SPE 149104

Cementation Exponent Estimation for Complex Carbonate Reservoirs Using a Triple Porosity Model Ali Al-Ghamdi, Roberto Aguilera and Christopher R. Clarkson, University of Calgary

Copyright 2011, Society of Petroleum Engineers

This paper was prepared for presentation at the SPE/DGS Saudi Arabia Section Technical Symposium and Exhibition held in Al-Khobar, Saudi Arabia, 15–18 May 2011. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at the SPE meetings are subject to publication review by Editoria l Committee of Society of Petroleum Engineers. Electronic reproduction, distribution, or s torage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and whom the paper was presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.

Abstract A previously defined triple porosity model is used to calculate the cementation exponent (m) of complex carbonate reservoirs

in the Middle East using well log data. The cementation exponent is usually affected in carbonate rocks by different types of

primary and secondary porosities. A combination of interparticle porosity, non-connected porosity (e.g., vuggy and fenestral)

and fractures increases the uncertainty in the estimation of m. Therefore, a well-defined petrophysical approach must start by

first understanding the rock’s fabric.

Initially, samples are classified into different flow units based on pore throat apertures at 35% cumulative pore volumes (rp35).

This classification is then extended to include variations in porosity types based on geological and petrophysical descriptions

of each rock. Each sample has different proportions of connected and non-connected porosities. These porosities are defined as

matrix, fractures and non-touching vugs (including fenestral porosity). The porosity types are extracted from well logs for the

whole reservoir section and are cross-checked against core samples and thin sections.

The value of m in a triple porosity system can be larger, equal, or smaller than the cementation exponent of only the matrix

blocks (mb). This variation depends on the relative contribution of natural fractures and non-touching vugs compared to the

composite triple porosity reservoir. A continuous curve of m values is obtained using this model. A good comparison has been

obtained between the results of this model and m values measured in the laboratory.

Estimation of variable m values within short distances in a given reservoir using the triple model is a significant development

in formation evaluation that helps reduce uncertainty in petrophysical calculations. The results increase the confidence level in

water saturation and reserves determinations.

Introduction

A broad assumption that is generally made in water saturation calculations is that the cementation exponent (m) is constant for

the whole reservoir interval. This assumption creates a large uncertainty in water saturation estimation in heterogonous

reservoirs. Figure 1 shows the error expected in water saturation calculations if the m value is under or over-estimated. A

small error in m causes significant impact by decreasing or increasing Sw. Since most carbonate reservoirs have heterogeneous

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rock properties due to microbial and diagenetic processes, changes in rock properties should be reflected in the value of m.

Archie’s cementation exponent (m) is defined as a parameter that is affected by connectivity of the pore system. The

cementation exponent depends on the grain and pore shapes and how they are connected (Salem and Chilingarian, 1999). The

generally accepted average value of m is 2, where it represents interparticle porosity (Archie, 1942). In fractured rocks, the

value of m tends to get smaller because the rocks have better connectivity for electrical current (Towle, 1962; Aguilera, 1976;

and Rasmus, 1983). These researchers suggest using parallel dual porosity systems for such rocks. In rocks with a high

percentage of non-touching vugs, the value of m tends to be higher than 2 as reported by Lucia (1983) and Focke and Munn

(1987). However, in carbonate reservoirs, fractures and vugs coexist with the matrix (inter and intraparticle connected)

porosity in different proportions that change with depth. Aguilera and Aguilera (2004) proposed a physical model of triple

porosity systems, which was subsequently improved by Al-Ghamdi et al., (2010) to account for the presence of matrix,

fractures and vugs.

The physical model of triple porosity systems allows the estimation of cementation exponent (m) for heterogeneous

formations. The model assumes non-connected (separate or non-touching) vugs, matrix and fractures that contribute to the

total porosity of the system. The assumption is made that the matrix and fractures have conductivities that are connected in

parallel. The combined matrix and fractures are connected in series with the non-connected vugs. The triple porosity system,

also referred to as the composite system in this paper, is given by the equation (Al-Ghamdi et al., 2010):

log

]/)1(

)1(log[22

2

bmbnc

ncnc

m

………. (1)

For optimum results, the physical model needs to be validated in complex triple porosity carbonate rocks. In this study,

matrix, fractures and vug porosities were estimated initially from petrographic work. This also helped to understand the

internal anatomy fabric of the rocks prior to evaluating the well logs. This approach provided reasonable estimates of the

cementation exponent (m) as a function of depth.

Rock Typing

Carbonate samples were collected from one of the Saudi Arabian fields. Geological descriptions of the reservoirs were

necessary to understand the pore structure before establishing the petrophysical rock classification. Reservoir A, Fig. 2,

consists of five packages that include peloid-microbial lump-intraclast or micritized ooid grainstones and micropeloidal

packstones. This reservoir has relatively small variations in terms of porosity and permeability; however, each package or rock

type has short-spacing variation in dissolution, pore types and cementation intensity. These variations are present together with

changes in vugs and micro-fractures intensity. Reservoir B, Fig. 2, is even more complex, and has a lower reservoir quality. It

consists of flat-laminated cryptmicrobial stromatolites, thrombolites, cabbage-head stromatolites and ooid-intraclast-molluscan

packstone/grainstones. These varieties of lithofacies increase the complexity of the pore types, cementation and petrophysical

rock properties, such as porosity, permeability and tortuosity.

Petrographic work was performed to understand rock texture and porosity types. Petrophysical rock properties need to be

linked to the geological descriptions, which can indicate the pore types and connectivity. Porosity, permeability and pore types

are related to geological lithofacies; however, this relationship can be distorted by factors like dissolution and cementation.

This distortion can have a positive or negative impact on reservoir quality. Figure 3 shows the distribution of porosities

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considered in this study as a function of rock types (RT). The oolitic grainstone (RT-1) has mainly interparticle porosity, while

the stromatolitic wackestone (RT-7) has mainly fenestral porosity. This knowledge helps to explain the poor fluid or electrical

connectivity in RT-7.

Various rock type classification techniques are compared (Lucia’s, Flow Zone Indicator (FZI), Winland/Aguilera rp35) in this

study to determine the best classification technique for these carbonate samples. The samples do not show any relationship

between interparticle porosity and permeability with respect to particle size as suggested by Lucia’s classification. Figure 4

shows different rock types in Lucia’s plot. The particles, based on petrographic work on thin sections, have approximately the

same size. Yet there is no correlation with that type of rock. This poor relationship can be related to the processes of rework,

dissolution and cementation that these carbonate rocks have experienced. In the flow zone classification method, Fig. 5, the

relationship between z and RQI can provide a general distinction between rock types; however, occasionally there is no RQI

(include permeability) difference with changing rock type. Different rock types show a wide range of values of z for the same

RQI values in Fig. 5.

Winland rp35 flow unit classification, Fig. 6, appears to provide the best result. The geological framework and the proportions

of fractures and non-touching porosity (e.g., vuggy and fenestral), which usually affects the conduction of fluids and electrical

current, are captured properly by this classification. The Winland technique calculates pore throat apertures (rp35) at 35%

cumulative pore volume and this agrees with what is reported from the geological descriptions. Figure 6 shows the different

rock types for the carbonate samples in this study. There is an excellent correlation with lithofacies changes described from

cores. For example, rock type 1 (RT-1) is described as micritised ooid to peloidintraclast grainstones, while the lower quality

rock types RT-3, 4 and 5 are degraded to microbial grainstone, microbial packstone and wackestone as shown in Fig. 7. The

changes in lithofacies are accurately predicted by the Winland rp35 classification. Sometimes the oolitic grainstones have lower

reservoir quality due to extensive precipitation of cementation. The degraded porosity and permeability was captured by the

Winland technique as well. In total, seven different rock types have been found in the Reservoir A and B carbonates used in

this study. RT-1 and 2 represent megaports (port = pore throat), RT-3 macroports, RT-4 and 5 mesoports, RT-6 microports and

RT-7 is seal rock. These different pore throats and their radii in microns are shown in Fig. 6.

Reservoir A consists of four petrophysical rock types, Fig. 8. RT-2 represents a clean peloidal grainstone and stromatoporoid

floatstone with very high porosity and permability. RT-3 represents microbial peloidal grainstone with lower rock quality due

to the pore-bridging microbial activity. RT-4 and 5 are microbial packstones and wackestones with fair to low rock quality

due to the increase of lime mud. Reservoir B consists of six petrophysical rock types with a more rapid change in rock types

and lower quality rocks than Reservoir A, Fig. 9. Reservoir B has the aforementioned rock types plus RT-1 (a super-K type of

rock) and RT-6, which is a very low quality rock. RT-1 is cement-free grainstone with some fractures. In general, Reservoir B

has more variety and rapid change in rock type than Reservoir A.

Triple Porosity Model Results

Different parameters (2, nc and f) in the triple porosity model, Eq. 1, have to be estimated to calculate the cementation

exponent (m). As a preliminary estimate, different porosity proportions are estimated visually from thin sections and m values

are calculated for every thin section (Al-Ghamdi et al., 2010). Estimation of non-connected porosity from thin sections is

complicated because of the 2D limitation; however, it is important to perform this step to understand the rock quality and the

pore types associated with these rocks.

The procedure for calculating different porosity proportions from logs is shown in Fig. 10. If we assume that sonic porosity

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accounts for matrix porosity, then subtracting the effective porosity (core measurements or logs) from the sonic porosity will

represent the fracture porosity (2), Eq. 2. Subtracting total porosity (ND or NMR porosity) from the effective porosity equals

the non-connected porosity (nc), Eq. 3. Matrix porosity (b), which is attached to the matrix volume only, can be calculated

knowing the other porosity proportions (2, nc and m). Knowledge of the pore types, as indicated above, of different

petrophysical rock types helps to validate the accuracy of the estimation from logs.

seff 2 …………. (2)

effnc …………. (3)

The log-derived cementation exponent (m) was generated using the aforementioned procedure and resulted in m values that

change with depth for Reservoir A and B, Figs. 8 and 9. The average m for Reservoir A is 2.19 and 2.25 for Reservoir B. To

validate this procedure, 25 samples from the two reservoirs were tested in the laboratory to estimate m values for the rocks.

Figure 11 shows that a good comparison was obtained between lab measurements and log estimations. The coefficient of

determination (R2 = 0.757) is reasonable when one takes into consideration the different scales between the logs and core plugs

(1.5” for core plugs and 6” for each point on the log). Subsequently, this scale difference is in favor of the log derived m (triple

porosity model) because water saturation is calculated at the same well log scale.

The continuous variable m estimated from logs was used with the triple porosity model to calculate water saturation as shown

in Figs. 8 and 9. This calculation is more reasonable and robust than water saturation calculated using a constant value of m.

It is well recognized that there can be significant differences in water saturation results from logs when the calculations are

carried out with constant and variable values of m using the triple porosity model. This difference increases with larger

contributions of non-connected porosity (nc) in the different rock types (Al-Ghamdi et al., 2010). In addition, reliable water

saturation calculations help in the identification of the fluid contacts.

Conclusions

1- The petrophysical model for triple porosity reservoirs discussed in this paper, with the support of detailed

petrographic work, provides a quick and robust method for estimating the cementation exponent (m) in complex

carbonate rocks.

2- Using a continuous log of m values reduces significantly the uncertainty in water saturation calculations. This is

because changes in rock types are accommodated in the calculated m values.

3- The Winland rp35 rock typing and flow unit technique provided the best results for the complex carbonate rocks

considered in this study.

Acknowledgment

We would like to thank Saudi Aramco for supporting this research and providing the study data. We also acknowledge the

Geoscience, and Chemical and Petroleum Engineering departments at the University of Calgary and our colleagues of the

GFREE research team at the University of Calgary for their help and support. We thank the Canadian Well Logging Society

(CWLS) for giving Ali Al-Ghamdi the CWLS Thesis Abstract Award for 2010/2011. The Thesis Abstract reflects some of

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Ali’s doctoral research discussed in SPE papers SAS-825 (presented at this meeting) and 132879 (in print: SPE Reservoir

Evaluation and Engineering – Formation Evaluation, 2011). Paradigm provided the software used in some of the

computations. Their contributions are gratefully acknowledged.

Nomenclature

- Total porosity, fraction

b - Matrix block porosity attached to the bulk Volume of the matrix system, fraction

eff - Effective porosity which include matrix and fracture porosities, fraction

m - Matrix block porosity attached to the bulk volume of the composite system, fraction

nc - Porosity of non-connected vugs attached to the bulk volume of the composite system, fraction

2 - Porosity of natural fractures attached to bulk volume of the composite system, fraction

z - Pore volume to grain volume ratio, fraction

RQI - Reservoir Quality Index, micron

rp35 - Pore-throat aperture corresponding to a mercury saturation of 35%, micron

References

Al-Ghamdi, A., Behmanesh, H., Qanbari, F., Chen, B., and Aguilera, R. 2010. An Improved Triple Porosity Model for

Evaluation of Naturally Fractured Reservoirs. Paper SPE-132879 presented at the Trinidad and Tobago Energy Resources

Conference, Port of Spain, Trinidad, 27-30 June. In print: SPE Res. Eval. & Eng. (2011).

Al-Husseini, M.I. and Matthews, R. K. 2008. Jurassic-Cretaceous Arabian Orbital Stratigraphy: The AROS-JK Chart.

GeoArabia, Vol. 13, No. 1, pp. 89-94.

Aguilera, R. 1976. Analysis of Naturally Fractured Reservoirs from Conventional Well Logs. J. Pet. Technol., Vol. 28, pp.

764–772.

Aguilera, R. 2002. Incorporating Capillary Pressure, Pore Throat Aperture Radii, Height Above Free Water Table, and

Winland r35 Values on Pickett Plots. AAPG Bulletin, Vol. 86, No. 4, pp. 605-624.

Aguilera, R.F. and Aguilera, R. 2004. A Triple Porosity Model for Petrophysical Analysis of Naturally Fractured Reservoirs.

Petrophysics, Vol. 45, No. 2, pp. 157-166.

Archie, G.E. 1942. The Electrical Resistivity Logs as an Aid in Determining Some Reservoir Characteristics, Trans. AIME

Vol. 146, pp. 54–62.

Amaefule, J.O., Altunbay, M., Tiab, D., Kersey, D.G. and Keelan, D.K. 1993. Enhanced Reservoir Description: Using Core

and Log Data to Identify Hydraulic (Flow) Units and Predict Permeability in Uncored Intervals/Wells. Paper SPE-26436, 68th

SPE Annual Technical Conference and Exhibition, Houston, Texas, October 3-6.

Focke, J.W. and Munn, D. 1987. Cementation Exponents in Middle Eastern Carbonate Reservoirs, SPE Form. Eval. Vol. 2,

pp. 155–167.

Lucia, F.J. 1983. Petrophysical Parameters Estimated from Visual Descriptions of Carbonate Rocks; a Field Classification of

Carbonate Pore Space. J. Pet. Technol. Vol. 23, pp. 629–637.

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Rasmus, J.C. 1983. A Variable Cementation Exponent, m, for Fractured Carbonates. The Log Analyst, Vol. 24, No. 6, pp. 13-

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Salem, H.S. and Chilingarian, G.V. 1999. The Cementation Factor of Archie’s Equation for Shaly Sandstone Reservoirs. J.

Pet. Sci. Eng. Vol. 23, No.2, pp. 83–93

Towle, G.H. 1962. An Analysis of the Formation Resistivity Factor-Porosity Relationship of Some assumed Pore Geometries.

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Fig. 1: Water saturation error as a function of the porosity exponent, m. For example at 10% porosity, if the correct value of m is 2.0 and the evaluation is performed using 1.7, the water saturation error is 29.2%.

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Fig. 3: Pore types observed from petrographic work on different rock types in different reservoirs.

Fig. 2: Jurassic to Cretaceous geologic column showing Reservoirs A and B position. Modified after Al-Husseini and Matthews, 2008.

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Fig. 4: A plot of inter-particle porosity vs. permeability does not show a distinctive relationship with the particle size for the seven carbonate rock types on Lucia’s plot. Rock types illustrated in this plot are based on petrophysical work and geological description.

Fig. 5: This flow zone indicator plot shows a wide range of z and RQI values for the four rock types.

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Fig. 6: Winland rp35 values (microns) show distinctive trends between porosity and permeability for each rock type. This rock type classification represents a solid methodology for use in petrophysical and engineering analysis.

Fig. 7: Carbonate rocks have tendency to change petrophysically within very small distances due to microbial and diagenetic processes. A-(RT-2), B-(RT-3), C-(RT-4), C-(RT-5).

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Fig. 8: Reservoir A log results. Track 1 Lithological components; Track 2 Depth scale; Track 3 GR and Caliper; Track 4 Raw porosity logs; Track 5 Calculated porosity; Track 6 rp35 petrophysical rock type; Track 7 Variable m curve obtained from the triple porosity model and lab-derived m; Track 8 Resistivity; Track 9 NMR pore size; Track 10 Calculated Sw (old and new); Track 11 NMR distribution; Track 12 Permeability (lab measurements and Facimage predicted).

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Fig. 9: Reservoir B log results. Track 1 Lithological components; Track 2 Depth scale; Track 3 GR and Caliper; Track 4 Raw porosity logs; Track 5 Calculated porosity; Track 6 rp35 petrophysical rock types; Track 7 Variable m curve obtained from the triple porosity model and lab-derived m; Track 8 Resistivity; Track 9 NMR pore sizes; Track 10 Calculated Sw (old and new); Track 11 NMR distribution; Track 12 Permeability (lab measurements and Facimage predicted).

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Fig. 11: Good relationship between m values measured in the lab and log-derived m. The scatter in the points is expected because of the different vertical measurement scales (Plugs represent 1.5” and log is 6”).

Fig. 10: Schematic diagram shows how to calculate different portions of the total porosity.