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Keywords: Reservoir characterization, rock typing, capillary tube model, permeability equation *) Student of Petroleum Engineering – Institut Teknologi Bandung **) Supervising Lecturer of Petroleum Engineering – Institut Teknologi Bandung INTRODUCTION Permeability is defined as the ability of porous rock to transmit fluids. Permeability is one of the most important parameters in reservoir characterization and description. The value of permeability is essential in reservoir management and field development. It is used to determine production rate, completion and perforation design, enhanced oil recovery patterns, and injection conditions (Ahmed et al., 1991). However, the in-situ measurement method for permeability is yet to be found, unlike porosity and fluid saturation where technology has allowed the determination of those parameters to be conducted within reasonable accuracy. On the other hand, the determination of permeability still requires coring or drill-stem testing (DST) (Timur, 1968). However, these two options cannot be done to the whole interval of a well due to the high cost. As an alternative, researchers have proposed several correlations to predict permeability from porosity and irreducible water saturation, among them are Tixier (1949), Timur (1968), and Coates (1974). Unfortunately, these correlations were derived empirically without considering geological aspects. Therefore, these correlations cannot be applied universally because permeability of a rock is determined by wide varieties of factors: pore size and geometry, pore size distribution, clay content, etc. (Rushing et al., 2009). Due to this complexity, it is necessary to find a suitable method which enables us to generate accurate permeability equation. OBJECTIVES 1. To apply a rock typing method derived from Capillary Tube Model to determine the rock types of a sandstone reservoir using Routine and Special Core Analysis, and geological data. 2. To develop a method to accurately predict permeability. BACKGROUND THEORY Rock Typing. One of the most acknowledged definition of rock types was given by Archie (1950), who define rock type as units of rock deposited under similar conditions which experienced similar diagenetic processes resulting in a unique porosity-permeability relationship, capillary pressure profile and water saturation for a given height above free water in a reservoir. By this definition we can infer that rock typing relates physical properties –i.e. porosity, permeability, water saturation- with geological characteristics of reservoir rocks. Therefore, rock typing should be the basis of permeability prediction. According to Rushing et al. (2009), there are three kinds of rock types: 2

•

Depositional. These rock types are defined within context of the large-scale geologic framework and represent the original rock properties present at deposition. Rock types are grouped according to similarities in composition, texture, sedimentary structure, and stratigraphic sequence as influenced by depositional environment, energy, and morphology. These parameters are evaluated from core descriptions. • Petrographic. These rock types are also grouped according to geological framework established from depositional rock types, but are based on a pore-scale microscopic imaging of the current pore structure as well as the rock texture and composition, clay mineralogy, and diagenesis. • Hydraulic. These rock types are quantified based on physical rock flow and storage properties as controlled by the pore structure. Correct identification of hydraulic rock types should result in a unique permeability-porosity relationship. Rock typing is important in establishing an appropriate reservoir zonation and should be in accordance with facies distribution in order to build good reservoir model. Rock typing, if it is applied properly, can be very effective in constructing consistent permeability and initial water saturation models for geological and reservoir-simulation modelling. This consistency will increase confidence in the hydrocarbon-in-place estimations and in the dynamic reservoir performance predictions (Guo et al., 2005). One of the most generally used methods in rock typing is J-function which was developed by Leverett (1941). The concept is that a single J-function curve is the representation for a group of rock samples having similar pore geometry, which is accomodated by the term (k/φ)0.5, and pore structure, which is indicated by a similar capillary pressure curve. Implicitly, Leverett's Jfunction concept stated that both pore geometry and pore structure play an important role in defining a rock type or a flow unit. Based on a set of mercury injection capillary pressure data, Permadi (2009) then stated that the term (k/φ)0.5 correlates very well with volumetric average of mode values of pore aperture size distribution. This average pore size was called as effective hydraulic diameter of the pores. The obtained empirical correlation, in terms of parameters that determines permeability, is exactly the same as theoretically derived equation for the capillary tube model. This suggests that capillary tube model could be applied as an approach in the characterization of pore geometry and pore structure which is essential in rock typing. Capillary Tube Model. Initially, capillary tube model equation was used to determine the permeability of a medium consisting of straight cylindrical capillary tubes. Later, this equation became the basic theory of Hydraulic Flow Unit which is used to predict the permeability of a porous medium. The following equation is proposed by Scheidegger (1960) to determine the permeability of a medium consisting of straight cylindrical capillary tubes: 𝑘 = φ 𝑑̅ 2 /32 ............................................... (1) When 𝑑̅ is in microns, φ is in fractions, and k in md, then Eq.1 becomes: 3

𝑘 = 31.6875 φ 𝑑̅ 2 ....................................... (2) For tortuous capillary tubes with tortuosity T, Eq.2 may be written as: 𝑘 = 𝐴 φ3 /(𝑇𝑆 2 ) .......................................... (3)

where 𝑇 =

𝐿𝑎

, 𝐿𝑎 is the average distance for fluid particles to travel through the tubes from inlet to outlet, L is the straight length of the medium, and 𝑆 = 4φ/𝑑̅ , which is the definition for specific surface area. A is a constant and 𝑇𝑆 2 is the internal characteristic of the tubes, representing the variation of tube sizes and the structure of the tubes, and determines how ease a fluid can pass through the tubes. The lower the value of 𝑇𝑆 2 the easier fluid passes through the tubes. For porous rocks, tortuosity T and specific surface area S are difficult to measure, but Eq.3 can be adopted and written in the following form: 𝑘 = 𝐶 φ3 or 𝐶 = 𝑘 ⁄φ3 ....................................................... (4) where C is pore structural parameter that takes tortuosity and specific surface area into account, as can be identified from Eq. 3 above, or may be simply called as hydraulic conductivity of the pores, and has the same unit as permeability k. Hydraulic conductivity increases as tortuosity and/or specific surface area decreases. Two rock samples may have the same values of C but the difference in the arrangements of grains, sorting, grain orientation, and other factors that affect the pore distribution could also result in different permeability between the two. On the previous section, it has been stated that both pore geometry and pore structural are two parameters that must be taken into account in rock typing. As an approach to this the theory, Eq. 4 shall be modified to separate the parameters representing pore geometry and pore structure. 𝐿

�𝑘�φ = φ √𝐶 ...............................................(5)

The left term at Eq. 5 is the parameter that represents pore geometry based on Leverett's proposal, and the right term is the parameter reflecting pore structural condition. Eq. 5 explicitly gives the idea that a log-log plot of (𝑘/φ )0.5 versus C of samples having similar pore geometry and pore structure shall exhibit a straight line with maximum slope of 0.5. It means that Eq. 5 may be applied in pore architectural identification, i.e. pore geometry and structure, of various rock samples in rock typing. DATA The data used in this study consists of rock samples originated from 3 wells located at Xfield. The rock samples were taken from a sandstone reservoir which is located in North West Java Basin, Indonesia. The depositional environment of the sandstone formation is fluvial-deltaic and lacustrine. The available data consists of 42 conventional core samples and 6 special core analysis (SCAL) from well X-2, 21 conventional and 19 sidewall core samples from well X-5, and 28 sidewall core samples from X-7. The core samples show a wide range of porosity and permeability values. The values of porosity range from 1.7% to 29.7%, while values of permeability range from 0.1 md to 488 md.

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Fig. 1 is a porosity-permeability plot that shows how the data points are scattered, and why predicting permeability based on a simple porosity-permeability relationship will not give satisfactory result. DATA PROCESSING Rock Typing. J-function plot, a widely used rock typing method, was made based on 6 samples from SCAL data (Fig. 2) and indicated that there were 2 rock types. Later, this result would be compared to the result of rock typing using log-log plot of (𝑘/φ )0.5 and C. Then, the values of (𝑘/φ )0.5 and C were plotted on a log-log scale (Fig. 3). Previously, the values of those two terms were calculated based on all core samples, i.e. routine and SCAL, where the term C was determined using this following equation: 𝐶 = 𝑘� .............................................(6) 1014φ3 where k is in milidarcy and φ is in fraction. In accordance with the J-function plot, 6 data points from SCAL samples in Fig. 3 also shows that there were 2 rock types. Meanwhile, data points from the routine core analysis were mildly scattered, thus drawing straight lines that identify all rock types was difficult, especially in the area where the straight lines seemed to cross each other. Core qualitative description - such as color, grain size, sorting, angularity, etc. - was opted to solve this problem due to unavailability of petrographical data. While identifying the geological description of each rock types, it was revealed that most of the sidewall core samples from well X-5 and X-7, which in Fig. 4 belongs RT-1, were actually indicates similar texture with RT-3. A study conducted by Webster et al. (1959) resulted in a conclusion that sidewall coring could shatter and readjust the grain arrangement of the samples as showed by Fig. 5. This phenomenon will result in the difference of measured rock properties between sidewall core and conventional core samples. This statement became our argument to exclude sidewall core samples from the rock typing phase. Finally, the identified rock types, as showed by Fig. 4 are as follows: • Rock Type 1 (RT-1) This rock type is the best among the identified rock types. Porosity ranges from 7.5% to 18.7% and permeability ranges from 5.2 md to 488 md. RT-1 is dominated by tuff sandstone with very fine to coarse grain, although small number of samples have medium to coarse grain size. • Rock Type 2 (RT-2) The porosity and permeability of RT-2 samples ranges from, consecutively, 2.6% to 27.1% and 0.55 md to 4.4 md. This rock type consists of various lithology which are andecitic sandstone with various grain size, tuff sandstone with very fine grain, and metamorphic tuff. • Rock Type 3 (RT-3) RT-3 has the worst quality of all identified rock types. The porosity ranges from 1.7% to 11.7% while the permeability ranges from 0.1 md to 0.45 md. This rock type

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is dominated by very-fine-grained tuff sandstone. Some other samples from this rock type belong to mudstone and andecitic sandstone. The number of rock types discovered using this method gives an interesting fact that rock typing using SCAL data, which is widely used in conventional rock typing method such as J-function, does not give reliable results all the time. This finding gives an idea that rock typing should be done based on routine core data, and later the results could be used as a reference in choosing core samples for special core analysis. In this way, SCAL data shall be available for each rock types. Table 1 exhibits the correlations between (𝑘/φ )0.5 dan C for each rock types, which take the form: b

k ...............................................(7) = a 3 φ 1014φ k

Normalization of Irreducible Water Saturation Values. Irreducible water saturation (Swirr) is one of the parameters used in the permeability equations. Normalization was necessary because routine core analysis gives invalid Swirr values. The water saturation given by routine core analysis is the residual water saturation of core samples, and those values are usually altered by two processes. First process is drilling fluid invasion due to the differential pressure across the well face. The differential pressure occurs because the pressure of mud column in the well is greater than the pressure exerted by fluid in the formation. As most drilling is done with waterbase mud, water filtrate invades the formation and displaces the original formation fluid. The second process is the gas expansion due to the constantly decreasing confining pressure as the core samples being brought to the surface. Fig. 6 shows the plot of Swirr versus porosity and permeability based on routine core analysis data. To achieve normalized Swirr values, plots of Swirr versus porosity (Fig. 7) and Swirr versus permeability (Fig. 8) were made based on 6 samples of special core analysis (SCAL) as SCAL is believed as a more reliable source of Swirr values. It is apparent that Swirr correlates better with permeability than with porosity, thus the normalization of Swirr values were attempted using this following equation: 𝑆𝑤𝑖𝑟𝑟 = 65.592 𝑘 −0.1914............................. (8) It is important to take note that the outcome of the normalization using Eq. 8 was just an approximation to the real Swirr values of each rock samples and that this equation is only suitable for the rock samples used in this study. Permeability Prediction. In this study, there were two that must be done to determine the permeability prediction correlations for each rock type. First, the powers of porosity (φ ) and Swirr were computed using these following equations: A=3−

0.5 ................................................... b

6

(9)

B=

0.5 ...................................................... (10) b×n

where n = 0.1914 (based on Eq. 8). Second, several data points were picked from each rock type to create a relationship between k and

φA

. In this study, data points used to generate permeability equation for RTSwirr B 1 were picked from SCAL data . Then, the correlations were determined by using Power Law regression as shown by Fig. 9 - 11. Those correlations take the form: Y

φA ........................................ (11) k = X B Swirr The permeability prediction correlations for each rock types are listed on Table 3, along with the calculated value of A and B using Eq. 9 and Eq. 10. Fig. 12 exhibits the result of the prediction using the method explained in this study, while Fig. 13 and Fig. 14 shows the comparison of prediction accuracy between this method and previous correlations. It is clear that this method shows its superiority over other correlations in predicting permeability. CONCLUSIONS 1. Log-log plot of (k/f)0.5 versus C = (k/f3) has been proved as an accurate tool for rock typing. 2. Based on the core description data, each rock type can be geologically distinguished from the others. 3. The methodology developed in this study has resulted in equations for accurate permeability prediction. 4. Permeability prediction should be based on rock types. 5. The resulted prediction shows its superiority over previous correlations in estimating permeability. RECOMMENDATIONS 1. This study proposed an idea that, unlike the conventional point of view, SCAL data is not essential in rock typing. Instead, this study proved that rock typing could be done using routine core data only, and the result could be used as a reference in choosing rock samples for special core analysis, therefore SCAL data could be generated for each existing rock type. 2. This method has been proved to be sufficiently accurate for samples with permeability values ranging from 0.1 md and higher. However, the applicability of this method still need to be tested with samples having sub-millidarcy permeability.

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NOMENCLATURE a = a constant, dimensionless A = porosity exponent, dimensionless b = hydraulic conductivity exponent, dimensionless B = irreducible water saturation exponent, dimensionless C = hydraulic conductivity, md 𝑑̅ = average diameter of capillary tubes, μm φ = porosity, fraction k = permeability, md L = length of a porous medium, unit of length L a = average distance flown by fluid particles through porous medium, unit of length S = specific surface area, μm2 T = tortuosity, dimensionless X = a constant, dimensionless Y = exponent, dimensionless

REFERENCES 1. Ahmed,U., Crary, S.F., Coates,G.R., Permeability Estimation : The Various Sources and Their Interrelationships, JPT, May 1991 2. Archie, G.E., Introduction to Petrophysics of Reservoir Rocks, AAPG Bull. (1950) vol. 34, 943-961 3. Coates, G.R. and Dumanoir, J.L., A New Approach to Improved Log Derived Permeability, Proc., SPWLA 14th Annual Logging Symposium, Lafayette, May 6-9, 1973 4. Guo, G., Diaz, M. A., Paz, F., Smalley, J., Waninger, E.A., Rock Typing as an Effective Tool for Permeability and Water-Saturation Modeling: A Case Study in a Clastic Reservoir in the Oriente Basin, SPE 97033 presented at SPE Annual Technical Conference, Oct. 9-12, 2005 5. Leverett, M.C., Capillary Behaviour in Porous Media, Trans. A.I.M.E, vol. 142, 341358 6. Permadi, P., Susilo, A., Permeability Predicition and Characeristics of Pore Structure and Geometry as Inferred from Core Data, Paper SPE 125350 presented at SPE/EAGE Reservoir Characterization & Simulation Conference, Abu Dhabi, UAE, Oct. 19 -21, 2009 7. Rushing, J.A., Newsham, K.E., Blasingame, T.A., Rock Typing – Keys to Understanding Productivity in Tight Gas Sands, Paper SPE 114164 presented at Unconventional Reservoirs Conference, Colorado, USA, Feb. 10-12, 2009 8. Scheidegger, A.E., The Physics of Flow Through Porous Media. University of Toronto Press, 1960

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9. Timur, A., An Investigation of Permeability, Porosity, and Residual Water Saturation Relationships, Proc. SPWLA 9th Annual Logging Symposium, New Orleans, June 2326, 1968 10. Tixier, M.P., Evaluation of Permeability From Electric-Log Resistivity Gradients, Oil & Gas J. (June 16, 1949) 48, No.6, 113-22 11. Torskaya, T., Jin, G., Torres-Verdin, C., Pore-Level Analysis of the Relationship Between Porosity, Irreducible Water Saturation, and Permeability of Clastic Rocks, SPE 109878, 2007 12. Webster, G. M., Dawsongrove, G. E., The Alteration of Rock Properties by Percussion Sidewall Coring, SPE 1159-G presented at Fall Meeting of Los Angeles Basin Section, California, Oct. 16-17, 1958 13. Wyllie, M.R.J. and Rose, W.D., Some Theoretical Considerations Related to Quantitative Evaluation of Physical Characteristics of Reservoir Rock from Electrical Log Data, Trans., AIME (1950) 189, 105-18

Rock Type

Straight Line Equation

RT-1

k = 5.109 φ 1014φ 3

0.453

k

k

k φ = 3.391 1014φ 3

0.196

RT-2 RT-3

k φ = 1.905 1014φ 3

0.128

k

Table 1. Straight line equation for each rock types. Jenis Batuan

A

RT-1

1.896

RT-2

0.449

RT-3

-0.906

B ∅𝟏.𝟐𝟗𝟔

𝒌 = 𝟗. 𝟕𝟒𝟒 �𝑺𝒘𝒊𝒓𝒓𝟑.𝟕𝟕𝟑 � ∅𝟎.𝟏𝟔

𝒌 = 𝟎. 𝟏𝟓𝟔 �𝑺𝒘𝒊𝒓𝒓𝟒.𝟕𝟓𝟖 � 𝟎.𝟎𝟑𝟐

𝒌 = ∅𝟎.𝟐𝟔𝟓 𝑺𝒘𝒊𝒓𝒓𝟔.𝟎𝟏𝟓

Table 2. The permeability equation for each rock types.

9

1000

100

k, 10 md 1

0.1 0

10

20

30

φ, %

40

Figure 1. Plot of porosity vs permeability based on routine core analysis data from Xfield.

180

5 7 13 20 21 43

160 140 120

J (Sw)

100 80 60 40 20 0 0

20

40

60

80

100

Sw, % Figure 2. Plot of J-function versus Sw based on 6 SCAL samples

10

100

(k/φ)0.5 10

Routine SCAL

1 0.1

1

10

C=

100

1000

A/(TS2)

Figure 3. Log-log plot between (𝒌/φ )𝟎.𝟓 and C based on Routine and SCAL data. 100

RT-1 : Tuff SD Very fine to coarse grain y= 5.035 x0.469 R2 = 0.918

(k/φ)0.5 10

y= 3.391 x0.196 R2 = 0.713

RT-2 : Met, Andecitic SD Medium to coarse grain y= 1.905 x0.128 R2 = 0.574

RT-3 : Mudstone, tuff SD Very fine to fine grain

1 0

1

10

C = A/(TS2)

RT-1 RT-2 RT-3

100

Figure 4. Log-log plot between (𝒌/φ )𝟎.𝟓 and C showing each rock types 11

1000

Figure 5. Comparison of thin section of conventional (left) and sidewall (right) core sample (Webster et al., 1959)

100 90 80

90 80

70

70

60

60

Swirr, %

Swirr, %

100

RT-1 RT-2 RT-3

50 40

50 40

30

30

20

20

10

10

0

0 0.1

1

10

100

1000

RT-1 RT-2 RT-3 0

k, md

10

20

30

Porosity, %

Figure 6. Swirr vs k plot (left) and Swirr vs φ (right) based on routine core analysis data.

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Figure 7. The relationship between Swirr and porosity based on SCAL data.

S = 1.69953331 r = 0.99831000

100 90 80

Swirr, %

70 60 50 40 30 20 10 0 0.0

0.1

1.0

10.0

100.0

1000.0

10000.0

k, md

Figure 8. The relationship between Swirr and permeability based on SCAL data.

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10000

1000 y = 9.7442x0.6704 R² = 0.9578

k 100 md 10

1 1

10

100

1000

10000

A = 1.934 B = 5.611

Figure 9. Power Law regression to determine the permeability equation for RT-1

10 y = 0.1564x0.3576 R² = 0.9851

k md 1

0.1 10

100

φ

1000 A

Swirr

B

10000

A = 0.409 B = 13.635

Figure 10. Power Law regression to determine the permeability equation for RT-2

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1

y = 0.0505x0.2927 R² = 0.9591 k md

0.1 1

10

100

1000

10000

A = -0.906 B = 20.559

Figure 11. Power Law regression to determine the permeability equation for RT-3

10000

k predicted, md

1000 100 10 1

RT-1 RT-2

0.1

RT-3 SCAL

0.01 0.01

0.1

1

10

100

1000

k core, md

Figure 12. Permeability prediction result

15

10000

10000

This Study

k predictted, md

1000

Tixier

100

Timur

10

Coates Torskaya

1 0.1 0.01 0.001 0.0001

0.00001 0.000001 1E-06

0.0001

0.01

1

100

10000

k core, md

Figure 13. A comparison of permeability prediction resulted from this method and other correlations (Routine Core data)

10000 1000

Tixier Timur Coates

k predicted, md

100 10

Torskaya This Study

1 0.1 0.01

0.001 0.001

0.01

0.1

1

10

100

1000

10000

k core, md

Figure 14. A comparison of permeability prediction resulted from this method and other correlations (SCAL data)

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