SPE Abstract. Introduction

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1 SPE Connate Water Saturation - Irreducible or Not: the Key to Reliable Hydraulic Rock Typing in Reservoirs Straddling Multiple Capillary Windows Chicheng Xu, SPE, The University of Texas at Austin; Carlos Torres-Verdín, SPE, The University of Texas at Austin; Qinshan Yang, The University of Texas at Austin; Elton Luiz Diniz-Ferreira, The University of Texas at Austin Copyright 013, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Annual Technical Conference and Exhibition held in New Orleans, Louisiana, USA, 30 September October 013. 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 does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage 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 SPE copyright. Abstract Irreducible water saturation is an important attribute to quantify reservoir petrophysical quality in terms of flow capacity. High in-situ capillary pressure causes connate water saturation in reservoir rocks to approach the irreducible stage, thereby providing a direct link between electrical and hydraulic conductivities. A new hydraulic rock typing method is developed by relating resistivity-saturation equations with core-calibrated Timur-Tixier s permeability model, both of which are expressions of porosity and irreducible water saturation in this special reservoir context. Petrophysical quantities equivalent to Leverett s reservoir quality index (RQI) and Amaefule s flow zone indicator (FZI) are derived from petrophysical analysis based solely on conventional logs, including gamma ray, neutron porosity, bulk density, and resistivity. We test the new method on a deltaic gas reservoir from offshore Trinidad (Columbus Basin). In the field case, rock typing accuracy based on the new rock typing method is improved by 1% in terms of their contingency coefficients with corebased hydraulic rock types. We also discuss the limitations of the new method in detecting and ranking reservoir rock types in complex contexts of reservoir saturation-height. A new concept, referred to as capillary window, is developed to categorize the applicability of the new rock typing method. At extremely high capillary pressure, irreducible water saturation of different rock types is shown to have significant overlapping, thereby introducing large uncertainty in rock typing. Across capillary transition zones, methods to correct for the presence of free water are necessary to extend the new rock typing method to multiple wells penetrating multiple capillary windows. In the aquifer window, the new method for rock classification is not practical because of the absence of capillary pressure. One important conclusion is that rock typing based on water saturation needs to be exercised with caution in different capillary windows to honor the reservoir s saturation-height behavior. Introduction Irreducible water saturation (S wirr ) is a well-established petrophysical quantity that has been routinely used to characterize reservoir rock quality. It has extensive petrophysical applications in permeability modeling (Tixier, 1949; Timur, 1968) and hydraulic rock typing (Buckles, 1965; Asquith and Gibson, 198). Irreducible water saturation is normally associated with the capillary pressure exerted on the rock-fluid system. It is defined as the pore volume of water that cannot be forced out of the pore system at a given threshold capillary pressure during a primary drainage process. This value is normally used to calculate total hydrocarbon volume in static reservoir modeling. Sometimes irreducible water saturation is interchangeable with critical water saturation, which is defined as the water saturation at which the corresponding water-phase relative permeability falls below a threshold value (Marschall et al., 1995). The latter value is often used to calculate water production in dynamic reservoir modeling. In theory, these two values are very close to each other. The spatial distribution of irreducible water in water-wet rocks has been studied in detail by Zhou et al. (000). Four different forms of trapped water are identified, namely (1) hydration water attached to clay surface area (Hill et al., 1979); () pendular rings due to irregular pore geometry; (3) water trapped in dead ends of the pore network system; and (4) water by-passed in pores during two-phase flow. Some publications categorize (1) as clay-bound water and generally group (), (3), and (4) as

2 SPE capillary-bound water (Peveraro and Thomas, 010). Figure 1 shows the model of pore-filling fluid in shaly sands. While clay-bound water remains truly immobile at reservoir conditions, capillary-bound water can be further reduced by exerting higher capillary pressure. The use of irreducible water saturation for hydraulic rock typing is based on the assumption that hydraulic radius of a rock is anti-correlated with the volume of water residing in small pores. Such a correlation has been proved valid in numerous field cases (Diniz-Ferreira and Torres-Verdín, 01; Xu and Torres-Verdín, 013a). In this paper, we present a detailed analysis of such correlation from a pore-scale view point. Figure 1 Model of pore-filling fluids in shaly sands (modified from Peveraro and Thomas, 010). Connate water saturation can be generally estimated from electrical resistivity measurements using Archie s equation (194) or its multiple variations, including those arising in shaly-sand analysis. In a reservoir with high in-situ capillary pressure, connate water saturation in reservoir rocks approaches the irreducible stage, thereby providing a link between electrical conductivity and hydraulic conductivity. In this paper, we compare irreducible bulk volume of water (BVW =φs w ) with other commonly-used rock typing attributes and then derive log attributes equivalent to Leverett s RQI and Amaefule s FZI for hydraulic rock typing. We test the new method in a deltaic gas reservoir from offshore Trinidad (Columbus Basin) and discuss the limitations of the new method in detecting and ranking reservoir rock types within complex reservoir saturationheight contexts. Rock Typing: Electrical vs. Hydraulic Electrical System. Irreducible water saturation has a direct physical causal impact on rock s electrical resistivity (inverse of conductivity), as indicated by Archie s equation (194): R = R S, (1) m n t wφ wirr where R is bulk electrical resistivity, t R w is electrical resistivity of connate water, φ is porosity in fraction and S wirr is irreducible water saturation in fraction, Winsauer s factor is set to 1.0, and m and n are porosity and saturation exponents, respectively. Higher irreducible water saturation entails higher electrical conductivity or lower resistivity. Hydraulic System. Irreducible water saturation has an indirect petrophysical correlation with rock s hydraulic conductivity. Higher clay-bound water is a direct consequence of higher clay volume concentration (Hill et al., 1979) and higher capillarybound water saturation indicates complex pore geometry and networks (Mohanty and Salter, 198). Higher clay volume concentration and complex pore geometry and network contribute together to a lower hydraulic conductivity or permeability. The relation between permeability and irreducible water saturation has been modeled in a general form (Tixier, 1949; Timur, 1968; Torskaya et al., 009): β φ k = α, () γ Swirr where k is permeability in Darcy,φ is porosity in terms of fraction of bulk volume and S wirr is irreducible water saturation in terms of fraction of pore space volume, α, β, and γ are core-calibrated constants. Under this model, the commonly-used BVW attribute can be associated with porosity and permeability by: or in logarithmic form, BVW 1/ γ β/ γ + 1 1/ γ = φswirr = α φ k, (3) 1 β 1 logbvw = log k + ( + 1) logφ + logα, (4) γ γ γ Table 1 lists the constants used in Tixier and Timur s original formulae. In both Tixier and Timur s formulae, γ is equal to

3 SPE , which ensures a direct anti-correlation between BVW and permeability (or hydraulic radius). Table 1: Exponential constants used in Tixier and Timur s original formulae. α β γ Tixier s Model Timur s Model Comparison of Rock Typing Attributes. Petrophysical attributes related to hydraulic radius are commonly used for corebased hydraulic rock typing, such as RQI (Leverett, 1941), Winland s R 35 (Pittman, 199), and FZI (Amaefule et al., 1993). Formula-wise, these three quantities are all functions of porosity and permeability measured with routine core analysis (Xu and Torres-Verdín, 01). Let stand for any of the above quantities. Their common formulae can be expressed as: log = x log k + ylogφ + z. (5) Noteworthy is that BVW in Eq. (4) also fits into the above general form. We compared the coefficients x, y, and z associated with these formulae in Table and found that absolute values of coefficients x are all close to 0.5, which has a wellestablished physical basis: permeability is proportional to the square of pore-throat radius. However, in the BVW formulae, the weighting factors for porosity are much higher than the other quantities. Figure shows the rock typing results achieved by clustering RQI and irreducible BVW respectively on a set of random porosity-permeability points. The two methods deliver essentially the same rock typing results. This exercise indicates that a good correlation exists between RQI and irreducible IBVW due to similarity in their mathematical expressions. Table : Coefficients of mathematical expressions associated with rock typing attributes. X y z Leverett s RQI Winland s R Amaefule s FZI variable BVW (Tixier) BVW (Timur) Figure Rock typing with RQI (upper panel) and BVW (lower panel) on a set of random porosity-permeability values. Derivation of Rock-Typing Attributes from Logs. From pore-scale understanding, BVW is associated with the small poresize mode of the rock while hydraulic radius is mainly determined by the large pore-size mode (Xu and Torres-Verdín, 013b). For rocks exhibiting simple pore geometries, these two quantities may correlate well to each other. However, such

4 4 SPE correlation may deteriorate in rocks that have undergone significant diagenesis. Therefore, quantities related to hydraulic radius are still preferred to perform rock classification whenever possible. In doing so, we combine Eqs. (1) and () to derive RQI and FZI as follows: β γ mγ φ R β t n n k = α = α( ) φ +, (6) γ S R wirr w and 1 γ β mγ 1 k R + t n n RQI = = α ( ) φ, (7) φ R w 1 γ β mγ 3 k 1 φ R + t n n FZI = = α ( ) φ (1 φ). (8) φ φ R w In Eqs. (7) and (8), only porosity and deep-sensing resistivity are required to calculate RQI and FZI, which enables log-based petrophysical rock classification based on hydraulic radius attribute. Field Case: Deltaic Gas Reservoir, Offshore Trinidad, Columbus Basin The formation under consideration is a sandstone unit deposited in a deltaic sedimentary system in the Columbus Basin, offshore Trinidad (Liu, 007; Xu et al., 013c; Hadibeik et al., 013). Different facies exhibit distinct grain-size distributions and clay volumetric concentrations, which result in different pore-size distributions (Xu et al., 013c). Therefore, a causeeffect relationship exists between depositional facies and hydraulic rock types. The reservoir is saturated with gas and was penetrated with a vertical key-study well drilled with synthetic oil-base mud (SOBM). Approximately 80 ft of whole core were acquired in the upper deltaic sequence for both geological and petrophysical studies. The cored zone was estimated to be at a height above the free-water level (HAFWL) between 400 and 500 ft. High in-situ capillary pressure between gas and water phases ensures that water saturation be close to irreducible saturation. Fluorescence analysis on slabbed whole core confirmed that invasion of SOBM during coring was negligible. Helium porosity, gas permeability (with Klinkenberg effect correction), and Dean-Stark water saturation were measured on 104 preserved core plugs, among which 11 core plugs were further subject to mercury injection capillary pressure (MICP) measurements and 4 core plugs were studied with a laser particle size analyzer (LPSA). The effects of mud-filtrate invasion on well logs are negligible due to very shallow radial length of invasion and absence of free water. Rock Typing from Core Measurements. We performed rock typing with Leverett s RQI calculated from routine porositypermeability data (Fig. 3a) and studied the core-measured water saturation of each rock type (Fig. 3b). It was found that BVW measured with Dean-Stark s method consistently correlated with rock types, i.e., better rock types were associated with lower BVW, while poorer rock types were associated with higher BVW (Fig. 3b). Figure 4 shows the Buckles plot constructed with core porosity and Dean-Stark water saturation, indicating a good correlation between rock types and BVW. The LPSA data from 4 core samples verify that grain size distribution on Wentworth scale (Wentworth, 19) and clay volumetric concentration are also closely related to hydraulic rock types (Fig. 5). In general, smaller median grain size indicates higher clay volumetric concentration and poorer hydraulic rock types. Figure 6 shows that MICP data also consistently correlate with the defined rock types. Better rock types generally exhibit larger major pore throat sizes. Table 3 summarizes the statistical variability of total porosity, absolute permeability, and Dean-Stark water saturation together with BVW for each rock type.

5 SPE (a) (b) Figure 3 (a) Porosity-permeability crossplot grouped according to rock types, and (b) box-plot of core-measured BVW grouped with rock types for the offshore Trinidad field case. Figure 4 Buckles plot constructed with core porosity and Dean-Stark water saturation for the offshore Trinidad field case.

6 6 SPE (a) (b) Figure 5 (a) Grain size distribution data grouped according to rock types, and (b) box plot of clay volumetric concentration grouped according to rock types for the offshore Trinidad field case. Figure 6 MICP data color-coded with classified rock types for the offshore Trinidad field case. RT-4 was not examined with MICP. Table 3: Statistical distributions of total porosity, absolute permeability, Dean-Stark water saturation and BVW, and volumetric clay concentration for each rock type in the offshore Trinidad field case. φ (frac) k (md) Dean-Stark S w (frac) Dean-Stark BVW (frac) C cl (frac) RT ± ± ± ± ± RT ± ± ± ± ± RT ± ± ± ± ± RT ± ± 0.70 ± ± ± 0.07

7 SPE Electrical-Hydraulic Model Calibration. Table 4 list the core-calibrated constants used in Eqs. (7) and (8). Archie s parameters originate from core electrical measurements and Timur-Tixier exponential constants are regressed from 104 core samples measured with routine porosity, permeability, and Dean-Stark water saturation. The Timur-Tixier exponents for this specific field case are quite different from the original formula, which suggests that the model itself should be calibrated on a field-by-field basis. Table 4: Core-calibrated constants used in Eqs. (7) and (8). m n α β γ With the given parameters in Table 4, Eqs. (7) and (8) can be simplified as and k R R RQI ( ) 0.65 ( ) φ R R 1 γ β mγ 1 + t n n 0.9 t 0.3 = = α φ = φ, (9) w w k 1 φ R R FZI ( ) (1 ) 0.65 (1 )( ) φ φ R R 1 γ β mγ 3 + t n n 0.1 t 0.3 = = α φ φ = φ φ. (10) w w Equations (9) and (10) calculate RQI and FZI explicitly from conventional logs including gamma ray, bulk density, neutron porosity, and resistivity. Inversion-Based Petrophysical Analysis. Thin beds are frequently encountered in this particular reservoir. We perform joint inversion of petrophysical properties using gamma ray, density, and resistivity logs based on a multi-layered earth model to minimize shoulder-bed effects (Liu, 007; Sanchez-Ramirez et al., 009). Figure 7 shows the well logs together with the results obtained from inversion-based petrophysical estimation. Permeability is estimated via Eq. (6) with the corecalibrated parameters described in Table 4. Estimated petrophysical properties agree with core data to a satisfactory level. Figure 7 Inversion-based petrophysical analysis and permeability modeling in the offshore Trinidad field case. Track 1: Gamma ray log; Track : Neutron (in apparent sandstone porosity units) porosity and bulk density logs; Track 3: Induction resistivity logs; Track 4: Shale volumetric concentration; Track 5: Porosity from both core and logs; Track 6: Water saturation from both core and logs; Track 7: Permeability from both core and logs. Depth index is in ft.

8 8 SPE Log-Based Rock Typing with RQI-FZI Attribute Clustering. We use Eqs. (9) and (10) to calculate RQI from logs as shown in Fig. 8, Track 4. Rock classification is then performed with k-means clustering (Press et al., 007) on log-derived RQI (Fig. 8, Track 7). For comparison, we also perform rock classification with k-means clustering on a combination of individual attribute including shale volume, total porosity, and water saturation (Fig. 8, Track 8). Contingency tables (Bishop et al., 1975) are used to quantify the agreement between core-derived and log-derived rock types in this paper. In a contingency table, the contingency coefficient, C, is defined as the ratio of diagonal elements to the total number of samples, and quantifies rock typing accuracy as C = χ, (11) N + χ whereas Cramer s V quantifies the strength of the dependence between two variables as V = χ NM ( 1), (1) where N is the total number of rock samples, χ is the Pearson s chi-squared parameter, and M is the number of rock types under comparison. Table 5 shows a contingency table that compares rock types estimated via clustering analysis of a combination of individual attributes including shale volume, total porosity, and water saturation to core-derived rock types; it indicates a low rate of agreement in terms of the contingency coefficient, roughly equal to 63.4%. Table 6 shows a similar contingency table comparing rock types estimated with the new method of clustering log-derived RQI to core-derived rock types. In this case, the rate of agreement increases to 75.4%, thereby effectively reducing the misclassification between neighboring rock types. Figure 8 Log-based rock typing in the offshore Trinidad field case. Track 1: Gamma ray log; Track : Neutron (in apparent sandstone porosity units) porosity and bulk density logs; Track 3: Induction resistivity logs; Track 4: Log-derived RQI; Track 5: Core-derived rock types; Track 6: Rock types derived from logs using log-derived RQI attribute; Track 7: Rock types derived from logs without using the log-derived RQI attribute. Depth index is in ft.

9 SPE Table 5: Contingency table of rock types determined with k-means clustering on shale volume, total porosity, and water saturation. (Cramer s V = 0.47; Contingency Coefficient C = 63.4%). CRT1-4 indicates core-based rock types; LRT1-4 indicates log-derived rock types. Rock Type CRT1 CRT CRT3 CRT4 Total LRT LRT LRT LRT4 0 6 Total Table 6: Contingency table of rock types determined with k-means clustering log-derived RQI. (Cramer s V = 0.66; Contingency Coefficient C = 75.4%). CRT1-4 indicates core-based rock types; LRT1-4 indicates log-derived rock types. Rock Type CRT1 CRT CRT3 CRT4 Total LRT LRT LRT LRT Total Capillary Window Categorization It should be noticed that the new method is only applicable within reservoir sections that exhibit no free or mobile water. In practice, it is necessary to carefully segment the reservoir into multiple capillary windows for implementation of different petrophysical workflows. In general, a hydrocarbon-bearing reservoir under hydraulic communication can be segmented into three capillary windows: irreducible window, transition window, and aquifer window. Figure 9 shows a schematic view of an ideal reservoir straddling multiple capillary windows. Next, we discuss the technical challenges associated with rock typing within each window. Figure 10 shows such a field example from the central North Sea (Xu and Torres-Verdín, 01). The top reservoir is at irreducible water stage and it crosses a 150 ft-thick transition zone above an active aquifer. Figure 9 Schematic view of an ideal reservoir straddling multiple capillary windows under hydraulic communication. Irreducible Window. Water saturation approaches very low values within the irreducible window, which gives rise to large uncertainty in estimating saturation from electrical resistivity measurements. In addition, irreducible water saturation of different rock types may exhibit large overlapping. In the example shown in Figure 3, rock types RT-1 and RT- have large overlapping within the low water saturation end while RT-3 and RT-4 have large overlapping within the high water saturation end. In this case, regrouping or rock types may be necessary for reliable interpretation. For the offshore Trinidad field example shown in this paper, grouping RT-1 and RT- together to constitute a good reservoir rock type may be sufficient in serving some reservoir characterization purposes.

10 10 SPE Figure 10 North Sea field example of a hydrocarbon-bearing reservoir straddling multiple capillary windows under hydraulic communication (Xu and Torres-Verdín, 01). The blue dashed line identifies the oil-water contact ascertained in this well from reservoir pressure data. Track 1: Gamma ray log; Track : Depth; Track 3: Neutron (in apparent sandstone porosity units) porosity, bulk density, and photoelectric factor logs; Track 4: Induction resistivity logs; Track 5: Core permeability; Track 6: Reservoir pressure. Transition Window. The presence of free water in the capillary transition zone breaks the correlation between electrical conductivity and hydraulic conductivity. As shown in Fig. 10, the change of water saturation versus reservoir column height significantly impacts the resistivity log, while reservoir rock types remain almost unchanged as evidenced by core porosity and permeability values. In this case, Xu and Torres-Verdín (01) proposed a correction method by linking Leverett s RQI with in-situ capillary pressure (P c ) and initial connate-water saturation (S w ) via the empirical J-function model (Darling, 005; Torres-Verdín, 01): 1 b Sw Swirr b Sw = Swirr + aj J( Sw) = ( ), (13) a together with Leverett s capillary pressure model, given by: k J S S S RQI = = cos = ( ) φ 1 ( w) w wirr σ cos b σ θ Pc a Pc θ, (14) where S w is initial water saturation, S wirr is irreducible water saturation (which is set to 0.01 lower than the minimum water saturation in the entire reservoir column, Darling, 005); a and b are constants derived from core-measured capillary pressure

11 SPE curves; σ cosθ is the product of interfacial tension and contact angle, which is assumed constant in the same reservoir; P c is in-situ reservoir capillary pressure in psi. However, the method assumes that the reservoir under analysis is hydraulically connected and underwent hydrocarbon migration similar to a primary drainage process. Complex hydrocarbon migration history may give rise to saturation hysteresis which could deviate from the saturation-height relation defined by primary drainage capillary pressure measurements. For example, in reservoirs with complex saturation history, a residual oil zone may form where capillary pressure is negative, which renders this method not applicable at all. In addition, reservoir compartmentalization originated by faults may disturb the reservoir pressure continuity, which imposes additional challenges when estimating in-situ capillary pressure. Aquifer Window. In an aquifer window, where rocks are 100% water saturated, electrical conductivity is only marginally sensitive to the pore system (Xu et al., 013d). NMR measurements are necessary for accurate hydraulic rock typing in an aquifer zone. Figure 11 shows a set of well logs acquired within an aquifer zone in the Gulf of Mexico (Xu et al., 013d). Resistivity logs do not exhibit significant variability. However, NMR logs including logarithmic-average T (TLM), bound fluid volume (BFV), and free fluid volume (CMFF) show good sensitivity to hydraulic rock types. We use two different workflows to classify rock types invoking the same k-means clustering algorithm (Press et al., 007). The first workflow uses NMR logs as input attributes to classify rock types. The second workflow uses resistivity logs as input attributes and invokes the same clustering algorithms to classify rock types. We found that rock classification results obtained with the first workflow (Track 7) exhibit higher resolution and variability than those obtained with the second workflow (Track 8). In other words, resistivity logs do not contribute as much useful information as NMR logs do for rock typing within a water zone. Figure 11 Comparison of resistivity- and NMR-derived rock types in a water-bearing zone. Track 1: Depth; Track : Gamma ray log; Track 3: Neutron (in apparent sandstone porosity units) porosity and bulk density logs; Track 4: Induction resistivity logs; Track 5: NMR T waveform logs; Track 6: NMR free-and bound-fluid volume logs; Track 7: NMR-derived rock types; Track 8: Resistivity-derived rock types. Conclusions Irreducible water saturation has a direct physical causal relationship with electrical conductivity and an indirect petrophysical correlation with hydraulic conductivity in clastic rocks. Consequently, it is possible to perform petrophysical rock classification based on water saturation when reservoirs are water-wet remaining at irreducible water saturation conditions. In the absence of free water, resistivity logs can be quantitatively used to estimate rock hydraulic capacity. However, irreducible water saturation characterizes the small pore-size mode while hydraulic rock types are classified by way of hydraulic radius, which is mainly conditioned by the large pore-size mode. Therefore, petrophysical quantities related to hydraulic radius should be preferentially used for rock classification. We developed a new log-based rock classification method linking

12 1 SPE Archie s equation and Timur-Tixier s permeability model which was verified in clastic reservoirs located within the irreducible window. The new method is not directly applicable to a capillary transition window due to the presence of free water. Strategies for correcting fluid effects on well logs were proposed by considering the saturation-height behavior of the reservoir. Within aquifer windows, electrical conductivity is only marginally sensitive to the pore size, which also renders resistivity logs non-diagnostic of different hydraulic rock types. NMR logs are suggested to be included for rock typing within aquifer windows. Integrated interpretation workflows are still necessary to implement reliable hydraulic rock typing in reservoirs straddling multiple capillary windows for field studies. Acknowledgments We would like to thank BP Trinidad and Tobago (BPTT) for providing the field data used for analysis and verification. The work reported in this paper was funded by The University of Texas at Austin s Research Consortium on Formation Evaluation, jointly sponsored by Afren, Anadarko, Apache, Aramco, Baker-Hughes, BG, BHP Billiton, BP, Chevron, China Oilfield Services, LTD., ConocoPhillips, ENI, ExxonMobil, Halliburton, Hess, Maersk, Marathon Oil Corporation, Mexican Institute for Petroleum, Nexen, ONGC, OXY, Petrobras, PTTEP, Repsol, RWE, Schlumberger, Shell, Statoil, Total, Weatherford, Wintershall and Woodside Petroleum Limited. Nomenclature a : Linear coefficient in empirical J function, [] b : Exponent in empirical J function, [] C : Contingency coefficient, [] C cl : Clay volumetric concentration, [frac] C sh : Shale volumetric concentration, [frac] D : Grain diameter, [mm] J : Leverett s J function, [] k : Permeability, [md] m : Archie s porosity exponent, [] M : Number of rock types, [] n : Archie s saturation exponent, [] N : Number of rock samples, [] P c : Capillary pressure, [psi] R 35 : Pore-throat radius at 35% non-wetting phase saturation, [μm] R t : Bulk electrical resistivity, [ohm.m] R w : Connate water resistivity, [ohm.m] S w : Water saturation, [frac] S wirr : Irreducible water saturation, [frac] T : NMR Transverse relaxation time, [ms] V : Cramer s V, [] x : Coefficient of permeability in rock quality, [] y : Coefficient of porosity in rock quality, [] z : Constant term in rock quality, [] α : Constant coefficient in Timur-Tixier s permeability model, [] β : Porosity exponential in Timur-Tixier s permeability model, [] γ : Saturation exponential in Timur-Tixier s permeability model, [] σ : Interfacial tension, [dyne/cm] θ : Contact angle, [degree] φ : Total porosity, [frac] : Symbol for quantifying rock quality, [] χ : Pearson s chi-squared parameter, [] List of Acronyms and Log Curve Mnemonics AHT10-90 : Array Induction Log (H) with Two Feet Resolution and inch Depth of Investigation AMP_DIST : NMR T Amplitude Distribution AT10-90 : Array Induction Log with Two Feet Resolution and inch Depth of Investigation BFV : Bound Fluid Volume BS : Bit Size BVW : Bulk Volume of Water

13 SPE CMFF : Free Fluid Volume CRT1-4 : Core-Derived Rock Types 1 to 4 ECGR : Environmental Corrected Gamma Ray Log FZI : Flow Zone Indicator HAFWL : Height Above Free Water Level HC : Hydrocarbon HCAL : Caliper Log HDRA : Density Correction Log Hg : Mercury HSK : Hill-Shirley-Klein K_Core : Core Permeability LPSA : Laser Particle Size Analyzer LRT1-4 : Log-Derived Rock Type 1-4 MICP : Mercury Injection Capillary Pressure NPHI : Neutron Porosity Log NRT : Non-Reservoir Rock Type PEFZ : Photo Electric Factor Log (High Resolution) Phi_Core : Core Porosity Res_Pressure : Reservoir Pressure RHOB : Bulk Density Log RHOZ : Bulk Density Log (High Resolution) RQI : Reservoir Quality Index RT : Rock Type SH : Shale SOBM : Synthetic Oil Base Mud TLM : Algorithmic Mean of NMR Transverse Relaxation Time (T ) TNPH_SS : Thermal Neutron Porosity (in Apparent Sandstone Porosity Unit) References Amaefule, J.O., Altunbay, M., Tiab, D., Kersey, D.G., and Keelan, D.K Enhanced Reservoir Description: using core and log data to identify hydraulic (flow) units and predict permeability in uncored intervals/wells. Paper SPE 6436 presented at the SPE Annual Technical Conference and Exhibition, Houston, Texas, 3-6 October. Archie, G.E The Electrical Resistivity Log as an Aid in Determining Some Reservoir Characteristics. Transactions of the AIME, 146(1): Asquith, G. B. and Gibson, C. R Basic Well Log Analysis for Geologists. 1st edition, American Association of Petroleum Geologists Publication. Bishop, Y. M. M., Fienberg, S. E., and Holland, P. W Discrete Multivariate Analysis: Theory and Practice. MIT Press. Buckles, R.S Correlating and Averaging Connate Water Saturation Data. Journal of Canadian Petroleum Technology, 9(1): 4-5. Darling, T Well Logging and Formation Evaluation. Gulf Professional Publishing. Diniz-Ferreira, E.L. and Torres-Verdín, C. 01. Improved Estimation of Pore Connectivity and Permeability in Deepwater Carbonates with the Construction of Multi-Layer Static and Dynamic Petrophysical Models. SPWLA 53rd Annual Logging Symposium, Cartagena, Colombia, 16-0 June. Hadibeik, H., Kwabi, E., Torres-Verdín, C., and Sepehrnoori, K Miscibility Effects of Oil-Base Mud and In-Situ Gas on Conventional Well Logs. 54 th SPWLA Annual Symposium, New Orleans, Louisiana, -6 June. Hill, H.J., Shirley, O.J., and Klein, G.E., Edited by Waxman, M.H., and Thomas E.C Bound water in shaly sands its relation to Qv and other formation parameters. The Log Analyst, XX(3): Leverett, M.C. 1941, Capillary Behavior in Porous Solids. Transactions of the AIME, 14(1): Liu, Z.P Joint Inversion of Density and Resistivity Logs for the Improved Petrophysical Assessment of Thinly-Bedded Clastic Rock Formations. M.S. Thesis, The University of Texas at Austin. Marschall, D., Gardner, J.S., Mardon, D., and Coates, G.R Method for Correlating NMR Relaxometry and Mercury Injection Data. Society of Core Analysts International Symposium, San Francisco, California, 7-10 September. Mohanty, K.K., and Salter, S.J Multiphase Flow in Porous Media: II. Pore-Level Modeling. Paper SPE MS presented at SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 6-9 September. Peters, E.J. 01. Advanced Petrophysics - Volumes 1 and. Greenleaf Book Group, Austin, Texas. Peveraro, R., and Thomas, E. C Effective Porosity: a Defensible Definition for Shaly Sands. SPWLA 51st Annual Logging Symposium, Perth, Australia, 19-3 June. Pittman, E.D Relationship of Porosity and Permeability to Various Parameters Derived from Mercury Injection-Capillary Pressure Curves for Sandstone. AAPG Bulletin, 76(): Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P Section 16.1: Gaussian Mixture Models and k-means Clustering, Numerical Recipes, The Art of Scientific Computing, 3rd Ed., New York: Cambridge University Press. Sanchez-Ramirez, J.A., Torres-Verdín, C., Wang, G., Mendoza, A., Wolf, D., Liu, Z., Schell, G Field Examples of the Combined

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