Black Oil Formulation Research Articles

A semi-analytical rate-transient analysis model for fractured horizontal well in tight reservoirs under multiphase flow conditions

Abstract Rate-transient analysis (RTA) has been widely applied to extract reservoir/fracture properties using analytical and semi-analytical methods with simplifying assumptions. However, current RTA models may lead to misdiagnosis of flow regimes and incorrect estimates of reservoir/fracture information when complex fracture network, multiphase flow, and pressure-dependent properties occur in tight reservoirs simultaneously. A semi-analytical model is developed to account for multiphase flow, complex fracture network, and pressure-dependent properties. The technique uses the black oil formulation and butterfly model to determine three nonlinear partial differential equations (PDEs) that describe the flow of oil, gas, and water in the reservoir with complex fracture network. A modified Boltzmann variable considering the heterogeneity of complex fracture network is proposed to convert the fluid flow PDEs to a set of ordinary differential equations (ODEs) that can be solved through the Runge-Kutta method. A new rate-transient analysis workflow is also developed to improve flow regime identification (ID) and the accuracy for tight oil reservoirs with complex fracture network. It is applied to a synthetic case with equivalently modeled complex fracture network and multiphase flow. The estimated fracture properties are in excellent agreement with model inputs.

Compositional Streamline-Based Modeling of Polymer Flooding Including Rheology, Retention, and Salinity Variation.

The chemical enhanced oil recovery (CEOR) technology that is most used worldwide is polymer flooding due to its proven commercial success at field scale, maturity, and versatility to combine with other technologies. So, there has been an increasing interest in expanding its applicability to more unfavorable mobility ratio conditions and adverse environments (such as high-temperature, high-salinity carbonate reservoirs, pH-sensitive polymers, and formations with active clays). Therefore, a requirement for successful field application is to find the design parameters of the process that balance material requirements and oil recovery benefits in a cost-effective manner, which is usually done through reservoir modeling. Polymer flooding predictive tools normally require detailed information and are based on time-consuming field reservoir simulations. Thus, for effective project management, a quick and sound tool is needed to screen for polymer flooding applications without giving up key physical-chemical phenomena that govern the oil recovery. In this research, we developed a two-dimensional polymer flooding model based on the streamlines approach. This is an alternative to having a multidimensional practical tool thoroughly representing the physical and chemical behavior of polymer flooding by considering key phenomena such as rheology behavior (shear thinning and shear thickening), salinity variations, permeability reduction, and polymer adsorption. Previously published streamline multidimensional models for polymer flooding lack the integrated modeling of the above-mentioned key phenomena. Additionally, the models to represent rheology and retention phenomena in the proposed tool consider a more complete description than the present streamline-based simulators. For the construction of streamlines, we considered a black oil formulation to estimate the pressure and saturation 2D distribution by applying the implicit in pressure and explicit in saturation method, coupled with an explicit formulation for the 2D composition computation. For saturation-composition along the streamlines, the 1D practical tool incorporated represents the polymer flooding key phenomena. The numerical algorithm used by the streamline-based tool is supported by laboratory experiments for waterflooding in homogenous porous media, analytical results for waterflooding in heterogeneous media, polymer flooding field scale simulation cases, and a CMG-STARS model built as a reference for waterflooding in both media (homogenous and heterogeneous) and for polymer flooding. The practical tool developed contributes to simplifying the upscaling from laboratory observations to field applications with better fitted numerical simulation models and to determining favorable scenarios; thus, it could assist in understanding how key parameters affect oil recovery without performing time-consuming CEOR simulations.

Correction to: Sequential fully implicit newton method for flow and transport with natural black-oil formulation

Correction to: Sequential fully implicit newton method for flow and transport with natural black-oil formulation

Sequential fully implicit newton method for flow and transport with natural black-oil formulation

Sequential fully implicit newton method for flow and transport with natural black-oil formulation

Dynamic PVT model for CO2-EOR black-oil simulations

A well-planned CO2EOR operation can help meet an ever-increasing need for energy and at the same time reduce the total CO2 footprint from the energy production. Good simulation studies are crucial for investment decisions where increased oil recovery is optimized and balanced with permanent CO2 storage. It is common to use a compositional simulator for CO2 injection to accurately calculate the PVT properties of the mixture of oil and CO2. Compositional simulations have significantly increased simulation time compared to blackoil simulations. Large simulation studies where many simulations are used either to represent uncertainty and/or optimize the results can thus be unpractical. On the other hand existing blackoil formulations often poorly represent the PVT properties of the oil-CO2 mixtures. We therefore present an extended blackoil formulation with dynamic blackoil properties that depends on the fraction of CO2 in the cell. These properties represents the density and viscosity of the hydrocarbon - CO2 mixture more accurately and thus give results closer to the compositional simulator. The dynamic blackoil functions are calculated from numerical slim-tube experiments based on one-dimensional equation-of-state (EOS) simulations. The same simulations also gives estimates of the minimum-miscibility pressure (MMP). We present examples based on data from the Fifth Comparative Solution Project: Evaluation of Miscible Flood Simulators, but uses CO2 as the injection gas. These examples shows that the new blackoil model gives results that are closer to compositional simulations compared to existing blackoil formulations. The model is implemented in the Flow simulator. The Flow simulator is developed as part of the open porous media (OPM) project and is an openly developed and free reservoir simulator that is capable of simulating industry relevant reservoir models with similar single and parallel performance as commercial simulators.

A phase I clinical trial to evaluate the safety of thymoquinone-rich black cumin oil (BlaQmax®) on healthy subjects: Randomized, double-blinded, placebo-controlled prospective study

Black cumin or black seed (Nigella sativa L.) is a popular medicinal herb and culinary spice belonging to Ranunculacea family. Thymoquinone (TQ) is the major active phytoconstituent in black cumin and is abundant in the volatile oil fraction. Though black cumin oil containing low TQ content (less than 1%) has been clinically investigated, clinical efficacy and safety data of TQ-rich oil is limited. A recent study with black cumin oil formulation containing 5% TQ (BCO-5) exhibited significant clinical efficacy to alleviate sleep disorders and stress. So, the present phase 1 randomized, double-blinded, placebo-controlled trial evaluated the safety of BCO-5 at a dose of 200 mg/adult/day for 90 days on healthy subjects (n = 70). Both the biochemical and hematological parameters were analysed along with the adverse events or side effects to establish the clinical safety of BCO-5. The study reported neither serious adverse side effects nor any significant alterations in the hematological parameters. The absence of significant changes in the biochemical parameters related to liver function (ALT, AST, ALP), renal function (serum creatinine and urea) were also observed. However, analysis of lipid profile showed a significant (P < 0.05) reduction in total cholesterol, LDL, VLDL and triglycerides, but within the normal range. In conclusion, BCO-5 is safe at 200 mg/adult/day for human consumption and may be clinically evaluated for various health beneficial pharmacological activities where black cumin oil has been shown to have positive effects.

Multiscale methods for model order reduction of non-linear multiphase flow problems

Numerical simulations for flow and transport in subsurface porous media often prove computationally prohibitive due to property data availability at multiple spatial scales that can vary by orders of magnitude. A number of model order reduction approaches are available in the existing literature that alleviate this issue by approximating the solution at a coarse scale preserving fine scale features. We attempt to present a comparison between two such model order reduction techniques, namely (1) adaptive numerical homogenization and (2) generalized multiscale basis functions. We rely upon a non-linear, multi-phase, black-oil model formulation, commonly encountered in the oil and gas industry, as the basis for comparing the aforementioned two approaches. An expanded mixed finite element formulation is used to separate the spatial scales between non-linear, flow, and transport problems. A numerical benchmark is setup using fine scale property information from the 10th SPE comparative project dataset for the purpose of comparing accuracies of these two schemes. An adaptive criterion is employed by both the schemes for local enrichment that allows us to preserve solution accuracy compared to the fine scale benchmark problem. The numerical results indicate that both schemes are able to adequately capture the fine scale features of the model problem at hand.

A semi-analytical approach for analysis of the transient linear flow regime in tight reservoirs under three-phase flow conditions

The majority of current techniques for production data analysis of hydraulically-fractured horizontal wells only consider single- or two-phase flow conditions. Three-phase flow is expected to occur in many practical scenarios of low-permeability reservoir production when water (frac fluid and/or formation) production is occurring along with hydrocarbon phases. In this paper, a new semi-analytical method is developed to allow production data analysis of wells producing from low-permeability (tight) reservoirs exhibiting three-phase during the transient linear flow period.The proposed technique is based on the modified black oil formulation and is developed by employing the Boltzmann transformation. The modified black oil formulation comprises three highly nonlinear Partial Differential Equations (PDE's) that describe the flow of water, oil and gas in the reservoir. The use of the Boltzmann transformation allows conversion of this set of governing fluid flow PDE's to a set of Ordinary Differential Equations (ODE's) that can be easily solved using numerical techniques such as the Runge-Kutta method. In this paper, oil relative permeability under three-phase flow conditions is modelled using Stone's well-known first model.A theoretical basis for the occurrence of straight lines on a plot of 1/q vs √t for any producing phase is provided herein. The slope of the line is a function of the flowing fluid properties, and the reservoir and fracture characteristics. One important advantage of using the Boltzmann transformation is that the linear flow parameter, xf√k, can be directly estimated as a part of the solution process without the need for defining any complex pseudo-variable transformations. The results demonstrate that the relative error in xf√k estimation is generally less than 10% for different fluid models and relative permeability curves. Moreover, the simultaneous solutions of the ODE's provide the pressure and phase saturations as unique functions of the Boltzmann variable; these can be used to find relationships between pressure and phase saturations that in turn can be utilized for other rate transient analysis applications. The derived pressure-saturation relationships are in excellent agreement with numerical simulation for different three-phase relative permeability models.The significance of this paper is that a new theoretical and practical framework is introduced for the first time to analyze three-phase production data for transient linear flow under constant flowing bottomhole pressure conditions. These conditions are of practical importance for many tight production scenarios where water, in addition to hydrocarbon phases, are mobile in the reservoir. The results are validated using numerical simulation.

ICM releases new details about showcase biorefinery

Coal bed methane (CBM) has received increasing attentions as a significant energy resource. Numerical modeling of the CBM recovery processes entails simulation of the complex coupled mechanisms, including desorption of methane from the coal matrix surface, diffusion of gas to coal cleats, and gas flow from coal cleats to the wellbore. Beyond these complex flowing mechanisms, it is crucially important to represent coal cleats, structural fractures, and/or hydraulic fractures realistically in CBM simulators as they provide flow channels and dominate CBM flow behaviors. Existing CBM simulators are typically extended from oil and gas reservoir simulators with either black-oil or compositional formulation, and sorption and desorption are usually modeled by the Langmuir isotherms. The concept of shape factor is commonly used to characterize the flow between matrix and cleats (or fractures). When the shape factor is treated as only a function of cleat spacing, the detailed characteristics of actual cleats (or fractures) are missing, including the spatial distribution of cleats and interconnectivity of cleats. In this study, we propose a new workflow to perform a 2-D coal bed methane recovery simulation with discrete fracture model (DFM) in consideration of both structural fractures (large-scale fractures) and cleats (small-scale fractures). There are two key steps in our approach. First, we use a detailed network of discrete fractures characterized from core samples to represent the actual distribution of identified cleats, and calculate the shape factor of the realistic cleated coal sample by running a flow simulation to pseudo-steady state. Second, we apply the shape factor to field-scale simulations in which large-scale fractures are modeled as DFM. For this purpose, we treat gas sorption and desorption as a “chemical reaction”, and we developed an extension to an existing geochemical-reservoir simulator. We implemented both a “pseudo-compositional” and a “full-compositional” module to study the effect of mass exchange between gas and aqueous phases. We validated our new formulation and simulator development from a benchmark case in which our simulation results show close agreement with commercial simulators. We also demonstrated the significance of modeling mass exchange between fluid phases on CBM recovery in some cases, which is commonly missing in most commercial simulators. Finally, we presented our workflow in modeling an enhanced CO2-ECBM recovery process to a complex fractured coal bed with both large-scale tectonic fractures and small-scale cleats.

A model for CO2 storage and seismic monitoring combining multiphase fluid flow and wave propagation simulators. The Sleipner-field case

The main objective of this paper is to use a flow simulator to represent the CO2 storage and combine it with a wave propagation simulator in order to obtain synthetic seismograms qualitatively matching time-lapse real field data. The procedure is applied to the Utsira formation at Sleipner field. The field data at the site available to us is a collection of seismic sections (time-lapse seismics) used to monitor the CO2 storage. An estimate of the CO2 injection rate and the location of the injection point are known. Using these data, we build a geological model, including intramudstone layers with openings, whose coordinates are defined by performing a qualitative match of the field seismic data. The flow simulator parameters and the petrophysical properties are updated to obtain CO2 saturation maps, including CO2 plumes, so that the synthetic seismic images resemble the real data. The geological model is based on a porous-media constitutive equation. It considers a poroelastic description of the Utsira formation (a shaly sandstone), based on porosity and clay content, and takes into account the variation of the properties with pore pressure and fluid saturation. Moreover, the model considers the geometrical features of the formations, including the presence of shale seals and fractures. We also assume fractal variations of the petrophysical properties. The numerical simulation of the CO2-brine flow is based on the Black-Oil formulation, which uses the pressure-volume-temperature (PVT) behavior as a simplified thermodynamic model. The corresponding equations are solved using a finite difference IMPES formulation. Using the resulting saturation and pore-pressure maps, we determine an equivalent viscoelastic medium at the macroscale, formulated in the space-frequency domain. Wave attenuation and velocity dispersion, caused by heterogeneities formed of gas patches, are described with White’s mesoscopic model. The viscoelastic wave equation is solved in the space-frequency domain for a collection of frequencies of interest using a finite-element iterative domain decomposition algorithm. The space-time solution is recovered by a discrete inverse Fourier transform, allowing us to obtain our synthetic seismograms. In the numerical examples, we determine a set of flow and petrophysical parameters allowing us to obtain synthetic seismograms resembling actual field data. In particular, this approach yields CO2 accumulations below the mudstone layers and synthetic seismograms which successfully reproduce the typical pushdown effect.

On the pressure-saturation path in infinite-acting unconventional liquid-rich gas reservoirs

Unconventional liquid rich natural gas reservoirs exhibit a number of unique technical challenges, including ultra-low rock permeability, which can lead to prolonged periods of infinite-acting flow. Despite this, traditional production data analysis techniques often assume boundary-dominated conditions, which may not be experienced by unconventional systems for very long stretches in their productive life. Analysis of two-phase flow and well production often relies on the use of two-phase pseudo-variables calculations for which the fluid saturation-pressure relationship must be estimated a priori. The de-facto assumption is that such a priori reservoir saturation-pressure dependency can be acquired from available constant volume depletion (CVD) or constant composition expansion (CCE) laboratory test results. As a result, the influence of reservoir characteristics or drawdown conditions on saturation-pressure path has not been rigorously investigated in general; and even less for the particular case of infinite-acting reservoir systems under linear flow regime, which is the most commonly observed flow regime in multi-fractured horizontal wells. In the present work, a recently developed semi-analytical solution for the multiphase black-oil formulation, which considers both pressure and liquid saturation as independent variables, is employed to investigate the influence of reservoir and well conditions on saturation-pressure path in linear infinite-acting liquid rich gas systems. Here, the effects of constant bottomhole flowing pressure, initial reservoir pressure, and relative permeability characteristics on pressure-saturation path are explored in a reservoir system. Results are compared to constant composition expansion (CCE) and constant volume depletion (CVD) tests, which are routinely invoked to estimate saturation-pressure path, and it is demonstrated that these tests provide very poor estimations of saturation-pressure path for all cases considered. In addition, saturation-pressure paths exhibit significant sensitivity to the parameters investigated, as a result of the significant interplay between liquid dropout and phase mobility. Finally, following the results of the sensitivity study, we use the concept of the compositionally-extended black-oil formulation to further study the physical mechanisms that control saturation-pressure path behavior, which are elucidated through an investigation of the in situ and flowing compositions of surface gas and surface oil pseudocomponents. The results of this paper indicate that traditional methods for estimation of the saturation-pressure path in liquid-rich unconventional systems cannot account for the influence of system parameters on liquid-phase dropout and condensate accumulation. Furthermore, production data analysis techniques must account for these dependencies to develop reliable reservoir forecasts and reserve estimations.

Effect of large gas-oil capillary pressure on production: A compositionally-extended black oil formulation

Pore sizes are typically on the order of nanometers for many shale and tight rock oil reservoirs. Such small pores can affect the phase behavior of in situ oil and gas owing to large capillary pressure. Current black-oil simulation practice is to alter the unconfined black-oil data for a fixed mean pore size to generate confined black-oil data with a suppressed bubble-point pressure. This approach ignores compositional effects on interfacial tension and the impact of pore-size distribution (PSD) with variable phase saturations on capillary pressure and phase behavior.In this paper, we develop a compositionally-extended black-oil model where we solve the compositional equations (gas, oil, and water components) directly so that black-oil data are a function of gas content in the oleic phase and gas-oil capillary pressure. The principle unknowns in the variable bubble-point fully-implicit formulation are oil pressure, overall gas composition, and water saturation. Flash calculations in the model are non-iterative and are based on K-values calculated explicitly from the black-oil data. The advantage of solving the black-oil model using the compositional equations is to increase robustness of the simulations owing to a variable bubble-point pressure that is a function of two parameters; gas content and capillary pressure. Leverett J-functions measured for the Bakken reservoir are used to establish the effective pore size-Pc-saturation relationship, where the effective pore size depends on gas saturation, which is the non-wetting phase saturation. The input fluid data to the simulator, e.g. interfacial tension (IFT), phase densities and viscosities, are pre-calculated as functions of pressure from the Peng-Robinson equation of state (PREOS) for three fixed pore sizes. During the simulation, at any pressure and saturation, fluid properties are calculated at the effective pore radius by using linear interpolation between these three data sets. We compare the results of the compositionally-extended black oil model with those of a fully-implicit eight-component compositional model that we have also developed. The results for the Bakken reservoir show that including PSD in the model can increase estimated recoveries by nearly 10% for initially undersaturated reservoirs while the increase can be over 100% for initially saturated reservoirs. Capillary pressure significantly increases the original oil-in-place (OOIP) for reservoirs that would otherwise be initially saturated leading to larger oil production.

A similarity method approach for early-transient multiphase flow analysis of liquid-rich unconventional gas reservoirs

Despite their increased role in the global energy supply, liquid-rich unconventional gas (LRG) resources present a number of technical challenges. Among them, traditional production data analysis methods fail to successfully estimate and forecast production behavior in these systems. This failure is directly related to the extensive early-transient infinite-acting behavior exhibited by these systems, and the added complexities involved with liquid dropout and ensuing multi-phase flow of gas and condensate. Traditional approaches are strongly biased toward single-phase and boundary-dominated analysis; and when multiphase flow is considered, required input data often include laboratory-estimated pressure-saturation data and/or producing gas-oil-ratio data. In the present work, a novel extension of the similarity variable transformation method is developed to forecast production behavior in these LRG systems. The methodology uses the black-oil fluid formulation and considers linear and radial flow regimes under constant bottom hole pressure (BHP) and constant gas flow rate well conditions. Using this method, the system of governing partial differential equations is reduced to a system of ordinary differential equations solved by well-known Runge–Kutta techniques without the need for linearization. It is demonstrated that reservoir pressure and saturation behavior can be forecast simultaneously, thereby eliminating the need for pressure-saturation relationship or producing gas-oil-ratio data as inputs to the model. In all cases explored, the similarity results compared well to numerically generated reservoir data for a variety of well BHP and gas flow rate specifications. Calculated well production metrics also successfully matched data sets, indicating that this approach can be straightforwardly extended to estimate production metrics of interest during early transient conditions, such as liquid and gas production rates or gas-oil-ratio. Results strongly suggest that the method developed here provides a rapid and robust alternative to numerical simulation for forecasting of LRG reservoir systems.

A general finite volume based numerical algorithm for hydrocarbon reservoir simulation using blackoil model

Purpose – The purpose of this paper is to present a detailed algorithm for simulating three-dimensional hydrocarbon reservoirs using the blackoil model. Design/methodology/approach – The numerical algorithm uses a cell-centred structured grid finite volume method. The blackoil formulation is written in a way that an Implicit Pressure Explicit Saturation approach can be used. The flow field is obtained by solving a general gas pressure equation derived by manipulating the governing equations. All possible variations of the pressure equation coefficients are given for different reservoir conditions. Key computational details including treatment of non-linear terms, expansion of accumulation terms, transitions from under-saturated to saturated states and vice versa, high gas injection rates, evolution of gas in the oil production wells and adaptive time-stepping procedures are elaborated. Findings – It was shown that using a proper linearization method, less computational difficulties occur especially when free gas is released with high rates. The computational performance of the proposed algorithm is assessed by solving the first SPE comparative study problem with both constant and variable bubble point conditions. Research limitations/implications – While discretization is performed and implemented for unstructured grids, the numerical results are presented only for structured grids, as expected, the accuracy of numerical results are best for structured grids. Also, the reservoir is assumed to be non-fractured. Practical implications – The proposed algorithm can be efficiently used for simulating a wide range of practical problems wherever blackoil model is applicable. Originality/value – A complete and detailed description of ingredients of an efficient finite volume-based algorithm for simulating blackoil flows in hydrocarbon reservoirs is presented.

A novel approach to model enhanced coal bed methane recovery with discrete fracture characterizations in a geochemical simulator

Abstract Coal bed methane (CBM) has received increasing attentions as a significant energy resource. Numerical modeling of the CBM recovery processes entails simulation of the complex coupled mechanisms, including desorption of methane from the coal matrix surface, diffusion of gas to coal cleats, and gas flow from coal cleats to the wellbore. Beyond these complex flowing mechanisms, it is crucially important to represent coal cleats, structural fractures, and/or hydraulic fractures realistically in CBM simulators as they provide flow channels and dominate CBM flow behaviors. Existing CBM simulators are typically extended from oil and gas reservoir simulators with either black-oil or compositional formulation, and sorption and desorption are usually modeled by the Langmuir isotherms. The concept of shape factor is commonly used to characterize the flow between matrix and cleats (or fractures). When the shape factor is treated as only a function of cleat spacing, the detailed characteristics of actual cleats (or fractures) are missing, including the spatial distribution of cleats and interconnectivity of cleats. In this study, we propose a new workflow to perform a 2-D coal bed methane recovery simulation with discrete fracture model (DFM) in consideration of both structural fractures (large-scale fractures) and cleats (small-scale fractures). There are two key steps in our approach. First, we use a detailed network of discrete fractures characterized from core samples to represent the actual distribution of identified cleats, and calculate the shape factor of the realistic cleated coal sample by running a flow simulation to pseudo-steady state. Second, we apply the shape factor to field-scale simulations in which large-scale fractures are modeled as DFM. For this purpose, we treat gas sorption and desorption as a “chemical reaction”, and we developed an extension to an existing geochemical-reservoir simulator. We implemented both a “pseudo-compositional” and a “full-compositional” module to study the effect of mass exchange between gas and aqueous phases. We validated our new formulation and simulator development from a benchmark case in which our simulation results show close agreement with commercial simulators. We also demonstrated the significance of modeling mass exchange between fluid phases on CBM recovery in some cases, which is commonly missing in most commercial simulators. Finally, we presented our workflow in modeling an enhanced CO 2 -ECBM recovery process to a complex fractured coal bed with both large-scale tectonic fractures and small-scale cleats.

Assessment of CO2 Injectivity and Storage Capacity in a Depleted Pinnacle Reef Oil Field in Northern Michigan

The Midwest Regional Carbon Sequestration Partnership is conducti ng a large-scale CO 2 injection test in a depleted Niagaran Pinnacle Reef in northern Michigan. The focus of the dynamic modeling tas k described in this paper is to evaluate the CO 2 injectivity and storage capacity of this closed carbonate reef structure. We discuss the history-matching process to characterize the closed reservoir model using primary and secondary recovery data and its validation with the field pressures in the current CO2 injection phase. Two alternative conceptual geologic models of the reef are constructed to evaluate the level of detail necessary to efficiently model dynamic reservoir behavior without compromising geologic accuracy. We find that our initial black oil formulation under-predicts reservoir pressure and hence over -predicts injectivity during the CO 2 injection phase. Transition to a compositional model is currently underway to better represent reservoir dynamics by effectively accounting for interphase and intercomponent mass transfer processes. Lessons learned from this exercise can be drawn upon for possible use in injectivity evaluation of other reefs in the region.

Modeling Steam-Assisted Gravity Drainage With a Black-Oil Proxy

Summary This paper describes an alternative approach to model steam-assisted gravity drainage (SAGD) with an isothermal black-oil (BO) reservoir simulator. The oil-viscosity reduction caused by heating in the actual SAGD process is emulated by a tuned saturated pseudo-oil viscosity relation in which solution gas/oil ratio (Rs) is used as a “proxy for temperature.” In the BO formulation, fully saturated oil viscosity (μo*) at reservoir pressure equals μo that would be attained at steam-chamber temperature (T*) in the actual SAGD process; initial oil viscosity (μoi) with initial Rs = 0 represents initial oil viscosity at reservoir temperature; and BO gas properties represent steam at T*. After careful analysis of the SAGD process, one finds that oil flows only along a narrow zone along the outer edge of the steam chamber—the “edge oil-flow zone.” The temperature gradient within this narrow zone is perpendicular to the oil-flow direction and is practically impossible to model with any precision because of the large temperature variation and dynamic steam-chamber shape over time. The BO-model solubility gradient also varies, analogous to temperature in a thermal model, from zero to fully saturated (Rs*) with an associated drop in oil viscosity from μoi to μo*. SAGD design requires many hundreds of runs to find operational conditions that maximize economic value (e.g., injector and producer location, rates, pattern spacing, and steam-chamber temperature T*). The proposed BO proxy model runs several times faster than a thermal model while maintaining similar performance behavior. The proxy-model saturated pseudo-oil viscosity μo(p) relation used is found by history matching a full-physics thermal-model performance prediction of oil rate, bottomhole flowing pressure, and cumulative oil for a 2D homogeneous model. We have found a single-constant μo(p) equation that yields a good match to thermal SAGD performance. The tuned pseudo-oil viscosity relation honors the measured initial reservoir and fully heated (at T*) oil viscosities. Its dependence on Rs is not physical, but reflects the use of Rs as a transform variable for temperature, capturing the strong spatial variation of temperature and oil viscosity within the localized steam/oil boundary region in which oil has been mobilized. The pseudo-oil viscosity relation, defined by a single empirical best-fit constant n—for a given T* and a set of thermal properties—appears to be applicable for a wide range of reservoir heterogeneity, injection and production rates, and well placement. Consequently, it should be possible to use the BO proxy model for SAGD optimization of T*, control rates, and injector/producer vertical-depth difference. We also see the potential of using the BO proxy model for solvent-based SAGD, with the pseudo-oil viscosity model depending on both T* and solvent; thermal compositional modeling is yet even slower and less suitable for optimization.

A numerical procedure to model and monitor CO2 sequestration in aquifers

Carbon Dioxide (CO2) sequestration into geologic formations is a means of mitigating greenhouse effect. In this work we present a new numerical simulation technique to model and monitor CO2 sequestration in aquifers. For that purpose we integrate numerical simulators of CO2-brine flow and seismic wave propagation (time-lapse seismics). The simultaneous flow of brine and CO2 is modeled applying the Black-Oil formulation for two phase flow in porous media, which uses the Pressure-Volume-Temperature (PVT) behavior as a simplified thermodynamic model. Seismic wave propagation uses a simulator based on a space-frequency domain formulation of the viscoelastic wave equation. In this formulation, the complex and frequency dependent coefficients represent the attenuation and dispersion effect suffered by seismic waves travelling in fluid-saturated heterogeneous porous formations. The spatial discretization is achieved employing a nonconforming finite element space to represent the displacement vector. Numerical examples of CO2 injection and time-lapse seismics in the Utsira formation at the Sleipner field are analyzed. The Utsira formation is represented using a new petrophysical model that allows a realistic inclusion of shale seals and fractures. The results of the simulations show the capability of the proposed methodology to monitor the spatial distribution of CO2 after injection.

Modeling of CO2 storage in aquifers

Storage of CO2 in geological formations is a means of mitigating the greenhouse effect. Saline aquifers are a good alternative as storage sites due to their large volume and their common occurrence in nature. The first commercial CO2 injection project is that of the Sleipner field in the Utsira Sand aquifer (North Sea). Nevertheless, very little was known about the effectiveness of CO2 sequestration over very long periods of time. In this way, numerical modeling of CO2 injection and seismic monitoring is an important tool to understand the behavior of CO2 after injection and to make long term predictions in order to prevent CO2 leaks from the storage into the atmosphere. The description of CO2 injection into subsurface formations requires an accurate fluid-flow model. To simulate the simultaneous flow of brine and CO2 we apply the Black-Oil formulation for two phase flow in porous media, which uses the PVT data as a simplified thermodynamic model. Seismic monitoring is modeled using Biot's equations of motion describing wave propagation in fluid-saturated poroviscoelastic solids. Numerical examples of CO2 injection and time-lapse seismics using data of the Utsira formation show the capability of this methodology to monitor the migration and dispersal of CO2 after injection.

Efficient Field-Scale Simulation of Black Oil in a Naturally Fractured Reservoir Through Discrete Fracture Networks and Homogenized Media

SummaryThis paper describes a hybrid finite volume method, designed to simulate multiphase flow in a field-scale naturally fractured reservoir. Lee et al. (WRR 37:443-455, 2001) developed a hierarchical approach in which the permeability contribution from short fractures is derived in an analytical expression that from medium fractures is numerically solved using a boundary element method. The long fractures are modeled explicitly as major fluid conduits. Reservoirs with well-developed natural fractures include many complex fracture networks that cannot be easily modeled by simple long fracture formulation and/or homogenized single continuity model. We thus propose a numerically efficient hybrid method in which small and medium fractures are modeled by effective permeability, and large fractures are modeled by discrete fracture networks. A simple, systematic way is devised to calculate transport parameters between fracture networks and discretized, homogenized media. An efficient numerical algorithm is also devised to solve the dual system of fracture network and finite volume grid. Black oil formulation is implemented in the simulator to demonstrate practical applications of this hybrid finite volume method.