Clay Minerals (1994) 29, 491-501

A N A L Y S I S OF P E R M E A B I L I T Y C O N T R O L S : A P P R O A C H

A N E W

C . A . C A D E , I . J . E V A N S AND S. L . B R Y A N T *

BP Exploration Operating Company Limited, Uxbridge, Middlesex, and *BP Chemicals, Grangemouth, UK

(Received 23 June 1993; revised 25 March 1994)

A B S T R A C T : By modelling a range of rock-forming processes such as compaction and various styles of cementation, a new understanding of how they affect pore-system geometry, and hence permeability, has been gained. For example, almost identical permeability-porosity trends result from progressive compaction or grain overgrowth cementation in a clean sandstone, and these trends are curvilinear on the traditional log-linear plot. The steepening which defines the curve marks the onset of pore-throat blocking. Other cement styles, such as pore-filling carbonates or grain-rimming clays, show different porosity-permeability trends. This new understanding can be used predictively (predicting permeability from predictions of grain size and diagenetic style), or as a tool for identifying the important permeability controls in a set of field data. This latter application is presented and illustrated using data from a variety of sandstone types. This approach has important advantages over commonly used multivariate statistical analysis approaches. It can quickly provide a good understanding of what are (and are not) the important controls on permeability. It also provides a basis for more focused and meaningful statistical analysis to quantify these controls.

The rate at which fluids can be p roduced f rom a porous sub-surface reservoir rock is f undamen- tally d e p e n d e n t on th ree parameters : the thick- ness of reservoir present , the pressure d rawdown which can be appl ied to the reservoir at the wel lbore , and the permeabi l i ty of the reservoir . As flow rates are an impor t an t con t r ibu to r to the economic viability of an oil or gas field, then the accurate predic t ion of permeabi l i ty ahead of drilling can have a major impact on business decisions such as prospect rank ing or appraisal well location.

For example , if a well in prospect X (Fig. 1), pene t ra t e s med ium grained sands tones with per- meabi l i t ies in the range 100 m D to 500 m D , can we predict permeabi l i ty o~ the reservoi r in pro- spect Y, which f rom geological models we bel ieve to be similar bu t f iner-grained? W h a t if the finer- gra ined sands tone in prospect Y has more quar tz cement , or conta ins less clay, or is be t t e r sor ted? Can we predict permeabi l i ty in prospect Y, based on measu red permeabi l i ty data f rom prospect X and our geological model?

To answer these quest ions , the relat ive impor- tance of different potent ia l controls on pe rmeab i - lity (such as grain size, sort ing, compac t ion and

different styles of cemen ta t ion ) mus t be estab- lished. The effect of the major controls on permeabi l i ty must then be quantif ied. Ident i fying the impact of these controls , b o t h individually and in combina t ion , is the key to permeabi l i ty predic t ion. If var ia t ion in the vo lume of carbo- nate cemen t in a reservoir rock has a much grea te r impact on permeabi l i ty than var ia t ion in grain size, but our ability to predict cemen t var ia t ion is l imited, then our ability to predic t permeabi l i ty is similarly l imited, However , if grain size is the dominan t control , and the geological model

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FIG. 1. Illustration of permeability situation (see text).

�9 1994 The Mineralogical Society

492 C . A . C a d e et al.

allows prediction of this parameter, then permea- bility prediction may be feasible.

R E V I E W O F P R E V I O U S W O R K

In numerous previous studies using statistical techniques, a strong correlation between permea- bility and porosity has been shown. An example is a study on the Cretaceous Travis Peak Formation in East Texas, USA (Dutton & Diggs, 1992). Using a data set of over 600 samples, the correlation coefficient of permeability on porosity is 0.79, higher than any other textural or diagene- tic parameters included in multiple regression. With this high correlation coefficient, it might be expected that predictions of porosity could be used to predict permeability. A cross-plot of the data from this study (Fig. 2), however, shows that, for a given porosity, permeability varies by c. three orders of magnitude. Porosity alone cannot, therefore, be used to predict permeability.

In a recent review, Bloch (1991) described two general approaches to predicting reservoir quality in sub-surface sandstones: empirical techniques and 'process-oriented' techniques. The work on the Travis Peak Formation is an example of the empirical approach to the quantification of per- meability controls for predictive purposes.

Empirical techniques use a calibration data set (e.g. data from core samples from a well in prospect X) and multiple regression analysis to

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FIG. 2. Cross-plot of porosity vs . permeability for Travis Peak Sandstone samples. Linear regression of porosity on permeability gives a correlation coefficient of 0.79 (Dutton

& Diggs, 1992).

determine the relationship between rock property variables and reservoir quality. Dutton & Diggs (1992) and Bloch (1991) described the most frequently used application of this approach, in which relationships between measured porosity and permeability (usually ambient helium poro- sity and single phase gas permeability), and textural and mineralogical variables (usually mea- sured on thin-sections) were investigated. Com- monly-used variables are grain size, sorting, the ratio of rigid to plastically-deformable grains, matrix clay content, volume of individual cements, total cement volume, and point-counted interparticle porosity. Bloch (1991) stated that multivariate statistical techniques will not work as a predictive tool in some situations (because the key permeability controls cannot themselves be predicted). However, he suggested that "despite its limitations, the empirical technique provides the only feasible approach to reservoir quality prediction". Dutton & Diggs (1992) concluded that predicting porosity using statistical analysis of a calibration data set may be feasible, but that prediction of permeability will have much lower success.

We suggest that this lack of success is largely a consequence of the interplay and overprinting of the various permeability controls. If all possible permeability controls are considered together, the statistical processing may show that both grain-size and quartz cementation are of moder- ate importance as permeability controls, as there is no strong relationship between either para- meter and permeability. However, within coarse or medium sand grain-size classes, the volume of quartz cement may be the dominant control on permeability. If the textural controls are first removed, then the important diagenetic overprint controls should become clearer.

A variation on the empirical approach is described by Ehrlich e t a l . (1991). Using the observation that, even in a single formation, permeability commonly varies by several orders of magnitude, they concluded that the configur- ation of porosity, rather than the absolute poro- sity value, is the control on permeability. To characterize the pore system configuration, Ehr- lich e t a l . (1991), made measurements of pores in two dimensions (on polished thin-sections) and combined these with pore-throat size distribution data (from mercury porosimetry) to develop a simple pore-system model. For selected data sets

Analysis of permeability controls

a good degree of fit between the simple pore- system model and measured permeability has been established.

While the method presented by Ehrlich et al. (1991) has merit in its focus on pore type and connectivity, it has limitations as a predictive tool. For predictic, n of permeability ahead of drilling, the criteria for success of any method must be that it establishes a quantitative link between meast:red permeability and other rock parameters, and that those correlative para- meters can themselves be predicted from a geological model. With the current level of understanding, it is very unlikely that we would be able to predict with confidence the pore-type and pore-throat size distribution parameters in an undrilled sandstone from a geological model.

The 'process-oriented' approach described by Bloch (1991) focuses on modelling diagenetic processes in an undrilled area, based on chemical and mathematical models, and the effects of those processes on reservoir quality. There are two important limitations to this approach. First, there is the uncertainty associated with the sub- surface geological model, and how that impacts on the thermodynamics and kinetics of the diagenetic model. Second, there is the lack of a detailed quantitative understanding of how diage- netic processes control permeability. To date, the quantification of the impact of specific controls, particularly diagenetic controls, has been either formation specific (and therefore not generally applicable) or very general. Ethier & King (1991) illustrated a general understanding of a variety of controls (Fig. 3), but with little or no quantitative detail, the value of such trends is limited.

To summarize, previous work on permeability controls has been limited by the lack of a i~ quantitative understanding of how textural, and / in particular, diage~aetic, permeability controls operate, and has been hampered by statistical approaches which consider all possible controls together. In this paper we present research findings which address the quantitative under- standing of permeability controls, and propose a modified approach to reservoir quality analysis which can improve predictive capability.

A N A L T E R N A T I V E A P P R O A C H

Our approach is based on a simple model of a sandstone, a sphere pack. Using a numerical

493

model of this sphere pack, we simulate diagenetic processes, such as compaction and various styles of cementation. Their progressive impact on porosity, and more importantly permeability, is measured. The result of these simulations is an improved understanding of the ways in which permeability is influenced by different diagenetic modifications. The controls are considered both in isolation and in combination. Over a full range of porosities (<5-36%), the effect of grain-size, compaction and the most commonly-occurring cement styles (overgrowths, pore-filling cements and grain-rimming clays), on the permeability of a simple sandstone, is established. The theoretical details of the modelling which provide the basis for this alternative approach are outlined in Bryant et al., (1993a,b). This paper builds on this work by demonstrating the application of the modelling results to the analysis of field datasets.

S P H E R E P A C K M O D E L L I N G O F S A N D S T O N E D I A G E N E S I S

A sphere pack forms the basis for our modelling. During research into the structure of liquids, Finney (1970) constructed a random pack of ball bearings. This was shaken during packing such that the porosity of the pack reached a minimum. The result was a random, close packing. All the bearings were the same size, and the pack

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Fro. 3. Diagram to illustrate an interpretation of the effects of various controls on porosity and permeability (after

Ethier & King, 1992).

494 C.A. Cade et al.

porosity was 36.2%. The pack was then impreg- nated with wax and dismantled, one bearing at a time, and the relative positions of all of the bearings measured. With the positions of all the grains known, and because all the spheres were the same size, the interparticle pore space is, a priori, completely characterized. We believe this to be the only real pore-system which has been so completely characterized, and it is this feature which allows the calculation of porosity and permeability. Permeabil i ty is calculated by a rigorous geometrical conversion of the Finney pore-system into a network comprising pores and connecting throats (Bryant et al., 1993a). These pore-throats, and more specifically their diameter and ' interconnectedness ' , are the key to sand- stone permeabili ty.

Using data from this pore-system, a range of different diagenetic processes has been model led (Fig. 4).

Compaction

due to gravitational loading during burial. We simulate this by re-scaling one of the co-ordinate axes in Finney's packing according to the formula z' = zo + )v(z-zo) where zo is an arbitrary reference value and ~. refers to the degree of compaction (Fig 4b). A physically realistic range for )v is 1.0 > )v > 0.7, corresponding to a 0-30% change in bulk volume. Our simulation of com- paction causes grains to interpenetrate , and this is analogous to pressure solution at grain contacts in rocks.

Solid overgrowth cementation

One of the most common styles of cementat ion in sandstones is the precipitation of solid over- growths on detrital grains (e.g. quartz and felds- pars). Overgrowth cements are simulated as concentric rims on exposed sphere surfaces in the sphere pack (Fig. 4c).

Compact ion is one of the most important processes of porosity reduction during sandstone diagenesis. It can be defined as reduction in porosity as a consequence of the reduction in bulk rock volume. The volume reduction is usually the result of vertical shortening, and that in turn is

a b

eli FIG. 4. Numerical simulation of geological processes. (a) 2D slice through a dense packing of equal spheres representing sediment of clean, well-sorted sand. (b) Compaction forces spheres closer together and interpenet- ration occurs. (c) Quartz overgrowths cement the com-

pacted packing together. (d) Pore-filling cement.

Microporous grain-rimming cements'

Several minerals form cements in sandstones which can be described as microporous grain rims. Examples are chlorite and illite. These typically form as blocky, fibrous or platy crystals which grow radially around detrital grains. In be tween the crystals there is enclosed microporo- sity, and the sizes of these pores are typically one or two orders of magnitude smaller than the intergranular pores. The permeabil i ty of the void space within the microporosity is negligible com- pared to that for the interparticle pore-space. Thus, when fluid moving through a pore-system encounters a grain r immed by cement of this type, the effect is similar to that of a solid overgrowth whose volume equates to that of clay and microporosity combined. We therefore model grain-rimming clay cements as microporous, but impermeable , overgrowth cements.

Pore-filling cements"

Several minerals precipitate as pore-filling, rather than grain-rimming, cements. Carbonates (e.g. calcite and siderite), and some clays (e.g. kaolinite) often occur in this form. We model this style of cement by completely filling randomly

Analysis of permeability controls

selected pores within the packing (Fig. 4d). These pores and their connecting throats are then unavailable for flow. A microporous pore-filling cement, such as kaolinite, is modelled in a manner analogous to the microporous grain rim.

Combined cases"

We have model led combined cases, e.g. a phase of compaction, followed by either a phase of overgrowth or pore-filling cementat ion, and progressive compact ion with pressure dissolved grain material (grain interpenetrat ion) reprecipi- tated on the grain surfaces.

Model results

It is well known that, for a given porosity, permeabil i ty will be lower in a finer grained sandstone than in one that is coarser grained (all else being equal), and that a pore-bridging clay such as illite is very effective in reducing permea- bility. The sphere pack modell ing provides physi- cal confirmation, explanation, and quantification of these controls, and provides similar insight into how other, previously less well understood, controls operate.

In each case, porosity is reduced incrementally according to the style of cementat ion and the resultant permeabil i ty is calculated (details of the calculation are lengthy and are given in Bryant et al., 1993b). We present the permeabil i ty-porosity trends which result from the simulations as lOgl0 permeabil i ty vs. porosity cross-plots. In Fig. 5, permeabil i ty is presented in the dimensionless form K/Ko where Ko is the initial permeabil i ty of the packing before compact ion a n d / o r cementa- tion. This initial permeabil i ty (in Darcies) depends on the size of the spheres in the packing such that Ko = 3 x 10 -3 r 2, where r is the sphere radius measured in microns. This expression is obtained from network model calculations and agrees with many measurements and semi-empir- ical expressions such as the Kozeny-Carman relationship (Carman, 1937). In other figures, particular grain-size cases are presented and permeabil i ty is not normalized to the initial value.

Compac~on

The trend of declining porosity and permeabil- ity for a progressively compacted sandstone is

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F[c. 5. Model-derived porosity-permeability trends for compaction, cementation, and a combination of these processes. Note that in this cross-plot, permeability is expressed as a ratio of original uncompacted/uncemented permeability. This removes any grain-size dependence. The dashed line shows the percentage of pore-throats blocked as

porosity decreases.

curved, with a maximum rate of change of slope at --12% porosity (Fig. 5). This steepening coin- cides with the porosity at which the blocking of pore-throats begins.

Overgrowth cementation

Progressive quartz style overgrowth cemen- tation produces an almost identical porosity- permeabil i ty trend to the compact ion trend (Fig. 5). Divergence of the compact ion and overgrowth trends only occurs below 5% poro- sity, and this divergence is small. Combinations of compaction and overgrowth cementat ion produce the same curved trend. The significance of this trend coincidence is that any divergence from the curve, for a given grain size and sorting class, must be due to controls other than compac- tion or quartz cementat ion.

Pore-filling cement

Progressive cementat ion by a pore-filling cement produces a steeper decline in permeabil i ty with porosity (Fig. 6a). The reason for this is that blocking of pore-throats occurs as soon as the first pore is cemented, rather than when porosity has

496

been reduced to --12% overgrowth cement.

C.A. Cade et al.

Grain-rimming clays

in the case of an

Grain-rimming clays also result in a steeper permeability decline than overgrowth cemen- tation (Fig. 6b) but for a different reason to pore- filling cement: The microporous grain rim behaves like a solid overgrowth, but the ineffec- tive porosity, while not contributing to permeabil- ity, nevertheless forms part of the total porosity. Thus for a given permeability, a sandstone with clay grain rims will have higher porosity than one with solid grain overgrowths.

The effect of grain size

Grain-size fundamentally controls the size of pores, and, more importantly, for permeability, the size of the pore-throats which connect adjac- ent pores. The effect of grain size on porosity and permeability reduction is investigated in our simulations. A range of sand grain-sizes has been selected to provide the scaling for the network model. Permeability is calculated from this network representation of the pore-system. Per- meability (in Darcies) is dependent on the size of the spheres in the pack such that Ko = 3 x 10 -3 r 2, where r is the sphere radius measured in microns. Note that in all of our simulations, the sorting of the pack is perfect (all grains of the same size).

The porosity-permeability decline trends which

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result from the simulation of compaction, for the selected range of grain sizes, are illustrated in Fig. 7a.

The effect of sorting

Permeability also depends on the grain size distribution (sorting). Since our modelling approach is based on a pack of identically-sized spheres, the effect of sorting is not accounted for. Modelling systems with a range of grain sizes is numerically complex, and requires further research. At present an empirical correction based on experimental data (Beard & Weyl, 1973) is used (Fig. 7b). This sorting correction does not affect the shape of the predicted trends, but changes the starting permeability value at 36% porosity.

Plastically-deformable grains

Many sandstones contain grains such as mud- stone clasts or metamorphic grains which will deform in a plastic manner during burial. Although we have not modelled a pack contain- ing such grains, we believe that the porosity- permeability trend would be similar to that for progressive pore-filling cementation. The reason for this suggestion is that as the plastic grains deform, they fill adjacent interparticle pore- space. This process will cause pore-throat block- ing earlier than with the quartz grain compaction case discussed earlier.

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Porosity (%) FIG. 6. Model-derived porosity-permeability trends for simulations of (a) pore-filling cementation and (b) grain-rimming

clay.

Analysis of permeability controls

A N A L Y S I S OF P E R M E A B I L I T Y C O N T R O L S

The approach

The geometry and scale of the primary interparticle pore-system is fundamentally controlled by the size of the sand grains which define it. Diagenet ic modifications are then over- laid on, or result in the deformation of, this primary pore-system template. Rather than carry out an overall , multivariate, statistical analysis on all possible permeabil i ty controls in a set of data, we propose that a bet ter result is achieved if the primary textural controls are removed from the analysis at the outset. Thus the first step in this approach is to split the sample data set into grain size (and, if possible sorting) classes. For each textural group, the porosity-permeabil i ty trend is solely the result of diagenetic modification. By displaying each grain size data group separately, with the model derived curves for the correspond- ing texture, a qualitative assessment of the permeabil i ty controls can be made. For a wide range of data sets, we have found that, with just this initial stage, a good insight is gained into what the important permeabil i ty controls are. This insight is the result of two simple steps, splitting the data by primary texture, and comparison with results of sphere pack modelling.

At the initial display stage, after textural splitting, several conclusions can be made about

497

the data set. Any data points failing well above the compact ion/overgrowth cement curve (i.e. higher permeabil i ty for a given porosity), should be carefully investigated for data quality. A common explanation for such points (low poro- sity but high permeabili ty) is the existence of an open fracture in the plug used for permeabil i ty measurement . This may be a natural fracture, or more likely it will have been induced during plug- cutting, but in ei ther case, such data should be removed from the data set before further analy- sis. The permeabil i ty of such plugs is dominated by the permeabil i ty of the fracture and not the surrounding matrix rock. For data points which fall just above the model curve, the quality of the grain size data should be checked. As it is based on a perfectly sorted sphere pack, the model curve provides an upper limit on porosity-per- meability values for a sand with that texture.

The general trend of the data within each grain size class should point to the important controls on permeability. If the data lies on or just below the model trend, and parallels that trend, then compaction and/or overgrowth cementat ion are probably the dominant controls. If the trend is steeper, then there must be some contribution from a pore-filling or microporous cement. It should be noted here that a steeper t rend does not preclude a contribution from overgrowth cemen- tation or compaction.

Af te r removing the influence of primary tex- tural controls, the diagenetic overprint can be

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C.A. Cade et al.

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FJ6.8. Fontainebleau Sandstone--porosity vs. permeability cross-plot showing the close correspondence between model predictions based on grain size and cement style, and

measured porosity-permeability data.

evaluated. This can be done by using multivariate statistical analysis, or by performing further data splits, e.g. by variation in the volume of carbonate cement. By using statistical analysis after the textural controls are removed, there is a much reduced possibility of an important diagenetic control on permeabil i ty being masked by a textural parameter , and vice versa. This approach to reservoir quality analysis is illustrated in the following case examples.

Case example 1--Fontainebleau Sandstone

The Oligocene Fontainebleau Sandstone, which outcrops in the Ile de France area, near Paris, is the rock on which the sphere pack modell ing results were first validated. It is a texturally and diagenetically simple quartz sand- stone, which is fine grained and well sorted. It is cemented almost exclusively by quartz. Samples show a wide range of porosity and permeabili ty. Using cathodoluminescence to distinguish grains from overgrowths, the average grain size is 190 ~tm, close to the value of 200 p.m reported by Cayeux (1929).

As the grain-size in this data set varies so little between samples, there is no need to carry out any split by texture. When the porosity-permeabi- lity data are displayed with the model-der ived trend for the compact ion/overgrowth cemen- tation case, an almost exact coincidence between

the data and the trend can be seen (Fig. 8). As the samples have all been subject to a comparable burial history, and have been buried to a maxi- mum depth of only a few hundred metres, it is concluded that the porosity-permeabili ty varia- tion is predominant ly due to variation in the volume of quartz overgrowth cement (c. 5-30% of the rock volume).

The close match between measured data from this real, albeit texturally and diagenetically simple, sandstone a n d our model-der ived trend provides confidence that the sphere pack model is successfully simulating results of real diagenetic

processes.

Case example 2--Garn Formation, Haltenbanken, Norway

The Middle Jurassic Garn Format ion occurs in wells from offshore western Norway, and com- prises sandstones deposited in a fluvial to shallow marine environment . It is one of the principal hydrocarbon reservoir units in the Hal tenbanken area (Ehrenberg, 1990). Median grain-size is typically in the range 0.3~0.5 mm (upper medium sand), and most samples are well to very well sorted. Ehrenberg (1990) presented a detailed analysis of the petrography and reservoir quality of sandstones from 16 wells. The burial depth of the Garn Format ion in these wells ranges between 1400 and 4000 m, and in the deeper wells, where temperatures have exceeded 140~ authigenic illite is an important diagenetic phase. Ehrenberg (1990) stated that the primary controls on porosity variation are compact ion and quartz cementat ion, and that permeabil i ty is a function of the remaining volume of intergranular macroporosity.

The textural and mineralogical data presented by Ehrenberg (1990) have been used to analyse average porosity-permeabili ty values for each well using the trend curves from the sphere pack modelling. This analysis is summarized in Fig. 9. The start point is a simple compact ion/quartz overgrowth cementat ion model t rend for the appropriate grain size, in this example, medium sand. Note that in this case, as with the Fontaine- bleau Sandstone, there is a relatively small spread of grain-size, so the textural split has not been essential. The sandstones from wells in which there are low abundances of authigenic illite show average porosity-permeabili ty values which fall

100000 Analysis of permeability controls" 499

Case example 3--Mississippian Sandstones, Endicott Field, Alaska, USA

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Porosity (%) Fro. 9. Porosity vs. permeability cross-plot for Garn Formation sandstones. Porosity-permeability values are averages for wells with different geographical locations and burial histories (data from Ehrenberg, 1989). The curves are model-derived and match the measured textural and diagenetic characteristics of the Garn Formation

sandstones.

on, or close to, this model trend. This supports the conclusions of Ehrenberg (1990) and provides further confirmation that our models are realistic representations of real sandstones. Also shown on Fig. 9 are two model trends for combined cases of compact ion/quartz cementat ion, followed by grain-rimming clay cementat ion. The two cases differ in the degree to which porosity is first reduced by compact ion/quartz cementat ion (to 25% in one case, and to 15% in the other).

As is the case in example 1, the model trends, constructed using textural data from thin- sections, and authigenic mineralogy data from X- ray diffraction analysis, provide a full explanation of the measured porosity-permeabili ty data ave- rages. The averages from the deeper wells with more illite are enclosed by the two combined mechanism model trends, in more detail, increas- ing illite content is reflected in progressively lower permeabilit ies.

Having explained the observed trends in the porosity-permeabili ty data using the model results, this understanding can be used predicti- vely. For example, if a Garn Format ion prospect is similar to the drilled occurrences, but with fine- sand grain size, then the model-der ived trends for that finer grain size, in combinat ion with burial history information, could be used to make a pre- drill reservoir quality prediction.

A large data set from Mississippian age sand- stones in a well in the Endicot t Field has been analysed using the model results. These sand- stones have a more complex suite of textural and diagenetic controls on reservoir quality than the preceding cases, and this is a 'blind' analysis, with no prior statistical work on permeabili ty controls.

Samples from this well show widely varying grain sizes, with average grain size ranging from fine-sand to very coarse sand or greater. The data set is first split by grain-size class (Fig. 10a). One model trend, for a moderately sorted, medium sandstone undergoing compaction/quartz cemen- tation is shown on the plot for guidance. From this initial plot several conclusions can be drawn. Firstly, within each grain-size class, the porosity- permeabil i ty trend is steeper than the simple model trend, indicating that the dominant reser- voir quality control(s) are pore-filling cemen- tation and/or pore-lining/filling clay. Secondly, there is considerable overlap between the grain- size classes, which indicates that the diagenetic controls on porosity and permeabil i ty have reached the stage of development where they mask the primary textural control. However , some remnant textural control is still evident: e.g. the very coarse sand samples have a higher permeabil i ty for a given porosity than the medium sand samples, whereas fine to medium sand grade samples have lower permeabili ty.

Having established that the textural effect has been largely, but not completely, swamped by the diagenetic overprint , each textural group in the data set is then analysed on its own, to establish what the important diagenetic controls on reser- voir quality are. The analysis of the medium sand grade sample set is illustrated in Fig. 10b.

The medium sand data points are coded by clay content (point-count data), and a clear relation- ship of decreasing permeabil i ty with increasing clay content can be seen. Several of the medium sand grade samples have porosity-permeabili ty values which fall on or close to the model compact ion/quartz cementat ion trend. As we would predict, these samples all have a low clay content, and there is a t rend for lower porosity corresponding with higher volumes of quartz cement. It can be concluded, therefore, that the major causes of reservoir quality variation in

5O0

these sandstones are variation in the volumes of quartz cement and pore-filling clay, which largely obscure the primary textural control.

D I S C U S S I O N

The three case studies described illustrate, for sandstones of varying textural and diagenetic complexity, how the sphere pack models replicate the results of diagenetic processes in real sand- stones. This has important consequences. The modell ing has provided a quantified under- standing of how different styles of cement or compaction influence pores and pore-throats. This understanding permits the identification of important reservoir quality controls from poro- sity-permeability trends. In simple sandstone systems, it may be possible to draw conclusions about controls using just the porosi ty-permeabi- lity data and textural information from cuttings, sidewall core or core description. Clearly, there is less uncertainty if more detailed petrographic data on texture and cements are available.

In numerous cases, with a wide range of sandstone types, the model trends have given a quick and accurate insight into the permeabil i ty controls. Taking the results a step further, sensiti- vities can be investigated, and predictions made. For example, for a given sandstone type, investi-

C . A . Cade et al.

gate the grain size or cement volume at which permeabili t ies are reduced below the threshold for economic flow rates can be investigated.

It should be emphasized that only single phase permeabil i ty has been model led to date. Potential extensions of this work include modell ing of packs with a range of grain sizes and two phase

permeability.

C O N C L U S I O N S

(1) By modell ing the results of compaction and various styles of cementat ion in a numerical sphere pack and calculating porosi ty-permeabi- lity trends for these diagenetic models, a good match between porosity-permeabili ty data for real and model sandstones has been achieved.

(2) The sphere pack models give an improved and quantified understanding of how a range of textural and diagenetic reservoir quality controls operate.

(3) Progressive compaction and quartz over- growth cementat ion produce almost identical porosity-permeabili ty decline trends.

(4) Pore-filling cements (such as carbonates) , and grain-rimming clays cause a steeper permea- bility decline trend with porosity than compaction or quartz cementat ion.

100000 ~ a

41 = FSK

loooo -JI o Ms K . / " |1 + M-C K m~

w t1" §

,

,oo. / ,k o

10 O ~ 0 10 20 30 40

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FIe. 10. Porosity vs. permeability cross-plots for Mississippian age sandstones from a well in the Endicott field, Alaska, USA; (a) plot illustrating the diagenetic overprint of the primary textural control on reservoir quality; (b) plot showing the

diagenetic controls operating within one grain-size class.

Analysis o f permeability controls

(5) The sphere pack modell ing has underl ined the importance of considering the primary (tex- tural), and secondary (diagenetic) controls on reservoir quality separately. By removing the textural control first, analysis of the diagenetic controls is facilitated.

(6) In order to analyse a set of data to establish the reservoir quality controls we suggest the first stage should be to split the data set by grain-size class (and if appropriate, sorting class). If textural control is still important , it will be evident after this split. Within each grain-size class, the diage- netic controls can then be evaluated, both qualita- tively using comparison with the model-der ived trends, and quantitatively using statistical analy- sis, independent of texture.

(7) In order to predict permeabil i ty ahead of drilling, it is necessary to be able to predict the controlling parameters . By combining the sphere pack model results with an approach which separates textural and diagenetic parameters , the potential for defining the important controlling parameters is maximized.

A C K N O W L E D G M E N T S

The permission of BP Exploration to publish the results and application of this research is acknowledged. In addition, permission has been granted by the Endicott partner, group: Exxon, Unocal, Amoco, BP, Arco, Cook Inlet, Nana and Doyon, to utilize data from this field.

R E F E R E N C E S

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