spe-1576-g-pa.pdf - OnePetro

PETROLEUM RESEARCH

Identification, Classification and Prediction of Reservior Nonuniformities Affecting Production Operations

Abstract

C. A. HUTCHINSON, JR. MEMBER AIME

C. F. DODGE

T. L. POLASEK JUNIOR MEMBER AIME

A study of sandstone outcrops typical of producing horizons has been undertaken to develop a method for predicting the size, shape and permeability contrast of reservoir nonuniformities. This paper is a progress report and presents the tentative conclusions reached from the study of several Cretaceous age outcrops in the Four Corners area and of the Woodbine outcrop around Dallas.

The results to date suggest that nonuniformities in sandstone reservoirs may be classified according to (1) depositional environment and (2) rock texture and cement content. Within a sandstone unit, there will be no drastic variations in permeability providing the cement content is not sufficient to control the permeability. For this noncement-controlled or texture-controlled permeability situation, up to a 5:1 ratio of maximum-to-minimum permeability is expected for measurements on 1 X 7h-in. core plugs. When the permeability of the sand is cement-controlled, the maximum-to-minimum ratio of permeability values within a sand unit may exceed 100:1.

Clean shale sections tend to be continuous over great distances, whereas sandy shale sections will be fairly continuous only in ripple-marked and horizontally bedded layers of the formation. In cross-bedded sandstones, the sandy shale sections will tend to be discontinuous.

The conclusions reached in this study so far suggest that, if the bedding, textural qualities and cement content are known in blanket sandstones, the sizes, shapes and permeability contrast of nonuniformities within the sandstone are predictable. The bedding, textural properties and cement content can be determined from well cores,

Introduction

This is a progress report on a major research study that is far from completion. The report is presented with the

Origmal manuscript received in Society of Petroleum Engineers office July 18 19,'0. Revised manuscript re<'eived Jan. 16. 1061. Paper presented at 35th Annual Fall Meeting of SPE Oct. 2-5, 1960, in Denver.

MARCH, 1961 SPE 1576-G

THE ATLANTIC REFINING CO. DALLAS, TEX.

ARLINGTON STATE COLLEGE ARLINGTON, TEX.

THE ATLANTIC REFINING CO. DALLAS, TEX.

hope that the limited accomplishments to date may impart worthwhile insight to some and that others of the industry will become sufficiently interested in this frontier of technology to lend their efforts to developing an understanding of reservoir nonuniformities and the engineering procedures for including their effects in reservoir performance.

The over-all problem can be expressed best by the following two questions. How can non uniformities be identified and classified as to degree and geometry? How can the degree of nonuniformity and the geometries of nonuniformities within a specific reservoir and formation be predicted?

The scope of this investigation is . being restricted to those nonuniformities felt to be significant to the petroleum engineer. This means that the study is concerned first with changes in permeability existing within the reservoir, how great these changes are and the general geometry (size and shape) of the permeability nonuniformities. This research does not include studies of either the very small-scale poreto-pore non uniformities or the differences existing between reservoirs because these areas already have received much attention by petroleum engineers and geologists in the past.

Simultaneously with furthering an understanding of the nonuniformities which may exist within a reservoir, the research study could result in the development of methods by which the nonuniformities of any specific reservoir can be predicted for engineering purposes. Obviously, no reservoir can ever be exposed physically so that its porous structure can be analyzed foot-by-foot or inch-by-inch to define the permeability nonuniformity. Present studies are restricted to deducing nonuniformities from a general geological background on the formation in question and from information available from well logs and cores. In addition, data from well behavior (build-up curves, etc.) and field performance tests are utilized in the deduction process. The present study has been undertaken with the thought that the non uniformity prognosis method must rely only on general geology and on data from cores and logs from the specific formation.

There are companion problems concerning reservoir

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non uniformities. What do the non uniformities of reservoirs do to the various oil recovery processes? How do they affect such test data as build-up curves? What processes can be designed to relieve or eliminate the adverse effects of non uniformities on these processes? However, a discussion of the progress made in solving these problems is beyond the scope of this report.

Significance of Problem

In general, it appears that reservoir nonuniformities adversely affect any secondary recovery operation, no matter what the nonuniformities are. Further, the adverse effects of nonuniformities are magnified significantly by the presence of an adverse mobility ratio. Now that interest in the adverse mobility ratio processes has increased, these nonuniformities may become disastrous. Recent reports on various applications of the gas-driven miscible-slug process and the solvent-bank process attribute failures or disappointing behavior of the processes to the reservoir nonuniformities. Thus, if the new, exotic recovery processes are to be used, an understanding of reservoir nonuniformities and their effects upon these processes must be developed. Disaster then can be averted by avoiding some reservoirs or, possibly, by modifying the processes so that the nonuniformities will not cause failures.

Object of the Research

The research program is designed to develop a method for predicting, perhaps on a statistical basis, the probability of the presence of reservoir nonuniformities of a certain type in any reservoir under consideration from the cores, logs and general geologic background of the reservoir. It is hoped that through this research more information can be obtained from the field data now being gathered. Through better understanding and statistical correlations based on core and log analyses, for example, a better picture possibly will be developed of the stratification which exists in a reservoir - thus allowing a better guess to be made of the formation's uniformity between wells in the tremendous volume of the reservoir not sampled by cores and logs.

Research Procedure

While searching the literature, it became plainly evident that there has been much speCUlation concerning reservoir nonuniformities - but very little research dealing with the character and measurement of these nonuniformities. Unfortunately, the tremendous amount of work conducted by geologists is not particularly applicable to reservoir engineering problems in fluid flow.

In selecting a plan for conducting the research, it was decided first to study in detail the outcrops of reservoir sands in areas where vast exposures were available. The procedure has been to study large exposures of sandstone outcrops, to observe the changes in rock lithology, and to sample and measure the changes in rock properties from location to location. From data obtained in this fashion, present sedimentation theories are being augmented to explain and characterize new findings. It is hoped that enough data can be obtained so that the non uniformity problem can be approached from a statistical aspect.

Work Program in Progress

At present, the research program is being confined to a study of nonuniformities in sandstones of shallow-marine

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origin. Over 80 per cent of the oil-producing sandstone reservoirs are shallow marine.'o Limestone reservoirs present a completely different nonuniformity problem - one which is yet to be approached. Although further knowledge of nonuniformities in other reservoir characteristics is desirable, the present investigation has been limited to permeability variations and to the causes for these variations within the formation.

Samples first were taken from the Woodbine formation in outcrops around Dallas, and then from four other formations of Cretaceous age in the blanket sand outcrops in the Four Corners area. The sands sampled were the Pictured Cliffs, Point Lookout, Gallup and Dakota formations, all relatively clean sands not significantly modified by ground water circulation. The sampled portions of the outcrops ranged in length from about 1,000-ft to 1 mile.

The sampling program should be extended to include examinations of dirtier sands and also to include lens and pinchout types of deposits.

Present Observations

Observations to date have been limited to blanket, shallow-marine sandstone deposits; of these, only the relatively clean (low shale content) formations have been sampled extensively.

The concept of the "geological unit of deposition" has been quite helpful in interpreting data obtained from the outcrop samples and in conceptually analyzing the nonuniformities to be expected. A sandstone formation may be composed of one or more units of deposition. A unit can be identified by three physical characteristics: (1) the unit will have the same type of bedding throughout; (2) the average grain size of core plug samples will not vary over about a factor of 1.8, and the grain-size distribution will vary only over a very limited range; and (3) the grain packing will be about the same throughout the unit. Observations show that from unit to unit there generally is a rather marked change in average grain size and grain size distribution and, at times, in packing. Within a unit, only a small variation exists.

A unit generally has wide areal extent in blanket sandstones. In a blanket sand with cross-bedding, the unit is a collection of lenses. Figs. 1 and 2 are photographs of cross-bedded outcrops showing the bedding and lenses. The lens can be quite small or it can be large, perhaps 1,000 ft in areal extent. Units of ripple-marked and horizontaIly bedded sandstones can be considered as layered systems. An example of ripple-marked bedding is shown in the photographs of Figs. 3 and 4.

Zones of shaly sand (much finer than average grain-size sand) occasionally were observed within a coarser-grained sandstone unit. These sandy shale zones, which will restrict vertical flow of fluids, tended to be continuous under some circumstances and discontinuous under others. In blanket sandstones horizontally bedded or ripple marked, the sandy shale tends to be continuous over great distances. When there is strong current cross-bedding, the sandy shale streaks tend to be discontinuous and may extend only a few tens of feet through the formation. In such cases a sandy shale streak will tend to be elliptical in both horizontal and vertical cross section.

Clean shale deposits tend to be continuous throughout a blanket-type deposit no matter what the bedding type. Thus, when clean shale is found in a core, even though

:!°References given at end of paper.

JOURNAL OF PETROLEUM TECHNOLOGY

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Fig. I - t;::ross-bedd ing in Webel' formation outcrop nea r Ran gely, Colo.

Fig. 2-Cross-bedding in Gallup formation outcrop near Farmington, N. M.

this shale streak be only I-in. thick, it probably will be continuous over thousands of feet.

The next observation concerns the permeability variation within a sand unit. From the standpoint of this discussion, exclude the permeability variation that exists between the sandy portion of the unit and any included sandy shale zones. Consider only the permeability as measured in I-in. core plug samples taken throughout the sandy portion of the unit. The cores were not oriented with respect to the bedding planes in cross-bedded sands. All of the cores, except for a few taken vertically, were taken parallel to the dip of the formation. The vertical and horizontal permeability values were very nearly identical except in ripplemarked units which contain many short, thin, shaly layers. For the most part, however, variations in horizontal permeability were investigated.

The degree of permeability variation in the sandy portion of the unit appears to depend primarily upon the cement content and the textural properties of the sand. When the cement content is high (over 25 per cent of the initial pore volume), the permeability variation also will be high -maybe a hundred-fold or more. When the cement content is low, the textural properties alone control the variation of permeability. The studies indicate that the permeability

MARCH, 1961

3- Ripp\ -marked bedd 'ng in outcrop near Duch esne,

Fig. 4-Side view of ripple-marked outcrop shown in Fig. 3.

VarIatIOn for these conditions will range from a minimum of about fivefold for sands with commonly found packing to about twenty-fold for extra-tightly packed grains. It is important to note that the permeability variations existing under these texture-controlling conditions are spaced essentially at random within the sandstone unit.

The information contained in the preceding discussion is illustrated graphically in Fig. 5, which shows the breakdown of the sandstone unit into the bedding-type and the permeability-control mechanisms. The data obtained to date have been summarized in Table l.

The preceding discussion has considered the permeability variation within units and the extent of units. A further concern would be the permeability variation between units. No correlation of this nature has been attempted, but it should be obvious that practically any variation is conceivable.

Interpretation

Most sedimentary material came from the continents, delivered to the seas by streams and rivers. Only a small amount resulted from weathering of the shore lines. Once the material is delivered to the sea, there is a sorting of particle size for sedimentation according to the water

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Sandstone Uni t

I Sandy Portion

I Random

I Sandy Shale Portion

Areal Extent of Inclusion

Permeability Variations

Cross

I Lens - to- Lens

.1 High

Cement Content

I

Texture Controlled

n Extra Common Tight . parng pacrng

I I

Bedding I

I Within-a-Lens

I High

Cement Content

I

Texture Controlled

n E~tra Common Tight . Packing Packing

I I ? krangeN7 krangeN2 krange",3 krange",2

Horizontal Bedding Ripple-marked Bedding

I High

Cement Content

I Texture Controlled

E~~mon Tight Packing parng I

? krange",5

Horizontal Bedding

Ripple-marked Bedding

I Tends to be cont inuous

All Cross

Bed ding

I Tends to be

discontinuous

Fig. 5-Generalizations on extent and permeability variations of sandstone units in blanket shallow-marine deposits.

velocity delivering each particle. Even in the bays and lagoons where water motion is slight, there is significant sorting of the sediments. Areas with almost still water will accumulate the silts and clays, and coarseness of the material sedimented increases with increasing water velocity. When sediments are carried into the open sea, a more thorough sorting process takes place. Large areas 10 to 20-miles wide will accumulate the sands, shales, or silts preferentially. In this type of environment, the blanket sands are formed. Here the grain sizes and sorting for anyone particular unit are confined to a fairly narrow range of values because of the significant amount of particle-size sorting accomplished.

During the long period of time over which a blanket sand was deposited, the area of the sea in which deposition was taking place moved, either regressing from the continent or transgressing upon it. The sand accumulation in each unit is really an accumulation of a series of layers. Here each unit can be visualized as a deck of cards, each card slightly offset from the card below it, with the offset resulting from the transgression and regression of the sea. The layers may all be the same, or one layer may vary from the next because of a change in the material deposited or because of an over-all change in the environment of deposition. When these changes occur, there is a change from one unit to the next. A second mechanism for change of unit is conceivable. The succeeding layers accumulating in one area of the sea may be essentially identical, but offset just slightly. In an adjacent area of the sea, a second unit, like a second deck of cards (also skewed), is being deposited and may be of different bedding. There will be an area of overlapping of the "decks". Thus, in this area of overlap, a vertical plane will contain two units. The San Juan basin in the Four Comers area contains excellent examples of the regressive and transgressive blanket sands."

Four fairly distinct types of bedding have been considered: horizontal bedding, ripple-marked bedding, weak current cross-bedding and strong current cross-bedding. Weak and strong current cross-bedding are only qualitative terms at present and are reflected in the angle of crossbedding. The more the bedding in the various lenses departs from the plane that was horizontal during deposition, the

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stronger the current cross-bedding. The bedding depends upon the water velocity, as does the grain size. Therefore, it is possible that the bedding type of a sample can be predicted by the grain size in that sample. At times it is difficult to determine bedding by examination of well

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Fig. 6-Correlation of permeability with other core properties.


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TABLE I-SUMMARY OF DATA FROM SAMPLING OUTCROPS OF SHALLOW-MARINE SANDSTONES, BLANKET-TYPE DEPOSITS.

Outcrop

Woodbine Upper Pictured Cliff Lower Pictured Cliff Point Lookout Gallup Dakota

15 mi. W, 15 mi. W, 17 mi. W, 25 mi. W, location Denton Cty, Tex. Farmington, N.M. Farmington, N.M. Farmington, N .M. Shiprock, N.M. 2 mi. W, Cortez, Colo.

Number of Units 1 1 2 3 1 1 Type Bedding Strong Current Weak Current Ripple-Marked & Weak Horizontal Horizontol Strong Current

Cross-Bedding Cross-Bedding Current Cross-Bedding Cross-Bedding Porosity Range, % 29.5 to 36 22.3 to 26.3 24.2 to 26 22.1 t025.1' 21.2 to 23.2 15.8 to 19.8 k Range, md 3,500 to 15,000 20 to 110 20 to 105 50 to 250' 50 to 550 150 to 2850 Max.-to-Min. k Ratio

(Sandy Parts) 4.3 5.5 5.2 5' 11 19 k Variation on

Adiacent Plugs, ratio <2 <2 <2 <2' 2 Sandy Shale Sampled [Not None Yes Yes None V., Y.s

Included in Properties)

Nature of Stone Friable Consolidated Consolidated Consolidated Consolidated Consolidated

Cement Content, by % wt Negligible Iron Negligible Negligible Negligible 4 0/ 0 Calcareous 2 0/ 0 Calcareous

Grain GMD, mm 0.14 to 0.22 0.065 to 0.088 0.062 to 0.082 0.087 to 0.11' 0.1 to 0.16 0.19 to 0.28

a ~ of Grain Sizes 0.15 to 0.55 0.6 to 0.85 0.5 to 0.75 0.53 to 0.78' 0.4 to 0.75 0.35 to 0.65

F, Ratio 5.2 to 7.2 11.5 to 16.2 11.4 to 14.8 13.5 to 18.5' 13.5 to 20 13.2 to 22.8 *Middle unit only

cores. From grain-size analysis, however, it appears that some further insight into the bedding can be gleaned.

The Unit

The geological unit of deposition has been chosen as a basis for interpreting the data_ The unit by definition has the same bedding throughout, indicating that current velocity and other depositional characteristics remained essentially the same while the unit was being deposited. With this in mind one would expect a limited variation in the grain size and grain-size distribution from point to point in the unit, with the exception of sandy shale inclusions. Therefore, one also would anticipate a limited and random variation in permeability from point to point within this unit. The sampling of outcrop units indicates that these permeability variations are random and in some cases limited in range, as expected.

The next step is to evaluate the characteristics, causes, and range of random permeability variations in core plug size samples. Under conditions where grain size and grainsize distribution alone control the permeability, the randem variation in permeability from location to location within the unit appears to be limited to a factor of approximately five, no matter what the bedding. When other factors control the permeability, this variation will be considerably greater.

In the sedimentation process for weak and strong current cross-bedded formations, there is considerably more sorting of grain sizes going on during deposition than in the deposition of a horizontally bedded or ripple-marked formation. Therefore, one might expect a greater uniformity within parts of the current cross-bedded formations, and this has been found to be true. Within each lens included in the cross-bedded units, the random permeability variation from point to point in core plug size samples will range only over the values of about a factor of two. From lens to lens there will be a random variation so that, over-all within the unit, a permeability variation on the order of a factor of five is found. Although this is the same variation found in horizontally bedded units, the two cases are not equivalent from a fluid-flow standpoint. Cross-bedded units should be the more unfavorable.

The conditions existing during. sedimentation also can be examined to obtain a concept of the areal extent of various types of units. For example, a clean shale can be deposited only in very calm waters; thus, the clean shales must be horizontally bedded, and it can be expected that they will be continuous over the entire area of deposition.

MARCH, 1961

At times there may be a change in the source material of a deposit such that, in addition to the normal largegrain sand, a greater proportion of silts and clays is deposited. This forms the sandy shale streaks. If the water velocity was such that the sandstone unit was being deposited horizontally or with ripple marks, the sandy shale will be deposited horizontally; thus, the sandy shale portion of this unit should be continuous over great distances. In cross-bedding where the current velocity is higher, the sandy shale should be deposited in the troughs between the temporary bars being formed and partially destroyed by shifts in currents in the over-all process of depositing the unit. Here, the sandy-shale parts of the unit should be discontinuous, elliptical deposits; and this has been observed in the outcrops. In the strong and weak current cross-bedded units, the sandy shale might be considered as simply another lens, but a peculiar lens because the grain size is below the normal range anticipated for inclusion within the unit.

Factors Determining Permeability and Permeability Variation

A reservoir core sample is too small to have statistical meaning in determining the permeability and permeability variation of a reservoir. Since the study is restricted to this sample, however, every possible bit of information must be gleaned from it. Thus, in addition to the permeability and porosity of a core plug, other factors relating to permeability and to the variation in permeability from location to location within a unit might be investigated. To determine whether or not such an approach is feasible or worthwhile, the factors that control permeability can be examined to find out how these factors vary from point to point and, perhaps even more important, why.

Three factors are important in establishing the permeability of a sediment. The first is grain size. The sediment will contain a range of grain sizes, which is characterized by a grain-size distribution factor and a geometric-mean grain diameter. The second factor is the degree of packing of the sand grains. The amount of packing that occurs upon deposition is a function of the current velocity, the angularity of the grains themselves and perhaps several other as-yet-unidentified factors. At present, the packing must be characterized indirectly. The third important parameter in determining permeability is the cementation and compaction of the sediment. These enter into the picture after the initial deposition.

Once a sand deposit is accumulated and buried by sub-

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sequent deposition, a texture-controlled permeability variation may be aggravated by compaction and cementation. The compaction begins almost immediately, and any clays present will deform to conform to the adjacent quartz grains. The clay probably increases the permeability variation only slightly because the' clays seem to be distributed in a relatively uniform manner throughout the sandy portion of the unit. The compaction of the quartz grains themselves first results in a closer arrangement of the particles. As the formation is buried to a great depth, a reduction in the original sandstone pore space is brought about by solid deformation of the quartz grains and solution of the quartz grains at the points of contact between them. The number of contacts per sand grain generally increases with increase in depth as the sand grains attempt to distribute the load of the overburden." By analysis of thin sections, it has been found that the percentage of reduction in porosity is greater for a fine-grained sandstone by the pressure solution and re-deposition of silica than for an adjacent coarse-grained sandstone under the same pressure solution and re-deposition." Therefore, silica cement will tend to aggravate the original random permeability variation.

Calcite, dolomite and anhydrite, as cementing materials within the sandy portion of the reservoir, appear to be randomly located and probably will have a random effect upon the permeability variation. Therefore, one would expect the range of permeabilities within the unit to be increased.

The degree of packing is dependent upon the angularity of the sand grains, the water motion during sedimentation and the particle-size distribution of the sand grains. If there is a random distribution of particle size as measured by mean grain diameter and grain-size distribution, a random degree of packing should at least be possible. In the loosely packed sandstones, this does not appear to affect the permeability variation significantly; in well packed sandstones such as the Dakota formation, on the other hand, packing apparently aggravates the permeability variation significantly.

Measurable Core Properties

As a matter of routine, porosity and permeability are measured on most core samples. In addition, other measured quantities can be used to relate texture and cement content to porosity and permeability. The formation resistivity factor F is a function of the texture (grain size, sorting and packing) and the compaction and cementation. The geometric-mean grain diameter (GMD) is a partial measure of texture. The standard deviation of the distribution of log, of grain size, (J'., is a measure of the grain sorting and also is in part a measure of primary texture. The standard deviation for a uniform system would be zero.

If independent correlations for permeability and porosity can be obtained with these other measurable core properties, one should be confident that the controlling parameters are being measured (though not necessarily directly). The following correlations have been developed from the data obtained in outcrop core sampling, as well as from other published core-analysis data. For permeability,

k a (GMD) (e-o.G ".) (F)-' (1)

where k = permeability,

GMD = geometric-mean grain diameter,

228

(J'I> = standard deviation for log, grain-size distribution, and

F = formation resistivity factor.

The equation for porosity is

rp a (F)-' (GMD)-' (2)

where rp = porosity and the other terms have the same meanings as in Eq. 1. These correlations are shown in Figs. 6 and 7.

This leads to an important, but very preliminary, correlation of the variance of permeability within the sandy portion of a unit with the characterizing core properties. The four points shown in Fig. 8 to form this correlation surely are too few, but the span and trend shown appear significant. From this correlation, or from its successor when more data are obtained, one of the major questions can be answered-What permeability variation (random) can be expected in the sandy portion of a given unit where the core properties have been measured?

Prognosis

The work reported here is only a start toward understanding the non uniformities that exist within reservoirs, toward identifying the causes of these nonuniformities and toward development of methods of predicting their presence and type in a specific reservoir. The data obtained and the concepts developed to date, though limited, are useful in the present unsophisticated form; for example, they can be used in the interpretation of permeability variations in core plugs taken from a well. If the permeability is not cement-controlled and the formation is loosely packed, a 5: 1 variation in core plug permeability will not be interpreted as evidence of stratification but, rather, more as the random permeability distribution expected in this sandstone unit. Other similar uses for these concepts and correlations, of course, are apparent.

At present, and probably after further work, the first step in classifying and quantifying the nonuniformity of a specific reservoir is to review the general geology background of the formation. Specifically, the sand first must be identified as a blanket sand, offshore bar, channel fill, etc. In some instances, this also will identify the probable bedding; for example, strong cross-bedding would be expected in an offshore bar. In other instances, such as the blanket sands reported here, the bedding must be determined from core examination, either by seeing the actual bedding or by deducing it from the geometric-mean grain diameter. The other core properties then should lead to a fuller understanding of the character of the formation through correlations such as those developed here.

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FIg. 7-Correlation of porosity with other core properties.


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Fig. 8-Correlation of permeability variation in the sandy portions of a unit with core properties.

References

1. Ball, M. W., Weaver T. J., Grider, H. D. and Ball, D. S.: "Shoestring Gas Fields of Michigan", Stratigraphic Type Oil Fields, A Symposium, AAPG, 237.

2. Barnett, D. G.: "O'Hern Field, Duval and Webb Counties, Texas", Stratigraphic Type Oil Fields, A Symposium, AAPG, 722.

3. Blaunstein, M. K.: "Relation of Petrology and Structure to Productivity in a Stratigraphic Trap, Lindermann (McMillian Sand) Oil Field, Runnels County, Texas", PhD Dissertation.

4. Cardwell, W. T. and Parsons, R. 1.: "Average Permeability in Heterogeneous Oil Sands", Trans., AIME (1945) 160, 34.

5. Casey, S. R. and Cantrell, R. B.: "Davis Sand Lens, Hardin Field, Liberty County, Texas", Stratigraphic Type Oil Fields, A Symposium, AAPG, 564.

6. Dillard, W R.: "Olymphic Pool, Hughes and Okfuskee Counties, Okla.", Stratigraphic Type Oil Fields, A Symposium, AAPG,456.

7. DIllard, W. R., Oak, D. P. and Bass, N. W.: "Chanute Oil Pool, Neasho County, Kansas, Water Flooding Operation", Stratigraphic Type Oil Fields, A Symposium, AAPG, 492.

8. Fettke, C. R.: "Music Mountain Oil Pool, McKean County, Penn.", Stratigraphic Type Oil Fields, A Symposium, AAPG, 492.

9. Fettke, C. R.: "Physical Characteristics of Bradford Sand, Bradford Field, Penn., and Relation to Production of Oil", Bull., AAPG (Feb., 1934) 18, No.2, 191.

10. Fraser, H. J.: "Experimental Study of the Porosity and Permeability of Clastic Sediments", Jour. of Geol. (1935) 43, Part 1,910.

11. Gaul, H. R. and Steward, R. H.: "Continental Terrace Sediments in the Northeastern Gulf of Mexico", Finding Ancient Shorelines, SEPM Special Pub. No.3.

12. Geology of Southwestern San Juan Basin, Second Field Conf., Four Corners Geol. Soc. (1957).

13. Graton, L. C. and Fraser, H. J.: "Systematic Packing of Spheres-With Particular Relation to Porosity and Permeability", Jour. of Ceol. (1935) 43, No.8, Part 1, 785.

MARCH, 1961

14. Griffiths, J. c.: "Grain-Size Distribution and Reservoir Rock Characteristics", Bull., AAPG (Feb., 1952) 36, No.2, 205.

15. Heald, M. T.: "Cementation of Simpson and St. Peter Sandstones in Parts of Oklahoma, Arkansas, Missouri", Jour. 0/ Geo!. (Jan., 1956) 64, No.1, 16.

16. Hutta, J. J.: Fabrzc and Permeability of Some Typical Sediments, Pennsylvania State U. Mineral Industries Experimental Station Bull., No. 68 (1955) 93-99.

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DISCUSSION

S. E. SZASZ MEMBER AIME

Taking into account reservoir inhomogeneities in reservoir engineering calculations probably will require a statistical approach. The problem seems in many ways similar to that of calculating the permeability of a porous medium from the characteristics of individual pores, without having to describe in detail each individual pore. Along these lines, we have used an approach based on Scheidegger's random walk model to calculate the behavior of a simple system involving elements of only three different permeabilities randomly distributed in a two-dimensional array. We found an over-all permeability of one-half the arith-

SINCLAIR RESEARCH LABORATORIES INC. TULSA, OKLA.

metic average. This result was confirmed by a network of resistors.

It is my hope that some degree of randomness can be defined, and perhaps calculated, from coefficients of correlation between permeability distributions in individual wells and that this degree of randomness then can be introduced into the mathematical treatment of reservoir behavior. It is true that until now our attention has been focused only on specific permeability, and not on fluid-fluid displacement; however, it seems logical to introduce further complications only step-by-step until a practical, satisfactory method can be developed to predict reservoir behavior.

AUTHOR'S REPLY TO S. E. SZASZ

Szasz points out one of the several possible approaches for solving the difficult problem of predicting reservoir behavior once the non uniformity character and degree of non uniformity are ascertained. Thus, Szasz's comments

C. A. HUTCHINSON, JR. (center) joined The Atlantic Refining Co. in Dallas in 1949 as an assistant research engineer. Since then he has served in a variety of positions, all in crude-oil production research. He holds BS

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relate more to what should be done next following the work described in the present paper. Of course, we will be most happy to see him, and others in the industry, undertake this type of work. ***

and MS degrees in chemical engineering and a BE degree from the U. of Colorado. C. F. DODGE (right) is an associate professor of geology at Arlington State College, Arlington, Tex. After receiving BS and MS degrees in geology from Southern Methodist U., he joined the Concho Petroleum Co. as a geologist. He assumed his present position on the faculty of Arlington State in 1957. T. L. POLASEK (left) is an associate research engineer with Atlantic in Dallas. He received BS and MS degrees in petroleum engineering from The U. of Texas in 1956 and 1957, respectively. He joined Atlantic following graduation as a junior research engineer, and since then has served in various capacities in reservoir engineering and reservoir mechanics.


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