Background

The 1984 Natl. Petroleum Council (NPC) studies of EOR [" The 1984 Natl. Petroleum Council Study on EOR: An Overview" (Aug. 1986JPT, Pages 869–74); "The 1984 Natl. Petroleum Council Estimate of Potential EOR for Miscible Processes" (Aug. 1986 JPT, Pages 875–82); and "The 1984 Natl. Petroleum Council Study on Pages 875–82); and "The 1984 Natl. Petroleum Council Study on EOR: Chemical Processes" (Aug. 1987 JPT, Pages 976–80)] was by far the most extensive evaluation of this important resource. It incorporated some 2,500 oil fields, each with more than 50 million bbl [8 × 106 m] of oil in place, comprising at least 73 % of all currently known oil in place in the U.S.

In addition to determining the remaining oil content by subtracting extrapolated ultimate waterflood oil recovery from oil in place, for a survey study, the task force made a laudable effort to place, for a survey study, the task force made a laudable effort to determine to a degree how the remaining oil content is distributed in the reservoir. In turn, that distribution was incorporated into a pre-diction of oil that might be recoverable by miscible displacemenor pre-diction of oil that might be recoverable by miscible displacemenor chemical flooding. The ingenious approach was to use a multilayer numerical reservoir simulator to determine an equivalent per-meability variation that would match the volumetric sweep efficienc per-meability variation that would match the volumetric sweep efficienc inferred by the gross volumetric and performance data of each reservoir. The model treated each reservoir as a five-spot waterflood with calculations made as follows:

  1. the relative-permeability/ frontal-drive aspect of the analyses incorporated results of some slim-tube waterflood tests;

  2. the areal sweep aspect of the water-flood used the numerical-model streamtube procedure;

  3. the vertical-sweep aspect of the waterflood was calculated as a 100-layer reservoir without crossflow; and

  4. the permeabilities assigned to the layers were assumed to have log-normal distribution.

The permeability distribution was varied until the model results yielded the same volumetric sweep efficiency as the field data. The resultant permeability distribution was expressed as a pseudo-Dykstra-Parsons permeability variation. If the derived pseudo-Dykstra-Parsons permeability variation. If the derived permeability variation was less than 0.5, a value of 0.5 was assumed permeability variation was less than 0.5, a value of 0.5 was assumed for all subsequent analyses.

The suggestion was made at a DOE/NIPER workshop on residual oil saturation that the DOE/NPC data base provided a very large source of information on residual oil saturations. I have obtained from the Bartlesville DOE office the final values of pseudo-Dykstra-Parsons permeability variations used. Table D-1 pseudo-Dykstra-Parsons permeability variations used. Table D-1 summarizes the distribution of permeability variations for sandstone reservoirs for those fields for which a value could be calculated. In 76% of the cases, the calculated pseudo-Dykstra-Parsons permeability variation exceeded 0.70.

In comparison with my published and unpublished detailed comparisons of actual performance of fluid-injection projects with core-permeability data, the permeability variations used in the NPC studare anomalous and exceedingly high. I respectfully suggest that con-sideration also be given to some alternative interpretations.

Methods of Averaging Core Permeabilities for Layers Permeabilities for Layers By the 1930's, selective shooting of water-injection wells was used to improve the effective-permeability profile. In 1946, Hurst and van Everdingen presented an analytic procedure for considering the areal-sweep aspects of dry gas in gas-condensate cycling projects and the first published calculation procedure for considering vertical sweep efficiency during parallel flow in noncommunicating layers. Their example appears to represent core analysis of a single well. There were no suggestions on averaging core analysis from many wells.

In 1946, Miller and Lents expanded the Hurst-van Everdingen method by developing a method of averaging permeabilities from cores of many wells at the same relative vertical position in the sand to assign permeabilities to the individual layers. The efficacy of their procedure was demonstrated by a favorable comparison between predictions from a 16-well average-permeability profile and the actual dry-gas dilution histories of observation wells in the Cotton Valley cycling project.

Standing et al. presented a similar analysis of cycling except that the permeabilities assigned to layers were selected from a smoothed log-normal frequency plot of permeabilities, a special slope of which has come to be known as permeability variation. In 1950, Dykstra and Parsons expanded this to model waterflooding of parallel noncommunicating layers in which the different mobilities of swept parallel noncommunicating layers in which the different mobilities of swept and unswept zones in a linear flood resulted in changing relative flow rates among the layers as the flood progresses. The procedure proposed for assigning permeabilities to layers was identical to that of Standing et al.

About the same time, Stiles presented his procedure of using permeability distribution in waterflood calculations. Part of it is permeability distribution in waterflood calculations. Part of it is similar to the Dykstra-Parsons procedure in that the permeabilities are to be arranged in sequential order for averaging in groups for individual layers, but he did not propose the next step of idealization to log-normal frequency distribution of permeabilities. In 1959, Prats et al. presented a study that combined many of the aspects of the Dykstra-Parsons and Stiles methods as applied to a five-spot waterflood and compared it with results of an actual waterflood.

Comparison With Gas-Condensate Cycling Projects

I heard the Miller-Lents presentation in 1946 and was impressed both by the logic of the procedure proposed for averaging core data of many wells by vertical position in the formation to assign per-meabilities to individual layers and by the excellent agreement between per-meabilities to individual layers and by the excellent agreement between the "prediction" by the procedure and the actual dry-gas dilution histories of observation wells in the Cotton Valley field. They stated that "data must be weighted with respect to areas of influence after being located vertically in a manner consistent with the relative geometric occurrence of the sample ... accurate vertical location of the data may be as significant as the value used." Later, when the Standing et al., Stiles, and Dykstra-Parsons procedures were published, I arranged the Cotton Valley permeability procedures were published, I arranged the Cotton Valley permeability data in serial order, divided them into 50 equal groups to assign permeabilities to layers, and repeated the cycling calculations. permeabilities to layers, and repeated the cycling calculations. Agreement with the actual dry-gas breakthrough and the subsequent dry-gas dilution histories of Cotton Valley observation wells was much poorer.

The difference between averaging permeabilities by position as proposed by Miller and Lents and by statistical frequency proposed by Miller and Lents and by statistical frequency distribution per se as proposed by Standing et al., Stiles, and DykstraParsons is illustrated in Fig. D-1 (modified from Miller and Lents).

The individual core permeabilities from 16 Cotton Valley wells are plotted vs. percentage vertical position in the Bodcaw sand. The plotted vs. percentage vertical position in the Bodcaw sand. The solid horizontal lines illustrate how the permeability data would be grouped for averaging by position for 10 layers. The vertical dashed lines illustrate how the same permeability data would be grouped for averaging by frequency distribution for 10 layers. The vertical distribution of data points between pairs of dashed lines demonstrates the aberration introduced by this averaging procedure compared with an idealized geologic model of at least many marine sediments being deposited in relatively parallel horizontal sequences.

Related papers: SPE 13239, SPE 13240, SPE 13241

Related discussions and replies:SPE 18397, SPE 20007, SPE 20009

 

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