Dispersion and Reservoir Heterogeneity

Arya, Atul; Hewett, Tom A.; Larson, Ronald G.; Lake, Larry W.

doi:10.2118/14364-pa

Cited by 216 publications

(130 citation statements)

References 20 publications

Supporting

Mentioning

120

Contrasting

Order By: Relevance

“…Edwards et al (1991) and many other authors (Didierjean 1997;Eidsath et al 1983;Souto and Moyne 1997) use this equation for periodic media and present 2D computational results also for higher Peclet numbers. The comparison with experimental values uses a standard plot of the longitudinal dispersion coefficient divided by the molecular diffusion coefficient versus the Peclet number (Arya et al 1988). A dissimilar definition of the dispersion tensor by the engineering and mathematics community, differing by a factor equal to the porosity, precluded until now a correct comparison between experimental and theoretical values obtained with homogenization (Tardif d'Hamonville et al 2007).…”

Section: Introductionmentioning

confidence: 99%

Computation of the Longitudinal and Transverse Dispersion Coefficient in an Adsorbing Porous Medium Using Homogenization

2011

View full text Add to dashboard Cite

This article compares for the first time, local longitudinal and transverse dispersion coefficients obtained by homogenization with experimental data of dispersion coefficients in porous media, using the correct porosity dependence. It is shown that the longitudinal dispersion coefficient can be reasonably represented by a simple periodic unit cell (PUC), which consists of a single sphere in a cube. We present a slightly modified and simplified approach to derive the homogenized equations, which emphasizes physical aspects of homogenization. Subsequently, we give full dimensional expressions for the dispersion tensor based on a comparison with the convective dispersion equation used for contaminant transport, inclusive the correct dependence on porosity. For the PUC of choice, the dispersion relations are identical to the relations obtained for periodic media. We show that commercial finite element software can be readily used to compute longitudinal and transverse dispersion coefficients in 2D and 3D. The 3D results are for the first time obtained at relevant Peclet numbers. There is good agreement for longitudinal dispersion. The computed transverse dispersion coefficients for a single sphere in a cube are much too low. The effect of adsorption on the dispersion coefficient is also studied. Adsorption does not affect the transverse dispersion coefficient. However, adsorption enhances the longitudinal dispersion coefficient in agreement with an analysis of homogenization applied to Taylor dispersion discussed in the literature.

show abstract

Section: Introductionmentioning

confidence: 99%

Computation of the Longitudinal and Transverse Dispersion Coefficient in an Adsorbing Porous Medium Using Homogenization

2011

View full text Add to dashboard Cite

show abstract

“…The result that Var(x) is proportional to <x> 2 , as established in dispersive transport in semiconductors [13,14], leads immediately to a dispersivity that is proportional to <x>, as is also known from groundwater studies [72]. While it has been reported [73,74] that the dispersion coefficient is typically a small power (sublinear) of time and that the dispersivity is roughly a linear function of x, the necessary consequence (as shown in Figure 7), is that the time for particles to reach a given distance x is a superlinear function of x, has been reported only once [75] (to our knowledge) for solute transport in porous media, but is well-known in dispersive transport [45][46][47][48][49][50]. In particular, we have then Var(x) <x> 2 and Var(x) t 1+δ , with δ 1 giving immediately t x 2/(1+δ) .…”

Section: Resultsmentioning

confidence: 81%

Saturation dependence of dispersion in porous media

2012

View full text Add to dashboard Cite

In this study, we develop a saturation-dependent treatment of dispersion in porous media using concepts from critical path analysis, cluster statistics of percolation, and fractal scaling of percolation clusters. We calculate spatial solute distributions as a function of time and calculate arrival time distributions as a function of system size. Our previous results correctly predict the range of observed dispersivity values over ten orders of magnitude in experimental length scale, but that theory contains no explicit dependence on porosity or relative saturation. This omission complicates comparisons with experimental results for dispersion, which are often conducted at saturation less than 1. We now make specific comparisons of our predictions for the arrival time distribution with experiments on a single column over a range of saturations. This comparison suggests that the most important predictor of such distributions as a function of saturation is not the value of the saturation per se, but the applicability of either random or invasion percolation models, depending on experimental conditions.

show abstract

“…1.5). If the permeable media were layered, there should be a significant difference in the values of echo and field dispersivities from Arya et al (1998). The results in Fig.…”

Section: Results and Discussion Task 1: Reduce Mmp With Gas Enrichmentmentioning

confidence: 88%

Development of More-Efficient Gas Flooding Applicable to Shallow Reservoirs

Rossen¹,

Johns²,

Pope³

2003

View full text Add to dashboard Cite

ABSTRACT:The objective of this research is to widen the applicability of gas flooding to shallow oil reservoirs by reducing the pressure required for miscibility using gas enrichment and increasing sweep efficiency with foam. Task 1 examines the potential for improved oil recovery with enriched gases. Subtask 1.1 examines the effect of dispersion processes on oil recovery and the extent of enrichment needed in the presence of dispersion. Subtask 1.2 develops a fast, efficient method to predict the extent of enrichment needed for crude oils at a given pressure. Task 2 develops improved foam processes to increase sweep efficiency in gas flooding. Subtask 2.1 comprises mechanistic experimental studies of foams with N 2 gas. Subtask 2.2 conducts experiments with CO 2 foam. Subtask 2.3 develops and applies a simulator for foam processes in field application.Regarding Task 1, several results related to subtask 1.1 are given. In this period, most of our research centered on how to estimate the dispersivity at the field scale. Simulation studies (Solano et al. 2001) show that oil recovery for enriched gas drives depends on the amount of dispersion in reservoir media. But the true value of dispersion, expressed as dispersivity, at the field scale, is unknown. This research investigates three types of dispersion in permeable media to obtain realistic estimates of dispersive mixing at the field scale.The dispersivity from single-well tracer tests (SWTT), also known as echo dispersivity, is the dispersivity that is unaffected by fluid flow direction. Layering in permeable media tends to increase the observed dispersivity in well-to-well tracer tests, also known as transmission dispersivity, but leaves the echo dispersivity unaffected. A collection of SWTT data is analyzed to estimate echo dispersivity at the SWTT scale. The estimated echo dispersivities closely match a published trend with length scale in dispersivities obtained from groundwater tracer tests. This unexpected result-it was thought that transmission dispersivity should be greater than echo dispersivity-is analyzed with numerical simulation.A third type of dispersive mixing is local dispersivity, or the mixing observed at a point as tracer flows past it. Numerical simulation results show that the local dispersivity is always less than the transmission dispersivity and greater than the echo dispersivity limits. It is closer to one limit or the other depending on the amount and type of heterogeneity, the autocorrelation structure of the medium's permeability, and the lateral 4 (vertical) permeability. The agreement between the SWTT echo dispersivities and the field trend suggests that the field data are measuring local dispersivities. All dispersivities appear to grow with length.Regarding Task 2, two results are described: 1) An experimental study of N 2 foam finds the two steady-state foam-flow regimes at elevated temperature and with acid, adding evidence that the two regimes occur widely, if not universally, in foam in porous media. 2) A simulation finds tha...

show abstract

Dispersion and Reservoir Heterogeneity

Cited by 216 publications

References 20 publications

Computation of the Longitudinal and Transverse Dispersion Coefficient in an Adsorbing Porous Medium Using Homogenization

Computation of the Longitudinal and Transverse Dispersion Coefficient in an Adsorbing Porous Medium Using Homogenization

Saturation dependence of dispersion in porous media

Development of More-Efficient Gas Flooding Applicable to Shallow Reservoirs

Contact Info

Product

Resources

About