This paper summarises the results of a benchmark study that compares a number of mathematical and numerical models applied to specific problems in the context of carbon dioxide (CO 2 ) storage in geologic formations. The processes modelled comprise ad-H. Class (B) · A. Ebigbo · R. Helmig · M. Darcis · B. Flemisch vective multi-phase flow, compositional effects due to dissolution of CO 2 into the ambient brine and nonisothermal effects due to temperature gradients and the Joule-Thompson effect. The problems deal with leakage through a leaky well, methane recovery enhanced P. Audigane BRGM, French Geological Survey, 410 Comput Geosci (2009) 13:409-434 by CO 2 injection and a reservoir-scale injection scenario into a heterogeneous formation. We give a description of the benchmark problems then briefly introduce the participating codes and finally present and discuss the results of the benchmark study.

Current macroscopic theories of two-phase flow in porous media are based on the extended Darcy's law and an algebraic relationship between capillary pressure and saturation. Both of these equations have been challenged in recent years, primarily based on theoretical works using a thermodynamic approach, which have led to new governing equations for two-phase flow in porous media. In these equations, new terms appear related to the fluid–fluid interfacial area and non-equilibrium capillarity effects. Although there has been a growing number of experimental works aimed at investigating the new equations, a full study of their significance has been difficult as some quantities are hard to measure and experiments are costly and time-consuming. In this regard, pore-scale computational tools can play a valuable role. In this paper, we develop a new dynamic pore-network simulator for two-phase flow in porous media, called DYPOSIT. Using this tool, we investigate macroscopic relationships among average capillary pressure, average phase pressures, saturation and specific interfacial area. We provide evidence that at macroscale, average capillary pressure–saturation–interfacial area points fall on a single surface regardless of flow conditions and fluid properties. We demonstrate that the traditional capillary pressure–saturation relationship is not valid under dynamic conditions, as predicted by the theory. Instead, one has to employ the non-equilibrium capillary theory, according to which the fluids pressure difference is a function of the time rate of saturation change. We study the behaviour of non-equilibrium capillarity coefficient, specific interfacial area, and its production rate versus saturation and viscosity ratio.A major feature of our pore-network model is a new computational algorithm, which considers capillary diffusion. Pressure field is calculated for each fluid separately, and saturation is computed in a semi-implicit way. This provides more numerical stability, compared with previous models, especially for unfavourable viscosity ratios and small capillary number values.

ABSTRACTwhere P n and P w are the average pressures of nonwetting and wetting phases, respectively; P c is capillary pressure, Capillary pressure plays a central role in the description of waterand S is the wetting phase saturation. A schematic depicflow in unsaturated soils. While capillarity is ubiquitous in unsaturated tion of P c vs. S curves is given in Fig. 1. depends on the flow dynamics-it depends on both the history and the rate of change of saturation. The dependence of capillary pressure-saturation curves on the his-C apillarity plays a central role in the description of tory of flow is known as capillary pressure hysteresis; multiphase (and unsaturated) flow in porous media. analyses, the theoretical basis and practical implications of capillaritythis is a well-known effect and has been the subject of In quantitative modeling of multiphase flow, a relationextensive investigations. The dependence of capillary ship is needed to describe capillary pressure as a funccurves on the rate of change of saturation is due to dytion of other medium properties. Although the underlynamic effects. It is much less known and is not quantified ing processes that determine the distribution of fluid properly. The latter effect is the subject of this study. phases in porous media are extremely complicated, the Another important parameter in the description of main theoretical and practical tool currently used to unsaturated flow is relative permeability, which is also quantify the capillary pressure function is an empirical considered to be a function of saturation. There are some relationship between capillary pressure and saturation indications that the relative permeability-saturation rein the form (see, e.g., Bear and Verruijt, 1987): lationship also shows hysteresis effects and may depend on the rate of change of saturation. These effects, how-P n Ϫ P w ϭ P c ϭ f(S) [1] ever, are less pronounced than in the case of capillary pressure. It must be noted that the dynamic effect con-S.M. Hassanizadeh, Section for Hydrology and Ecology; Faculty of sidered in this paper is different from the flow-rate deCivil Engineering and Geosciences, Delft University of Technology;pendence of the relative permeability coefficient. It is

Capture and subsequent injection of carbon dioxide into deep geological formations is being considered as a means to reduce anthropogenic emissions of CO2 to the atmosphere. If such a strategy is to be successful, the injected CO2 must remain within the injection formation for long periods of time, at least several hundred years. Because mature continental sedimentary basins have a century-long history of oil and gas exploration and production, they are characterized by large numbers of existing oil and gas wells. For example, more than 1 million such wells have been drilled in the state of Texas in the United States. These existing wells represent potential leakage pathways for injected CO2. To analyze leakage potential, modeling tools are needed that predict leakage rates and patterns in systems with injection and potentially leaky wells. A new semianalytical solution framework allows simple and efficient prediction of leakage rates for the case of injection of supercritical CO2 into a brine-saturated deep aquifer. The solution predicts the extent of the injected CO2 plume, provides leakage rates through an abandoned well located at an arbitrary distance from the injection well, and estimates the CO2 plume extent in the overlying aquifer into which the fluid leaks. Comparison to results from a numerical multiphase flow simulator show excellent agreement. Example calculations show the importance of outer boundary conditions, the influence of both density and viscosity contrasts in the resulting solutions, and the potential importance of local upconing around the leaky well. While several important limiting assumptions are required, the new semianalytical solution provides a simple and efficient procedure for estimation of CO2 leakage for problems involving one injection well, one leaky well, and multiple aquifers separated by impermeable aquitards.

Molecular and culture-based methods were used to investigate the microbial diversity in produced water obtained from the high-temperature Troll oil formation in the North Sea. 16S rRNA gene libraries were generated from total community DNA, using universal archaeal or bacterial oligonucleotide primer sets. Sequence analysis of 88 clones in the bacterial library indicated that they originated from members of Firmicutes (48 sequences), Bacteroidetes (17 sequences), delta-Proteobacteria (15 sequences), Spirochaetes (5 sequences), Thermotogales (2 sequences) and gamma-Proteobacteria (1 sequence). Twenty-two sequences in the archaeal library were close relatives to members of the genera Methanococcus (18 sequences), Methanolobus (3 sequences) and Thermococcus (1 sequence). Most of the bacterial sequences shared less than 95% identity with their closest match in GenBank, indicating that the produced water harbours a unique community of novel bacterial species or genera. Members of the thermophilic genera Thermosipho, Thermotoga, Anaerophaga and Thermovirga were isolated. The Troll formations are not injected with sea water. Thus, dramatic changes of the in situ conditions have been avoided, and a common source of continuous contamination from injection water can be excluded. However, the majority of the organisms detected in the gene libraries were most closely related to cultivated organisms with optimum temperatures for growth well below the in situ reservoir temperature (70 degrees C), indicating that produced water from the Troll platform harbours a substantial amount of non-indigenous organisms. This was confirmed by the isolation of a number of mesophilic and moderately thermophilic organisms that were unable to grow at reservoir temperature.

We develop an Eulerian-Lagrangian localized adjoint method (ELLAM) to solve two-dimensional advection-diffusion equations with all combinations of inflow and outflow Dirichlet, Neumann, and flux boundary conditions. The ELLAM formalism provides a systematic framework for implementation of general boundary conditions, leading to mass-conservative numerical schemes. The computational advantages of the ELLAM approximation have been demonstrated for a number of one-dimensional transport systems; practical implementations of ELLAM schemes in multiple spatial dimensions that require careful algorithm development are discussed in detail in this paper. Extensive numerical results are presented to compare the ELLAM scheme with many widely used numerical methods and to demonstrate the strength of the ELLAM scheme.

Abstract. Traditional two-phase flow models use an algebraic relationship between capillary pressure and saturation. This relationship is based on measurements made under static conditions. However, this static relationship is then used to model dynamic conditions, and evidence suggests that the assumption of equilibrium between capillary pressure and saturation may not be be justified. Extended capillary pressure-saturation relationships have been proposed that include an additional term accounting for dynamic effects. In the present work we study some of the underlying pore-scale physical mechanisms that give rise to this so-called dynamic effect. The study is carried out with the aid of a simple bundle-of-tubes model wherein the pore space of a porous medium is represented by a set of parallel tubes. We perform virtual two-phase flow experiments in which a wetting fluid is displaced by a non-wetting fluid. The dynamics of fluid-fluid interfaces are taken into account. From these experiments, we extract information about the overall system dynamics, and determine coefficients that are relevant to the dynamic capillary pressure description. We find dynamic coefficients in the range of 10 2 − 10 3 kg m −1 s −1 , which is in the lower range of experimental observations. We then analyze certain behavior of the system in terms of dimensionless groups, and we observe scale dependency in the dynamic coefficient. Based on these results, we then speculate about possible scale effects and the significance of the dynamic term.

ABSTRACTwhere P n and P w are the average pressures of nonwetting and wetting phases, respectively; P c is capillary pressure, Capillary pressure plays a central role in the description of waterand S is the wetting phase saturation. A schematic depicflow in unsaturated soils. While capillarity is ubiquitous in unsaturated tion of P c vs. S curves is given in Fig. 1. depends on the flow dynamics-it depends on both the history and the rate of change of saturation. The dependence of capillary pressure-saturation curves on the his-C apillarity plays a central role in the description of tory of flow is known as capillary pressure hysteresis; multiphase (and unsaturated) flow in porous media. analyses, the theoretical basis and practical implications of capillaritythis is a well-known effect and has been the subject of In quantitative modeling of multiphase flow, a relationextensive investigations. The dependence of capillary ship is needed to describe capillary pressure as a funccurves on the rate of change of saturation is due to dytion of other medium properties. Although the underlynamic effects. It is much less known and is not quantified ing processes that determine the distribution of fluid properly. The latter effect is the subject of this study. phases in porous media are extremely complicated, the Another important parameter in the description of main theoretical and practical tool currently used to unsaturated flow is relative permeability, which is also quantify the capillary pressure function is an empirical considered to be a function of saturation. There are some relationship between capillary pressure and saturation indications that the relative permeability-saturation rein the form (see, e.g., Bear and Verruijt, 1987): lationship also shows hysteresis effects and may depend on the rate of change of saturation. These effects, how-P n Ϫ P w ϭ P c ϭ f(S) [1] ever, are less pronounced than in the case of capillary pressure. It must be noted that the dynamic effect con-S.M. Hassanizadeh, Section for Hydrology and Ecology; Faculty of sidered in this paper is different from the flow-rate deCivil Engineering and Geosciences, Delft University of Technology;pendence of the relative permeability coefficient. It is