Classification of the average capillary pressure function and its application in calculating fluid saturation

PETROLEUM EXPLORATION AND DEVELOPMENT Volume 39, Issue 6, December 2012 Online English edition of the Chinese language journal Cite this article as: PETROL. EXPLOR. DEVELOP., 2012, 39(6): 778–784.

RESEARCH PAPER

Classification of the average capillary pressure function and its application in calculating fluid saturation HU Yong1,*, YU Xinghe1, CHEN Gongyang2, LI Shengli1 1. School of Energy Resources, China University of Geosciences, Beijing 100083, China; 2. College of Computer Science, Yangtze University, Jingzhou 434023, China

Abstract: When reservoir heterogeneity is strong, there is a great error between the calculated oil saturation based on the J-function and the actual oil saturation interpreted by logging. Aimed at this problem, a reservoir quality index is proposed to classify the average mercury curves, and the reservoir quality index model and original oil saturation model are established, by experimental measurement and numerical simulation with an illustration of an oilfield in the Pearl River Mouth Basin. The oil saturation calculated with this method accords closely with that interpreted by logging, it is a reliable method to show the properties of strongly heterogeneous reservoirs. In addition, this paper proposes a comprehensive utilization of mercury curve and mercury-ejection curve fitting J-function in establishing the saturation model of bound water, movable water, residual oil, movable oil. Considering the influences of such factors as reservoir quality index and clay content on mercury-ejection efficiency, “mercury-ejection index” is used to classify the average mercury-ejection curves and a movable oil saturation model is established, which provides basis for the calculation of recoverable reserves and the research of residual oil distribution. Key words: J-function; saturation model; mercury curve; mercury-ejection curve; reservoir quality index; mercury-ejection index

Introduction Of three-dimensional geological models of reservoir, the oil saturation model is of great significance in reservoir evaluation and geological reserves estimation. In recent years, researchers often use stochastic modeling method to establish oil saturation model based on the results of well log interpretation. But studies show that there is great difference between most of the established model and the actual oil reservoir saturation distribution. The reason is that the distribution of the oil saturation is more related to the microscopic structure of the rock in addition to following the laws of geostatistics to some extent, and being affected by facies, lithology and porosity. It is mainly the function of rock capillary pressure [13]. In actual work, we usually get water saturation first, and then get oil saturation after mathematical conversion. In this paper, the reservoir quality index is used to classify the J-function curves (average capillary pressure curves), and fit water saturation function, respectively, for each category, for the establishment of the original oil saturation model. The authors also try to make use of the mercury curve and the mercury-ejection curve to fit J-function, and get the fluid saturation such as bound water, movable water, residual oil and movable oil saturation.

1 J-function and average capillary pressure curves Cores that are different in physical characteristic must be different in capillary pressure curves also. The capillary pressure curve measured in laboratory can only describe the characteristics of the sampling points of reservoir. Therefore, we need to process the rock capillary pressure curves using equation (1), i.e., J(Sw) function [45]. Relatively concentrated in shape, the processed rock curves can reflect the average characteristics of reservoir. pc J (Sw ) K I (1) V cosT pc ( U w  U o ) gH (2)

The general method of getting oil saturation using J(Sw) function is to fit the J-Sw data of all the rock samples, and get the average water saturation relationship (3) which can represent the entire reservoir [68]; some scholars fit the saturation relationship of each rock sample, and then get the average water saturation relationship with the arithmetic mean of the coefficients a, b [911]; eventually we translate water saturation to the reservoir’s original oil saturation [45, 12]. S w aJ b (3)

Received date: 06 Feb. 2012; Revised date: 07 July 2012. * Corresponding author. E-mail: [email protected] Foundation item: Supported by the Open Project of State Key Laboratory of Petroleum Resources and Prospecting (KFKT 2010001). Copyright © 2012, Research Institute of Petroleum Exploration and Development, PetroChina. Published by Elsevier BV. All rights reserved.

HU Yong et al. / Petroleum Exploration and Development, 2012, 39(6): 778–784

2 Classification of average capillary pressure curve When the reservoir heterogeneity is strong, that is, the change of the reservoir quality index (Irq= K / I ) is large, whether fit all the samples J-Sw data or fit J-Sw data of each sample and then get the arithmetic mean of the coefficient (Fig. 1), the resulted J-function would be difficult to represent the capillary pressure curve of all the rock samples, and cannot effectively describe reservoir heterogeneity. Hence the water saturation calculated by this mean would have big error. The equations 1 and 2 show that J(Sw) function takes the rock porosity, permeability and oil height etc into comprehensive consideration [8]. It is approximately expressed as the function of the reservoir quality index (Irq= K / I ) when the oil height changes little in the same reservoir. Experiments have proved that Irq value [13] can reflect pore structure characteristics of rock very well. The larger the Irq value, the smoother the pore throat surface, and the stronger the microscopic homogeneity, and the better reservoir properties of the rocks. On the contrary, the smaller the Irq value, the less smooth the pore throat surface, and the stronger micro-heterogeneity, and the worse the reservoir properties of the rocks. Therefore, average capillary pressure curves are classified according to Irq value in this paper. The study area, in an oil field in the Pearl River Mouth Basin, is of braided river delta facies, where a couple of oil-bearing layers have been found vertically, with channel sand as the major reservoir. Delta plain facies are rather thick, up to 30 meters, with good physical properties and strong

Fig. 2

Fig. 3

homogeneity (Figure 2a); while the reservoirs are mostly thinner in the delta front facies with the average thickness of less than 4 m and minimum thickness of less than 1 m, relatively poor in physical property and strong in heterogeneity (Figure 2b), where the reservoirs account for 70% of the total oil reservoirs, but reserves are only 30% to 35% of the whole area. This study involves 33 average capillary pressure curves (Figure 3) with Irq value from 0 to 4, among which three samples were from thick layers (3
Fig. 1

Average capillary pressure curve

Reservoir rock slices of an oilfield (10×2.5) in Pearl River Mouth Basin

Relationship between reservoir quality index and average capillary pressure curve

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condition and good reservoir property; while the cores with low Irq value display the exact opposite characteristics of the capillary pressure curve, suggesting poor-sorting and small pore throats. Domestic and foreign scholars have not yet classified average capillary pressure curves. In line with the actual situation of the study area, the authors divide the average capillary pressure curves into four types (Figure 3b) according to the Irq value interval which the morphology relative concentrated area belongs to, by considering the curve's SK and sorting (0< Irq İ1, 1 < Irqİ2, 2 < Irqİ3, 3 < Irq <4), and then fit water saturation equation type by type. This study establishes the reservoir quality index model (Figure 4) after establishing reservoir physical model (porosity, permeability model), and gets the final reservoir original oil saturation using different saturation equations for different ranges of reservoir quality index (Figure 5). Water saturation curves calculated by J-function and from log interpretation were compared (Figures 6 and 7), a, b, c are thin layers and d is a thick layer. It is found that the thin layers show quite different Irq value and strong heterogeneity and the thick layer is opposite. Figure 6 shows the results of all fitted capillary pressure curves by one function And there is little error in the thick layer, but quite big error in the thin layers. Therefore, saturation fitted by one function has significant error when Irq value is quite different, not applying to reservoirs with strong heterogeneity. Figure 7 shows the result calculated by saturation equations according to Irq type. It is found that the saturation calculated by J-function and log interpretation is in good agreement whether for thick layer or thin layer, especially the thin layers see obvious drop in error.

Fig. 6

It is proved that this method can effectively improve the accuracy of saturation calculation and characterize oiliness of reservoir of strong heterogeneity.

3

Establish other fluid saturations with J-function Most domestic and foreign scholars get water saturation

Fig. 4

Reservoir quality index model

Fig. 5

Original oil saturation model

Comparison of the logging water saturation with water saturation calculated by average J-function

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HU Yong et al. / Petroleum Exploration and Development, 2012, 39(6): 778–784

Fig. 7

Comparison of the logging water saturation with water saturation calculated by average J-function

using equation 3, while they haven’t made further research into the calculation methods of other fluid saturation [611, 1418]. Some scholars believe that the water saturation calculated by the J function is actually movable water saturation (equation (4)), which does not contain irreducible water saturation [4] (the total water saturation can be calculated by equation (5)), therefore, the result from this conversion is not the original oil saturation. S wn aJ b (4)

Sw

S wn (1  S wc )  S wc

(5)

J-function fitting in essence is to describe water saturation by mathematical methods combining multiple parameters. If replace the water saturation with other fluid saturation, the J-function fitting can be regarded as the fitting of J-function with that kind of fluid saturation. Different fluid saturation function can be established if J-function is fitted with different fluid saturation, thereby establish various types of fluid saturation models, such as movable water saturation, irreducible water saturation, movable oil saturation and residual oil saturation models. The displacement capillary pressure curve can reflect the minimum residual wetting phase saturations (for water-wet reservoir, commonly known as the irreducible water saturation) and non-wetting phase residual saturation (namely the residual oil saturation). The difference between the maximum mercury saturation and the residual mercury saturation is mercury-ejection saturation on the capillary pressure curves, so the ratio of the mercury volume exit after decompression and the total mercury volume injected before decompression is called mercury-ejection efficiency Ew [3]:

Ew

S max  S r u 100% Smax

(6)

Mercury-ejection efficiency is a laboratory result, which reflects the maximum oil recovery of the non-wetting phase under ideal conditions and the oil displacement efficiency of water driving oil in the water-wet oil reservoir. So mercury-ejection efficiency can be used to roughly evaluate reservoir recovery. However, the author believes that the mercury-ejection efficiency Ew only reflects the overall recovery efficiency of a piece of rock sample. The mercury-ejection efficiency is different in different part of the rock sample and the oil recovery is also different because of the uneven pore distribution in rock and different throat size and pore throat radius is in normal distribution [14]. Pore radius can be regarded as a function of the capillary pressure, so mercury-ejection capillary pressure curve can also be expressed as a function of the recovery factor, which provides a more elaborate calculation method for further understanding of the recovery factor of the rock of different structure, and which also provides a new way for researching the relationship between the recovery and pore structure and fluid property. Although we can establish a function of the recovery factor, in practical work, sometimes we would rather like to learn about the oil saturation, especially the distribution of movable oil [19]. The residual non-wet phase still does not exit when mercury retire completes is the captured residual non-wet phase which remains in the core of reservoir from the mercury-ejection curve. The difference between mercury saturation and residual mercury saturation of rock samples is the ratio of dischargable mercury volume and the total pore volume under different capillary pressure condition. If the rock

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sample is hydrophilic, the excluded amount of mercury is the amount of mobile oil in water flooding. So the multi-mercuryejection curves are averaged using J-function to get the equation of movable oil saturation, and then the movable oil saturation model is established to get recovery factor model by mathematical conversion. However, it is found that the function established, different from the mercury curve, is not distributed in consistent with the Irq value, in the process of establishing the function of the movable oil saturation using mercury-ejection curve. Both macro recovery and mobile oil saturation under different pressure conditions have little to do with the Irq value (Figures 8 and 9). It proved the presence of rock samples which are similar in mercury curve shape but quite different in mercury-ejection curve. It further reflects the complexity of pore structure of reservoir rock, which is significantly influenced by clay minerals [20]. Domestic and foreign researches on mercury-ejection curve also have confirmed this [2126]. In comparison with actual core which is costly to collect and has measurement error, man-made core samples can have predetermined clay composition and content, micro-porosity, surface properties, making study easier. Therefore, artificial rock samples can be used to carry out fine study. Some scholar studied the mercury-ejection efficiency of artificial rock samples [27], which shows that the mercury-ejection efficiency is mainly affected by the clay property and content, and the surface properties of rock samples as well. Clay minerals are layered and chai- layered silicate, less than 2 m in

size, high in specific surface, strong in adsorptive power to cations, and complicated in distribution form, they may hinder the flow of non-wet phase fluid. The mercury-ejection efficiency will increase significantly when the clay content drops. Using six mercury-ejection curves and considering the effect of Irq and clay content (Vc) in this study, mercury-ejection index is represented by ln( I rq / Vc ) . The mercury-ejection index in Figure 8 reflects the recovery factor of different rock samples, the lower the index, the higher the recovery. In saturation modeling, we divide the mercury-ejection curve into three types according to the distribution area of the mercury-ejection curve in the figure, namely according to the mercury-ejection index (0.690.79, 0.981.04, 1.051.21). And then movable oil saturation model was established by fitting movable oil saturation equation type by type (Figure 10). The movable oil saturation model above-mentioned can give reservoir ultimate recoverable reserves and ultimate recovery factor by conversion. And comparing this data with the ultimate recovery factor predicted by the law of reservoir production decline (Table 1), the error is small on the whole, which proves the reliability of the method and the reasonableness of the movable oil saturation model, so it can be used to calculate the recoverable reserves and research the distribution of the remaining oil.

4

Conclusions

J-function is an effective tool for the average of the capillary pressure curves. But when the reservoir heterogeneity is strong, each rock sample has different J-function curve shape. The stronger the heterogeneity, the greater the difference in curve shape, and in this case, the difference between the

Fig. 8 Relationship between movable oil saturation and J-function Fig. 10 Table 1

Movable oil saturation model Reservoir ultimate recovery

Cumulative pro- Recoverable Predicted recov- Predicted Oil duction in the dec- reserves/ ery by production recovery by layer line period/104 m3 104 m3 decline rule/% J-function/%

Fig. 9 Crossplot of rock recovery factor and reservoir quality index

a

779.33

2 974.33

61.52

62.31

b

499.12

2 694.12

55.72

54.62

c

201.32

2 396.32

49.56

49.81

d

921.80

3 116.80

64.46

64.81

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fitting oil saturation using a J-function and the actual saturation would be significant. Considering rock porosity and permeability comprehensively, the reservoir quality index can give quantitative evaluation of the reservoir, and the oil saturation model is established that can reflect reservoir heterogeneity. In addition, the method to establish saturation model of bound water, movable water, residual oil, movable oil using mercury curve and mercury-ejection curve is put forward. Taking factors that affect the ejection efficiency such as the reservoir quality index and clay content into comprehensive consideration, the mercury-ejection curves are classified by mercury-ejection index, and then we can fit a more accurate J-function of the movable oil saturation, so that it can reflect the distribution of the reservoir fluid in complex geological conditions. Comparison of the water saturation curves calculated by classified J-function with the curves by log interpretation, and comparison of the ultimate recovery calculated by classified J-function with the ultimate recovery predicted by the law of production decline show that the classification the paper proposed and the saturation model are reasonable.

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Nomenclature

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J(Sw)—J-function, dimensionless;

67–69.

pc—capillary pressure, Pa;

[11] Lu Bo, Li Zhi, Zhang Xingchao. A method for calculating

—oil-water interfacial tension, N/m;

average capillary pressure curve and its application. Inner

—wetting contact angle, (q);

Mongolia Petrochemical Industry, 2010, 36(24): 208–210.

K—air permeability, m2;

[12] Bear J. Dynamics of fluids in porous media. New York:

¶—porosity, %; ²w—density of water, kg/m3; ²o—density of oil, kg/m3;

American Elsevier, 1972. [13] Yu Xinghe. Basis of hydrocarbon reservoir geology. Beijing: Petroleum Industry Press, 2009.

g—acceleration of gravity, 9.8 m/s2;

[14] He Gengsheng. Petrophysics. Beijing: Petroleum Industry

H—oil height, m;

Press, 1994.

a, b—coefficient;

[15] Rojas A. Application of J-functions to prepare a consistent

Swn—movable water saturation, %;

tight gas reservoir simulation model: Bossier field. SPE

Swc—irreducible water saturation, %;

138412, 2010.

Sw—total water saturation, %;

[16] Elgaghah S A, Tiab D, Osisanya S O. A new approach for

Ew—mercury-ejection efficiency; Smax—maximum amount of mercury can enter rock samples, mL;

obtaining J-function in clean and shaly reservoir using in situ

Sr—residual amount of mercury in rock samples, mL;

measurements. Journal of Canadian Petroleum Technology,

Somümovable oil saturation, %;

2001, 40(7): 30–37. [17] Garrouch A A. A modified Leverett J-function for the Dune

Erürecovery factor, %.

and Yates carbonate fields: A case study. Energy & Fuels,

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