Spatial averaging of transmissivity in heterogeneous fields with flow toward a well

Desbarats, A. J.

doi:10.1029/91wr03099

Cited by 84 publications

(84 citation statements)

References 20 publications

(16 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Consistent with Matheron they found that for fixed Ao, k, increases toward as .,/Ao + 0, and decreases and (4) asymptotically approaches F: @e., ensemble harmonic average of ko(X)) as .,/Ao + w . For similar flow conditions, Desbarats (1992b) modeled Le as a weighted spatial geometric average where the log permeabilities were weighed by the inverse square of their distance from the well.…”

Section: Model Comparisonmentioning

confidence: 99%

“…Where simplifjring assumptions concerning the spatial structure of the porous medium can be made and flows are uniform, upscaled permeability estimates are derived directly through analytical solutions (e.g., Gutjahr et al, 1978, Dagan, 1981Gelhar and Axness, 1983;Deutsch, 1989;Rubin and Gomez-Hernandez, 1990;Desbarats, 1992a). Where non-uniform flows are encountered a single effective permeability value can no longer be defined that is dependent soIely on the statistical properties of the permeability; rather, upscaling must explicitly account for the flow conditions unique to the problem (e.g., Ababou and Wood, 1990;Desbarats, 1992b;Indelman and Abramovich, 1994;Sanchez-Vila, 1997). For cases involving complicated heterogeneities andor flows numerical solutions to the upscaling problem are necessitated (e.g., White and Home, 1987;I Kitanidis, 1990;Durlofsky, 1991).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Untitled

Tidwell

Wilson

1999

Mathematical Geology

View full text Add to dashboard Cite

To physically investigate permeability upscaling over 13,000 permeability values were measured with four different sample supports (Le., sample volumes) on a block of Berea Sandstone. At each sample support spatially-exhaustive permeability data sets were measured, subject to consistent flow geometry and boundary conditions, with a specially adapted minipermeameter test system.Here, we present and analyze a subset of the data consisting of 2304 permeability values collected from a single block face oriented normal to stratification. Results reveal a number of distinct and consistent trends (i.e., upscaling) relating changes in key summary statistics to an increasing sample support. Examples include the sample mean and semivariogram range that increase with increasing sample support and the sample variance that decreases. To help interpret the measured mean upscaling we compared it to theoretical models that are only available for somewhat different flow geometries. The comparison suggests that the non-uniform flow imposed by the minipermeameter coupled with permeability anisotropy at the scale of the local support (i.e., smallest sample support for which data is available) are the primary controls on the measured upscaling. This work demonstrates, experimentally, that it is not always appropriate to treat the local-support permeability as an intrinsic feature of the porous medium; that is, independent of its conditions of measurement.

show abstract

Section: Model Comparisonmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Untitled

Tidwell

Wilson

1999

Mathematical Geology

View full text Add to dashboard Cite

show abstract

“…To date, such efforts have relied on theoretical constructs coupled with mathematical modeling. One of the most widely recognized examples is the inverse distance squared weighting of heterogeneities by radial flow to a well [CaMwell and Parsons, 1945;Desbarats, 1992a]. Oliver [1990] used a perturbation approach to calculate the weighting function for permeability estimates derived from the semilog plot of drawdown versus time for nonsteady pump test data.…”

mentioning

confidence: 99%

What does an instrument measure? Empirical spatial weighting functions calculated from permeability data sets measured on multiple sample supports

Tidwell¹,

Gutjahr²,

Wilson³

1999

Water Resources Research

View full text Add to dashboard Cite

Abstract. With the aid of linear filter theory we analyze 13,824 permeability measurements to empirically address the question, What does an instrument measure? By measure we mean the sample support or sample volume associated with an instrument, as well as how the instrument spatially weights the heterogeneities comprising that sample support. Although the theoretical aspects of linear filter analysis are well documented, physical data for testing the filtering behavior of an instrument, particularly in the context of porous media flow, are rare to nonexistent. Our exploration makes use of permeability data measured with a minipermeameter on a block of Berea sandstone. Data were collected according to a uniform grid that was resampled with tip seals of increasing size (i.e., increasing sample support). Spatial weighting (filter) functions characterizing the minipermeameter measurements were then calculated directly from the permeability data sets. In this paper we limit our presentation to one of the six rock faces, consisting of 2304 measurements, as the general results for each rock face are similar. We found that the empirical weighting functions are consistent with the basic physics of the minipermeameter measurement. They decay as a nonlinear function of radial distance from the center of the tip seal, consistent with the divergent flow geometry imposed by the minipermeameter. The magnitude of the weighting function decreases while its breadth increases with increasing tip seal size, reflecting the increasing sample support. We further demonstrate, both empirically and theoretically, that nonadditive properties like permeability are amenable to linear filter analysis under certain limiting conditions (i.e., small variances). Specifically, the weighting function is independent of the power average employed in its calculation (e.g., arithmetic versus harmonic average). Finally, we examine the implications of these results for other instruments commonly employed in hydraulic testing (e.g., slug and pump tests). Introduction Questions concerning what is actually measured by an in-In this way, the weighting function 13mo explicitly accounts for the influence of the measurement process on the value of k m.

show abstract

“…In general, the different methods used in upscaling parameters like absolute permeability or transmissibility and relative permeability can be classified based on what is being upscaled and the technique used (see reviews by Smith, 1991;Desbarats, 1992;King et al 1995;Christie, 1996;Renard and Marsily, 1997;Chiles and Delfiner, 1999). In single-phase upscaling, the absolute permeability or transmissibility of the geologic model is upscaled, while in multi-phase in addition upscaling the absolute permeability or transmissibility, the relative permeabilities and capillary pressure are upscaled.…”

Section: General Upscaling Methodsmentioning

confidence: 99%

Upscaling for Thermal Recovery

Abubakar¹,

Muggeridge²,

King³

2014

SPE International Heavy Oil Conference and Exhibition

View full text Add to dashboard Cite

Thermal recovery is one of the most widely applied EOR methods worldwide. It is used mainly to improve the recovery of more viscous oils. Heat is used primarily to reduce the viscosity of oil but may also improve recovery by other mechanisms such as oil expansion, steam distillation and reduction in capillary forces. As a result, the prediction of thermal recovery performance requires more complex and computationally demanding numerical simulations than is the case when evaluating a waterflood. The simulator has to evaluate the impact of both heat transfer and compositional behaviour on the fluid flows.In most cases the engineer will have to use coarser grids in the simulation models than would be needed for a waterflood in order to keep simulation times within acceptable limits. However, it has been shown in the modelling of other EOR processes that in fact much finer grids may be needed to capture the frontal dynamics of the displacement than would be the case in waterflooding. As a result, the simulation of steamflooding on the field scale is unlikely to capture the impact of small scale heterogeneity on flow, as well as being severely affected by numerical dispersion. The ideal solution is to use homogenization to capture the effects of sub-grid-block heterogeneity combined with advanced numerical techniques such as dynamic/adaptive gridding or higher order schemes to reduce the impact of numerical diffusion and dispersion. However, such methods are not currently available in the commercial simulators available to most engineers.The alternative is to use upscaling, but as yet there are no upscaling methodologies suitable for thermal oil recovery methods. Upscaling is a way of altering the inputs to numerical flow models so that simulations run on a coarse grid. These will a) predict the impacts on flow of sub-grid heterogeneity (homogenization) and b) will be less affected by numerical dispersion. For waterflooding this is typically achieved by calculating the effective absolute permeability for each coarse grid cell. In many cases, it is also necessary to upscale the well index and the transmissibilities of the well blocks. Upscaling the absolute permeability, the well index and the well block transmissibilities, ensures that the overall pressure drop for single phase flow between wells is correctly predicted in the coarse grid, whilst upscaling the relative permeabilities ensures that the two-phase flow effects (pressure drop, breakthrough time and water cut development) are correctly modelled. Although there is a significant literature on single-phase upscaling and the development of pseudo relative permeabilities for waterflooding applications, these methods do not capture the heat transport or the impact of temperature on the oil mobility. ivIn this research, a combination of pseudoisation procedures (by making reasonable assumptions) with the Buckley-Leverett solution approximated for thermal EOR processes is used to derive analytical pseudo-relative permeabilities for both hot water and steam ...

show abstract

Spatial averaging of transmissivity in heterogeneous fields with flow toward a well

Cited by 84 publications

References 20 publications

Untitled

Untitled

What does an instrument measure? Empirical spatial weighting functions calculated from permeability data sets measured on multiple sample supports

Upscaling for Thermal Recovery

Contact Info

Product

Resources

About