Using the Inertial Coefficient, B, To Characterize Heterogeneity in Reservoir Rock
1987; Linguagem: Inglês
10.2523/16949-ms
Autores Tópico(s)Enhanced Oil Recovery Techniques
ResumoUsing the Inertial Coefficient, B, To Characterize Heterogeneity in Reservoir Rock S.C. Jones S.C. Jones Core Research, Div. of Western Atlas Search for other works by this author on: This Site Google Scholar Paper presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas, September 1987. Paper Number: SPE-16949-MS https://doi.org/10.2118/16949-MS Published: September 27 1987 Cite View This Citation Add to Citation Manager Share Icon Share Twitter LinkedIn Get Permissions Search Site Citation Jones, S.C. "Using the Inertial Coefficient, B, To Characterize Heterogeneity in Reservoir Rock." Paper presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas, September 1987. doi: https://doi.org/10.2118/16949-MS Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAll ProceedingsSociety of Petroleum Engineers (SPE)SPE Annual Technical Conference and Exhibition Search Advanced Search SPE MemberAbstractNew data, relating the inertial coefficient, P, or the Klinkenberg slip factor, b, to the characteristic length,, are presented for core plugs from several reservoirs. These are useful for estimating flow performance of wells.The group, bko, which is the characteristic length dimension in a Reynolds number for porous media, should be proportional to the k/o characteristic length approaches proportionality for the most permeable samples, but deviates badly for tighter plugs. A multi-layer flow model is developed that demonstrates that the departure is due to the non-linear dependence of inertial resistance on permeability variations in a core plug. Thus the measurement of p provides a very sensitive indication of permeability heterogeneity, on a core-plug level.IntroductionForchheimer in 1901 discovered that the pressure gradient required to sustain a high flow rate through a porous medium is higher than Darcy's equation would predict. The deviation increased with increasing flow rate. He attributed the excess gradient required, to inertial flow resistance, which is proportional to pv2. He also proposed an additional cubic term for very high flow rates.Cornell and Katz determined inertial coefficients, or 'turbulence factors' for a variety of reservoir rocks and correlated their results with permeability. Tek, et. al. presented a correlation involving permeability and porosity. Firoozabadi and Katz compare correlations of several authors. Noman, et. al. measured inertial coefficients from tests in high-rate gas wells and compared them to laboratory-measured coefficients with fair success.Geertsma showed that the ratio of pko to k/o is a constant for unconsolidated media, drawing on Ergun's relationships. Macdonald, et. al. also discussed the Ergun equation. Ezeudembah and Dranchuk established a physical basis for Forchheimer's cubic term. Finally, Evans and coworkers have discussed the effect of liquid saturation on the 'non-Darcy flow coefficient'.None of these authors has suggested that the inertial coefficient, p, is strongly influenced by the degree of permeability heterogeneity in a reservoir rock, nor that heterogeneity may be the reason why all correlations involving p exhibit so much scatter. This is the goal of the present paper.THEORETICAL CONSIDERATIONSThe inertial coefficient, P, is defined by the Forchheimer equation, which for one-dimensional flow is:(1)The factor 3.238 × 10-8 is required for dimensional consistency when the units are those given in the nomenclature. The v in Eq. 1 is the Darcy velocity, q/A, which is based on the superficial cross-sectional area. When the inertial term, pv2, becomes negligibly small (at low fluid velocities and/or densities), Eq. 1 reduces to the more familiar Darcy equation.According to Eq. 1, part of the pressure gradient across a core plug is due to viscous flow, and the remainder results from inertial dissipation. To compare the magnitude of these effects, it is instructive to factor the viscous term from the right-hand side of Eq. 1:(2)P. 165^ Keywords: effective inertial coefficient, permeability, dimension, correlation, inertial coefficient, flow rate, resistance, flow in porous media, fluid dynamics, coefficient Subjects: Reservoir Fluid Dynamics, Flow in porous media This content is only available via PDF. 1987. Society of Petroleum Engineers You can access this article if you purchase or spend a download.
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