This paper presents the predictions and calculations of the phase equilibria of oil, gas and water/brine mixtures where the oil and gas are modeled by a cubic equation of state and where the gas solubility in the aqueous phase is estimated from Henry's law. Henry's law constants for a variety of compounds of interest to the petroleum industry are correlated against pressure and temperature. The scaled-particle theory is used to take into account the presence of salt in the aqueous phase. An extensive match of experimental data is presented, showing the adequacy of the proposed model for Henry's law constant.On donne dans ce travail les pridictions et les calculs d'kquilibre de phase des mClanges pktrole, gaz et eau-saumure, 00 le pktrole et les gaz sont reprksentis par une Cquation d'itat cubique et ou la solubilite des gaz dans la phase aqueuse est estimie a I'aide de la loi d'Henry. Les constantes de Henry sont corrClCes pour une large gamme de composis d'intiret pour I'industrie pktroliere, en fonction de la pression et de la tempkrature. On utilise la thiorie des particules ajusties pour tenir compte de la prisence de sel dans la phase aqueuse. On prksente une vaste comparaison de donnies expkrimentales qui montre la validiti du modkle propost5 pour les constantes de la loi d'Henry. ater exists abundantly in hydrocarbon reservoirs, either where y,, denotes the mole fraction of component i in phase m. K,,, = yIw/y,e 486 THE

This paper describes a fully coupled geochemical compositional Equation-of-State (EOS) compositional simulator for the simulation of CO2 storage in saline aquifers. The simulator (GEM-GHG) models the following phenomena:convective and dispersive flow in porous media;phase equilibrium between the oil, gas and aqueous phase;chemical equilibrium for reactions between the aqueous components andmineral dissolution and precipitation kinetics. For numerical robustness and stability, all equations are solved simultaneously. The simulator is applied to the simulation of typical field-scale CO2 sequestration processes, showing the migration of CO2(g) and CO2(aq), the dissociation of CO2(aq) into HCO3 and its subsequent conversion into carbonate minerals. Convection of high-density plumes of CO2-rich brine in conjunction with CO2 mineralization around the plumes is illustrated. Introduction Because of the climatic warming effect of CO2, CO2 storage is essential for reducing greenhouse effects. Gunter et al.1 provided a critical look at capacities, retention times, rates of uptake and costs for CO2 disposal in different classes of CO2 sinks in Canada. Sedimentary basins such as depleted oil and gas reservoirs and aquifers are potential sites for storage. Deep aquifers seem to be the most promising sites for CO2 storage2,3 as they are widely distributed, underlie most point sources of CO2 emission and are not limited by the reservoir size as in the case of depleted oil and gas reservoirs. Tanaka et al.4 discussed several structures for CO2 storage in Japan. These consist of (1) oil and gas reservoirs with neighboring aquifers, (2) aquifers in anticlinal structures, (3) aquifers in monoclinal structures on land and (4) aquifers in monoclinal structures offshore. Oil and gas reservoirs with neighboring aquifers in category 1 are still active and will be producing for some time in the future. When depleted, these reservoirs can be used for underground natural gas storage, instead of CO2 storage. Consequently, aquifers in categories (3) and (4) are the most attractive candidates for CO2 sequestration. Koide et al.5–6 provided additional discussions of the merit of storing CO2 in deep saline aquifers around the world in general and in Japan in particular. Baklid et al.7, Kongsjorden et al.8, and Chatwick et al.9 described the Sleipner Vest CO2 storage project in the North Sea. The rich gas of the Sleipner Vest Field contains sizable amounts of CO2 (9%). CO2 is removed using an activated amine and reinjected into an aquifer in the Utsira formation. Emberley et al.10 discussed the CO2 storage process in the CO2-EOR injection project in Weyburn, Saskatchewan, Canada. van der Meer11 reviewed significant milestones and successes achieved in underground CO2-storage technology over the past few years. All underground options including aquifer storage, EOR processes, CO2 storage in depleted gas and oil fields, and Enhanced Coalbed Methane are reviewed. He noted that Sleipner project has proven to be a successful storage project. CO2 has high density and high solubility in the aqueous phase at the high pressures that exist in deep aquifers. There are two ways in which CO2 can be trapped in aquifers:structural (or hydrodynamic) trapping andmineral trapping. The first process consists of trapping CO2 into a flow system with low flow velocity over geological periods of time. The second process converts CO2 to carbonate minerals and renders it immobile. The latter is very desirable as CO2 is sequestered in a form that is harmless to the environment. Wawersik et al.12 provide a comprehensive review of the physics and research needs related to the terrestrial sequestration of CO2 that highlight the importance of structural and mineral trapping. Geomechanics also plays an important role as the pressure increase due to the injection of CO2 may exceed the yield point of the cap rock or sealing faults. This will result in the undesirable leakage of CO2 into the environment.

A robust and efficient method for solving the equations corresponding to an equation-of-state compositional model is described. The method is developed for an adaptive-implicit simulator where only a small number of blocks need to be solved implicitly, while the remaining blocks are solved in an explicit manner. The salient features of the method is the decoupling of the solution of flow equations from the flash calculations. This allows an easy implementation of powerful flash- calcualtion schemes in the simulator. The adaptive-implicit approach is compared to a fully implicit approach and an explicit-transmissibility approach by using the Third SPE Comparative Solution Project. Results show that the adaptive-implicit approach is about twice as fast as the other two methods. Introduction Most EOS compositional models described in the literature use explicit transmissibilities. Because of the complexity of the equations and the use of large numbers of components (around 10), the explicit formulation has been the only feasible approach to field-scale simulation. This was demonstrated in the Third SPE Comparative Solution Project, where all the simulators used were explicit. The drawback of the explicit formulation is the timestep size limitation, which excludes its application in coning studies. Some attempts have been made to develop a fully implicit EOS compositional model. However, the application of such a model was restricted to very small problems (3 components and 80 blocks in Reference 2; and 3 components and 64 blocks in Reference 3), and no field-scale runs were reported. Recently, Bertiger and Kelsey described the use of the adaptive-implicit method in an EOS compositional model. The adaptive-implicit method introduced by Thomas and Thurnau is based on the idea that at a given time during a simulation, only some blocks need to be solved implicitly, while the remaining blocks are solved explicitly. Thus during a simulation, blocks will be switched automatically from explicit to implicit to allow the use of large timesteps. The alignment of equations and variables used by Bertiger and Kelsey 4 is similar to that of Coats. Their test examples were also restricted to relatively small systems (5 components and 56 blocks; 3 components and 150 blocks). This paper describes a robust and efficient formulation of an adaptive-implicit EOS compositional model. The salient features of the formulation are the selection of primary equations and variables, and the decoupling of the solution of the flow equations from the flash calculations. The flow equations are converged with Newton's method, while the phase-equilibrium equations can be solved by any technique (e.g., Newton's method and quasi-Newton successive substitutions). This is a departure from previous Newton's method approaches to compositional simulation where the flow and phase-equilibrium equations are converged simultaneously. These approaches are described by Fussell and Fussell and Young and Stephensons for explicit-transmissibility models and by Coats and Chien et al. for fully implicit models. The desirable features of the present approach are discussed later. The use of either analytical or numerical derivatives in the Jacobian construction has been a point of contenttion. Numerical differentiation is easy to program and does not require extensive revision of the code when property correlations are changed. However, it is computationally more time-consuming than analytical differentiation, especially in the evaluation of of equation-of-state fugacity derivatives. This paper shows a differentation method where both analytical and numerical differentationare used at different places to take advantage of both schemes. P. 395⁁

This paper describes a thermodynamic model for asphaltene that captures the behavior of asphaltene precipitation during primary depletion. Precipitation occurs above the saturation pressure, reaches a maximum value around the saturation pressure, and decreases as the pressure drops further. The precipitated asphaltene is represented as a pure solid, with the oil and gas phases modeled with an equation of state (EOS). A validation of the model with experimental data is reported. A study of the sensitivity of the model to different parameters is described. Introduction Asphaltene precipitation from reservoir fluids. during oil production is a serious problem because it can result in plugging of the formation, wellbores and production facilities. Asphaltene precipitation may occur during primary depletion or during the displacement of oil by rich gas or C02. de Boer et al. observed that reservoirs that experience asphaltene precipitation during primary depletion usually have the following characteristics:The fluid in place is light to medium oil with small asphaltene content.The initial reservoir pressure is much larger than the saturation pressure.Maximum precipitation occurs around the saturation pressure. Heavier crudes that contain a larger amount of asphaltene have very little asphaltene precipitation problems as they can dissolve more asphaltene. The region where asphaltene precipitation occurs is bound by the asphaltene deposition envelope (ADE). Fig. 1 shows an ADE and PT saturation curve for a typical oil. Precipitation occurs above the saturation pressure (upper ADE pressure), reaches a maximum value around the saturation pressure, and decreases as pressure drops further. Precipitation ceases as pressure drops below the lower ADE pressure. Above the saturation pressure, the precipitation is solely due to pressure, while below the saturation both pressure and composition affect the precipitation behavior.

An efficient modelling technique based on the representation of the precipitated asphaltene as a pure dense phase is presented. The success of the approach is based on the division of the heaviest component in the oil into a nonprecipitating and a precipitating component.The characterization of these components is discussed. This model was able to make quantitative predictions of experimental data from the literature as well as additional data from industry. This was achieved with only a small number of adjustable parameters (two or three). The mechanistic aspect of the model with regards to colloidal nature of asphaltene/resin micelles is also discussed. An algorithm for three-phase flash calculations with asphaltene precipitation is described.