HPAM-Cr (III) polymer gel plugging efficiency to CO2 and water during a water-alternating-gas (WAG) process. Berea Sandstone cores with the permeability range of 107 to 1225 md were used to evaluate the plugging performance in terms of residual resistance factor and breakthrough pressure, which is the minimum pressure required for CO2 to enter the gel-treated cores. We compared the pressure gradient from the near-wellbore to far-field with the gel breakthrough pressure, from which we analyzed under which conditions the gel treatment could be more successful. Results show that HPAM-Cr (III) polymer gel has higher breakthrough pressure in the low-permeability cores. The polymer gel can reduce the permeability to water much more than that to CO2. The disproportionate permeability reduction performance was more prominent in low-permeability cores than in high-permeability cores. The gel resistance to both CO2 and brine significantly decreased in later cycles. In high-permeability cores, the gel resistance to CO2 became negligible only after two cycles of water and CO2 injection. Because of the significant reduction of pressure gradient from near-wellbore to far-field in a radial flow condition and the dependence of breakthrough pressure on permeability and polymer concentration, we examined hypothetical reservoirs with no fractures, in which impermeable barriers separated high- and low-permeability zones and in which the gel was only placed in the high-permeability zone. We considered two scenarios: CO2 breaking through the gel and no CO2 breakthrough. No breakthrough represents the best condition in which the gel has no direct contact and can be stable in reservoirs for long. In contrast, the breakthrough scenario will result in the gel's significant degradation and dehydration resulting from CO2 flowing through the gel, which will cause the gel treatment to fail.

Quantifying Oil-Recovery Mechanisms during Natural-Gas Huff ‘n’ Puff Experiments on Ultratight Core Plugs

Abstract: Despite promising natural gas huff ‘n’ puff (HnP) field-pilot results, the dominant oil-recovery mechanisms during this process are poorly understood. We conduct systematic natural-gas (C1 and a mixture of C1/C2 with the molar ratio of 70:30) HnP experiments on an ultratight core plug collected from the Montney tight-oil formation, under reservoir conditions (P = 137.9 bar and T = 50°C). We used a custom-designed visualization cell to experimentally evaluate mechanisms controlling gas transport into the plug during injection and soaking phases and oil recovery during the whole process. The tests also allow us to investigate effects of gas composition and initial differential pressure between injected gas and the plug (ΔPi = Pg−Po) on the gas-transport and oil-recovery mechanisms. Moreover, we performed a Péclet number, NPe, analysis to quantify the contribution of each transport mechanism during the soaking period. We found that advective-dominated transport is the mechanism responsible for the transport of gas into the plug at early times of the soaking period (NPe = 1.58 to 3.03). When the soaking progresses, NPe ranges from 0.26 to 0.62, indicating the dominance of molecular diffusion. The advective flow caused by ΔPi during gas injection and soaking leads to improved gas transport into the plug. Total system compressibility, oil swelling, and vaporization of oil components into the gas phase are the recovery mechanisms observed during gas injection and soaking, while gas expansion is the main mechanism during depressurization phase. Overall, gas expansion is the dominant mechanism, followed by total system compressibility, oil swelling, and vaporization. During the “puff” period, the expansion and flow of diffused gas drag the oil along its flowpaths, resulting in a significant flow of oil and gas observed on the surface of the plug. The enrichment of injected gas by 30-mol% C2 enhances the transport of gas into the plug and increases oil recovery compared to pure C1 cases.