Appropriate Choice of Average Pressure for Upscaling Relative Permeability in Dynamic Flow Conditions

Nordbotten, Jan Martin; Nogues, J. P.; Celia, Michael A.

doi:10.2118/113558-pa

Cited by 6 publications

(5 citation statements)

References 26 publications

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“…For this reason, we have used the arithmetic averaging method in this article. We are aware that Nordbotten et al () have discussed alternative ways of averaging capillary pressure and relative permeability data; however, they were not attempted in this article.…”

Section: Modeling Strategymentioning

confidence: 99%

A numerical study of dynamic capillary pressure effect for supercritical carbon dioxide‐water flow in porous domain

et al. 2014

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Numerical simulations for core‐scale capillary pressure (Pc)‐saturation (S) relationships have been conducted for a supercritical carbon dioxide‐water system at temperatures between 35°C and 65°C at a domain pressure of 15 MPa as typically expected during geological sequestration of CO2. As the Pc‐S relationships depend on both S and time derivative of saturation ( ∂S/∂t) yielding what is known as the “dynamic capillary pressure effect” or simply “dynamic effect,” this work specifically attempts to determine the significance of these effects for supercritical carbon dioxide‐water flow in terms of a coefficient, namely dynamic coefficient (τ). The coefficient establishes the speed at which capillary equilibrium for supercritical CO2 (scCO2)‐water flow is reached. The simulations in this work involved the solution of the extended version of Darcy's law which represents the momentum balance for individual fluid phases in the system, the continuity equation for fluid mass balance, as well as additional correlations for determining the capillary pressure as a function of saturation, and the physical properties of the fluids as a function of temperature. The simulations were carried out for three‐dimensional cylindrical porous domains measuring 10 cm in diameter and 12 cm in height. τ was determined by measuring the slope of a best‐fit straight line plotted between (1) the differences in dynamic and equilibrium capillary pressures true(Pc,dyn−Pc,equtrue) against (2) the time derivative of saturation (dS/dt), both at the same saturation value. The results show rising trends for τ as the saturation values reduce, with noticeable impacts of temperature at 50% saturation of aqueous phase. This means that the time to attain capillary equilibrium for the CO2‐water system increases as the saturation decreases. From a practical point of view, it implies that the time to reach capillary equilibrium during geological sequestration of CO2 is an important factor and should be accounted for while simulating the flow processes, for example, to determine the CO2 storage capacity of a geological aquifer. In this task, one would require both the fundamental understanding of the dynamic capillary pressure effects for scCO2‐water flow as well as τ values. These issues are addressed in this article. © 2014 American Institute of Chemical Engineers AIChE J 60: 4266–4278, 2014

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Section: Modeling Strategymentioning

confidence: 99%

A numerical study of dynamic capillary pressure effect for supercritical carbon dioxide‐water flow in porous domain

et al. 2014

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“…These relationships can have a critical effect on the simulation of propagation of drawdown outward from these wells. A further requirement is the employment of suitable "dynamic pseudo-relative permeability" functions, or "pseudos" as these are often called in the petroleum literature (Kyte and Berry 1975;Stone 1991;Barker and Thibeau 1997;Hewett and Archer 1997;Darman et al 2002;Gasda and Celia 2005;Nordbotten et al 2010). To the authors' knowledge these matters have received no attention in either the CBM reservoir modeling or CBM regional impact assessment modeling literature.…”

Section: Introductionmentioning

confidence: 99%

Some Challenges Posed by Coal Bed Methane Regional Assessment Modeling

et al. 2014

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Coal measures (coal bearing rock strata) can contain large reserves of methane. These reserves are being exploited at a rapidly increasing rate in many parts of the world. To extract coal seam gas, thousands of wells are drilled at relatively small spacing to depressurize coal seams to induce desorption and allow subsequent capture of the gas. To manage this process effectively, the effect of coal bed methane (CBM) extraction on regional aquifer systems must be properly understood and managed. Groundwater modeling is an integral part of this management process. However, modeling of CBM impacts presents some unique challenges, as processes that are operative at two very different scales must be adequately represented in the models. The impacts of large-scale gas extraction may be felt over a large area, yet despite the significant upscaling that accompanies construction of a regional model, near-well conditions and processes cannot be ignored. These include the highly heterogeneous nature of many coal measures, and the dual-phase flow of water and gas that is induced by coal seam depressurization. To understand these challenges, a fine-scale model was constructed incorporating a detailed representation of lithological heterogeneity to ensure that near-well processes and conditions could be examined. The detail of this heterogeneity was at a level not previously employed in models built to assess groundwater impacts arising from CBM extraction. A dual-phase reservoir simulator was used to examine depressurization and water desaturation processes in the vicinity of an extractive wellfield within this fine-scale model. A single-phase simulator was then employed so that depressurization errors incurred by neglecting near-well, dual-phase flow could be explored. Two models with fewer lithological details were then constructed in order to examine the nature of depressurization errors incurred by upscaling and to assess the interaction of the upscaling process with the requirement for adequate representation of near-source, dual-phase processes.

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“…By averaging microscale forms, TCAT ensures that the information in the equations that result is consistent between equations and across scales. This eliminates the procedure of introducing ad hoc definitions of quantities [98, 129] that, while seemingly offering some advantage for the study of one aspect of a problem, actually introduce inconsistencies elsewhere. Knowledge of larger scale equilibrium conditions also serves as an aid in rearranging entropy producing terms in an entropy inequality into force-flux pairs.…”

Section: Features Of the Tcat Approachmentioning

confidence: 99%

Averaging theory for description of environmental problems: What have we learned?

Gray

Miller

Schrefler

2013

Advances in Water Resources

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Advances in Water Resources has been a prime archival source for implementation of averaging theories in changing the scale at which processes of importance in environmental modeling are described. Thus in celebration of the 35th year of this journal, it seems appropriate to assess what has been learned about these theories and about their utility in describing systems of interest. We review advances in understanding and use of averaging theories to describe porous medium flow and transport at the macroscale, an averaged scale that models spatial variability, and at the megascale, an integral scale that only considers time variation of system properties. We detail physical insights gained from the development and application of averaging theory for flow through porous medium systems and for the behavior of solids at the macroscale. We show the relationship between standard models that are typically applied and more rigorous models that are derived using modern averaging theory. We discuss how the results derived from averaging theory that are available can be built upon and applied broadly within the community. We highlight opportunities and needs that exist for collaborations among theorists, numerical analysts, and experimentalists to advance the new classes of models that have been derived. Lastly, we comment on averaging developments for rivers, estuaries, and watersheds.

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Appropriate Choice of Average Pressure for Upscaling Relative Permeability in Dynamic Flow Conditions

Cited by 6 publications

References 26 publications

A numerical study of dynamic capillary pressure effect for supercritical carbon dioxide‐water flow in porous domain

A numerical study of dynamic capillary pressure effect for supercritical carbon dioxide‐water flow in porous domain

Some Challenges Posed by Coal Bed Methane Regional Assessment Modeling

Averaging theory for description of environmental problems: What have we learned?

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