SPE Formation Evaluation

Transcription

1 Cementation Exponents in l\/iidcile Eastern Carbonate Reservoirs J.W. Focke Qatar General Petroleum Corp. SPE Formation Evaluation

2 ^mfe = effective water resistivity in the flushed zone, O-m RQ = resistivity of the fully water-bearing formation, 0-m Rt = resistivity of the hydrocarbon-bearing formation, fi-m i?,^ = resistivity ofthe formation water, fi-m R^a = resistivity of the flushed zone around the wellbore, fi-m S/j = 1 5,= hydrocarbon saturation, % Sw = water saturation, % Sxo = water saturation in the flushed zone, % 0 = porosity, % *ln the original Archie equation, F^ was empirically related to porosity, F =M()>"'. This equation was later generalized to Ff,=bl4>'", where b is a parameter of mathematical convenience; It should not be confused with the geometric pore factor (tortuosity factor), G. **/ Is empirically related to the water saturation, IR = MS^". Combination of these equations yields the basic equation to calculate water saturation In a hydrocarbonbearing formation: S ={\br J<t>'"R,\)'"" See Eq. 12. Acknowledgnfients We thank the Qatar General Petroleum Corp. for providing support and permission to publish this paper and M.M. de Monchy, U. KnoUmayer, P.M. George, and A.B. Graper (Qatar General Petroleum Corp.), L.J.M. Smits, C. Moens, and E. De Wolf (Shell Intl. Petroleum Mij.), R.W. Eade and T.T. Dziuba (Shell Canada), M. Watfa (Schlumberger, Middle East), and several anonymous reviewers for valuable comments and suggestions. Heferences 1. Archie, G.E.: "Electrical Resistivity Log as an Aid in Determining Some Reservoir Characteristics," Trans., AIME (1942) 146, Archie, G.E.: "Electrical Resistivity as an Aid in Core Analysis Interpretation," Bull., AAPG (1947) 31, Archie, G.E.: "Introduction to Petrophysics of Reservoir Rock," Bull., AAPG (1950) Archie, G.E.: "Classification of Carbonate Reservoir Rocks and Petrophysical Considerations," BM//., AAPG (1952) 36, Perez-Rosales, C: "Generalization of the Maxwell Equation for Formation Resistivity Factors," 7Pr (July 1976) Perez-Rosales, C: "On the Relationship Between Formation Resistivity Factor and Porosity," SPEJ (Aug. 1982) Mendelson, K.S. and Cohen, M.H.: "The Effect of Grain Anisotropy on the Electrical Properties of Sedimentary Rocks," Geophysics (mi) 47, No 2, Wyllie, M.R.J, and Gregory, A.R.: "Formation Factors of Unconsolidated Porous Media; Influence of Particle Shape and Effect of Cementation," JPT (April 1953) ; Trans., AIME, Wöbking, H.i "Zur Kritik des sogenannten Zementationsfaktor," Gerlands Beitr. Geophys., Leipzig (1972) 81, Sherman, M.M.: "The Determination of Cementation Exponents Using High-Frequency Dielectric Measurements," The Log Analyst (Nov.-Dec. 1983) Winsauer, W.O. et al.: "Resistivity of Brine Saturated Sands in Relation to Pore Geometry," Bull., AAPG (1952) 36, Ransom, R.C: "A Contribution Toward a Better Understanding ofthe Modified Archie Formation Resistivity Factor Relationship," The Log Analyst (March 1984) Choquette, P.W. and Pray, L.C: "Geological Nomenclature and Classification of Porosity in Sedimentary Carbonates," Bull, AAPG (1970) 54, Wyllie, M.R.J, and Rose, W.D.: "Some Theoretical Considerations Related to the Quantitative Evaluation of Physical Characteristics of Reservoir Rock from Electrical Log Data," JPT (April 1950) ; Trans., AIME, Rasmus, J.C: "A Variable Cementation Exponent, m, for Fractured Carbonates," Tlw Log Analyst (Nov.-Dec. 1983) Sen, P.N., Scala, C, and Cohen, M.H.: "A Self-Similar Model for Sedimentary Rocks with Application to the Di-electric Constant of Fused Glass Beads," Geophysics (1981) 46, Asquith, G.B.: "Handbook of Log Evaluation Techniques for Carbonate Reservoirs," Methods in Exploration, AAPG, Tulsa, OK (1985) No. 5, Anderson, W.G.: "Wettability Literature Survey Part 3: The Effect of Wettability on Electrical Properties of Porous Media," JPT (Dec. 1986) Brie, A., Johnson, D.L., and Nurmi, R.D.: "Effect of Spherical Pores on Sonic and Resistivity Measurements," Trans., SPWLA Logging Symposium, Dallas (1985) 1, paper W, Lucia, F.G.: "Petrophysical Parameters Estimated from Visual Descriptions of Carbonate Rocks, a Field Classification of Carbonate Pore Space," 7Pr (March 1983) Rasmus, J.C. and Kenyon, W.E.: "An Improved Petrophysical Evaluation of Oomoldic Lansing-Kansas City Formations Utilizing Conductivity and Dielectric Log Measurements," Trans., SPWLA Logging Symposium, Dallas (1985) paper V. 22. Watfa, M.: "Important Variables in Carbonate Interpretations," Schlumberger, Paris (1985). 23. Amin, A.T., Watfa, M., and Awad, M.A.: "Accurate Estimation of Water Saturations in Complex Carbonate Reservoirs," paper SPE presented at the 1987 SPE Middle East Oil Technical Conference and Exhibition, Bahrain, March Borai, A.M.: "A New Correlation for Cementation Factor in Low- Porosity Carbonates," paper SPE presented at the 1985 SPE Annual Technical Conference and Exhibition, Las Vegas, Sept Neustaedter, R.H.: "Log Evaluation of Deep Ellenburger Gas Zones," paper SPE 2071 presented at the 1968 SPE Deep Drilling and Production Symposium, Monahans, TX, March Focke, J.W. and Munn, D.: "Cementation Exponents (m) in Middle Eastern Carbonate Reservoirs," paper SPE presented at the 1985 SPE Middle East Oil Technical Conference and Exhibition, Bahrain, March Guillote, J., Schrank, J., and Hunt, E.: "Smackover Reservoir, Interpretation Case Study of Water Saturation Versus Production," Trans., Gulf Coast Assn. of Geological Societies (1979) 29, Mitchell-Tapping, H.J.: "Petrophysical Evaluation of the Smackover Oomouldic Porosity of East Texas and Southern Arkansas," The Log Analyst (1983) 24, No. 4, Dorfman, M.H.: "Discussion of Reservoir Description Using Well Logs," ipr (Dec. 1984) SI Metric Conversion Factors ft X 3.048* in. X 2.54* 'Conversion factor Is exact. E-01 = m E+00 = cm SPEFE Original manuscript received In the Society of Petroleum Engineers office March 6, Paper accepted for publication July 23,1986. Revised manuscript received Sept. 22,1986. Paper (SPE 13735) first presented at the 1985 SPE Middle East Oil Technical Conference and Exhibition held In Bahrain, March SPE Formation Evaluation, June

3 Cementation Exponents in i\1iddle Eastern Carbonate Reservoirs J.W. Focke,* SPE, Qatar General Petroleum Corp. D. Munn/ * SPE, Qatar General Petroleum Corp. Summary. The cementation exponent, m, is a major factor of uncertainty in the calculation of hydrocarbon/ water saturation in heterogeneous carbonate reservoirs. Hydrocarbon saturations as high as 70 or 80%, calculated with the conventional value m=2, may disappear completely with m values of 3 and 4 (Fig. 1), which are quite common in carbonate rocks. Laboratory data obtained in heterogeneous carbonate reservoirs often show a wide scatter (Fig. 2). Constant (average) m values are usually used in spite of such scatter, and data points with m values much higher than the average value are often rejected to obtain straight-line trends. This paper presents the results of a study of the relationship between variable m values measured on core plugs and detailed carbonate rock types. The scatter in the data is analyzed in terms of rock type. We conclude that the high m values are often representative for specific rock types and that these values should not be rejected but applied selectively in log analysis over those intervals where these rock types occur. Fig. 17 Application of variable m for a reservoir containing moldic limestones and dolomite grainstones. The hatched area represents the reduction In calculated hydrocarbon saturation as a result of applying variable m values (as compared to a constant value of 2); the shaded area represents the additional reduction, which is obtained by applying an n value of 3 Instead of 2. This leads to a practical method whereby more representative values for m can be given for particular reservoir intervals. Rock types with intergranular porosity and sucrosic dolomites show m values close to 2. Rock types with matrix porosity only, such as mudstones and wackestones, also show m values close to 2. Rock types with both matrix and vuggy or moldic porosity show m values generally greater than 2, in proportion to the amount of unconnected porosity, but no firm values can be provided. Fractured and fissured rock types may have m values less than 2 that theoretically could become as low as 1. Moldic lime (oolitic) grainstones show m values that range from about 1.8 at 5 % porosity to 5.4 at 35 % porosity. Trends can be given as relationships between Fj^ and 0 or m and </>. The scatter in the data has been reduced by distinguishing four permeability classes that represent pore-type variations within the group of moldic grainstones. Further research into the physical mechanism of electrical conductance of moldic rocks is recommended. Moldic dolomite (oolitic) grainstones show trends similar to the moldic lime grainstones, except that permeabilities are generally higher and m values are lower, probably because of more open textures in the (recrystallized) cement. An average m value of 2.4 is suggested for this rock type, subject to the qualifying remark above. To apply these values or trends, heterogeneous carbonate reservoirs have to be split into layers (intervals) on the basis of dominant rock type (porosity type) by core studies and integrated reservoir geologic and petrophysical modeling to allow different parameters, such as m values, to be applied in each layer. The EPT appears to be very promising in deriving m values from logs, but further confirmation is required. Nomenclature b = intercept of an extrapolated trend line on a logarithmic F;^-vs.-porosity plot with the 100% porosity axis Fj^ = formation resistivity factor=i?o/^iv* = resistivity index=7?^//?^** k = permeability, md m = cementation exponent (lithological exponent) n = saturation exponent Rmf - resistivity of the mud filtrate, fi-m Introduction The cementation exponent (lithological exponent), m, plays an important role in the calculation of hydrocarbon/water saturations from electrical wireline logs, with the Archie equation, Fj^=RtlRw = '^IV^ As calculated from laboratory measurements on core plugs, in varies considerably in complex lithologies. In carbonates, the variation in m is very large. As a result, the use of average values, even if based on many laboratory measurements, and particularly the use of the literature value m=2, may lead to large inaccuracies in the calculated saturations. Geologic analysis of several hundreds of samples on which formation resistivity experiments have been performed showed that more accurate values for m can be given if a distinction is made between detailed rock types. Rock types with mainly interparticle or intercrystalline porosity (e.g., grainstones and sucrosic dolomites) show m values close to 2. Rock types with more tortuous and/or poorly interconnected porosity (e.g., moldic lime grainstones), however, show well-defined trends of increasing m with increasing porosity. In several cases the m value ranged from about lat 5% porosity to 5.4 at 35% porosity. Similar trends, but with narrower ranges, were found for more complex and mixed porosity types. Scatter can be reduced further by distinguishing between permeability classes. The physical mechanism of electrical conductance in moldic rocks is still not well understood and réquires further field and laboratory research. The electromagnetic propagation (EPT) log has been a promising tool (in conjunction with standard electrical and porosity logs) for deriving m in hydrocarbon-bearing zones, a normally difficult task with standard techniques (e.g., resistivity logs, Pickett plots, and sonic logs), and good confirmation has been obtained from core data in *Now with Petroleum Development Oman. **Now with Shell UK Exploration and Production, London. Copyright 1987 Society of Petroleum Engineers some cases. Many assumptions, however, need to be made, and it is considered too early to generalize these results. Middle Eastern carbonate reservoirs are very heterogeneous in terms of rock types. Application of the defined average values and trends therefore requires the reservoir to be split into layers on the basis of the dominant rock type (porosity type) within each layer and the selective application of different petrophysical parameters. Layering can be defined on the basis of cores and/or logs or a detailed geologic field model that allows layers and rock types to be identified by log correlation calibrated with cores. Such field models require an integrated and coordinated effort by geologists, petrophysicists, and reservoir engineers and should lead to reconciliation between data sets that, in heterogeneous reservoirs, often appear to be conflicting (e.g., saturations from logs compared to capillary pressure curves, and/or well testing results). The m value is only one of many parameters that affect such comparisons. The Archie Relation Although Archie * described the relationship between the formation resistivity factor, FR, and porosity, ^, as being exponential, FR = IIV\ (1) based on empirical observations mainly on sandstones, he was aware of the occurrence of variations and scatter and that these are related to rock variations in heterogeneous reservoirs.^"* He recognized that m was not constant and that the term "cementation factor" implied some relationship between m and the degree of cementation in sandstones. Numerous papers ^"^^ have attempted to provide a proper theoretical background for the observed relations and generally have focused on the tortuosity and/or the degree 166 SPE Formation Evaluation, June 1987 SPE Formation Evaluation, June

4 VJ V ' V O Vo - \ ' O o o O Ooo O o < O o\ O <S>,\p 100.? O O \ - o ' t O Y 0 oo\ " DOLOMITES INTER PARTICLE POROSITY ov O \ \o O \ \ ] O \ ioo Sw Qt m = 2(b -=1,0 = 2) O \ o\ \. \ POROSITY (*/.) MOLDIC POROSITY P0R0SITY(7o) Fig. 16 The effect of increasing effective overburden pressure on calculated m (core data), showing the very strong effect if moldic porosity is present. Black dots are ambient conditions and open circles are effective overburden pressure. Sw at m=2(b=l,n = 2) Fig, 1 The effect of changing m on the calculated water saturation Is shown, with a base case of m = 2, and for two given porosities. At 30% porosity (dashed lines), a hydrocarbon saturation of 70% would be reduced to 0 by changing m from 2 to 4. of effectiveness (interconnection) of the pore system. Many of these papers refer to ideal systems (such as glass beads), not to complex systems like carbonate rocks, and therefore leave doubt regarding their theoretical application in practical reservoir evaluation. Scattered data points on F^j-vs.-</> crossplots have traditionally been approximated by straight lines, with a combination of values (constants) for m and for b, the intercept of the trend line with the 100%-porosity axis (b^l). This relationship is known as the modified Archie equation: FR=b/r' (2) The best-known example of such a trend is probably the Humble equation" for certain sandstone reservoirs: =0.62/02.15 (3) POROSITY ( % ) ALL DATA AT EFF. OVERBURDEN PRESSURE Fig. 2 FR measurements (at effective overburden stress) obtained on core plugs from a single reservoir in a single well show the meaningless scatter obtained in a heterogeneous reservoir. Such a straight-line trend on a log plot of vs. 4» with a constant for m and b (b^l) has the same effect as applying a variable m value (atz? = l) at different porosity values. Because m is usually an independent input parameter in the Archie saturation equation (porosity values being derived from different logs), calculated m values (atb=l) are presented in this paper (plotted vs. porosity) alongside the more traditional FR-\S.-4> plots. These separate m plots are also convenient in determining the effect of different m values on the calculated water/hydrocarbon saturation by use of a diagram such as that shown in Fig. 1. The physical meaning of m or b and their relationship with pore geometry are undoubtedly of interest; under carefully controlled conditions (such as simplistic pore geometry and no conductive minerals), m can be related to grain shape, while the value of b can be shown to deviate from 1 in the presence of solid conductors or semiconductors. '2 Carbonates are generally too heterogeneous to allow simple generalizations. This paper intends to differentiate carbonate reservoir rocks into natural groups on the basis of genetic porosity types as a step toward defining practical guidelines regarding parameters to be used in day-to-day wireline log interpretation. Methods All available plugs used in the past for FR measurement from reservoirs offshore Qatar, covering a large number pected. In rocks that have both moldic and intergranular porosity (e.g., rim-cemented moldic grainstones), it is obviously the presence of intergranular porosity that causes the permeability to be higher and the m value to be lower than that of a comparable rock with only moldic porosity. Log evaluation problems have been frequently recognized in reservoirs containing moldic oolitic limestones, with many reported cases of water production from interpreted hydrocarbon-bearing reservoirs. 17,27,28 ^.j^jg respect, parts ofthe Smackover and Lansing Kansas City formations in the U.S. display striking similarities to the moldic oolitic reservoir shown in Figs. 13 and 17. Various field methods have been developed for these cases, usually based on specific logs and local log parameters with narrowly defined conditions of mud filtrate and formation water resistivities. These methods may or may not be successful in certain cases. The possible advantage of using the data as presented in this study is that they are based on observed trends for rock types and genetic porosity types that are essentially the same worldwide. For example, it can be expected that well-developed moldic limestones, with textures similar to those described in this paper and of typical low permeability, would display similar trends of steeply increasing m values with increasing porosity in other reservoirs. Also, the proposed method conforms to the traditional Archie equations and parameters ((j), b, m, Rg, Rf, R^, and n) i.e., it allows general application, in principle, unconstrained by local conditions. Application of the Results The essence of this paper is that different petrophysical parameters should be used for different rock types, with particular reference to formation resistivity. A similar approach is required for other reservoir properties, such as capillary pressure curves. To apply these parameters in formation evaluation, the reservoir must be split into layers on the basis of the dominant rock type. Layers can be defined on the basis of cores, if available, logs (log rock typing), and/or a detailed field model based on cores, logs, correlation, and a conceptual depositional and diagenetic model. Defining layers and applying parameters will always require an integrated and coordinated effort from various disciplines. Fig. 17 shows an example reservoir that has been divided into dolomite layers where porosity is mainly intergranular and intercrystalline and oolitic limestone layers with mainly moldic porosity. The hatched area shows the significant reduction in hydrocarbon saturation resulting from the application of the trends for the moldic limestone proposed in this study. The shaded area represents the additional reduction obtained from using a value of 3 instead of 2 for the saturation exponent, n. This shows that variations in the saturation exponent as observed in moldic limestones (n may vary from 1.5 to 3.5 according to laboratory measurements at ambient conditions) also have a significant effect. The relationship between n, which is sometimes considered as a special case of m (Ref. 12), and rock types is more complex than between m and rock types. The value of n is affected not only by various rock properties, largely unknown, but also by wettability and therefore the chemistry of the hydrocarbons, their interaction with the rock, physical conditions in the reservoir, and saturation history. As a result, study of n is seriously hampered by the absence of reliable reservoir-condition laboratory techmques.^^ We believe that applying petrographically analyzed core data to heterogeneous carbonate reservoirs in conjunction with modern wireline logs provides a better basis to derive a more accurate and reliable formation evaluation and reservoir description. Conclusions Formation resistivity factor (FR, m) data in carbonate reservoirs show large variations that can be largely resolved by distinguishing detailed rock and porosity types. 156 SPE Formation Evaluation, June 1987 SPE Formation Evaluation, June

5 EFFECTIVE OVERBURDEN PRESSURE (PSI) Fig. 15 Porosity and as a function of increasing effective overburden pressure, sliowing tlie strong effect on F if moldic porosity is present. bilities as reported previously provides strong reasons to continue investigation of EPT use for this purpose. Discussion Rock Types With Predominant Interparticulate Porosity. Lime and dolomite grainstones with intergranular porosity (Rock Types 1 and 2), dolomites with intercrystalline porosity (Rock Type 3), and rock types with only matrix porosity (Rock Type 6) show consistent m values close to 2 for porosities from 5 to 35 %. At low porosities (<5%), m values tend to be less than 2 (Fig. 4b), which is contrary to the expectation that wellcemented and therefore low-porosity samples have more tortuous porosity systems and m values greater than 2. It is possible that microfractures (either induced or natural) are responsible for the low m values, but we have not found evidence supporting such fractures. Low m values from low-porosity carbonates have also been reported elsewhere in the Arabian Gulf. ^^ The general equation given for low-porosity carbonates in service-company charts* does not appear to be applicable for these rocks. Rock Types With Moldic Porosity. The results of this study have shown that high m values are related to low permeabilities and the relative amount of moldic porosity in the sample. We have previously assumed that the moldic porosity would be effectively isolated and that electrical pathways would bypass the moldic porosity (Fig. 8 in Ref. 26), It is difficult, however, to believe that the moldic pores would be totally sealed and ineffective. This would be inconsistent with the fact that the original grains *This equation, m = /0, was originally proposed witli particular (and exclusive) reference to the Ellenburger deep gas zones and later published (Ref. 24). It subsequently appeared In Schlumberger chart books and manuals as a much more generalized Shell formula for low-poroslty carbonates. This generalization would appear to be Inappropriate. have become so effectively leached, and it would also be difficult to understand how hydrocarbons could ever penetrate these pores. If these pores are totally sealed, resistivity logs would not be able to differentiate between fluids within these pores. Given the high residual hydrocarbon saturations seen by the EPT in the flushed zone shown in Fig. 13 (which implies that hydrocarbons are present inside the moldic pores because cores show that practically all porosity is moldic in these zones), the good match between m values derived from the EPT (partially hydrocarbon-bearing) and laboratory data (fully waterbearing) would also be very difficult to explain if the moldic pores are totally sealed. Interesting research results suggest that the effect on electrical conductivity is more a function of pore shape than of connection and that spherical porosity (such as oomoldic porosity) adds very little to the bulk conductivity of the rock, even in the connected, brine-filled case. It appears that some petrophysical aspects of moldic rocks are not well understood. In view of the common occurrence of moldic porosity in carbonate (as well as in some clastic) reservoirs throughout the world, we strongly recommend further research into the physical mechanism of electrical conductance in these rocks, including combined laboratory and field investigations that use cores, electrical logs, and nonelectrical logs that may be useful in providing independent hydrocarbon information. Early results of such comparisons (Figs. 13 and 14) are certainly promising the match between core and log data is too consistent to be coincidental (the match is good over long intervals, representing different rock types, porosity, and permeability ranges) but it is clearly too early to generalize the results. Note the behavior of the moldic lime grainstones under increasing effective overburden pressure. In rock types with intergranular or intercrystalline porosity, the increase in FR with increasing effective overburden is clearly related to the compressibility of the rock, as shown by the concurrent stabilization of FR and porosity, usually within the first 200 psi [1379 kpa] of applied effective pressure (Fig. 15). For moldic limestones, however, FR, which is already at much higher levels at ambient conditions, continues to rise significantly even after porosity ceases to decline significantly. This probably means that, as pressure rises, more of the micropores (which are probably flat in shape) between the cement crystals close. Such closure would not result in any significant decline in PV (compressibility) but would affect a rise in resistivity by a drastic increase in the tortuosity within the rock matrix. This behavior, therefore, appears to confirm the overriding effect of the rock matrix on the resistivity of the bulk sample as compared to the moldic pores. The sensitivity of FR to overburden pressure in moldic limestones affects the calculated m values, as shown in Fig. 16. Clearly, laboratory measurements on core plugs should always be done under effective overburden pressure in addition to ambient and intermediate pressures if the presence of these more complex rock types is suspected. The intermediate-pressure results are useful from a quality-control viewpoint because they allow the detection of sample failure and pore collapse, which occurs commonly in these carbonates. The differentiation in m values by permeability in moldic rock types shows that a relation exists between conductivity to fluids and to electrical currents, as can be ex- of wells and reservoirs, were petrographically analyzed in thin sections and the data plotted separately, according to categories based on rock type (lithology) and porosity type. The porosity type is by far the most important parameter in regard to reservoir properties. Archie's own carbonate rock classification,^ although very useful in wellsite geology, does not include a genetic porosity classification and therefore is not adequate in the study of reservoir properties. The porosity type is emphasized in this study. A simplified schematic of the major genetic porosity types used in this paperis presented in Fig. 3. The permeability of each sample was determined before the FR measurement was performed. FR was measured at a range of pressures, including the effective overburden pressure prevailing in the reservoir from which the sample was taken. Various plug sizes up to 4 in. [10 cm] in diameter were used. Most data refer to clean carbonate rock; for some chalky samples with small quantities of clay minerals, minor corrections were applied on the basis of measured cation exchange capacity. In clean carbonates, FR does not appear to be affected by the brine's resistivity; however, anhydrite-bearing plugs many suffer from strong dissolution effects, depending on the brine composition. Simulated formation water was used in all laboratory measurements. Results Rock Types 1 through 3. Rock Types 1 and 2, lime and dolomite grainstones with intergranular porosity (Fig. 3a), and Rock Type 3, sucrosic dolomites with intercrystalline porosity and crystal textures that are usually very open (Fig. 3b), show a very similar resistivity response because they all have an interparticle porosity type (particles are grains or crystals). Therefore, the results for these rock Fig. 3 Genetic classification of porosity type correlated with rock types: (a) Intergranular (lime and dolomite grainstones, Rock Types 1 and 2; (b) intercrystalline (sucrosic dolomites, Rock Type 3); (c) moldic (moldic oolitic limestone and dolomite grainstones, Rock Types 4 and 5); (d) matrix or chalky (mudstones, chalks. Rock Type 6); (e) moldic or vuggy in addition to matrix (vuggy packstones and wackestones, Rock Type 7); and (f) fracture or fissure porosity (Rock Type 8). Fig. 4 FR and m (b = 1) vs. (p for limestone and dolomite grainstones with intergranular porosity and sucrosic dolomites with intercrystalline porosity (Rock Types 1 through 3). Symbols refer to different wells and reservoirs. 164 SPE Formation Evaluation, June 1987 SPE Formation Evaluation, June

6 POROSITY (%) P0R0SITY(7o) Fig. 5 and m (b = 1) vs. (p for moldic limestones (Rock Type 4), Permeability Class 1. Symbols refer to different wells. Dashed curve on the FR plot is equivalent to the straightline trend on the m plot. types have been combined into one figure (Fig. 4), although such a combination may not be acceptable for other reservoir properties, such as porosity/permeability relations or capillary pressure curves. As shown by Fig. 4a, these rock types show a straight-line relationship between FR and 0 with m=2 at b=l, which, of course, is represented by a linear plot of calculated m values vs. 4» (Fig. 4b). At low porosities (below about 5%), however, m values appear to be consistently less than 2, which will be discussed later. Rock Type 4. By contrast, Rock Type 4 comprises moldic lime grainstones with well-developed, moldic ("vuggy") porosity (Fig. 3c) and shows very significant variations, with m ranging from about 2.0 to 5.4 (Fig. 5). This rock type represents a complete diagenetic inversion whereby the original porosity (between the grains) was destroyed by cement and the grains themselves were dissolved to form the current porosity. Note in Fig. 3c that moldic porosity of this kind is very poorly interconnected, which has a major effect on the reservoir properties of this rock. The petrographic study of thin sections clearly shows that the highest m values are associated with samples having the best developed and largest amount of moldic porosity. We prefer the term moldic rather than vuggy for this porosity type to indicate the actual origin of the pores, which result when a particle dissolves and leaves behind its original shape. We separated the resistivity data for moldic limestones into four permeability classes to reduce to some extent the very wide scatter in the data. Fig. 5a presents all available data for moldic limestones with a permeability less than 0.1 md and shows the following trend: =670/0-0'22 (4) This trend, with a high value for the intercept b and a negative m value, may appear provocative; however, it adequately represents the fact that m values become larger with increasing total porosity of the sample. This is shown in Fig. 5b, where the same data are plotted as m (b=l) vs. 0. These data show a straight-line trend as follows. 772 = (5) The compatibility of the two trends (Eqs. 4 and 5) can be seen by plotting the equivalent curve of the straightline trend from Fig. 5b on Fig. 5a (dashed line). Such an equivalent curve has the advantage of satisfying the basic requirement of F;^ approaching infinity at very low porosities and unity at a porosity of 100%. It is clear, however, from comparing the straight line with the dashed curve in Fig. 5a that, for purposes of saturation calculation, the effect of using a combination of fixed values for 771 and b (Eq. 4) or a variable m (Eq. 5) is the same within the porosity range ofthe data (i.e., 5 to 35%). Eq. 5 do^ not lead to a better or more reliable relationship when compared with Eq. 4, which is derived by a direct regression of FR on porosity, weighted toward the higherporosity region. Similar results, but less steep trends, are obtained for the remaining moldic limestones. For Permeability Class 2 (/:=0.1 to 1 md), the following trends are given (Fig. 6). and F^=7O/0ö'46 (6) 772= (7) 158 SPE Formation Evaluation, June 1987 One example of successful application of the EPT, whereby laboratory and log-derived data were determined for a cored well, is given in Fig. 13. Note the general agreement between log- and core-derived 772 values. In cases where 722 from the core is higher than the 722 from EPT (e.g.. Samples 19, 24, and 26), 0 measurement from the core is also higher, and the discrepancy probably reflects thin, highly porous beds not resolved by the porosity logs. Note the much higher movable hydrocarbon fraction in the dolomites as compared to the limestones, and the mirror effect between the EPT 722 curve and the 0 log, reflecting the relation between 722 and 0 (see Fig. 14). A comparison of all available core data on one selected rock type (moldic limestone) with log data is given in Fig. 14. The results appear very promising, although we stress that the currenfly available data set is limited. Improved evaluation based on dielectric logs has also been reported from other reservoirs. 2' Note that several assumptions have to be made, including the value of n in the flushed zone, the effective salinity of the water in the flushed zone and its electromagnetic propagation time, and the effect of the different tools investigating different volumes of rock (see Refs. 22 and 23 for a more detailed explanation of the EPT). It is usually assumed that 72=2, which even in clean carbonates may not be accurate, particularly if the reservoir is not water-wet. On the other hand, even in such cases, 72 may be close to 2 in the flushed zone because the value of 72 changes with the water saturation and probably approaches a value of 2 (in clean carbonates) at higher water saturations. It is important to realize that in such cases, different values for 72 may apply in the invaded zone and in the virgin formation, because 72 is a function of saturation. These assumptions present limitations to the technique for deriving 722 from the EPT and prevent generalization of results. However, the good match between core and log data occurring over extended intervals and covering a variety of rock types, porosities, and permea- MOLDIC LIMESTONES EPT DATA 92 e e e %-! 5 I'O LOG POROSITY (Vo) Fig. 13 Depth plot showing lithology, porosity, immobile (black) and movable (shaded) hydrocarbons as a fraction of porosity, and m based on the EPT as generated by Schlumberger GLOBAL evaluation. Circles represent core data. MOLDIC LIMESTONES CORE DATA e e e» CORE POROSITY (% ) Fig. 14 Crossplots of m vs. (p from logs (left) and cores (right). Note the general agreement. m values from EPT are based on the Schlumberger GLOBAL evaluation, with one data set per foot. SPE Formation Evaluation, June

7 a K) POROSITY (%) POROSITYC/o) Fig. 6 Ffl and m (b = 1) vs. cp for moldic limestones (Rock Type 4), Permeability Class 2. Symbols refer to different wells. Dashed curve on the F plot Is equivalent to the straightline trend on the m plot. For Permeability Class 3 (/:=! to 100 md), the follow- For Permeability Class 4 (A:> 100 md), the following ing trends apply (Fig. 7): trends are suggested (Fig. 8): Fig. 12 Lucia plot showing the relationship between m and the ratio of unconnected (vuggy) to total porosity; (b) the same plot extended to incorporate results for moldic limestones. =59/00-32 (8) F;? =7.3/00-68 (10) logs and cores. Fig. 11 should be adapted when data from other regions become available. m From Logs. Under certain circumstances, FR and m can be derived directly from resistivity and porosity logs in zones that are fully water bearing if the water resistivity is known. In heterogeneous reservoirs, however, this technique is often not useful because values derived from water zones cannot be applied in other zones of the reservoir without the knowledge that the rock type is exactly the same. For similar reasons, the use of the Pickett plot^'' is often also unsatisfactory in these reservoirs. The interpretation of such a plot is made more difficult because points that represent hydrocarbon-bearing intervals are affected by the saturation exponent n (note the effect of wettability on n).^^ Another way to obtain an indication of m from logs is to determine the amount of unconnected porosity (sometimes referred to as secondary porosity) as a fraction of the total porosity, from the sonic log and the density/neutron logs, and by using the Lucia plot (Fig. 12a). A maximum m value of about 3 is suggested by this plot for an unconnected/total porosity ratio of 0.75 (i.e., 75% of the total porosity is unconnected). The well-developed moldic limestones described in this paper (Rock Type 4 in Fig. 3c, the lowest-permeability class) would have a ratio of close to unity (nearly 100% unconnected porosity; the volumetric contribution ofthe microporosity between the cement crystals is negligible). Therefore, they would all plot at the very top ofthe Lucia graph, regardless of their total porosity value. As we have seen (Fig. 5b), however, the m value of these samples is a function of total porosity. On the basis of these data, the Lucia plot can be extended as suggested in Fig. 12b by the inclusion of the moldic limestone points at the top of the graph, depending on their porosity value. Lines can be postulated (dashed line in Fig. 12b) to represent m values as a function of both total porosity and the ratio of unconnected/total porosity. These dashed lines are supported by very limited data and should be regarded as speculative. Applying the Lucia plot is limited, however, by the fact that both standard laboratory methods and the sonic log data seem to respond accurately to the total porosity, including the secondary porosity, in moldic oolitic limestones (see also Ref. 17). Promising results in obtaining m from logs in the (hydrocarbon-bearing) reservoir have been achieved with the EPT log. The tool provides a saturation value in the flushed zone independent from the electrical logs. Its depth of investigation is very shallow. As a result, the EPT has a very good vertical resolution, although this effect is reduced by the lesser vertical resolution of the porosity tools (which are required for the calculation of m). With S^o from EPT (corrected for salinity effects), 0 from the porosity logs, Rj^^ from a resistivity tool, and the effective resistivity of the water in the flushed zone (derived from R, f with correction for mixing with formation water), m can be calculated from the Archie equation: S,o"=RmfeKr'R.o) (12) I POROSITY (%) P0R0SITY(7o) Fig. 7 F and m (b = 1) vs. (p for moldic limestones (Rock Type 4), Permeability Class 3. Symbols refer to different wells. Dashed curve on the F^ plot is equivalent to the straightline trend on the m plot. 162 SPE Formation Evaluation, June 1987 SPE Formation Evaluation, June

8 10 zo IOC ^ POROSITY (7.) POROSITY (%) Fig. 8 Ffl and m (Jt) = 1) vs. (p for moldic limestones (Rock Type 4), Permeability Class 4. Symbols refer to different wells. Dashed curve on the plot Is equivalent to the straightline trend on the m plot. Fig. 10 Ffl and m vs. (p for rock types with matrix or chalky porosity only (Rock Type 6). Symbols refer to different wells and reservoirs. An average of 2.0 is suggested. The trends for Permeability Class 2 (Eqs. 6 and 7) would also fit the total (undifferentiated) data set for moldic limestones, and would therefore be suitable for application if no data on permeability are available. Rock Type 5. Rock Type 5 is formed by moldic dolomites, which are very similar to the moldic limestones o except that recrystallization into dolomite has taken place. Crossplots of the available data (Fig. 9) suggest similar trends of m values increasing with increasing porosity, as well as some differentiation with permeability (lowerpermeability samples generally have higher m values than higher-permeability samples). However, the trends are not as clear as those of the moldic limestones. The possible reasons for this difference are discussed later. On the basis of available data, a constant average m value of 2.4 is suggested as a currently reasonable representative for this rock type. Rock Type 6. Rock Type 6 is formed by mudstones and chalks that have matrix porosity (Fig. 3d) without any significant moldic, vuggy, fracture, or fissure porosity. A crosspiot (Fig. 10) shows m values as reasonably constant at around 2.0. Rock Type 7. Rock Type 7 consists of vuggy (moldic) packstones and wackestones that have unconnected or poorly connected porosity in addition to matrix (chalky) porosity (Fig. 3e). This tends to increase m above 2, depending on the amount and degree of interconnection of the vuggy porosity in the rock. The current data are limited, and only a very provisional trend line has been added for this rock type in Fig M " ' POROSITY (%) POROSITY { /.) Fig. 9 Ffl and m (ö = 1) vs. (p for moldic dolomites (Rock Type 5). Symbols refer to different permeability classes. Trends of increasing m with increasing porosity are suggested, similar to those shown for the moldic limestones but less well developed. An average constant m of 2.4 is suggested as reasonably representative for this rock type. Rock Type 8. Rock Type 8 comprises rocks with fracture and fissure porosity (Fig. 3f). Very few consistent laboratory data are available for this rock type. We have excluded most data from fractured plugs on the suspicion that the fractures are induced. The general area of naturally fractured and fissured rocks, as indicated in Fig. 11, is based on literature data and the fact that m values are decreased (toward a theoretical value of unity) by straight pathways present in the rock that also depend on orientation. Fig. 11 combines the results for each ofthe rock types. It should be stressed that while these trends are averages that are underlain by scatter, the value of the plot is to provide separate trends for natural groups based on genetic pore types, and not to advocate the absolute validity of the trends themselves, which should not be applied elsewhere without supportive evidence and confirmation from 1.0 I M ninni^ lill lill iiniiiwip^ I I I I n ni MIIIIIII llllllii^ «"«nn"^ POROSITY ( % ) Fig. 11 A combined Ffl-vs.-(p plot shows the trends suggested for rock types: (1,2) lime and dolomite grainstones, intergranular porosity; (3) sucrosic dolomite, intercrystalline porosity; (4a) moldic limestones, lc<0.1 md; (4b) moldic limestones, /f = 0.1 to 1 md; (4c) moldic limestones, /f=1 to 100 md; (4d) moldic limestones, lf>100 md; (5) moldic dolomites; (6) rocks with only matrix (chalky) porosity; (7) rocks with vuggy and moldic porosity in addition to matrix porosity; and (8) fractured rocks. 160 SPE Formation Evaluation, June 1987 SPE Formation Evaluation, June