modeling fluid saturation

This paper was prepared for presentation at the 2005 SPE International Student Paper Contest at the SPE Annual Technical Conference and Exhibition being held in Dallas, Texas, 9-12 October 2005. This paper was selected for presentation by merit of placement in a regional student paper contest held in the program year preceding the International Student Paper Contest. Contents of the paper, as presented, 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.

Abstract Laboratory derived capillary pressure data can be seen as an important tool for the purpose of establishing water saturation-height relationships as a function of rock type, forming the basis for a number of petroleum engineering and geoscience estimates. A modified ‘FZI-λ’ method, capable of giving better estimates of fluid distribution for Australian reservoirs, is proposed. The new methodology is particularly well suited for interpolating among different lithologies and diverse rock types as evident from a comparison with other methods reported in the literature, using a case study of the Griffin area fields.

Reconciliation of capillary pressure data with core and log data can be advantageous for better reservoir description. In this work, the Carman-Kozeny (C-K) equation based Hydraulic Flow Zone Unit (HU or FZU) methodology has been found ideal in characterizing geologic depositional environments and modelling fluid saturation profiles. For this purpose, the concept of ‘Global Characteristic Envelopes’ (GCEs) has been introduced, to analyse geological and petrophysical characteristics and for the integration and correlation among the wells. Capillary pressure data, based on such FZU and depositional grouping, may be further used for modeling saturation profiles over the uncored intervals and allows meaningful averages to be assigned for geocellular modeling and reservoir simulation. Introduction Formation characteristics, both qualitative and quantitative, are used by geologists, petrophysicists and reservoir engineers. As such, laboratory derived capillary pressure data is important in the derivation of water saturation-height relationships as a function of rock type (or lithology) and prevailing reservoir and fluid conditions. While knowledge of fluid wettability conditions and the shape of capillary pressure curves are important, specific rock properties and grain / pore parameters may generally be of equal importance. The quantification of the latter by means of a Carman-Kozeny

based Hydraulic Flow Zone Unit (FZU) methodology can be most advantageous in characterizing various depositional environments and modeling saturation trends.

Conventional saturation-height methods used by the oil and gas industry are critically compared in terms of advantages and disadvantages for a data set for the Griffin area fields. After systematic data validation and processing, quality laboratory capillary pressure data, corrected for specific reservoir situations, is translated into height above free water level (FWL) at reservoir conditions. In a first attempt to derive such profiles, the popular Leverett J-function approach was used to generate universal, normalized saturation curves for the field; however, the results could not bridge across the diversity of rock types. Johnson’s method of utilizing averaged permeability and the more recent Skelt-Harrison method were also unable to model core derived saturation profiles adequately.

To overcome the above limitations, a modified ‘FZI-λ’ approach was developed, using a hydraulic radius based FZU methodology, emphasizing the flow behaviour of rocks. Saturation profiles were created for the Griffin area fields and their validity was checked against saturation profiles interpreted from petrophysical logs. Statistical and error measurement techniques were also used in comparing results from the various methods.

Furthermore, it is shown how such saturation modeling forms part of an integrated approach where core data, petrophysical log interpretation and geological models may be combined into a framework of Global Characteristic Envelopes (GCEs). These GCEs provide information about geological attributes, diagenetic variations and petrophysical characteristics, reflecting sorting, compaction, variations in grain characteristics, pore structure, and energy of deposition for a particular depositional environment under consideration. This FZU methodology allows correlation and integration among Griffin wells, where average properties for each zone, including expected saturation profiles, may be extended over uncored intervals and nearby wells. Such systematic approach in utilizing FZUs, including a number of enhancements and additions to the standard methodology, has resulted in an overall improved method that is able to integrate geological, petrophysical and engineering aspects.

SPE-99285-STU (Student 4)

An Integrated Method for Modeling Fluid Saturation Profiles and Characterising Geological Environments Using a Modified FZI Approach: Australian Fields Case Study S. Biniwale, SPE, Australian School of Petroleum, The U. of Adelaide

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Hydraulic Flow Zone Unit Concepts In recent years, an increasing number of publications have highlighted the merits of hydraulic flow zone unit concepts in fluid flow characterization of porous media. They reveal that reservoirs are indeed heterogeneous and non-uniform systems that are typically comprised of multiple, more homogeneous subgroups referred as flow units (1). Ebanks (2) introduced the concept of Hydraulic Flow Zone Units (HU or FZU) from a geological viewpoint, considering a representative elementary volume within the total reservoir rock, which could be mappable and correlatable in terms of lithofacies. On the other hand, Amaefule et al. (3) explained flow units as a subset of lithofacies, where lithofacies are characterized by macroscopic attributes of lithology, texture, nature of bedding contact and sedimentary structures, partially as a result of original deposition and subsequent modification or diagenesis, such as compaction and cementation (1).

The first, more quantitative ideas were described by Kozeny (4) and Carman (5), giving a theoretical foundation for the dependence of permeability on pore structure and resulting in the so-called Carman-Kozeny (C-K) equation, generally given by:

⎟⎟⎠

⎞⎜⎜⎝

⎛

−= 222

3 1)1( gvse

e

SFk

τφφ

………………..……. (1)

where, k = Permeability, µm2 φ = Effective porosity, fractional bulk volume Fs = Shape factor (2 for a circular cylinder) τ = Tortuosity Sgv = Surface area per unit grain volume, µm-1

Conventional core analysis data is often in a first pass analyzed with simple porosity-permeability cross plots. Behrenbruch and Biniwale (6) have shown the use of the C-K equation offers further insight into rock pore structures and depositional environments. However, the first more practical petroleum engineering applications using distinct zones (hydraulic units), providing information about depositional and diagenetic controls on pore geometry, were given by Amaefule and Barr (3, 7). They used a modified C-K equation that includes a log-log plot of the ‘Reservoir Quality Index’ (RQI), which is related to the hydraulic radius and a ‘Normalized Porosity Index/Porosity Group’ (PG), where φ is the porosity as a fraction. These relationships may be summarized as follows:

⎟⎟⎠

⎞⎜⎜⎝

⎛−

=e

ez 1 φ

φφ ……………………………………………. (2)

e

mdkmRQIφ

µ )(0314.0)( = …………………..……...…. (3)

⎟⎟⎠

⎞⎜⎜⎝

⎛=

gvs SFmFZI

τµ 1)( ………………..……………..…. (4)

FZI RQI z logloglog += φ …………………………. (5) When RQI is plotted against PG, the relationship results in

a straight line with a unit slope and the intercept defines the characteristic ‘Flow Zone Indicator’ (FZI). This offers flexibility for a practical implementation of the C-K equation without exact determination of parameters such as pore throat shape factor, tortuosity and surface area. Characterisation of Geological Environments

While in many instances, practitioners have used the C-K equation in a more mechanistic manner, to identify rock similarities, Behrenbruch and Biniwale (6) have presented a more systematic approach in analyzing flow zone units. They have proposed a classification framework, emphasizing the importance of properly integrating geological knowledge, for clastic formations that may be generally applied. This modified FZU methodology considers depositional environments as the highest level of classification and incorporates rock type (i.e. grain size, sorting, bedding and diagenesis) as a secondary classification. Therefore, from a practical perspective, following modified definition of hydraulic units is proposed: “Hydraulic Units are lithologically unique geological layers or lithofacies (or simply facies), as manifested by petrological characteristics, and are correlatable in terms of the hydraulic radius, by strict adherence to geology.”

“Global Characteristic Envelopes” (GCEs) for characterising geological depositional environments, which address the large number of rock attributes in a systematic and hierarchical manner, is the key feature of such FZU methodology. Biniwale and Behrenbruch (8) report the comparison, and describe the analysis, of a large data set covering several Australian offshore basins. Therefore, GCEs may be seen as an aid in FZU modeling, by mapping regions or envelopes in the C-K space as a function of geological depositional environments.

Altunbay and Barr (9) were first to describe factors affecting hydraulic qualities of rocks, mainly controlled by pore geometry, which in turn is a function of mineralogy (type, abundance, morphology and location relative to pore throats) and texture (grain size, grain shape, sorting and packing). All these attributes are primarily influenced by geological deposition and subsequent diagenesis, consequently controlling reservoir quality. Such depositional trends and diagenetic aspects are then generally responsible for the location of individual FZUs within a particular characteristic envelope, and conclusions may be further supported by using photomicrographs and SEMs.

Saturation Profile Modelling The accurate determination of saturation-height relationships, based on individual facies, is an important prerequisite for the delineation of hydrocarbons within a reservoir (10). Capillary pressure data and saturation-height relationships form the basis for a number of engineering and geoscience applications. Several methods are available in the literature for determining

SPE Student Paper 3

field-wide saturation-height functions based on capillary pressure data and log derived data, mainly utilizing parameters related to rock typing, porosity and permeability, all for the purpose of grouping similar relationships (11-18). Many of these methods, in addition to averaging methods and parameter grouping, use curve fitting and curve smoothening techniques, in which original data may be more or less honoured. Leverett-J Method:

Leverett (15) is generally regarded as the first person to introduce an equation, widely known as the Leverett-J function for normalization of capillary pressure data, assuming a close relationship between porosity and permeability: ………….…………………….. (6) Sw represents water saturation for a given capillary pressure, Pc is capillary pressure at any height above the free water level in psia, σ is the interfacial tension (dyne/cm), k is permeability in md and φ as the porosity as a fraction. signifies the mean hydraulic radius. By grouping rock types of similar pore structure, the ‘J-function’ attempts to convert all capillary pressure data, as a function of water saturation, to a universal curve. However, this generalized method often gives poor results for diverse rock types and is also inappropriate for a large range of permeability values.

Johnson’s Method:

Johnson (16) proposed ‘permeability-averaged’ technique, grouping capillary pressure data on the basis of permeability, for saturation modeling. Water saturation and permeability relationship can be approximated by straight lines on a log-log plot and can be represented by reduced major axis regression analysis as described by the equations:

….………….……….. (7)

…………..……... (8) Equation 8 represents the empirical correlation used by Johnson, correlating capillary pressure and height above Free Water Level (FWL) with water saturation and core permeability. The constants A, B and C are derived from a series of capillary pressure plots. Although, this technique is relatively simple and does not require irreducible water saturation (Swir) values, it is not universally applicable and fails to adequately predict saturations for lower permeability values and short distances above the FWL. Skelt-Harrison Method:

Based on Thomeer’s original set of pore geometrical factors, relating saturation to capillary pressure, the Skelt- Harrison (17, 18) method uses both capillary pressure and log-derived data for saturation modeling. The general form of the relationship, relating saturation with height above FWL, is given by:

….…………..……….. (9)

Where, H is the height above the FWL and a, b, c and d are

constants determined by regression and optimization of core and log data. Each data point may be assigned different weighting during curve fitting, to honor the data in case of large fields or for refined reserves calculations. Although this method provides better flexibility and a more practical approach, the link to permeability is less clear. Lambda Function: Field and experimental results show that a lambda function approach tends to fit most capillary pressure relationships very well. In the Leverett-J function a relationship between permeability and porosity is needed, together with knowledge of aerial variation of these parameters (19). This aerial variation may be addresses by dividing rocks into effective porosity or permeability classes as proposed by the ‘Lambda function’. There are various forms of the lambda equation available in the literature, which may be written as: …….………….….………….. (10) …………...…….….………….. (11)

Where a, b and λ are regression constants, dependent on porosity and permeability relationships. Sw is generally expressed as a fraction of pore volume, h is the height above the FWL. The approach was developed to better describe the shape of capillary pressure curves, representing both longer and shorter transition zones and the formulation works well for prediction but is less satisfactory for Swir predicting the entire capillary pressure curve. Modified ‘FZI-λ’ Function A flow zone unit approach, being closely associated with geological and petrophysical parameters, has been used for saturation modeling. A modified ‘FZI-λ’ method has, therefore, been proposed and compared with other saturation prediction models. The new model may be described as follows: .….………...……….. (12) Sw is expressed as a fraction of the pore volume and A, Hd and λ are parameters, being simple functions of FZI, as follows: ……………...….……………...….. (13)

……………...….…………..…….. (14) …………...….…………..…….. (15)

where, H = the height above the free water level

φθσkPcSJ w cos

)( =

φ/k

bkaS w += )log()log()log()log( kAPBS C

cw −= −

c

wh dHbaSS ⎟

⎠⎞

⎜⎝⎛

+−

=−= exp1

λ−= haS w

bhaS w += − λ

λ−−= )( dw HHAS

2

1AFZI

AA =

2

1λ

λλFZI

=

2

1Hd

FZIHH =

4 SPE Student Paper

Pd = the pore entry pressure. Hd = the entry height, equivalent height at which oil first enters the pores, equating to the pore entry pressure. A1, A2, λ1, λ2, H1 and H2 are specific constants, evaluated from capillary pressure data and determined by optimization techniques, being specific for each field. Parameter Hd offers more flexibility for handling various entry heights in modeling. Using FZI also allows for a direct link with other parameters that characterize a particular zone, e.g. relative permeability or other petrophysical parameters. This method gives more realistic saturations, even close to the FWL where other methods are less satisfactory. Based on Brooks and Corey’s equation, Udegbunam and Amaefule (21) have utilized a similar formulation (Equations 14 and 15), relating the terms λ and Pd with FZIs.

This modified method uses FZI as a correlation parameter for saturation modeling, which automatically incorporates the hydraulic radius (Leverett J function), porosity grouping (lambda function) and offers flexibility for tuning specific relationships using regression and optimization techniques (Skelt-Harrison method). Overcoming shortcomings of earlier methods, the improved methodology offers a better solution for saturation modeling.

Griffin Area Fields: Case Study Geology and Stratigraphy

The Griffin area fields are located in the southern Carnarvon basin, offshore Western Australia and mainly consist of three fields: Griffin, Chinook and Scindian. The Griffin main structure lies along a northeast-southwest Triassic high trend known as the Alpha Arch (6, 22, 23). The main producing reservoir zones are the Birdrong and Zeepard formations trapped in early Cretaceous sediments, as shown in Fig. 1. The Mardie Greensand together with the Muderong shale acts as a seal for the pay zone. The Zeepaard formation is of excellent reservoir quality and is the primary reservoir, separated from the relatively poor quality Birdrong formation by the Intra-Valanginian unconformity. The location of wells and the distribution of oil in each of the reservoirs is shown in Fig. 2. While natural edge water has been effective, resulting in a high recovery factor for the generally good quality Zeepaard formation, a number of shale and low permeability barriers have resulted in uneven displacement. By contrast, the overlying Birdrong formation shows much more heterogeneity and facies variation, where average formation characteristics are relatively poor (8, 25). Data Validation and Analysis Validation is the most important step before processing conventional core analysis data, in order to generate reliable results (24). For every well in the Griffin area, the core analysis data validation step was carried out, and all data is categorised into various classes, as explained in previous publications (6, 8). The main data class omitted from analysis consists of non-reservoir data (data with exceptionally low permeability and/or porosity), atypical data (data which appears atypical or

non-representative for a particular deposition) and scattered data (data scattering on both porosity-permeability and C-K plots). In total, 5-10% of data has been removed from the analysis and the remaining dataset was used for further, detailed analysis and study (8, 24).

In terms of capillary pressure plugs, 21 samples were available for the Griffin area fields, mainly from Griffin-1, 2, 3, Ramillies-1 (downthrown edge block to the Griffin main field) and Scindian-2, see Fig. 2. The above mentioned validation methodology was extended over the entire data set and also for validating Special Core Analysis (SCAL) results for various depositional environments. Capillary pressure plug samples for the Griffin-2 well are shown in Table-1 and the figures 3 and 4 are presented in order to give some appreciation for the SCAL validation methodology, for Griffin-2. The larger symbols indicate SCAL samples and the relative affinity of such samples with other conventional core analysis samples is a measure of their representativeness for a particular formation interval (depositional environment). More specifically, SCAL samples 18 and 21 (Figures 3 and 4), are not representative of the geological interval considered. For sample 21, porosity and permeability values are relatively higher (Figure 3) and a higher RQI value is indicated in the C-K plot of Figure 4, whereas sample 18 shows poor quality, even less than average quality for the group, meaning that the SCAL analysis results for this plug are likely to be non-representative for the overall group. In these cases, the mentioned SCAL sample results require adjustment before being used in upscaling and reservoir simulation (26). Careful review of conventional core analysis data can thus be invaluable in validating the applicability of special core analysis derived relationships, such as relative permeability, and this has largely been the impetus for the current study.

Characterization of Geologic Depositional Environments

As per common practice, porosity-permeability cross plots were first created to identify clustering of various facies for specific depositional environments. Following the FZU methodology described, tentative clusters are then translated into the C-K space. As mentioned above, the Zeepard formation is of very good quality, particularly when compared to the poorer Birdrong formation, and this difference can be clearly seen from Fig.5, where the bold lines indicate FZI lines for the Zeepard Formation and the dotted lines indicate FZI lines corresponding to the Birdrong formation. In addition to showing the GCE for the Griffin area fields, Fig. 5 also demonstrates quality zonation, ranging from Q1 (best) to Q5 (poorest). The Zeepard formation falls into Q1-Q3, which consists of a highstand system tract and is mainly dominated by stacked distributary channels, with FZI values ranging from 5-50 (8, 25). On the other hand, the Birdrong Formation falls into Q3-Q5 zones, developed from a combination of lowstand and transgression systems and is dominated by interbedded fine-grained sandstones and claystones, being characteristic of poor quality, lower shoreface deposition.

Correlation among wells: Griffin-1, 2 and 3 is shown in Figs. 6 and 7, where initial correlation has been based on

SPE Student Paper 5

geological deposition and is subsequently compared with petrophysical log correlation. In Fig. 6, FZI values are compared with the gamma ray logs for each well, showing a good correspondence between the two. In Fig. 6, geologically correlatable zones are shown by dotted lines and shows zones with similar FZI values have been integrated and are represented by single, straight lines as shown in Fig. 7.

Based on log correlation, Fig. 7 shows a stratigraphic cross section, referenced to the marker shale layer 4.1. Cored intervals and corresponding depths are shown in the Fig. 7. Major shale breaks are indicated by dark dotted lines, with shale layer 4.1 being cored in Griffin-1 and Griffin-2 wells. It can be concluded that the HU3 zone in Griffin-2 and 3 wells is correlatable and the same zone could be identified as the HU5 in the Griffin-2 well, represented by number 15. This zone is correlatable due to geologic similarity as indicating similar FZI values, which could be traced back to C-K space, as marked by line 15 shown in Fig. 5. After the similar analysis, the other correlatable zones, with similar geological depositions and overall same flow properties, are indicated by FZI lines marked by 8, 9, 12, 13 and 19. After establishing such correlation and integration the relationships can be extended over uncored intervals of wells.

Fluid Saturation Modelling

Table 1 summarizes drainage capillary pressure laboratory data for Griffin-2. All data was first corrected for laboratory conditions and then translated to specific reservoir situations by using following equation.

……..…….……………….. (16)

Where σ is interfacial tension between the fluids in dynes/cm, θ is the contact angle relating wettability and rock-fluid interaction in degrees. It is realized that there is some uncertainty in appropriate interfacial tension and contact angles, as well as conversion between different pressure conditions, giving to a systematic shift in correlations (10, 16). Fig. 8 gives a comparison of drainage capillary pressure data for laboratory conditions (represented by solid lines) and the corresponding reservoir conditions (indicated by symbols).

Similar to the validation procedure described for the SCAL (relative permeability) explained above, capillary pressure plugs were also first screened. Atypical plug samples are indicated within boxes in the respective figures. Data for reservoir conditions is then translated to height above the free water level (FWL).

The comparative saturation modeling study has been carried out for the Griffin-2 well. Initially, the Leverett-J function approach was used for generating normalized capillary pressure curves as shown in Fig. 9, indicating that there are different rock types present and realistically saturation for these groups could not be modeled by assuming one universal saturation curve. Porosity, permeability or facies grouping would be expected to give some improvement, but in general this method is not adequate for diverse rock types.

As saturation is closely linked to permeability, permeability grouping was carried out and relationships with saturation are plotted on log-log plots as proposed by Johnson (16). Figures 10 and 11 indicate results derived for Griffin-2 using Johnson’s averaged permeability method. Fig. 11 indicates predicted saturation compared with respective measured values. For very low and very high permeability plugs, one can see a good match, but otherwise the method fails to predict the overall saturation trend. Another shortcoming observed for this method is that for low permeability and shorter height above the FWL, the method predicts saturation values greater than one.

It was found that the Skelt-Harrison method generally works better than the two techniques discussed above, at least for Griffin-3 and Ramillies-1; however, for Griffin-2 this method failed to give satisfactory saturation profiles that match measured values. Up to 15 m above the FWL, a reasonable match is indicated, but for greater heights above the FWL and lower quality samples, the match deviates significantly, as presented in Fig. 12. This has led to an attempt to devise an improved formulation using Lambda functions and permeability grouping, as shown in Fig. 13. However, at distances of more than 40 m above the FWL the method still fails to model saturations accurately.

Fig.14 shows saturations modeled for the Griffin-2 well using a modified FZI-λ method. In this case, results show a satisfactory match with the measured saturation values, underpredicting saturation slightly at elevated distances above the FWL. However, overall saturation trends could be modeled quite accurately, for different values of FZI and permeability, when compared to the other methods. As further validation of this match, capillary saturation profiles were compared to log derived saturation profiles. Fig.15 shows such comparison for zones 2 and 4, showing good agreement. Zone 1 is constituted mainly of poor quality Birdrong formation with very few data points available in cored intervals, making it difficult to correlate predicted saturations with log derived profiles. The modified FZI-λ method was also applied to Griffin-3 and Ramillies-1 wells, where predicted saturations show a very good match with measured values, Figs. 16 and 17.

Statistical Comparison of Saturation Prediction Methods

Fig. 26 gives a comparative overview of the saturation modeling methods: Leverett-J function, Johnson’s method, Skelt-Harrison and modified FZI-λ methods, where the intention is to produce a plot of height above FWL against water saturation using porosity, permeability or FZU as a third parameter axis. Leading up to this final result, Figs. 18, 20, 22 and 24 show plots that compare model predicted water saturation with saturation determined from core. As evident, the modified FZI-λ method gives the best results with R2 (correlation coefficient) values ranging from 0.98-1, followed by the Skelt-Harrison method, whereas the other two methods indicate lesser correlation.

( )( ) ⎥

⎥⎦

⎤

⎢⎢⎣

⎡=

)(

)()()( cos

cos

lab

reslabcresc PP

θσθσ

6 SPE Student Paper

Differences between water saturation predicted by each model and core measured saturations can be seen on histograms plots on a comparable basis in Figs. 19, 21, 23 and 25. The superior performance of the modified FZI-λ method is indicated in plots of Figs. 24 and 25, with mean difference 0.0014 and standard deviation of 0.0016. Table 2 presents a comparison of error metrics for the described methods, where the modified FZI-λ method has performed the best with a mean average error (MAE) of 0.000136 and root mean square error (RMSE) of 0.0088 for the Griffin-2 well. Similarly, in case of the Griffin-3 and Ramillies-1 wells, modified FZI-λ method show most excellent results with high correlation coefficient and the lowest values for MAE and RMSE.

Fig. 27 summarises the multidisciplinary approach advocated, reconciling geology (G1-G4: showing core analysis, facies zonation techniques, photomicrographs and SEMs), reservoir engineering (R1-R2: capturing porosity-permeability and C-K relationships) and petrophysics (P1-P4: integrating capillary pressure and log data with modified FZI-λ approach). This integration of disciplines is thus paramount in providing consistent and meaningful averages of data that may be assigned to grid blocks for geo-cellular modeling and in reservoir simulation. In offering greater flexibility for modeling various relationships, the improved saturation modeling method is able to give an extra dimension to formation evaluation techniques.

Summary and Conclusions 1. A practical and theoretically based, improved flow zone

unit (FZU) approach has been outlined, which represents an ideal method for characterizing formations and modeling saturation profiles. It leads to enhanced reservoir description, by integration of various core analysis results utilizing a multidisciplinary approach that covers geology, petrophysics and reservoir engineering.

2. A systematic data validation and analysis technique has been proposed for conventional core and SCAL sample data, where the determination of representative relationships for SCAL samples is of paramount importance.

3. “Global Characteristic Envelopes” (GCEs), having a unique classification scheme potential, may be of considerable assistance in depositional characterisation and the analysis of major controlling factors of reservoir quality, as demonstrated by the Griffin area case study.

4. Adhering strictly to geological interpretation, the modified FZU methodology has been found to be useful for correlation and integration among wells, as exemplified by the Griffin area case study.

5. A modified FZI-λ saturation-height function approach, which automatically incorporates the hydraulic radius and porosity grouping, has been presented. Superiority of the functional form is manifested by the statistical comparison with other published methods, where this method offers greater flexibility and accuracy for treating diverse lithologies, as shown for the selected Griffin area fields.

Acknowledgments The author would like to gratefully acknowledge the sponsors: BHP Billiton, ChevronTexaco, Santos Ltd and Woodside Energy for their financial support and permission to publish their data and analysis results. The author would also like to thank Prof. Peter Behrenbruch for his enormous support and valuable technical guidance in writing this paper. References 1. Amaefule, J. O. and Keelan, D. K.: “Mature Niger Delta

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24. Biniwale, S.: “Hydraulic Flow Zone Unit Characterisation and Mapping for Australian Geological Depositional Environments” PhD Thesis, The University of Adelaide, Australia.

25. Workman, L. J., Slate, T.V. and Oke, B.F.: “The Griffin Development- Flying high on infill success,” paper SPE 77920 presented at the 2002 Asia Pacific Oil and Gas Conference and Exhibition, Melbourne, Australia, Oct. 8-10.

26. Goda, H. and Behrenbruch, P.: “Using a modified Brooks-Corey Model to study oil-water relative permeability for diverse pore structures” paper SPE 88521, presented at the 2004 Asia Pacific Oil and Gas Conference and Exhibition, Perth, Australia, Oct. 18 –20.

* Non-representative plug samples with atypical trends for normal saturation profilesTable 1: Drainage capillary pressure laboratory data after FZI and depositional grouping, Griffin-2 well

**

Table 2: Comparison between modified FZI- λ method and other Conventional Methods for Griffin 2, 3 and Ramillies-1

Well Error Measurements

Leverett-J Function

Johnson’s Method

Skelt-Harrison Method

Modified FZI-λ Method

Griffin-2 R2 0.90 0.88 0.94 – 1.00 0.98 – 1.00

Griffin-2 MAE 0.000037 0.03580 0.01927 0.000136

Griffin-2 RMSE 0.0667 0.0846 0.0508 0.0088

Griffin-3 R2 0.77 -- 0.87 0.98

Griffin-3 MAE 0.0000279 -- -0.000063 -0.0000436

Griffin-3 RMSE 0.0977 -- 0.0729 0.0379

Ramillies-1 R2 0.93 -- 0.91 0.99

Ramillies-1 MAE 0.000558 -- 0.207 -0.000182

Ramillies-1 RMSE 0.0577 -- 0.0819 0.0165

8 SPE Student Paper

Fig. 2: Griffin Area- Zeepaard reservoir top structure mapFig. 1: Griffin Area - Stratigraphy

Fig. 3: Data Validation and SCAL sample representiveness; porosity-permeability cross plot, Griffin-2 well.

Note: Samples within boxes indicate non-representative plug samples

SPE Student Paper 9

Fig. 4: Data Validation and SCAL sample representiveness; Carman-Kozeny plot, Griffin-2 well.


Fig. 5: Hydraulic zonation by quality; Carman-Kozeny plot, integrating Griffin area wells.

10 SPE Student Paper

Fig. 6: Correlation within Griffin area wells1, 2 and 3; gamma ray and flow zone indicator vs. depth

Fig. 7: Birdrong and Zeepard Formations – stratigraphic cross section, integrating FZUs within Griffin area wells.

SPE Student Paper 11

Fig. 8: Drainage capillary pressure; comparison at laboratory and reservoir conditions, Grifin-2 well.

Note: Plug Samples within boxes indicate atypical saturation trends

Fig. 9: Leverett-J function; normalized capillary pressure, Griffin-2 well.


Fig. 10: Johnson’s method; straight line relationship between saturation and permeability, Griffin-2 well.

Fig. 11: Johnson’s method; normalized capillary pressure saturation modeling, Griffin-2 well.


Points from drainage capillary pressure data Corresponding saturation prediction (calculated)


Fig. 13: Lambda function (using permeability grouping); saturation modeling, Griffin-2 well.


Fig. 12: Skelt-Harrison method; capillary pressure saturation modeling, Griffin-2 well.



Fig. 15: Modified ‘FZI-λ’ method (using FZI and depositional environments grouping); comparison with log saturation, Griffin-2 well.

Fig. 14: Modified ‘FZI-λ’ method (using FZI and depositional environments grouping); saturation modeling, Griffin-2 well.



Fig. 16: Modified ‘FZI-λ’ method (using FZI and depositional environments grouping); saturation modeling, Griffin-3 well.

Non-representative plug sample


Fig. 17: Modified ‘FZI-λ’ method (using FZI and depositional environments grouping); saturation modeling, Ramillies-1 well.

Non-representative plug sample



Fig. 20: Comparison between Johnson’s function predicted water saturation and core derived saturation, Griffin-2 well.

Fig. 21: Difference between Johnson’s function predicted water saturation and core derived saturation, Griffin-2 well.

Johnson’s Function Mean = 0.0358 Std Dev = 0.0771

Fig. 22: Comparison between Skelt-Harrison function predicted water saturation and core derived saturation, Griffin-2 well

Fig. 23: Difference between Skelt-Harrison function predicted water saturation and core derived saturation, Griffin-2 well

Skelt-Harrison Function Mean = 0.019 Std Dev = 0.0536

Fig. 18: Comparison between Leveret-J function predicted water saturation and core derived saturation, Griffin-2 well.

Fig. 19: Difference between Leveret-J function predicted water saturation and core derived saturation, Griffin-2 well.

Leverett- J Function Mean = 0.00004 Std Dev = 0.0671


Fig. 26: Comparison of various methods for saturation modeling

After Biniwale and Behrenbruch (2005)

Fig. 24: Comparison between modified FZI-λ function predicted water saturation and core derived saturation, Griffin-2 well.

Fig. 25: Difference between modified FZI-λ function predicted water saturation and core derived saturation, Griffin-2 well.

Modified FZI-λ FunctionMean = 0.0014 Std Dev = 0.0016


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