Kristian Jessen - Academia.edu (original) (raw)
Papers by Kristian Jessen
All Days, Oct 3, 1999
This paper presents a new approach for constructing approximate analytical solutions for 1D, mult... more This paper presents a new approach for constructing approximate analytical solutions for 1D, multicomponent gas displacement problems. The solution to mass conservation equations governing 1D dispersion-free flow in which components partition between two equilibrium phases is controlled by the geometry of key tie lines. It has previously been proven that for systems with an arbitrary number of components, the key tie lines can be approximated quite accurately by a sequence of intersecting tie lines. As a result, analytical solutions can be constructed efficiently for problems with constant initial and injection compositions (Riemann problems). For fully self-sharpening systems, in which all key tie lines are connected by shocks, the analytical solutions obtained are rigorously accurate, while for systems in which some key tie lines are connected by spreading waves, the analytical solutions are approximations, but accurate ones. Detailed comparison between analytical solutions with both coarse-and fine-grid compositional simulations indicates that even for systems with nontie-line rarefactions, approximate analytical solutions predict composition profiles far more accurately than coarse-grid numerical simulations. Because of the generality of the new approach, approximate analytical solutions can be obtained for any system having a phase behavior that can be modeled by an equation of state. The construction of approximate analytical solutions is shown to be orders of magnitude faster than the comparable finite difference compositional simulation. Therefore, the new approach is valuable in situations requiring fast compositional solutions to Riemann problems are required.
All Days, Nov 11, 2007
The amount of wetting phase that is recovered by gravity drainage when the displacing fluid is no... more The amount of wetting phase that is recovered by gravity drainage when the displacing fluid is not in chemical equilibrium with the initial fluid involves a complex interplay of gravitational, diffusive, and capillary forces. Recently, in Part 1 in a series of papers, we proposed analytic solutions for capillary/gravity equilibrium (CGE) in compositional gravity drainage, and estimated the total recovery of wetting phase. In Part 2 we presented the results of experiments in an analog brine/isopropanol/iso-octane system (with non-parallel tie lines) in which the vertical profile of the components was measured destructively after 3 weeks of drainage. The condensing drainages compared favorably to the CGE solution and the vaporizing drainages to analytical solutions for advection dominated transport. Here we present numerical simulations of compositional gravity drainage. We find that the CGE solutions are approached asymptotically as the simulation grid is refined for a simplified phase diagram. For vaporizing drainages, a bank of wetting fluid is found to be created from early times in the drainage through wetting fluid imbibing back into swept regions. We show that including hysteresis in the capillary pressure curve limits the creation of the wetting fluid bank. We compare the numerical simulations to the experimental observations, and find the simulations match well for condensing drainages, but not for vaporizing drainages, similar to that seen for the CGE solutions.
Proceedings, Apr 14, 2015
ABSTRACT Molecular diffusion can play a significant role in oil recovery during gas injection in ... more ABSTRACT Molecular diffusion can play a significant role in oil recovery during gas injection in fractured reservoirs. Diffusion of gas components from a fracture into the matrix extracts oil components from matrix and delays, to some extent, the gas breakthrough. This in turn increases both sweep and displacement efficiencies. In current simulation models, molecular diffusion is commonly modeled using a classical Fick's law approach with constant diffusion coefficients. In the classical Fick's law approach, the dragging effects (off-diagonal diffusion coefficients) are neglected. In addition, the gas-oil diffusion at the fracture-matrix interface is normally modeled by assuming an average composition at the interface which does not have a sound physical basis. In this paper, we present a dual-porosity model in which the generalized Fick's law is used for molecular diffusion to account for the dragging effects; and gas-oil diffusion at the fracture-matrix interface is modeled based on film theory in which the gas in fracture and oil in the matrix are assumed to be at equilibrium. A novel shape factor is also introduced for gas-oil diffusion based on film theory. Diffusion coefficients are calculated using the Maxwell-Stefan model and are pressure, temperature and composition dependent. A time-dependent transfer function is used for matrix-fracture exchange in which the shape factor is adjusted using a boost factor to differentiate between the transfer rate at early and late times. Field-scale examples are used to demonstrate that the dragging effects (off-diagonal diffusion coefficients) can significantly impact the oil recovery during gas injection in fractured reservoirs. It is also shown that using proper physical models for matrix-fracture interactions (film theory for gas-oil diffusion and transfer function with boost factor) can considerably affect the simulation results as compared to conventional models. We also show that miscibility is not developed in the matrix blocks even at pressures above minimum miscibility pressure (MMP) when molecular diffusion is the main recovery mechanism during gas injection in fractured reservoirs. The work presented in this paper is directly applicable to the study and design of gas injection processes in fractured reservoirs through an improved understanding of the effect of diffusion and matrix-fracture interactions on these processes.
Injection of CO2 into deep unminable coal seams is an option for geological storage of CO2. In ma... more Injection of CO2 into deep unminable coal seams is an option for geological storage of CO2. In many industrial settings, pure CO2 streams are expensive to obtain and a mixture of CO2 and N2 would be less expensive. New analytical solutions are presented for two-phase, four-component flow with volume change on mixing in adsorbing systems. Analytical solutions have been reported previously for single-phase three-component gas flow (Zhu et al.) and for multicomponent flow of incompressible fluids with adsorption (Johansen and Winther, Dahl et al., Shapiro et al.). In this paper, we analyze the simultaneous flow of water and gas containing multiple adsorbing components by the method of characteristics. Mixtures of N2, CH4, CO2 and H2O are used to represent the ECBM-flue gas process. The displacement behavior is demonstrated to be strongly dependent on the relative adsorption strength of the gas components. N2 and CO2 recover CH4 through different mechanisms: CO2 preferentially adsorbs onto the coal surface, resulting in a shock solution; while N2 displaces CH4 by reducing the partial pressure of CH4, resulting in a rarefaction solution. When mixtures of N2 and CO2 are injected, the displacement exhibits both shock and rarefaction features. For CO2-rich flue gas, a path that includes a switch between branches of non-tieline paths is observed, a feature not previously reported for gas-liquid displacements. In these solutions, an additional key tieline, at which the switch between non-tieline paths occurs, is required. In the shock along this tieline, the non-tieline eigenvalues of injection and initial segments and the tieline shock velocity are equal. Analytical solutions to ECBM processes provide insight into the complex interplay among adsorption, phase behavior and convection. Improved understanding of the physics of these displacements will aid in developing more efficient and physically accurate techniques for predicting the fate of injected CO2 in the subsurface.
All Days, May 5, 2016
Methane (CH4) is the largest component of the natural gas produced from shale rocks. Although met... more Methane (CH4) is the largest component of the natural gas produced from shale rocks. Although methane accounts for 87-96 mol% of the gas from these rocks, other components including hydrocarbons such as ethane (C2H6) and propane (C3H8), nitrogen (N2) and helium (He) are also found in the gas produced. Methane and the various heavier hydrocarbons are stored in an adsorbed state in the micro and mesopores of the shale rocks, and as free gas in the fracture networks. Though convective and diffusive transport accounts for the short-term behavior in gas production, desorption is thought to dominate the long-term dynamics of shale-gas generation. The key objective of this study is the investigation of adsorption/desorption and diffusive transport phenomena of methane/hydrocarbon mixtures in shale-gas rocks. We focus our attention on the pure components of methane and ethane and their binary mixtures, since ethane is typically the second largest component in shale gas, and is thought to compete for the same adsorption sites in shale-gas rocks as methane. We study the adsorption/desorption behavior of this mixture (and its individual components) in ground shale rock samples using thermogravimetric analysis (TGA). The sorption isotherms generated are important to predict the gas storage capacity of the shale samples, while the study of adsorption/desorption dynamics/kinetics help us understand the role of desorption during the later times of gas production. A dynamic Langmuir-type sorption model is proposed, that allows us to isolate desorption kinetics from diffusive mass transfer. This, in turn, facilitates our modeling and interpretation of the experimental observations. The experimental observations and their interpretation pave a path to improve the interpretation of production data from shale-gas wells by leveraging an improved understanding of desorption dynamics and mass transfer of natural gas mixtures in shale.
International Journal of Greenhouse Gas Control, 2013
In this work, we investigate the impact of co-current to counter-current flow reversals on the mi... more In this work, we investigate the impact of co-current to counter-current flow reversals on the migration dynamics of a non-wetting phase plume in a porous medium. The presented results and observations have direct application to CO 2 injection into saline aquifers where a less dense CO 2 -rich plume migrates during and following the injection period. Counter-current gravity segregation experiments were performed in a vertical glass-bead pack with brine and iC 8 as analog fluids to mimic the behavior of a CO 2 /brine system of relevance to CO 2 sequestration processes. Four-electrode resistivity measurements were used to monitor the migration of the non-wetting phase (iC 8 ) by relating the resistivity index (RI) to the brine saturation. The observations are compared with numerical calculations to demonstrate that standard co-current relative permeability measurements are inadequate to reproduce the experimental observations. A reduction in the relative permeability of both phases, in particular for the non-wetting phase, is required to improve the agreement between experimental observations and numerical calculations. Numerical calculations based on co-current input data predicts a much faster migration of the non-wetting phase to the top of the column than what is observed in the segregation experiments. Our findings demonstrate that counter-current flow affects the phase's mobilities, because of interfacial coupling, and should therefore be considered in the modeling of injection/storage of CO 2 in saline aquifers: simulation of CO 2 /brine dynamics based on co-current relative permeability measurements is likely to render estimates of migration time/distance in significant error.
Energies, Nov 25, 2020
This study provides the engineering science underpinnings for improved characterization and quant... more This study provides the engineering science underpinnings for improved characterization and quantification of the interplay of gases with kerogen and minerals in shale. Natural nanoporous media such as shale (i.e., mudstone) often present with low permeability and dual porosity, making them difficult to characterize given the complex structural and chemical features across multiple scales. These structures give nanoporous solids a large surface area for gas to sorb. In oil and gas applications, full understanding of these media and their sorption characteristics are critical for evaluating gas reserves, flow, and storage for enhanced recovery and CO 2 sequestration potential. Other applications include CO 2 capture from industrial plants, hydrogen storage on sorbent surfaces, and heterogeneous catalysis in ammonia synthesis. Therefore, high-resolution experimental procedures are demanded to better understand the gas-solid behavior. In this study, CT imaging was applied on the sub-millimeter scale to shale samples (Eagle Ford and Wolfcamp) to improve quantitative agreement between CT-derived and pulse decay (mass balance) derived results. Improved CT imaging formulations are presented that better match mass balance results, highlighting the significance of gas sorption in complex nanoporous media. The proposed CT routine implemented on the Eagle Ford sample demonstrated a 17% error reduction (22% to 5%) when compared to the conventional CT procedure. These observations are consistent in the Wolfcamp sample, emphasizing the reliability of this technique for broader implementation of digital adsorption studies in nanoporous geomaterials.
Industrial & Engineering Chemistry Research, Oct 30, 2020
CO 2 geological storage in deep saline formations is considered a promising method to mitigate an... more CO 2 geological storage in deep saline formations is considered a promising method to mitigate anthropogenic CO 2 emissions and, thereby, minimize changes to the Earth's atmosphere. A fundamental understanding of CO 2 mass transfer and sorption phenomena in brine-saturated reservoir formations is necessary to understand the long-term fate of injected CO 2 as it is subjected to different (physical, dissolution, and mineral) trapping mechanisms. In this work, we investigate CO 2 sorption in brinesaturated and dry Mt. Simon sandstone samples via in situ Fourier transform infrared spectroscopy (FT-IR) at elevated pressures, ranging from 0.3 to 8.3 MPa, at a temperature of 50 °C. The FT-IR spectra of bulk-phase CO 2 were simultaneously recorded under the same conditions. For bulk-phase CO 2 , we observed, in agreement with past studies, a doublet peak at 2361 and 2336 cm -1 and another peak (ν 2 bending mode) at 667 cm -1 . With increasing pressure, the position of the peak at 667 cm -1 remains invariant; however, when crossing into the supercritical region, the doublet peak degenerates onto a single peak at 2336 cm -1 with a barely visible shoulder at 2361 cm -1 . The bulk CO 2 data provide a perfect fit for Beer's law for the whole range of pressure conditions. For the dry sample, the IR spectrum is experimentally indistinguishable from the bulk CO 2 spectrum, signifying that if physical adsorption occurs to any significant extent, the adsorbed CO 2 molecules are not substantially more rotationally constrained than the dense bulk CO 2 molecules. For the brine-saturated sample, we observe a strong band centered at 2342 cm -1 and a small companion peak at 2360-2361 cm -1 that degenerates into a barely visible shoulder peak at higher pressures. The 2342 cm -1 band has been previously observed by other investigators for CO 2 dissolved in bulk water/brine as well during its adsorption on a variety of other wet natural porous media. We observe no peaks corresponding to bicarbonate or carbonate bulk species, which correlates well with the prior literature on similar low-pH aqueous solutions. The integrated peak area for the CO 2 sorbed in the brine-saturated sample correlates linearly with its solubility in the same bulk brine, as measured separately via a PVT-cell approach. This validates the accuracy of both techniques and the potential of the FT-IR method to be used in the study of mass transfer and adsorption in such systems. To that effect, a simple mathematical model is presented to analyze the FT-IR data to determine the CO 2 effective diffusivity in the brine-saturated sandstone sample.
Industrial & Engineering Chemistry Research, Nov 20, 2015
As the primary mechanism of gas storage in shale, sorption phenomena of CH4 and other hydrocarbon... more As the primary mechanism of gas storage in shale, sorption phenomena of CH4 and other hydrocarbons in the micropores and mesopores are critical to estimates of gas-in-place and of the long-term productivity from a given shale play. Since C2H6 is another important component of shale gas, besides CH4, knowledge of CH4–C2H6 binary mixture sorption on shale is of fundamental significance and plays a central role in understanding the physical mechanisms that control fluid storage, transport, and subsequent shale-gas production. In this work, measurements of pure component sorption isotherms for CH4 and C2H6 for pressures up to 114 and 35 bar, respectively, have been performed using a thermogravimetric method in the temperature range (40–60 °C), typical of storage formation conditions. Sorption experiments of binary (CH4–C2H6) gas mixtures containing up to 10% (mole fraction) of C2H6, typical of shale-gas compositions, for pressures up to 125 bar under the aforementioned temperature conditions have also been co...
Transport in Porous Media, Oct 12, 2007
... 1993). Seri-Levy and Avnir used Monte Carlo simulations of gas–solid systems are to examine g... more ... 1993). Seri-Levy and Avnir used Monte Carlo simulations of gas–solid systems are to examine gas adsorption on rough surfaces of various geometries. ... 123 Page 10. 150 K. Jessen et al. 3.2 Carbon Dioxide Displacement An ...
Proceedings of SPE Annual Technical Conference and Exhibition, Oct 1, 2005
Accurate performance prediction of miscible enhanced-oilrecovery (EOR) projects or CO 2 sequestra... more Accurate performance prediction of miscible enhanced-oilrecovery (EOR) projects or CO 2 sequestration in depleted oil and gas reservoirs relies in part on the ability of an equation-of-state (EOS) model to adequately represent the properties of a wide range of mixtures of the resident fluid and the injected fluid(s). The mixtures that form when gas displaces oil in a porous medium will, in many cases, differ significantly from compositions created in swelling tests and other standard pressure/volume/temperature (PVT) experiments. Multicontact experiments (e.g., slimtube displacements) are often used to condition an EOS model before application in performance evaluation of miscible displacements. However, no clear understanding exists of the impact on the resultant accuracy of the selected characterization procedure when the fluid description is subsequently included in reservoir simulation. In this paper, we present a detailed analysis of the quality of two different characterization procedures over a broad range of reservoir fluids (13 samples) for which experimental swellingtest and slimtube-displacement data are available. We explore the impact of including swelling-test and slimtube experiments in the data reduction and demonstrate that for some gas/oil systems, swelling tests do not contribute to a more accurate prediction of multicontact miscibility. Finally, we report on the impact that use of EOS models based on different characterization procedures can have on recovery predictions from dynamic 1D displacement calculations.
Proceedings of SPE/DOE Symposium on Improved Oil Recovery, Apr 1, 2006
This paper investigates the accuracy of first-and high-order numerical methods in simulating enha... more This paper investigates the accuracy of first-and high-order numerical methods in simulating enhanced condensate processes in 1D, 2D, and 3D. We compare the predictions of a standard single point upwind (SPU) scheme with a third-order accurate finite difference (FD) simulator based on a third-order essentially nonoscillatory (ENO) flux reconstruction with matching temporal accuracy. We include physical dispersion in the mathematical model of these multiphase, multicomponent systems. The comparisons demonstrate that SPU schemes may fail to predict the formation of the mobile liquid bank at the leading edge of the displacement unless an impractical number of gridblocks is used in the simulations. In contrast, the high-order FD simulator is demonstrated to accurately predict the liquid bank at much lower grid resolution, providing for a more efficient simulation approach. In 2D displacement calculations with gravity included, the CPU requirement of the SPU scheme was found to be more than 50 times larger than for the ENO scheme for a given level of accuracy. In 2D vertical cross-sections, the predicted component recovery is demonstrated to vary upward of 8% depending on the selected numerical scheme for a given grid resolution and dispersivity. In these settings, the SPU solutions converge to the ENO results upon significant grid refinement. In 3D displacement calculations, the magnitude of the predicted condensate bank is also found to be very different depending on the selected numerical scheme. Relative to the 2D displacement calculations, condensate banking and gravity segregation is observed to have less impact on the process performance prediction because of the permeability configuration in the 3D model used here, but it could have a high impact in different settings. We include an explicit representation of longitudinal and transverse dispersion in the porous medium to demonstrate the grid resolution required to resolve physical dispersion at a given simulation length scale, and to show that condensate banks can also form in more realistic dispersive systems. Grid-refinement studies in 1D and 2D demonstrate, again, that the ENO scheme outperforms the SPU scheme for a given Peclet (Pe) number. Converged solutions are obtained with the ENO scheme using a relatively small number of grid cells. In addition, we show the behavior of the two schemes for varying Peclet numbers on a fixed simulation grid. For this grid, the ENO scheme is shown to be sensitive to the Peclet number, signifying that physical dispersion is not overwhelmed by numerical diffusion. For the SPU scheme, however, the solutions are almost independent of the Peclet number, which indicates that numerical diffusion dominates.
AGU Fall Meeting Abstracts, Dec 1, 2005
AGU Fall Meeting Abstracts, Dec 1, 2007
ABSTRACT
Journal of Colloid and Interface Science, Feb 1, 2007
Abstract This comment points out an error of interpretation of experimental results reported in [... more Abstract This comment points out an error of interpretation of experimental results reported in [J. Colloid Interface Sci. 299 (2006) 321–331].
Numerical simulation of flow and mass transfer in fractured reservoir is challenging due to the c... more Numerical simulation of flow and mass transfer in fractured reservoir is challenging due to the complexity of the fracture networks. To handle the geological complexity, dual-porosity models are often used to approximate such reservoir settings. In dual-porosity models, it is assumed that two domains, a high permeability flowing domain (fracture) and a low permeability stagnant domain (matrix) are in communication and that viscous flow is marginal in the stagnant domain.In commercial reservoir simulation tools, transfer rates between the flowing and the stagnant domains are commonly modeled using the Warren and Root approach, where no attempt is made to a solve diffusion equation within each matrix block and a quasi-steady state transfer is assumed between the two domains. Previous research has demonstrated that such a simplification does not correctly represent the mass transfer between the domains. A more accurate approach to modeling transfer rates in such settings is to discretize the matrix blocks. However, this approach reduces the computational efficiency of large scale implicit reservoir simulation, due to the associated significant increase in the number computational cells.In this work, we present a semi-analytical approach to model multicomponent molecular diffusion within each matrix block in a coarse-scale simulation model and develop equations for time-dependent transfer functions between the flowing and stagnant domains. The time-dependency of the transfer functions are formulated based on initial and average compositions of the domains. Generalized Fick's law is used to describe the diffusive fluxes to account for dragging effects between components. Analytical and semi-analytical solutions to the multicomponent mass transfer equations are obtained through linearization and eigenvalue decomposition of the diffusion coefficient matrix.To demonstrate the accuracy of the proposed semi-analytical approach, various examples are presented. In these examples the results of the suggested approach are compared to the Warren-root model, analytical solutions and high-resolution fine-scale results for different of fluid compositions and geometries. We demonstrate that the proposed approach (coarse-scale modeling with time-dependent transfer functions) accurately represents the analytical solution, at a significantly lower CPU time requirement relative to high-resolution fine-scale models. Furthermore, we compare the proposed approach to experimental observations of mass transfer in a binary (CO2-Brine) system to further validate the precision of the proposed model.A novel and consistent matrix-fracture transfer function for coarse-scale models is introduced in this paper using semi-analytical solutions to multicomponent diffusive mass transfer. In the proposed approach, the inaccuracies of the conventional representation of diffusive mass transfer in dual-porosity models are resolved, while eliminating the need for further discretization of the matrix blocks. This allows for accurate, yet efficient simulation of diffusive mass transfer in fractured reservoirs.
Industrial & Engineering Chemistry Research, Mar 16, 2016
Production of oil and gas from unconventional source rocks (shales) has increased significantly i... more Production of oil and gas from unconventional source rocks (shales) has increased significantly in recent years, reflecting a shift in the focus of the oil and gas industry from conventional to unconventional oil/gas resources. An improved insight into the pore structure characteristics of these important porous materials will enable a better understanding and further optimization of the production behavior from such vast hydrocarbon resources. In particular, characterization of porosity and permeability of shales is the key to accurately estimating the initial oil and gas in place and fluid flow through these rocks. However, evaluating the pore structure of shales presents technical challenges due to the presence of a range of pores, from the nanometer to the micrometer size. Characterization of the entire range of pore sizes requires an all-inclusive study employing a variety of techniques. Such an integrated approach is followed in this work to understand the pore structure of Monterey shale samples as...
Transport in Porous Media, Aug 15, 2014
Accurate upscaling of highly heterogeneous subsurface reservoirs remains a challenge in the conte... more Accurate upscaling of highly heterogeneous subsurface reservoirs remains a challenge in the context of modeling of flow and transport. In this work, we address this challenge with emphasis on the representation of the displacement efficiency in coarse-scale modeling. We propose a dual-porosity upscaling approach to handle displacement calculations in high resolution and highly heterogeneous formations. In this approach, the pore space is arranged into two levels of porosity based on flow contribution, and a dual-porosity dual-permeability flow model is adapted for coarse-scale flow simulation. The approach uses fine-scale streamline information to transform a heterogeneous geomodel into a coarse dual-continuum model that preserves the global flow pathways adequately. The performance of the proposed technique is demonstrated for two heterogeneous reservoirs using both black oil (waterflooding) and compositional (gas injection) modeling approaches. We demonstrate that the coarse dual-porosity models predict the breakthrough times accurately and reproduce the post-breakthrough responses adequately. This is in contrast to conventional single-porosity upscaling techniques that overestimate breakthrough times and displacement efficiencies (sweep). By preserving large-scale heterogeneities, coarse dual-porosity models are demonstrated to be significantly less sensitive to the level of upscaling, when compared to conventional single-porosity upscaling. Accordingly, the proposed upscaling approach is a relevant and suitable technique for upscaling of highly heterogeneous geomodels.
All Days, Oct 3, 1999
This paper presents a new approach for constructing approximate analytical solutions for 1D, mult... more This paper presents a new approach for constructing approximate analytical solutions for 1D, multicomponent gas displacement problems. The solution to mass conservation equations governing 1D dispersion-free flow in which components partition between two equilibrium phases is controlled by the geometry of key tie lines. It has previously been proven that for systems with an arbitrary number of components, the key tie lines can be approximated quite accurately by a sequence of intersecting tie lines. As a result, analytical solutions can be constructed efficiently for problems with constant initial and injection compositions (Riemann problems). For fully self-sharpening systems, in which all key tie lines are connected by shocks, the analytical solutions obtained are rigorously accurate, while for systems in which some key tie lines are connected by spreading waves, the analytical solutions are approximations, but accurate ones. Detailed comparison between analytical solutions with both coarse-and fine-grid compositional simulations indicates that even for systems with nontie-line rarefactions, approximate analytical solutions predict composition profiles far more accurately than coarse-grid numerical simulations. Because of the generality of the new approach, approximate analytical solutions can be obtained for any system having a phase behavior that can be modeled by an equation of state. The construction of approximate analytical solutions is shown to be orders of magnitude faster than the comparable finite difference compositional simulation. Therefore, the new approach is valuable in situations requiring fast compositional solutions to Riemann problems are required.
All Days, Nov 11, 2007
The amount of wetting phase that is recovered by gravity drainage when the displacing fluid is no... more The amount of wetting phase that is recovered by gravity drainage when the displacing fluid is not in chemical equilibrium with the initial fluid involves a complex interplay of gravitational, diffusive, and capillary forces. Recently, in Part 1 in a series of papers, we proposed analytic solutions for capillary/gravity equilibrium (CGE) in compositional gravity drainage, and estimated the total recovery of wetting phase. In Part 2 we presented the results of experiments in an analog brine/isopropanol/iso-octane system (with non-parallel tie lines) in which the vertical profile of the components was measured destructively after 3 weeks of drainage. The condensing drainages compared favorably to the CGE solution and the vaporizing drainages to analytical solutions for advection dominated transport. Here we present numerical simulations of compositional gravity drainage. We find that the CGE solutions are approached asymptotically as the simulation grid is refined for a simplified phase diagram. For vaporizing drainages, a bank of wetting fluid is found to be created from early times in the drainage through wetting fluid imbibing back into swept regions. We show that including hysteresis in the capillary pressure curve limits the creation of the wetting fluid bank. We compare the numerical simulations to the experimental observations, and find the simulations match well for condensing drainages, but not for vaporizing drainages, similar to that seen for the CGE solutions.
Proceedings, Apr 14, 2015
ABSTRACT Molecular diffusion can play a significant role in oil recovery during gas injection in ... more ABSTRACT Molecular diffusion can play a significant role in oil recovery during gas injection in fractured reservoirs. Diffusion of gas components from a fracture into the matrix extracts oil components from matrix and delays, to some extent, the gas breakthrough. This in turn increases both sweep and displacement efficiencies. In current simulation models, molecular diffusion is commonly modeled using a classical Fick's law approach with constant diffusion coefficients. In the classical Fick's law approach, the dragging effects (off-diagonal diffusion coefficients) are neglected. In addition, the gas-oil diffusion at the fracture-matrix interface is normally modeled by assuming an average composition at the interface which does not have a sound physical basis. In this paper, we present a dual-porosity model in which the generalized Fick's law is used for molecular diffusion to account for the dragging effects; and gas-oil diffusion at the fracture-matrix interface is modeled based on film theory in which the gas in fracture and oil in the matrix are assumed to be at equilibrium. A novel shape factor is also introduced for gas-oil diffusion based on film theory. Diffusion coefficients are calculated using the Maxwell-Stefan model and are pressure, temperature and composition dependent. A time-dependent transfer function is used for matrix-fracture exchange in which the shape factor is adjusted using a boost factor to differentiate between the transfer rate at early and late times. Field-scale examples are used to demonstrate that the dragging effects (off-diagonal diffusion coefficients) can significantly impact the oil recovery during gas injection in fractured reservoirs. It is also shown that using proper physical models for matrix-fracture interactions (film theory for gas-oil diffusion and transfer function with boost factor) can considerably affect the simulation results as compared to conventional models. We also show that miscibility is not developed in the matrix blocks even at pressures above minimum miscibility pressure (MMP) when molecular diffusion is the main recovery mechanism during gas injection in fractured reservoirs. The work presented in this paper is directly applicable to the study and design of gas injection processes in fractured reservoirs through an improved understanding of the effect of diffusion and matrix-fracture interactions on these processes.
Injection of CO2 into deep unminable coal seams is an option for geological storage of CO2. In ma... more Injection of CO2 into deep unminable coal seams is an option for geological storage of CO2. In many industrial settings, pure CO2 streams are expensive to obtain and a mixture of CO2 and N2 would be less expensive. New analytical solutions are presented for two-phase, four-component flow with volume change on mixing in adsorbing systems. Analytical solutions have been reported previously for single-phase three-component gas flow (Zhu et al.) and for multicomponent flow of incompressible fluids with adsorption (Johansen and Winther, Dahl et al., Shapiro et al.). In this paper, we analyze the simultaneous flow of water and gas containing multiple adsorbing components by the method of characteristics. Mixtures of N2, CH4, CO2 and H2O are used to represent the ECBM-flue gas process. The displacement behavior is demonstrated to be strongly dependent on the relative adsorption strength of the gas components. N2 and CO2 recover CH4 through different mechanisms: CO2 preferentially adsorbs onto the coal surface, resulting in a shock solution; while N2 displaces CH4 by reducing the partial pressure of CH4, resulting in a rarefaction solution. When mixtures of N2 and CO2 are injected, the displacement exhibits both shock and rarefaction features. For CO2-rich flue gas, a path that includes a switch between branches of non-tieline paths is observed, a feature not previously reported for gas-liquid displacements. In these solutions, an additional key tieline, at which the switch between non-tieline paths occurs, is required. In the shock along this tieline, the non-tieline eigenvalues of injection and initial segments and the tieline shock velocity are equal. Analytical solutions to ECBM processes provide insight into the complex interplay among adsorption, phase behavior and convection. Improved understanding of the physics of these displacements will aid in developing more efficient and physically accurate techniques for predicting the fate of injected CO2 in the subsurface.
All Days, May 5, 2016
Methane (CH4) is the largest component of the natural gas produced from shale rocks. Although met... more Methane (CH4) is the largest component of the natural gas produced from shale rocks. Although methane accounts for 87-96 mol% of the gas from these rocks, other components including hydrocarbons such as ethane (C2H6) and propane (C3H8), nitrogen (N2) and helium (He) are also found in the gas produced. Methane and the various heavier hydrocarbons are stored in an adsorbed state in the micro and mesopores of the shale rocks, and as free gas in the fracture networks. Though convective and diffusive transport accounts for the short-term behavior in gas production, desorption is thought to dominate the long-term dynamics of shale-gas generation. The key objective of this study is the investigation of adsorption/desorption and diffusive transport phenomena of methane/hydrocarbon mixtures in shale-gas rocks. We focus our attention on the pure components of methane and ethane and their binary mixtures, since ethane is typically the second largest component in shale gas, and is thought to compete for the same adsorption sites in shale-gas rocks as methane. We study the adsorption/desorption behavior of this mixture (and its individual components) in ground shale rock samples using thermogravimetric analysis (TGA). The sorption isotherms generated are important to predict the gas storage capacity of the shale samples, while the study of adsorption/desorption dynamics/kinetics help us understand the role of desorption during the later times of gas production. A dynamic Langmuir-type sorption model is proposed, that allows us to isolate desorption kinetics from diffusive mass transfer. This, in turn, facilitates our modeling and interpretation of the experimental observations. The experimental observations and their interpretation pave a path to improve the interpretation of production data from shale-gas wells by leveraging an improved understanding of desorption dynamics and mass transfer of natural gas mixtures in shale.
International Journal of Greenhouse Gas Control, 2013
In this work, we investigate the impact of co-current to counter-current flow reversals on the mi... more In this work, we investigate the impact of co-current to counter-current flow reversals on the migration dynamics of a non-wetting phase plume in a porous medium. The presented results and observations have direct application to CO 2 injection into saline aquifers where a less dense CO 2 -rich plume migrates during and following the injection period. Counter-current gravity segregation experiments were performed in a vertical glass-bead pack with brine and iC 8 as analog fluids to mimic the behavior of a CO 2 /brine system of relevance to CO 2 sequestration processes. Four-electrode resistivity measurements were used to monitor the migration of the non-wetting phase (iC 8 ) by relating the resistivity index (RI) to the brine saturation. The observations are compared with numerical calculations to demonstrate that standard co-current relative permeability measurements are inadequate to reproduce the experimental observations. A reduction in the relative permeability of both phases, in particular for the non-wetting phase, is required to improve the agreement between experimental observations and numerical calculations. Numerical calculations based on co-current input data predicts a much faster migration of the non-wetting phase to the top of the column than what is observed in the segregation experiments. Our findings demonstrate that counter-current flow affects the phase's mobilities, because of interfacial coupling, and should therefore be considered in the modeling of injection/storage of CO 2 in saline aquifers: simulation of CO 2 /brine dynamics based on co-current relative permeability measurements is likely to render estimates of migration time/distance in significant error.
Energies, Nov 25, 2020
This study provides the engineering science underpinnings for improved characterization and quant... more This study provides the engineering science underpinnings for improved characterization and quantification of the interplay of gases with kerogen and minerals in shale. Natural nanoporous media such as shale (i.e., mudstone) often present with low permeability and dual porosity, making them difficult to characterize given the complex structural and chemical features across multiple scales. These structures give nanoporous solids a large surface area for gas to sorb. In oil and gas applications, full understanding of these media and their sorption characteristics are critical for evaluating gas reserves, flow, and storage for enhanced recovery and CO 2 sequestration potential. Other applications include CO 2 capture from industrial plants, hydrogen storage on sorbent surfaces, and heterogeneous catalysis in ammonia synthesis. Therefore, high-resolution experimental procedures are demanded to better understand the gas-solid behavior. In this study, CT imaging was applied on the sub-millimeter scale to shale samples (Eagle Ford and Wolfcamp) to improve quantitative agreement between CT-derived and pulse decay (mass balance) derived results. Improved CT imaging formulations are presented that better match mass balance results, highlighting the significance of gas sorption in complex nanoporous media. The proposed CT routine implemented on the Eagle Ford sample demonstrated a 17% error reduction (22% to 5%) when compared to the conventional CT procedure. These observations are consistent in the Wolfcamp sample, emphasizing the reliability of this technique for broader implementation of digital adsorption studies in nanoporous geomaterials.
Industrial & Engineering Chemistry Research, Oct 30, 2020
CO 2 geological storage in deep saline formations is considered a promising method to mitigate an... more CO 2 geological storage in deep saline formations is considered a promising method to mitigate anthropogenic CO 2 emissions and, thereby, minimize changes to the Earth's atmosphere. A fundamental understanding of CO 2 mass transfer and sorption phenomena in brine-saturated reservoir formations is necessary to understand the long-term fate of injected CO 2 as it is subjected to different (physical, dissolution, and mineral) trapping mechanisms. In this work, we investigate CO 2 sorption in brinesaturated and dry Mt. Simon sandstone samples via in situ Fourier transform infrared spectroscopy (FT-IR) at elevated pressures, ranging from 0.3 to 8.3 MPa, at a temperature of 50 °C. The FT-IR spectra of bulk-phase CO 2 were simultaneously recorded under the same conditions. For bulk-phase CO 2 , we observed, in agreement with past studies, a doublet peak at 2361 and 2336 cm -1 and another peak (ν 2 bending mode) at 667 cm -1 . With increasing pressure, the position of the peak at 667 cm -1 remains invariant; however, when crossing into the supercritical region, the doublet peak degenerates onto a single peak at 2336 cm -1 with a barely visible shoulder at 2361 cm -1 . The bulk CO 2 data provide a perfect fit for Beer's law for the whole range of pressure conditions. For the dry sample, the IR spectrum is experimentally indistinguishable from the bulk CO 2 spectrum, signifying that if physical adsorption occurs to any significant extent, the adsorbed CO 2 molecules are not substantially more rotationally constrained than the dense bulk CO 2 molecules. For the brine-saturated sample, we observe a strong band centered at 2342 cm -1 and a small companion peak at 2360-2361 cm -1 that degenerates into a barely visible shoulder peak at higher pressures. The 2342 cm -1 band has been previously observed by other investigators for CO 2 dissolved in bulk water/brine as well during its adsorption on a variety of other wet natural porous media. We observe no peaks corresponding to bicarbonate or carbonate bulk species, which correlates well with the prior literature on similar low-pH aqueous solutions. The integrated peak area for the CO 2 sorbed in the brine-saturated sample correlates linearly with its solubility in the same bulk brine, as measured separately via a PVT-cell approach. This validates the accuracy of both techniques and the potential of the FT-IR method to be used in the study of mass transfer and adsorption in such systems. To that effect, a simple mathematical model is presented to analyze the FT-IR data to determine the CO 2 effective diffusivity in the brine-saturated sandstone sample.
Industrial & Engineering Chemistry Research, Nov 20, 2015
As the primary mechanism of gas storage in shale, sorption phenomena of CH4 and other hydrocarbon... more As the primary mechanism of gas storage in shale, sorption phenomena of CH4 and other hydrocarbons in the micropores and mesopores are critical to estimates of gas-in-place and of the long-term productivity from a given shale play. Since C2H6 is another important component of shale gas, besides CH4, knowledge of CH4–C2H6 binary mixture sorption on shale is of fundamental significance and plays a central role in understanding the physical mechanisms that control fluid storage, transport, and subsequent shale-gas production. In this work, measurements of pure component sorption isotherms for CH4 and C2H6 for pressures up to 114 and 35 bar, respectively, have been performed using a thermogravimetric method in the temperature range (40–60 °C), typical of storage formation conditions. Sorption experiments of binary (CH4–C2H6) gas mixtures containing up to 10% (mole fraction) of C2H6, typical of shale-gas compositions, for pressures up to 125 bar under the aforementioned temperature conditions have also been co...
Transport in Porous Media, Oct 12, 2007
... 1993). Seri-Levy and Avnir used Monte Carlo simulations of gas–solid systems are to examine g... more ... 1993). Seri-Levy and Avnir used Monte Carlo simulations of gas–solid systems are to examine gas adsorption on rough surfaces of various geometries. ... 123 Page 10. 150 K. Jessen et al. 3.2 Carbon Dioxide Displacement An ...
Proceedings of SPE Annual Technical Conference and Exhibition, Oct 1, 2005
Accurate performance prediction of miscible enhanced-oilrecovery (EOR) projects or CO 2 sequestra... more Accurate performance prediction of miscible enhanced-oilrecovery (EOR) projects or CO 2 sequestration in depleted oil and gas reservoirs relies in part on the ability of an equation-of-state (EOS) model to adequately represent the properties of a wide range of mixtures of the resident fluid and the injected fluid(s). The mixtures that form when gas displaces oil in a porous medium will, in many cases, differ significantly from compositions created in swelling tests and other standard pressure/volume/temperature (PVT) experiments. Multicontact experiments (e.g., slimtube displacements) are often used to condition an EOS model before application in performance evaluation of miscible displacements. However, no clear understanding exists of the impact on the resultant accuracy of the selected characterization procedure when the fluid description is subsequently included in reservoir simulation. In this paper, we present a detailed analysis of the quality of two different characterization procedures over a broad range of reservoir fluids (13 samples) for which experimental swellingtest and slimtube-displacement data are available. We explore the impact of including swelling-test and slimtube experiments in the data reduction and demonstrate that for some gas/oil systems, swelling tests do not contribute to a more accurate prediction of multicontact miscibility. Finally, we report on the impact that use of EOS models based on different characterization procedures can have on recovery predictions from dynamic 1D displacement calculations.
Proceedings of SPE/DOE Symposium on Improved Oil Recovery, Apr 1, 2006
This paper investigates the accuracy of first-and high-order numerical methods in simulating enha... more This paper investigates the accuracy of first-and high-order numerical methods in simulating enhanced condensate processes in 1D, 2D, and 3D. We compare the predictions of a standard single point upwind (SPU) scheme with a third-order accurate finite difference (FD) simulator based on a third-order essentially nonoscillatory (ENO) flux reconstruction with matching temporal accuracy. We include physical dispersion in the mathematical model of these multiphase, multicomponent systems. The comparisons demonstrate that SPU schemes may fail to predict the formation of the mobile liquid bank at the leading edge of the displacement unless an impractical number of gridblocks is used in the simulations. In contrast, the high-order FD simulator is demonstrated to accurately predict the liquid bank at much lower grid resolution, providing for a more efficient simulation approach. In 2D displacement calculations with gravity included, the CPU requirement of the SPU scheme was found to be more than 50 times larger than for the ENO scheme for a given level of accuracy. In 2D vertical cross-sections, the predicted component recovery is demonstrated to vary upward of 8% depending on the selected numerical scheme for a given grid resolution and dispersivity. In these settings, the SPU solutions converge to the ENO results upon significant grid refinement. In 3D displacement calculations, the magnitude of the predicted condensate bank is also found to be very different depending on the selected numerical scheme. Relative to the 2D displacement calculations, condensate banking and gravity segregation is observed to have less impact on the process performance prediction because of the permeability configuration in the 3D model used here, but it could have a high impact in different settings. We include an explicit representation of longitudinal and transverse dispersion in the porous medium to demonstrate the grid resolution required to resolve physical dispersion at a given simulation length scale, and to show that condensate banks can also form in more realistic dispersive systems. Grid-refinement studies in 1D and 2D demonstrate, again, that the ENO scheme outperforms the SPU scheme for a given Peclet (Pe) number. Converged solutions are obtained with the ENO scheme using a relatively small number of grid cells. In addition, we show the behavior of the two schemes for varying Peclet numbers on a fixed simulation grid. For this grid, the ENO scheme is shown to be sensitive to the Peclet number, signifying that physical dispersion is not overwhelmed by numerical diffusion. For the SPU scheme, however, the solutions are almost independent of the Peclet number, which indicates that numerical diffusion dominates.
AGU Fall Meeting Abstracts, Dec 1, 2005
AGU Fall Meeting Abstracts, Dec 1, 2007
ABSTRACT
Journal of Colloid and Interface Science, Feb 1, 2007
Abstract This comment points out an error of interpretation of experimental results reported in [... more Abstract This comment points out an error of interpretation of experimental results reported in [J. Colloid Interface Sci. 299 (2006) 321–331].
Numerical simulation of flow and mass transfer in fractured reservoir is challenging due to the c... more Numerical simulation of flow and mass transfer in fractured reservoir is challenging due to the complexity of the fracture networks. To handle the geological complexity, dual-porosity models are often used to approximate such reservoir settings. In dual-porosity models, it is assumed that two domains, a high permeability flowing domain (fracture) and a low permeability stagnant domain (matrix) are in communication and that viscous flow is marginal in the stagnant domain.In commercial reservoir simulation tools, transfer rates between the flowing and the stagnant domains are commonly modeled using the Warren and Root approach, where no attempt is made to a solve diffusion equation within each matrix block and a quasi-steady state transfer is assumed between the two domains. Previous research has demonstrated that such a simplification does not correctly represent the mass transfer between the domains. A more accurate approach to modeling transfer rates in such settings is to discretize the matrix blocks. However, this approach reduces the computational efficiency of large scale implicit reservoir simulation, due to the associated significant increase in the number computational cells.In this work, we present a semi-analytical approach to model multicomponent molecular diffusion within each matrix block in a coarse-scale simulation model and develop equations for time-dependent transfer functions between the flowing and stagnant domains. The time-dependency of the transfer functions are formulated based on initial and average compositions of the domains. Generalized Fick's law is used to describe the diffusive fluxes to account for dragging effects between components. Analytical and semi-analytical solutions to the multicomponent mass transfer equations are obtained through linearization and eigenvalue decomposition of the diffusion coefficient matrix.To demonstrate the accuracy of the proposed semi-analytical approach, various examples are presented. In these examples the results of the suggested approach are compared to the Warren-root model, analytical solutions and high-resolution fine-scale results for different of fluid compositions and geometries. We demonstrate that the proposed approach (coarse-scale modeling with time-dependent transfer functions) accurately represents the analytical solution, at a significantly lower CPU time requirement relative to high-resolution fine-scale models. Furthermore, we compare the proposed approach to experimental observations of mass transfer in a binary (CO2-Brine) system to further validate the precision of the proposed model.A novel and consistent matrix-fracture transfer function for coarse-scale models is introduced in this paper using semi-analytical solutions to multicomponent diffusive mass transfer. In the proposed approach, the inaccuracies of the conventional representation of diffusive mass transfer in dual-porosity models are resolved, while eliminating the need for further discretization of the matrix blocks. This allows for accurate, yet efficient simulation of diffusive mass transfer in fractured reservoirs.
Industrial & Engineering Chemistry Research, Mar 16, 2016
Production of oil and gas from unconventional source rocks (shales) has increased significantly i... more Production of oil and gas from unconventional source rocks (shales) has increased significantly in recent years, reflecting a shift in the focus of the oil and gas industry from conventional to unconventional oil/gas resources. An improved insight into the pore structure characteristics of these important porous materials will enable a better understanding and further optimization of the production behavior from such vast hydrocarbon resources. In particular, characterization of porosity and permeability of shales is the key to accurately estimating the initial oil and gas in place and fluid flow through these rocks. However, evaluating the pore structure of shales presents technical challenges due to the presence of a range of pores, from the nanometer to the micrometer size. Characterization of the entire range of pore sizes requires an all-inclusive study employing a variety of techniques. Such an integrated approach is followed in this work to understand the pore structure of Monterey shale samples as...
Transport in Porous Media, Aug 15, 2014
Accurate upscaling of highly heterogeneous subsurface reservoirs remains a challenge in the conte... more Accurate upscaling of highly heterogeneous subsurface reservoirs remains a challenge in the context of modeling of flow and transport. In this work, we address this challenge with emphasis on the representation of the displacement efficiency in coarse-scale modeling. We propose a dual-porosity upscaling approach to handle displacement calculations in high resolution and highly heterogeneous formations. In this approach, the pore space is arranged into two levels of porosity based on flow contribution, and a dual-porosity dual-permeability flow model is adapted for coarse-scale flow simulation. The approach uses fine-scale streamline information to transform a heterogeneous geomodel into a coarse dual-continuum model that preserves the global flow pathways adequately. The performance of the proposed technique is demonstrated for two heterogeneous reservoirs using both black oil (waterflooding) and compositional (gas injection) modeling approaches. We demonstrate that the coarse dual-porosity models predict the breakthrough times accurately and reproduce the post-breakthrough responses adequately. This is in contrast to conventional single-porosity upscaling techniques that overestimate breakthrough times and displacement efficiencies (sweep). By preserving large-scale heterogeneities, coarse dual-porosity models are demonstrated to be significantly less sensitive to the level of upscaling, when compared to conventional single-porosity upscaling. Accordingly, the proposed upscaling approach is a relevant and suitable technique for upscaling of highly heterogeneous geomodels.