by B.Granier
This paper presents a case study of rock-typing drawn from an integrated reservoir study on layer-cake reservoirs in field "A", offshore Abu Dhabi. In many case studies, a K/Ø cross-plot for each rock-type provides a trendline that is used to derive the permeability K as a function of the porosity Ø. However, the rock-type classification we arrived at shows that these parameters are not correlated. Each rock-type is characterized by distinct Gaussian distributions for both log K and Ø. This leads us to a new and promising approach providing an easy way of up scaling as it suggests using a single geometric mean permeability value and the corresponding standard deviation (variance, or coefficient of variation) for each rock-type.
Introduction
In his pioneering work, G.E. ARCHIE [1950] draws up the fundamentals of rock-type classification. Any porous network is related to its host rock fabric, therefore petrophysical parameters, such as porosity (Ø), permeability (K), and saturation (S), are controlled by pore sizes, distribution, and interconnection for any given 'type of rock'. The goal of reservoir characterization is to predict the spatial distribution of such petrophysical parameters at field scale.
In field "A", offshore Abu Dhabi (United Arab Emirates), the studied interval consists of a series of layer-cake reservoirs bracketed by a shale-dominated formation "A" above, which forms the regional seal, and a mainly dense limestone-dominated formation "F" below. In terms of reservoir, it was classically divided into 4 main zones (Fig. 1) labeled from "B" for the upper to "E" for the lower. Sequence stratigraphy helped us to delineate 16 operational units (Fig. 1), the boundaries of which are either sequence boundaries, transgressive surfaces, or maximum flooding surfaces. The layering used in the latest reservoir model results from the combination of both the generalized stratigraphic framework and the rock reservoir characteristics. It consists of ten layers from top to bottom of (Fig. 1):
Whereas sequence stratigraphy helps to design realistic, geologically constrained, reservoir architectures, the rock-types provide the building blocks to be input to the reservoir models. The present study focuses on these building blocks and more precisely on their relation to petrophysical parameters.
While examining the "rock type-porosity-permeability relation", G.E. ARCHIE [1950] stated that "a broad relationship exists between porosity and permeability of a formation" (a 'formation' sensu G.E. ARCHIE is a 'type of rock' or 'rock-type'). In his conclusions, he also wrote "The relations between rock characteristics should be thought of as trends" and even added that "Actually, these may be expressed by mathematical formulae". Subsequent workers overlooked some aspects of the paper, elaborated on these statements, and concluded with drawing trendlines on K/Ø cross-plots and using K/Ø transforms to predict K from either the total or the effective Ø. The present study addresses a different approach to the "rock type-porosity-permeability relation".
Summary of the methodology
Per definition, rock-typing should be based on cored wells. It is basically a 3-step approach. Preliminary rock-type identification is undertaken by use of thin section and conventional core analyses. Then or in parallel, it has to be related to Hg injection curves. Our database includes:
When a method is established for cored intervals where most data can be collected, this rock-typing should ideally be extrapolated to uncored intervals / wells through wireline information. In the studied case, statistical analyses were undertaken prior to this last step as they have proven to help in developing the final rock-type classification.
Preliminary rock-typing (from thin sections and conventional core analyses)
First, it should be pointed out that in the studied case there is not much separate-vug porosity in our reservoir layers. In any case, separate vugs do not contribute significantly to permeability [LUCIA, 1995].
Second, some permeability measurements need to be discarded. The plug descriptions given by the contractor often mention the occurrence of joints (stylolite, fracture, etc.). In such case, measured permeabilities might be overestimated by a factor of ten to a hundred as it can be demonstrated by comparison with the values of unaffected samples with similar rock-fabric. In the studied case, most measured K values higher than 5 mD have proven to result from a plug failure during or before the measurement. They usually represent less than 3 % of the samples.
Third, we have to bear in mind that a plug is not necessarily homogenous; it might cover several rock-fabrics (e.g. burrowed facies, boundstone with matrix, …). Therefore in the case of a heterogeneous plug, though the corresponding thin section might display a single texture, the plug measurements should ideally not be taken into account. For example, plugs taken from Rudist facies in the zones "C" to "E" commonly include large shell fragments, and the matrix permeability, i.e. the host rock permeability, may be underestimated in the conventional measurements ("Comet effect" on K/Ø frequency maps per layer or on K/Ø cross-plot: Fig. 4; "Manhattan effect" on 3D K/Ø histograms: Fig. 14-15).
As a matter of fact, the permeability range we are dealing with is very narrow; consequently there is little range available within which to define several rock-types. Conventional core and petrographical analyses of some 5000 samples have led us to segregate 3 groups of lithotypes / rock-types:
each of which covers from 1 to 4 lithotypes.
(*): 1 Darcy = 0.9869 µm2.
The first group covers 4 lithotypes, which are the worst in terms of reservoir characteristics:
The second group corresponds to R-chalk, i.e. Nannofossil ooze matrix with fair to high porosity values, but very low permeability values. It is restricted to the zone "B", i.e. the layer 1.
The third group includes 2 lithotypes, which are the best in terms of reservoir characteristics:
The layering classification into permeable or impermeable operational units has been defined to honor both the sequence stratigraphy (the 'envelopes') and the dominant rock-type (the 'contents'). In order to simplify (up-scale), we considered that a single "dominant" rock-type characterizes each layer. K/Ø cross-plot per layer (Fig. 4) and petrographic analyses give good support to this preliminary rock-type classification. We also observe that RR has slightly different behaviors in the zone "C" (above) and the zones "D-E" (below); this is possibly related to distinct depositional environments and diagenetic overprints.
Towards a refined rock-typing (from Hg injection data)
Permeability / rock-type is primarily related to the pore-throat network, i.e. size, number, shape, and arrangement of pore-throats:
Pore-throat sizes can be estimated from the Hg injection curves (**) though these curves only give an apparent distribution [WARDLAW & TAYLOR, 1976].
(**): E.W. WASHBURN [1921] first suggested the use of mercury injection as a laboratory method for determining the pore throat size distribution in rocks. Assuming the flow channels in the porous core sample may be represented by a bundle of straight capillary tubes in parallel, with the spaces between the tubes sealed by a cementing material, the WASHBURN equation can be expressed as Pc = -2g (cos Q /r) where Pc = capillary pressure (dynes/cm2), g = surface tension of Hg = 480 dynes/cm, Q = contact angle of Hg in air = 140°; and r = radius of aperture for a cylindrical pore throat. Thus, r (mm) = 107.744/Pc (psia)
Various cross-plots using factors (***) derived from the Hg injection curves (BRC, r35, etc.) illustrate that pore-throat size is the main factor controlling permeability (Fig. 2). The apparent scatter of the data is partly due to the fact that different increments in Hg injection pressure were used at the time of measurement by different laboratories. These factors might also help to sort the samples (Table 1).
(***): r35 represents the apparent radius at 35% Hg injection [PITTMAN, 1992] while BRC is an average radius also derived from the Hg injection curve.
In the studied case, 65 Hg injection curves were available (but 4 permeability measurements were missing as the corresponding plugs were broken: Table 1); after screening, 7 measurements only were discarded (using a rule of the thumb, when BRC >> r35: Table 1, Fig. 3). When we consider the histograms 'apparent pore-throat size' versus 'apparent percentage of pore volume' per layer (Fig. 8-13), i.e. per "dominant" rock-type, the following points can be highlighted:
Further investigations on the rock-typing (using statistical analyses)
As mentioned above, there are some variations within the lithotype RR that might justify splitting it depending on whether the sample was taken from the zone "C" or from the zones "D-E". However thin sections in carbonate rocks are usually not less than 30 mm thick, the largest pore entry radius derived from the Hg injection data for the current study never exceed 2 mm (and rarely 1 mm). Consequently pore throats were not visible in our thin sections. Therefore, the method that was used was to examine permeability and porosity distributions within each layer ("dominant" rock-type). 2D histograms (Fig. 8-13) show that:
Frequency maps and 3D histograms (Fig. 14-15) show that:
In conclusion, RR has to be split into RR-0.45 (= RR-"D-E") and RR-0.25 (= RR-"C") which form 2 distinct rock-types. A good match was obtained with measured depth wireline log Sw using a separate 'Sw versus height' equation for each rock-type:
where h (ft), Sw and Ø (fractions).
We also decided to unite R-stylo and RR-0.45 into a single rock-type as the pore volume reduction is probably restricted to the immediate vicinity of the solution seams. That is we assumed that this reduction is only accompanied by a correlative reduction of the number of passages between pores (pore-throats). Should it be accompanied by a reduction in the size of the passages between pores, the 2 lithotypes would have had to remain distinct and therefore to be ascribed to distinct rock-types.
Conclusion (towards a new approach of rock-typing)
G.E. ARCHIE's seminal paper [1950] was partly misinterpreted. When he wrote: "The relations between rock characteristics should be thought of as trends. Actually, these may be expressed by mathematical formulae", he immediately added the following warnings: "however, the formulae can not be applied in a rigid manner (…). It must be kept in mind that appreciable deviations from the average trend may occur".
In many studies, rock-type classifications conclude with drawing trendlines on K/Ø cross-plots and using K/Ø transforms to predict K from either the total or the effective Ø. In the studied case, statistics show that the two ranges of data do not move together; the best fits have low coefficients of determination (r2 < 0.5). The present study addresses this problem with a different and promising approach: each rock-type appears to be characterized by Gaussian distributions of both log K and the interparticle Ø (which in the studied case almost equals the total Ø, and the two parameters are not correlated (Fig. 14-15). These distributions are the basis for rock-typing. Such an approach has been used earlier to describe flow in heterogeneous media [WARREN & PRICE, 1961]. It is recommended to investigate further how it can be applied to slightly more homogenous media, such as a single rock-type, and how the use of a geometric mean permeability value for a given rock-type effectively affects reservoir models and simulations.
Acknowledgements
The author would like to thank the Management of Abu Dhabi Marine Areas - Operation Company (ADMA-OPCO) and Abu Dhabi National Oil Company (ADNOC) for their permission (Ref. No.: E/OFFSH/SPG/530/99) to publish this paper.
References
ARCHIE G.E. [1950].- Introduction to petrophysics of reservoir rocks. Bulletin of the American Association of Petroleum Geologists, Tulsa, vol. 34, N° 5, p. 943-961.
LUCIA F.J. [1983].- Petrophysical parameters estimated from visual descriptions of carbonate rocks: a field classification of carbonate pore space. Journal of Petroleum Technology, vol. 35, Nº 3, p. 629-637.
PITTMANN E.D. [1992].- Relationship of porosity and permeability to various parameters derived from mercury injection-capillary pressure curves for sandstone. Bulletin of the American Association of Petroleum Geologists, Tulsa, vol. 76, N° 2, p. 191-198.
WARREN J.E. & PRICE H.S. [1961].- Flow in heterogeneous porous media. Society of Petroleum Engineers Journal, September 1961, p. 153-169.
WASHBURN E.W. [1921].- Note on a method of determining the distribution of pore sizes in a porous material. Proceedings of the National Academy of Science, vol. 7, p. 115-116.
Table and figures
Table 1: List of the available Pc curves.
Figure 1: Combination of operational units and rock-/litho- types into reservoir layers.
Figure 2: BRC/K cross-plot for the 65 samples used for Hg injection. Caption: diamonds = discarded samples; dots = remaining samples.
Figure 3: BRC/ r35 cross-plot for the 65 samples used for Hg injection. Caption: diamonds = discarded samples; dots = remaining samples.
Figure 4: K/Ø cross-plot per layer (i.e. per "dominant" rock-type). All samples with a GEX (Gas Expansion) porosity.
Figure 5: Hg injection data: 'apparent pore-throat-size' (mm) versus 'pore volume Hg saturated' (%). Caption: dotted grey for R-chalk ("B"); black for RR-0.25 ("C"); black-ticks for RR-0.45 ("D-E"); white for discarded samples. It should be histograms; curves are used for display only!
Figure 6: Hg injection data: 'apparent pore-throat-size' (mm) versus 'pore volume Hg saturated' (%), cumulative. Dashed horizontal line at 35% Hg injection. It should be histograms; curves are used for display only!
Figure 7: Hg injection data: 'apparent pore-throat-size' (mm) versus 'total volume Hg saturated' (%), cumulative. It should be histograms; curves are used for display only!
Figure 8: Permeability histogram for RR-0.25 ("C") in layer 2 (all wells).
Figure 9: 3D permeability histograms RR-0.25 ("C") in layer 2 (each well).
Figure 10: Permeability histogram for RR-0.45 ("D") in layer 7 (all wells).
Figure 11: 3D permeability histograms for RR-0.45 ("D") in layer 7 (each well).
Figure 12: Permeability histogram for RR-0.45 ("E") in layer 10 (all wells).
Figure 13: 3D permeability histograms for RR-0.45 ("E") in layer 10 (each well).
Figure 14: 3D K/Ø histogram for RR-0.45 ("D-E") (901 samples).
Figure 15: As above, K/Ø scales in reverse order.