Summary History matching of a steam-assisted-gravity-drainage (SAGD) reservoir requires a large ensemble size for proper uncertainty assessment, which ultimately results in high computational cost. Therefore, it is necessary to reduce the number of realizations for SAGD-reservoir simulation purposes. In this paper, a novel sampling method (based on the probability-distance-minimization method) to generate an initial ensemble of reduced size is discussed. This method considers multiple static measurements and geological properties and uses Kantorovich distance to quantify the probability distance between the original ensemble and the reduced ensemble, which is later optimized by use of the mixed-integer linear-optimization (MILP) technique. To show the effectiveness of the method, we have shown history matching of an SAGD reservoir using the smaller size initial ensemble derived from the proposed method and compared with the original ensemble. For history matching, the ensemble Kalman filter (EnKF) has been used because of its ability to assimilate data for large-scale nonlinear systems. Results are compared with several other methods, such as importance sampling, kernel K -means clustering, and sampling by use of orthogonal ensemble members. The robustness and usefulness of each method for generating an improved initial ensemble of reduced size are analyzed on the basis of two criteria: (1) Does the smaller ensemble retain the same statistical distribution characteristics as the original ensemble, and (2) does the smaller ensemble improve the performance of history matching? In general, we conclude that the improved, smaller initial ensemble created by use of the proposed method retains the best statistical characteristics of the original ensemble. Also, it provides better performance compared with other ranking methods in sampling and history matching using EnKF. Finally, the proposed method can reduce the computing cost significantly without compromising uncertainty in the forecast model, which allows for real-time updating at smaller time intervals.

Summary There is now an array of analytical, semianalytical, and empirical forecasting methods that can be used to history match and forecast multifractured horizontal wells (MFHWs) completed in low-permeability (tight) reservoirs. Recent developments in analytical modelling have extended model application to cases in which the fracture geometry associated with MFHWs is complex. However, analytical modelling is still primarily limited to single-phase-flow problems, which is very restrictive, and potentially inaccurate, for tight oil and liquid-rich gas reservoirs flowing at less than saturation pressure. In this work, a semianalytical method is presented for history matching and forecasting MFHWs with simple and complex fracture geometry completed in tight, black-oil reservoirs and flowing at less than the bubblepoint pressure. The linear-to-boundary (LTB) model, commonly used to model flow in the inner (stimulated) region of an MFHW, is altered to account for two-phase flow of oil and gas. The enhanced-fracture-region (EFR) case, in which both stimulated and nonstimulated regions contribute to flow, is approximated (empirically) by superposition of two modified LTB models (one representing the inner fractured region and the other the outer, nonstimulated region), and similarly altered to account for two-phase flow. An important observation is that, for MFHWs flowing at less than bubblepoint at constant flowing bottomhole pressure during transient linear flow, the slope of the square-root-of-time plot for both oil and gas phases is constant [i.e., gas/oil ratio (GOR) is constant]. The slope and intercept of the square-root-of-time plot for the primary phase (e.g., oil in the cases studied) can therefore be used to generate a forecast during the transient linear-flow period for oil and for gas (by assuming constant GOR). For boundary-dominated flow, a robust method for forecasting gas and oil was developed using material balance for both phases combined with a modified productivity-index equation that accounts for multiphase flow. A fully implicit approach has been used to solve the flow equations for oil and gas. The new modified LTB and EFR models simplify forecasting considerably for low-permeability black-oil reservoirs exhibiting multiphase flow behaviour, relative to numerical simulation, although they are not as rigorous. The new models can, however, be tied directly to the results of rate-transient analysis and are flexible enough to be applied to common conceptual models used in the literature for forecasting MFHWs under certain conditions. The new modified LTB model has been compared with both simulated and field examples. The initial results demonstrate that transient- and boundary-dominated-flow periods for oil and gas are reasonably matched with the new approach, although slight mismatches may occur, particularly during early boundary-dominated flow. The limits of the new forecasting method will continue to be explored in future work.

Summary Unconventional reservoirs require extensive hydraulic-fracturing treatments to produce fluids economically and efficiently. The main purpose of such treatments is to create complex fracture networks with high-conductivity paths deeper into the nonstimulated reservoir regions. Proppants play an important role in maintaining good-quality fracture conductivities, which then greatly affect long-term production performance. In addition, research on proppants has shown a reduction in conductivities under downhole stresses and multiphase-flow behaviours. Therefore, it is important to study the effect different proppants and conductivities have on production performance through actual field cases. To evaluate the production performance of wells completed with different proppants, the authors proposed an integrated work flow for characterization and simulation of unconventional reservoirs. This work flow is unique because of the stochastic fracture-network-generation algorithms and improved unstructured-grid-generation techniques. Both analysis of field-production data and numerical simulations were performed on eight wells in the CAPA field of North Dakota. For the field-data analysis, three public-data resources were reviewed to prepare a summary of reservoir properties, fracture properties, proppant properties, and production history. For the numerical simulations, all the wells were modelled and simulated with the proposed work flow. Finally, sensitivity analyses were carried out to investigate the effects of fracture conductivities and natural fractures. After completing the field-case studies and reservoir simulations, it was concluded that with the same fracture design, higher fracture conductivity improves production performance. Pumping a smaller volume of upgraded proppants with higher conductivity not only improves long-term production performance, but also justifies the additional costs and reduces the overall operation time of the entire hydraulic-fracturing job. The stimulated reservoir volume was greatly increased, as was the production performance, where natural fractures exist. In this paper, field-data analysis was applied in the Bakken to demonstrate the integrated unconventional work flow. The proposed unstructured-gridding algorithms can be incorporated into any preprocessor to handle complex networks. Reservoir, fracture, and proppant characterization and reservoir simulation of the field cases can help engineers prepare and interpret simulation input and output.

Summary With the current interest in exploiting thin unconsolidated heavy-oil reservoirs, cold heavy-oil production with sand (CHOPS) can be considered to be a promising primary-recovery technique. However, it offers low recovery factors (~5-15%) and creates a complex network of high-permeability channels known as workholes, while simultaneously changing formation compressibility and in-situ stress conditions. Eventually, development of such a network would lead to a softer layer within the shallow unconsolidated reservoir, which can carry less of the overburden stress. Further development of such reservoirs is usually achieved through enhanced-oil-recovery (EOR) applications in the form of cyclic solvent stimulation within an economic framework. Cyclic loading and unloading of this EOR technique make it even more difficult to predict the recovery performance. In this study, a 3D geomechanical model was used to calculate the stress distribution in a history-matched field in Alberta with 15 producers. The fractal patterns generated from the diffusion-limited-aggregation (DLA) algorithm were used to represent the wormhole network with different strength properties. Foamy behaviour of heavy oil was modelled with the help of a set of kinetic reactions. The hydro-geomechanical model was then used for field-development planning, reservoir management, and assessment of near-wellbore regions during cyclic injection and production. The fieldwide deformation and stress changes were analyzed in deep overburden, caprock, and reservoir to show the influence of local stress orientations in soft and stiff layers. Next, we considered a sector model with a single well. The model introduced was used to assess EOR processes with different solvent streams. While light hydrocarbon components help to repressurize the formation, the heavier components seem more effective in heavy-oil dilution. This occurred while stress arching redistributed the cyclic injection/production-induced stresses to flow around soft inclusions. Although it is difficult to obtain data to calibrate the 3D hydro-geomechanical model, it allows for reliable investigation of reservoir performance and provides deeper insight than does the use of flow simulation alone. The assessment of the potential of geomechanics can ascertain whether a more-detailed modelling is necessary.

Summary Vapour extraction (VAPEX) is a nonthermal process using vapourized solvents, with promising potential to reduce steam consumption in heavy-oil recovery. The key recovery mechanisms are convection and molecular diffusion enhanced by various spreading mechanisms [e.g., capillarity and velocity variations at the micro and macroscale (i.e., dispersion and mixing)]. The efficiency of diffusion/dispersion depends significantly on reservoir heterogeneities, which exhibit a wide range of length scales. This paper demonstrates a procedure for quantifying the scaling characteristics of effective mass transfer accounting for heterogeneities based on the volume-averaging approach. Volume averaging is a mathematical technique used to derive continuum equations at coarse scales given representative transport equations at fine scales. Although treatment of transport problems has been published in the past, application to stochastic geological systems is limited. In the proposed procedure, results from a fine-scale numerical flow simulation reflecting the full physics of VAPEX over a small element of the reservoir are integrated by use of the volume-averaging technique to provide effective description of mass transfer at the coarse scale. Scaling characteristics of effective mass transfer are investigated systematically for different heterogeneity distributions. Results show (1) spatial variability of effective-mass-transfer coefficients increases as a solvent chamber advances through the reservoir; (2) mean and variance of effective-mass transfer vary with length scale in a fashion similar to that of recovery statistics; and (3) variability in effective-mass transfer is a strong nonlinear function of heterogeneity. An original contribution is to provide a general framework for developing scaling relationships of effective mass transfer in VAPEX accounting for reservoir heterogeneities. It also presents an important potential in modelling of other solvent-injection applications. Results demonstrate that effective-mass transfer varies with length scale and heterogeneity; hence, it should be represented properly for accurate prediction of recovery performance in simulations using scaled-up reservoir models.

Summary Thermal gas/oil gravity drainage (T-GOGD) is an attractive enhanced-oil-recovery method applicable to naturally fractured reservoirs (NFRs). The process is applied successfully in Qarn Alam, a heavy-oil field in Oman. This paper presents a case study featuring dynamic-modelling optimization and uncertainty-analysis workflow for T-GOGD in a bitumen-bearing fractured reservoir on the basis of realistic 3D fracture characterization. In T-GOGD, the fractures are displaced to steam to provide a (matrix) gravity-drainage potential while heating the reservoir at the same time. One of the recovery mechanisms associated with T-GOGD is thermal expansion, which can result in high initial rates, but may cause plugging of the fracture system in the case of extraheavy oil (bitumen) if the expanded oil cools down before it is being produced. This situation requires short-distance well configurations and/or steam-stimulation cycles to establish communication. In an NFR, steam vapour occupies the fracture system while oil drains through the matrix, increasing the area for heat transfer with respect to the steam-chamber case; the process therefore differs significantly from steam-assisted gravity drainage, and a different production function applies. Shell’s in-house reservoir simulator MoReS with advanced dual-permeability capability is used to model development of T-GOGD in a bitumen reservoir employing 3D element-of-symmetry (EOS) models. A realistic fracture-characterization and -modelling process is described. The geometrical well configuration and operating schedule and strategy are optimized on an economic function for a deterministic subsurface realization. Using an uncertainty-analysis work flow, cumulative distribution functions of recovery and steam/oil ratio (SOR) are generated. Finally, robust optimization is explored by use of an economic objective function. The study concludes that (1) relatively large well spacing is feasible while injector/producer horizontal well offset is necessary to avoid steam channeling to the producer well, (2) live steamproduction control is a robust operating strategy, (3) performance is most sensitive to matrix permeability and oil viscosity, and (4) vertical fracture connectivity plays an important role in the process performance. T-GOGD has significant potential to develop the bitumen resource in naturally fractured carbonates.

Summary Every simulation engineer wishes to simulate large full-field models, but historically reservoir simulation of the steam-assisted-gravity- drainage (SAGD) process has been constrained to single-well models up to a single pad. Models of these sizes provide valuable information and have helped to assess the development potential of reservoirs. These models may be used for reservoir management and to support the decision-making process for the design of the initial completion, operating strategy, and multipad wind-down evaluations, and also qualitatively assess the uncertainty in the SAGD forecast under different geological settings. However, in many cases we are left with the question of how multiwell and multipad communications ultimately affect performance at the well-pair scale. Because of technological constraints with computer hardware and simulation technology, running extremely large multipad models has been until recently largely impractical, especially when trying to run multiple scenarios to better understand the impact of geological and operational uncertainty. In this paper, we present a new and practical workflow that makes running extremely large multipad, multimillion-grid-cell SAGD models a reality. The three major steps of the workflow are (1) generating simulation-friendly geomodels, (2) use of experimental design and 3D submodels on the basis of SAGD performance index (SPI) for numerical tuning, and (3) use of 2D cross sections and SPI to develop dynamic grid-refinement-parameter values for the full 3D model. All of these steps are intended to improve the numerical stability and run time of multipad SAGD simulation models. A 24-SAGD-well-pair model with 2.52 million gridblocks was simulated for 10 years of forecast. The reservoir is geologically complex and highly heterogeneous. We discuss some of the important aspects that need to be accounted for when simulating large-scale SAGD models. Using this new workflow, the simulation run time was reduced from 42 days to 7 days on eight central processing units (CPUs)—a six-time speedup. The resulting run time is short enough to facilitate multirealization simultaneous runs using eight CPUs, hence maximizing the throughput and minimizing the simulation cycle time. This new workflow can be easily replicated and, more importantly, automated to reduce engineering time requirements. While this paper focuses on the SAGD process, this methodology is completely generic in that it can be applied to any large data set for any process. Details will differ depending on the process, but the workflow will be the same.

Summary Practical methods of operating dual-/triple-tubing strings, on the basis of temperature monitoring that is currently available, to achieve uniform steam-chamber development and enhanced production in a steam-assisted-gravity-drainage (SAGD) process, are presented. The work is motivated by the fact that numerous operators use dual-tubing strings for designing and optimizing steam-chamber development. Flow in the region of the SAGD horizontal well pair is often irregular, and dual-tubing strings may help to even out and improve both injection and production. Problems that operators have with multiple tubing strings in wells include their control and design. In this work, the injector and the producer will have two tubing strings each: one landed at the toe and the other at the heel. Control points are applied on each injection tubular. Injection at these control points is regulated by a proportional- integral-derivative (PID) feedback controller monitoring temperature differences between injected and produced fluids. A brief examination and discussion of the performance of control points in the production tubulars are also included. The PID controller will attempt to accomplish two goals: (i) to achieve evenness in injection and production conformance along both wells and (ii) to enforce a specified temperature offset between the injector and producer in order to improve oil production and reduce steam production and injection. Sensitivity of the feedback controller will be examined for (a) heterogeneity where several synthetic permeability patterns will be tested to gauge the effectiveness of coping with reservoir complexity, (b) update frequency where a comparison will be made between instantaneous and periodic updating of the controller error terms, and (c) ability of the controller to cope with early temperature rises in produced fluids. Well monitoring is accomplished through the use of high-temperature fibre-optic temperature sensing that is currently available. Results and further discussion are offered on whether an additional tubular landed at the midpoint of both wells will benefit production from a heterogeneous reservoir.

Summary Air-injection-based recovery processes are receiving increased interest because of their high recovery potentials and applicability to a wide range of reservoirs. However, most operators require a certain level of confidence in the potential recovery from these (or any) processes before committing resources, which can be achieved with the use of numerical reservoir simulation. In a previous paper, (Gutiérrez et al. 2009) it was proposed that after successful laboratory testing, analytical calculations and semiquantitative simulation models would be used for pilot design and further optimization of the actual operation. However, the specific steps for building the field-scale-simulation models were not addressed explicitly. This paper discusses a detailed workflow that can be followed to engineer an air-injection project using thermal reservoir simulation. The first step of the simulation study involves the selection of a kinetic model that either can be developed specifically for the reservoir in question or taken from public literature. Second, the oil would be characterized in terms of the same pseudocomponents employed by the kinetic model, and relevant pressure/volume/temperature (PVT) data would be matched to develop a fluid model for the thermal simulator. This new fluid model is used in the field-scale-simulation model to history match the production history (i.e., before air injection) of the field. Third, relevant combustion-tube tests would be history matched to validate the kinetic model and refine the thermal data that would be entered into the field-scale model. Finally, the results and knowledge gained from the combustion-tube match(es) are applied to the field-scale model with the proper upscaling of some parameters. This simulation model would aid in selecting optimum well locations and operating strategies of the pilot. It would then be refined as the actual operation progresses to enhance its predictability and allow further optimization of the project. Technical considerations, advantages, and limitations of each step of the workflow are discussed in detail. This paper also presents workflow variations and recommendations applicable to new and already-mature air-injection projects for which simulation models are being developed.

Summary An ensemble-based history technique has been applied to implicitly estimate three-phase relative permeability curves from production data. A power law representative of relative permeability curves is used. Both endpoints and shape factors of relative permeability curves are included in state vectors that are updated sequentially by assimilating observation data. This method has been validated by accurately evaluating relative permeability in a synthetic reservoir with 2D, three-phase flow. It is shown from the synthetic case that good estimation of relative permeability curves can be obtained by assimilating the observed oil rates, gas/oil ratios, and bottomhole pressures of production wells. Both shape factors and endpoints of relative permeability curves are accurately evaluated; however, a larger ensemble size is needed to avoid filter divergence. Compared with the existing implicit methods, the ensemble-based history matching technique does not require the gradient of the objective function, which makes the technique easy to implement.

Summary The vapour extraction (VAPEX) process, as a nonthermal process, may be suitable for the recovery of heavy oil and bitumen. In this process, the injected solvent diffuses into the heavy oil/bitumen, reduces its viscosity, and drains it to the producing well. The VAPEX process is more acceptable than other processes because of its environmental friendliness, low capital and operating costs, and suitability for thin reservoirs. Most of the efforts in the modelling of the VAPEX process have concentrated on the application of fluid-flow equations to the solvent and the diluted oil inside each gridblock used in the simulation of the VAPEX. This is adequate when very fine gridblocks are chosen to simulate the process in which the boundary layer (transition zone) occurs over a number of gridblocks. Fine gridblocks, however, require a large amount of simulation time, which is not applicable for field-scale simulation even with today's computing power. To deal with this problem, a new approach is introduced that is based on the application of the fluid-flow equations to three phases: solvent, diluted oil, and heavy oil/bitumen. With this approach, it becomes possible to have mobile solvent, mobile live oil, and immobile or slow-moving heavy oil/bitumen inside a gridblock. The main feature of the proposed model is its ability to capture the boundary layer within a gridblock, making very fine gridblocks unnecessary in the simulation of the VAPEX process. In addition, this approach can be applied to model the viscous fingering inside gridblocks.

Summary A numerical fully implicit nonisothermal wellbore/reservoir simulator is developed. The model entails simultaneous solution of transient coupled mass-, momentum-, and energy-balance equations within the wellbore; energy-balance equations for the tubular and cement materials and the formation surrounding the wellbore; and mass-balance and flow-rate/pressure equations for the reservoir formation. A wellbore heat-loss model that is a strong feature of this study is developed and employed in the model to improve the accuracy of the simulator and to be able to estimate the casing temperature and formation-temperature distribution. The model formulation is completed with an equation of state (EOS) to estimate fluid properties and appropriate friction-factor correlations in the wellbore tubing to compute the frictional pressure drop for different flow regimes. The developed model has several applications in the petroleum industry, particularly in the gas-well testing design and interpretation of both isothermal and nonisothermal gas reservoirs. This nonisothermal simulator is validated through comparisons to both analytical models and an equivalent numerical isothermal coupled wellbore/reservoir simulator that is also developed in this paper. Applications of this simulator to analyzing gas-well testing problems, in addition to several important observations, are extensively studied in Part 2 of this research work (Bahonar et al. 2010). Currently, it has been well accepted that the applicability and significance of a reservoir simulator depend on the behaviour of the wellbore and interaction between the wellbore and reservoir. A robust, accurate coupled wellbore and reservoir simulator is an invaluable tool for the petroleum engineer to help the petroleum industry understand production behaviour, make a meaningful prediction, and make correct decisions in all field-development and production stages.

Summary The Tommy Lakes field is located in northeastern British Columbia, Canada, and is one of the largest Middle Triassic gas pools within the western Canada sedimentary basin (WCSB). The major gas-production formation (Halfway/Doig reservoirs) at the Tommy Lakes field corresponds to shoreface sands with permeabilities ranging between 0.1 and 3 md, and porosities of 3 to12%. For the purpose of production optimization and field development, a full-field reservoir model was developed with the integration of advanced reservoir characterization, hydraulic-fracture modelling, and history-matching techniques. This study presents an integrated workflow for modelling the low-permeability Doig gas reservoir. A stochastic geostatistical reservoir model was developed on the basis of concepts emanating from an outcrop analogue analyzed with terrestrial light detection and ranging (LiDAR) technology and 60 wells that represent the fundamental rock characteristics, structure, facies? proportions, and petrophysical properties of the Doig anomalously thick sandstone bodies (ATSBs). Structural tops were interpreted from well logs and permeability/porosity relationships established from quantitative log analysis and core/log calibration. Facies were identified in cored intervals and were further grouped into four lithofacies. An artificial neural network (ANN) was used for training the logs of key wells [gamma ray (GR), neutron porosity (NPHI), and bulk density (RHOB)] and populating the facies distribution of uncored wells. Facies-based log-derived porosity, permeability, shale volume, and water saturation were assigned to gridblocks using sequential Gaussian simulation (SGS). Finally, the Monte Carlo simulation approach was used to rank the key variables affecting original gas in place (OGIP) in the uncertainty and optimization process. Flow-based techniques were used for upscaling reservoir properties into the coarse simulation grid. The full-field simulation model was calibrated with buildup data and hydraulic-fracture modelling of single wells. Production of the Doig channel from commingled wells was allocated systematically in order to achieve a good match of the gas-production history and bottomhole pressures. Sensitivity analysis of fracture half-length and its impact on ultimate gas recovery was investigated. This concluded with an integrated development strategy. It is concluded that integration of multiple domains leads to a valid full-field reservoir model, which is critical in developing an integrated strategy, predicting reservoir performance, and optimizing gas production.

Summary Because more and more wells have been put in operation, an accurate modelling of wellbore flow plays a significant role in reservoir simulation. One requirement of a wellbore model is its ability to trace various flow boundaries in the tubing, such as those created by phase or flow regime changing. An algorithm of dynamic gridding is applied to the wellbore flow model coupled with Stanford?s general purpose research simulator (GPRS), which has the capability to simulate the isothermal black oil reservoir model to obtain detailed information that explains such important quantities as flow pattern and mixture velocity in any specific location of wellbore. A significant problem in this case is how to calculate fluid and velocity properties with a fine grid (segment) on the boundaries of different flow regimes in the wellbore. Local dynamical segment refinement in the well can accurately and effectively handle this problem. This wellbore model includes mass conservation equations for each component and a general pressure drop relationship. The multiphase wellbore flow is represented using a drift-flux model, which includes slip between three fluid phases. The model determines the pressure, mixture flow velocity, and phase holdups as functions of time and the axial position along the well or alleviation depth. In addition, this model is capable of generating automatically adaptive segment meshes. We apply the black oil model to the simulation of several cases of isothermal dynamical local mesh refinement, and compare the results with fixed coarse and fine meshes. The experiments show that using local segment refinement can yield accurate results with acceptable computational time.

Summary Material balance has long been used in reservoir engineering practice as a simple yet powerful tool to determine the original gas in place ( G ). The conventional format of the gas material balance equation is the simple straight line plot of p / Z vs. cumulative gas production ( G p ), which can be extrapolated to zero p / Z to obtain G . The graphical simplicity of this method makes it popular. The method was developed for a "volumetric" gas reservoir. It assumes a constant pore volume (PV) of gas and accounts for the energy of gas expansion, but it ignores other sources of energy, such as the effects of formation compressibility, residual fluids expansion and aquifer support. It also does not include other sources of gas storage, such as connected reservoirs or adsorption in coal/shale. In the past, researchers have introduced modified gas material balance equations to account for these other sources of energy. However, the simplicity of the p / Z straight line is lost in the resulting complexity of these equations. In this paper, a new format of the gas material balance equation is presented, which recaptures the simplicity of the straight line while accounting for all the drive mechanisms. It uses a p / Z ** instead of p / Z . The effect of each of the previously mentioned drive mechanisms appears as an effective compressibility term in the new gas material balance equation. Also, the physical meaning of the effective compressibilities are explained and compared with the concept of drive indices. Furthermore, the gas material balance is used to derive a generalized rigorous total compressibility in the presence of all the previously mentioned drive mechanisms, which is important in calculating the pseudotime used in rate transient analysis of production data.

Summary Gas hydrates are a potentially vast untapped source of natural gas. Recent numerical and field studies suggest the Mallik gas-hydrate field in Canada's Mackenzie Delta may represent a technically producible and potentially economically viable reservoir of natural gas. Our initial reservoir simulations using a kinetic reaction approach indicate that gas evolution and transport within porous geologic reservoirs have a significant effect on fluid production characteristics, while field and laboratory data suggest that significant amounts of evolved gas can be trapped for some time within the reservoir, depending on the field operation. In this work, we invoke modelling concepts extensively employed in quantifying gas ex-solution from viscous oils to further assess the kinetic behaviour of gas-hydrate ex-solution through depressurization. Here, the gas bubbles can be categorized into three groups with explicit transport behaviour: small bubbles (water phase), large bubbles (immobile) and connected bubbles (or free gas). These concepts allow the development of a new set of kinetic reactions for hydrate dissociation: one representing the (possibly delayed) conversion of hydrate into water and dispersed gas bubble phases, and one representing the evolution from dispersed bubbles to connected bubbles. These reactions can effectively capture the nonequilibrium fluid-flow behaviour observed in field production tests. For modelling of the transport phenomenon, we assumed two explicit mobility formulations: (1) trapped bubbles (no mobility) and a flowing water phase and (2) large connected gas bubbles and flowing water (with relative mobility). Relative mobility can be estimated by using traditional gridblock-relative permeability curves. We then develop a simple mechanistic gas bubble trapping tool as a function of the capillary number, which can easily be incorporated into our numerical simulator. This entrapment of the nonwetting gas-phase results in higher values of critical gas saturation. Two case studies based on alternative representations of a Mallik-like gas-hydrate reservoir demonstrate that significant errors can result in reservoir modelling if these fluid transport phenomena are not adequately represented in numerical simulations. Aspects of the model developed here have been applied to history matching and prediction of natural gas recovery from a clastic, sand-dominated reservoir at the Mallik site.

Summary The flow in regions of oil and gas reservoirs that are dominated by gravity segregation can occur through two different mechanisms. First, all reservoir fluid phases, possibly oil, gas and water, might move through the same pores. One or more phases might move upward while the others move countercurrently downward, in the same pores. If such a mechanism were valid, Darcy's law could be applied uniformly over large areas of the reservoir to provide average-phase velocities, just as if the flows were the result of pressure-induced convection. However, a second mechanism is also possible. The phases might be segregated such that some pores carry the upward flowing phases, while other pores carry downward flows. When this mechanism is valid, Darcy's law applies only locally to the upward or downward regions of flow. The two mechanisms result in substantially different phase velocities. Simulators, including those available commercially, generally assume the first mechanism (i.e., uniform, countercurrent flow throughout each simulation cell). This paper describes an experimental study in which two-phase flow velocities were measured as the phases moved through a bed of small, uniform glass beads, as the result of gravitational forces only. The resulting velocities were more consistent with those predicted for segregated flows of Mechanism 2 compared with those of the commonly assumed homogeneous flows of Mechanism 1. These results suggest that greater accuracy in reservoir simulation may be achieved by including segregated flow in areas of the reservoir where gravity segregation predominates.

Summary Geostatistical models of reservoir properties are high resolution with many grid cells; it is impractical to use them directly in flow simulation because of computational costs. Upscaling techniques are applied to average small-scale permeability values to larger flow simulation blocks. In cases where unstructured grids are used or the geological features inside the gridblock are not aligned with the block geometry, symmetric or full-permeability tensors arise instead of a simple diagonal tensor. A method is presented to calculate the permeability tensor for an unstructured gridblock to account for the small-scale heterogeneity information inside the gridblock. Single-phase flow-based upscaling is performed based on random boundary conditions and the effective tensor permeability is found through an optimization technique. Full, symmetric and diagonal permeability tensors are calculated for 2D and 3D blocks and sensitivity analysis is performed.

Summary Among the three types of geological CO 2 sequestration (mature oil and gas fields, unminable coalbeds and deep saline formations), depleted gas condensate reservoirs are particularly interesting. First, because of the high-compressibility of gas, these reservoirs have larger storage capacity than oil reservoirs or aquifers. Second, the condensate that has dropped out from the gas phase during natural depletion will re-vaporize because of re-pressurization of the reservoir and by miscibility with the injected CO 2 . This condensate can be recovered from producing wells and leaves more pore volume for available storage of CO 2 . The objective of this study is to investigate the CO 2 storage capacity in different formation types, for different levels of CO 2 purity and different injection schedules. To this aim, we analyzed the injection of a CO 2 -based stream into a depleted gas condensate reservoir and into a saline aquifer using a compositional reservoir simulation model. The dynamics of the reservoir impose a minimum period of injection that is required in order for the storage scheme to benefit from 100% of the reservoir storage capacity. Hence, over and above a certain CO 2 injection rate, it becomes meaningless to invest in bigger compressors to increase this rate to reduce the time of injection. When the CO 2 stream contains impurities, such as N 2 or methane, the storage capacity of the reservoir decreases proportionally to the impure stream's compressibility factor and its concentration of impurities. This finding suggests that an economic optimum between the costs of separation, compression and injection can be determined. Finally, the mass of CO 2 sequestrated per pore volume in the equivalent aquifer model is approximately 13 times lower that of the depleted gas condensate reservoir model. This confirms that, because of their low overall compressibility, aquifers offer a far lower ratio of CO 2 stored per pore volume than depleted gas condensate reservoirs. However, aquifers tend to have a far larger extent, which often compensates somewhat for this lower ratio and therefore provides storage for significant volumes of CO 2 .

Summary Accurate characterization of sub-surface oil reservoirs is an essential prerequisite to the design and implementation of enhanced oil recovery (EOR) scenarios. Specifically, in reservoir characterization, integrating static and dynamic data into reservoir models to construct accurate and realistic models has received considerable attention. Unlike most of the conventional geostatistical approaches of integrating data into reservoir models that are based on semi-variograms (two-point statistics) as a measure of spatial connectivity, a complete multiple-point (MP) statistic framework is presented in this paper. In contrast to two-point statistic methods, MP statistics-based methods are capable of reproducing curvilinear geological structures. The algorithm starts with extracting MP statistics from training images (TI) using an optimal spatial template. After collecting different patterns and building the MP histogram, the pattern reproduction process commences. This process begins from data locations and then grows to fill the whole reservoir domain. The algorithm accounts for three main practical issues: uncertainty in geological scenarios, scanning template and non-stationarity. The MP statistics algorithm (growthsim) is capable of integrating data from multiple data sources. Among these data types is dynamic data or flow history. The conventional approach to integrate production information into reservoir models is by iterative perturbation of the reservoir model until the production history of the reservoir is matched. Iterative methods have been applied till date to random fields that are completely characterized by a two-point co-variance function. In contrast, this paper presents a forward modelling approach that investigates history matching within a MP modelling framework. A novel technique implemented in this research is based on the merging of MPs inferred from history matched and geological models. Pattern growth is performed subsequently by sampling from the merged MP histograms. History matched models using the presented approach show an excellent agreement with underlying geological descriptions and match production history.