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Reservoir zonation based on statistical analyses: A case study of the Nubian sandstone, Gulf of Suez, Egypt
Journal of African Earth Sciences 124 (2016) 199e210
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Journal of African Earth Sciences journal homepage: www.elsevier.com/locate/jafrearsci
Reservoir zonation based on statistical analyses: A case study of the Nubian sandstone, Gulf of Suez, Egypt Mohamed S. El Sharawy a, *, Gamal R. Gaafar b a b
Geophysical Sciences Department, National Research Centre, Cairo, Egypt PETRONAS Carigali Sdn Bhd, Kuala Lumpur, Malaysia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 April 2016 Received in revised form 20 September 2016 Accepted 21 September 2016 Available online 21 September 2016
Both reservoir engineers and petrophysicists have been concerned about dividing a reservoir into zones for engineering and petrophysics purposes. Through decades, several techniques and approaches were introduced. Out of them, statistical reservoir zonation, stratigraphic modified Lorenz (SML) plot and the principal component and clustering analyses techniques were chosen to apply on the Nubian sandstone reservoir of Palaeozoic e Lower Cretaceous age, Gulf of Suez, Egypt, by using five adjacent wells. The studied reservoir consists mainly of sandstone with some intercalation of shale layers with varying thickness from one well to another. The permeability ranged from less than 1 md to more than 1000 md. The statistical reservoir zonation technique, depending on core permeability, indicated that the cored interval of the studied reservoir can be divided into two zones. Using reservoir properties such as porosity, bulk density, acoustic impedance and interval transit time indicated also two zones with an obvious variation in separation depth and zones continuity. The stratigraphic modified Lorenz (SML) plot indicated the presence of more than 9 flow units in the cored interval as well as a high degree of microscopic heterogeneity. On the other hand, principal component and cluster analyses, depending on well logging data (gamma ray, sonic, density and neutron), indicated that the whole reservoir can be divided at least into four electrofacies having a noticeable variation in reservoir quality, as correlated with the measured permeability. Furthermore, continuity or discontinuity of the reservoir zones can be determined using this analysis. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Reservoir zonation Statistical analysis Permeability Electrofacies
1. Introduction Studying of the reservoir rocks has been associated with some terms such as facies, lithofacies, petrofacies, rock types, hydraulic flow units and electrofacies. The most widely used definition of facies was introduced by Reading (1978): facies should ideally be a distinctive rock which forms under certain conditions of sedimentation reflecting a particular process or environment. Lithofacies were defined by Dorfman et al. (1990) as “mappable stratigraphic units, laterally distinguishable from the adjacent intervals based upon lithologic characteristics, such as mineralogical, petrographical, and paleontological signatures that are related to the appearance, texture, or composition of the rock”. Similar rock types have also been defined as geological facies or simply facies. Petrofacies are defined as intervals of rocks with similar average
* Corresponding author. E-mail address: [email protected] (M.S. El Sharawy). http://dx.doi.org/10.1016/j.jafrearsci.2016.09.021 1464-343X/© 2016 Elsevier Ltd. All rights reserved.
values in pore throat radius, thus having similar fluid flow characteristics (Porras et al., 1999). Other similar definitions have been referred to as petrophysical rock types, reservoir rock types, and static rock types. Rock type is defined 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 (Gunter et al., 1997). This definition also indicates that rocks should be grouped according to physical properties controlling fluid storage, flow, and distribution (Rushing et al., 2008). They further differentiated rock types into depositional, petrographic and hydraulic units. The hydraulic flow unit (HFU) is defined as a mappable portion of the total reservoir, within which geological and petrophysical properties that affect the flow of fluids, are consistent and predictably different from the properties of other reservoir rock volumes (Ebanks et al., 1992). The term electrofacies was introduced by Serra and Abbott (1980) to define a set of log responses that characterizes a bed and permits it to be distinguished from the others. The aim of electrofacies
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Table 1 Statistics of the routine core data in the studied wells. Well
Well Well Well Well
No. of samples
A B C #Ref#
158 94 80 514
Core permeability
Core porosity
Min
Max
Avg.
Min
Max
Avg.
0.07 0.46 0.07 0.01
1568 1610 177 1050
425.5 198 13.7 68.7
8 6.8 1.2 2.7
24 22 17.2 20.4
16.2 16.3 9.13 13.4
2 L X mi 2 1 4X W¼ Kij Ki N L i¼1 j¼1
R¼
BW B
Khi Ki > identification is to correlate them with lithofacies that are identified from core or outcrop (Doveton, 2014). Electrofacies can be used also to assign relationships for each rock type such as porosity/ permeability equations (Stinco, 2006). Lee and Datta-Gupta (1999) and Perez et al. (2005) used electrofacies in predicting permeability. Kadhodaie-Ikhchi et al. (2013) integrated electrofacies and hydraulic flow unit concept to identify reservoir characterization. In 1958, Beghtol applied a modification of variance statistical analysis to zonation of the petroleum reservoir to determine the fluid flow pattern. In order to achieve his goal, he used core permeability data for eight closely spaced wells. After four years, Testerman (1962) published his statistical reservoir zonation study. He used variance technique and core permeability data to drive zonation in four adjacent wells. The technique was based on the premises that the variation is minimized within the zones and maximized between the zones. He introduced the following four equations to prove continuity or discontinuity in the zones across the studied wells:
" # L 2 X 1 B¼ mi Ki: K:: L 1 i¼1
(1)
(2)
(3) sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 1 þ szðv; pÞ 2 nh ni
(4)
where B ¼ the variance between zones, L ¼ the number of zones, i ¼ the summation index for the number of zones, j ¼ the summation index for the number of data within the zone, mi ¼ the number of data in the ith zone, Ki: ¼ the mean of the permeability data in the ith zone, K:: ¼ the over-all mean of the data in the well, W ¼ the pooled variance within zones, N ¼ the total number of data, the kij's ¼ the permeability data, R ¼ the zonation index. Khi ¼ the arithmetic average of the permeability data of the hth zone in one well, Ki: ¼ the arithmetic average of the permeability data of the ith zone in an adjoining well, nh and n, ¼ the number of data in the hth and ith zones, s ¼ the standard deviation S of all the permeability data from the reservoir, z ¼ a constant tabulated as a function of the number of data, the number of zones and a probability level. v and p are used to identify z-values as functions of the probability level. Harter (1960) provided a table of z-values. Hawkins and Merriam (1974) used gamma ray, conductivity and
Fig. 1. Well e to e well correlation of the studied reservoir. It can be noted that the lowermost part is occurred in all wells except for well X1. Meanwhile the upper part in well # Ref# is absent in other wells. This may be attributed to non deposition.
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Dip angle and direction 0
10
20
30
Rock Unit
201
this study, the main purpose is using a variety of statistical analyses techniques to zone the Nubian sandstone reservoir in the Southern Gulf of Suez, Egypt.
Rudeis
1.1. Data and methods
Nukhul
10612
10695
Nubia Sandstone
Fault
Unconformity
10808 Fig. 2. Dipmeter of well B showing the following: 1) Drag fault zone associated with normal fault in which the pre e rift sequence except for the lower part of the Nubia sandstone interval was missed. 2) Possible unconformity between zone I and zone II.
resistivity logs for zonation of the stratigraphic sequences based on multivariate techniques. Recently, Li et al. (1995) and Li and Beckner (2000) extended Testerman's approach to global upscaling in which they used three-dimensional unequal spaced grid cells to capture reservoir heterogeneities residing in geologic models. In
Three adjacent wells, A, B, and C, are used in this study. The average distance between the wells is 1.29 km. Well A encountered about 366 ft thick of the Nubia sandstone. About 180 ft have undergone routine core analyses, including air permeability, porosity, fluid saturation and grain density. Well B encountered about 90 ft thick in which most of the interval has undergone routinely cored analyses. Well C encountered about 229 ft thick, in which only the lowermost 80 ft were cored and analyzed (Table 1). Beside the routine core analysis data, geophysical well logging data was available. This data includes gamma ray, density, neutron, and sonic logs. Two additional uncored wells in the same field (X1 and X2) were used to test the validity of the applied techniques. Another cored well, located north of the studied field, was chosen to verify the obtained results. The methodology used in the current work includes the following steps: the first step is an environmental correction of the well logs data. The environmentally corrected data was then depth matched with the core data. For Testerman technique, the permeability data in original order were divided into two possible two zones using Equations (1)e(3) for a single well. The index of zonation “R” is the criterion used to indicate the best division. According to Testerman (1962), R index, which ranges between 0 and 1.0, indicates how closely the division corresponds to homogeneous zones. The closer the index is to 1.0, the more homogeneous the zones are. Therefore, the larger index denotes the best division into two zones and is retained for comparison with other indices. Repeating Equations (1)e(3) is done for the further division until reaching either two cases. The First case is when the new R is less than the previous one. The second case is when the difference between the two alternating indices is less than 0.06. In these two cases, no further division must be applied. After dividing each well into zones, Equation (4) is used to identify continuity or discontinuity of the zones. Other reservoir properties were used to zone, such as porosity, density, interval transit time, acoustic impedance (AI) and reflection coefficient (RC). The second method used principal component and cluster analyses to petrophysically zone the reservoir into electrofacies based on well logging data. The third method was based on classifying the reservoir into flow units using the Modified Stratigraphic Lorenz (MSL) plot as described by Gunter et al. (1997). The method depends on using core porosity and permeability, in which cumulative storage capacity “(Fh)cum” and cumulative flow capacity “(kh)cum” can be determined. The following equations were used for this purpose (Maglio-Johnson, 2000):
ðFhÞcum ¼ F1ðh1h0Þ þ F2ðh2h1Þ þ … þ Fkiðhi hi 1Þ Fkiðhi hi 1Þ
Table 2 Final zonation of reservoir permeability data. Zone
Zone mean, md
Number of data
(2,A) (1,A) (1,B) (1,C) (2,B) (2,C) (1,# Ref.#) (2, #Ref.#)
539.7 295.8 295.3 177 48 11.8 88.6 16.2
84 74 57 1 37 78 373 141
Note that (2, A) means well A and zone 2, and so on. In other words letter refers to well and number refers to zone.
(5)
where Ф is fractional porosity. h is a thickness of the sample interval.
ðkhÞcum ¼ k1ðh1h0Þ þ k2ðh2h1Þ þ … þ kiðhi hi 1Þ kiðh1 hi 1Þ
(6)
where k is permeability in md, 2. Results and discussions The studied Nubia sandstone reservoir represented one of the
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Table 3 Results of examination of continuity and discontinuity of zones based on core permeability data. Zone
Mean
Number of data
p
z
Fp
(2,A)
(1,A)
(1,B)
(1,C)
(2,B)
(2,A) (1,A) (1,B) (1,C) (2,B) (2,C)
539.7 295.8 295.3 177 48 11.8
84 74 57 1 37 78
2 3 4 5 6 7
2.77 2.92 3.02 3.09 3.15 3.19
722.9 762.1 788.2 806.4 822.1 832.5
2163.5 2014.1 509.9 3524.2 4747.8
4.0 166.9 1740.5 2475.0
165.85 1656.58 2300.84
180.02 232.14
256.46
Legend: p ¼ is used to identify z-values as functions of the probability level. z ¼ a constant tabulated as a function of the number of data, the number of zones and a probability level. Fp ¼ is the product of z- values times standard deviation (s).
Well A
1.25 Km
Well B 10700
10750
Zone I
Zone I 10750 10800 Zone II 10800
Well C
1.125 K m
1.5 K
m
10850
10650 Zone II
Fig. 3. Results of reservoir zonation based on Testerman (1962) technique using core permeability.
most important reservoirs in the prolific Gulf of Suez Province, Egypt. The geologic age extended from Cambrian to Lower Cretaceous deposited in continental to fluvial braided systems. The Nubia sandstone is resting unconformably on Precambrian basement rocks and overlain unconformably by Upper Cretaceous deposits. Due to the reservoir sediments being usually unfossiliferous, its age is under debate. Several classifications were adopted for the Nubia sequence (Hermina et al., 1989). The thickness of the Nubia sequence generally decreased from north to south as a response to the southward regression phase as well as the prevailing tectonic regime. Several tectonic activities and unconformities occurred during deposition of the Nubia sandstone sequence (Barakat et al., 1986; Patton et al., 1994; El Heiny et al., 1998 and Omran and El Sharawy, 2014). Generally, three factors can be considered to control the encountered thicknesses in the drilled wells in the southern Gulf of Suez. The first one is the normal decrease in thickness towards the south. The second is the erosion processes and the third factor is the location of the drilled well relative to the tilted fault
blocks, which formed as a response to the Oligocene e Miocene Gulf of Suez rifting. Therefore, the drilled well may be encountered the only lowermost part of the reservoir due to faulting effect rather than erosion process. This situation can be observed in the studied wells, especially in well B (Figs. 1 and 2). Well e to e well correlation using gamma ray and sonic logs shows that the lowermost part is correlated in the studied wells except for well X1 (Fig. 1). It can be noted also that the upper part reference well is not correlated in the other wells, almost due to non deposition. As a response to the Tertiary Gulf of Suez rifting, the pre- rift stratigraphic sequence is highly affected by the complicated tectonic activities that were dominant during the Suez rift stages which resulted in tilt e fault blocks with different sizes. So, missing parts are expected in the pre- rift sequence in response to fault cutting rather than facies changes or erosion processes. The main part of the reservoir is faulted out in well B as well as the uppermost part in well C. Applying the first three equations of Testerman technique for
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203
Fig. 4. Dipmeter of wells C, X1 and X2 showing the possible unconformity within the Nubia sandstone.
well A yielded two zones (1, A) and (2, A), with zonation index (R) ¼ 0.95. Such zonation occurred at depth 10,795 ft. The value of the zonation index indicated that further zonation is meaningless in which the difference between this value and the new one will be less than 0.06. Well B has divided also into two zones (1, B) and (2, B), with R ¼ 0.96. Such separation of zones occurred at 10,766 ft depth. For well C, the separation into two zones has occurred just after the first data point with R ¼ 0.97, at 10,608 ft depth, which means no further zonation is necessary. After zonation of the individual reservoir into possible zones, the next step is to identify if these zones are continuous or not. In order to do that Equation (4) is used with the following steps: 1. Rank the means of well zones in descending order (Table 2). 2. Calculate Equation (2) using all permeability data in the three wells yielding W ¼ 68110.75.
3. Calculate the standard deviation for W value in step two, pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi yielding s ¼ 68110:75 ¼ 260:98 4. Select z e values from Harter (1960) for 95% probability level. 5. Multiply z e values by the standard deviation to get F'p ¼ sz,p 6. Examine the significant differences among the well e zone means (Table 3). This Table indicated that the comparison is significant until zone (2, B). Therefore, the first four zones represented a continuous zone (zone I) while the last two zones represented another continuous zone (zone II). This means that zones (1, A) and (2, A) are merged in one zone. Therefore, the cored interval of well A represented one zone while the cored interval in the other two wells represented two zones (Fig. 3). Geologically, zones I and II seem to be separated by an unconformity, as indicated by dipmeter data (Figs. 2 and 4). The cored interval in well C represented only the lowermost part
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Fig. 5. Dipmeter, well logs response, cored interval and electrofacies in well # Ref.#. The sequence is divided into two zones based on core permeability. The same result was obtained by using reflectance coefficient in term of energy ('R). The two zones seem to be separated by unconformity. High permeability is associated with blue and green colours, while low permeability is associated with red and yellow colours. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Table 4 Two zones are the result with each reservoir property but the separation is always occurred at different depth. Reservoir properties
Core permeability, K Core Porosity, Ф Bulk Density, rb Interval transit time, Dt Acoustic impedance, AI reflectance coefficient expressed in term of energy, R0
Depth of separation for the identified two zones Well A
Well B
Well C
Ref# well
Well X1
Well X2
10,795 10,768 10,576 10,705 10,717 10,617
10,757 10,733 10,732 10,701 10,733 10,698
10,608 10,658 10,662 10,608 10,512 10,686
11,074 10,874 10,595 10,585 10,594 11,072
Not cored Not cored 9814 9963 9967 9877
Not cored Not cored 10,333 10,330 10,330 10,364
of the Nubia sandstone sequence as shown in Fig. 1. On the other hand, the core plugs in well A covered an interval within the middle part. As shown, the reservoir thickness increases gradually from well B to well A with a medium thickness in well C. The question now is whether there are other zones if the whole interval was
tested in well A, which represented the thickest reservoir amongst studied wells. The answer can be obtained through two ways. The first way is achieved through permeability prediction of the uncored interval using empirical models, multiple regression analysis and/or artificial intelligence methods such as fuzzy logic
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205
Table 5 Results of examination of continuity and discontinuity of zones based on core porosity data (Ф). Abbreviations as in Table 3. Zone
Mean
Number of data
p
z
Fp
(1,a9a)
(1,a2a)
(2,a2a)
(2,a9a)
(1,a3b)
(1,a9a) (1,a2a) (2,a2a) (2,a9a) (1,a3b) (2,a3b)
17.92 16.8 15.86 15.62 11.66 4.57
37 51 107 57 51 30
2 3 4 5 6
2.77 2.92 3.02 3.09 3.15
6.7 7.0 7.3 7.4 7.6
7.3 15.3 15.4 41.0 76.8
7.8 8.7 36.7 75.2
2.07 34.91 77.29
29.05 69.28
43.58
Well A
1.25 Km
Well B 10700
Zone I 10750
Zone I 10750 10800 Zone II 10800
Zone II
1.5 K
m
10850
Well C
1.1 25 Km
Zone I 10650 Zone II
Fig. 6. Results of reservoir zonation based on Testerman (1962) technique using core porosity.
and neural network. In this way, uncertainty will be presented depending on the strength of the prediction. The second way is using a reference well that contains cored interval covering the whole thickness in the studied wells. This reference well #Ref# is located about 11 km north well A (Fig. 1). This well encountered about 707 ft thick of the Nubia sandstone reservoir, in which about 600 ft thick were cored (Fig. 5). Applying the Testerman technique in this well also yielded two zones. As shown in Fig. 5, the two zones are separated by a possible unconformity. Therefore, two zones are the optimal division for this reservoir. In his approach, Testerman mentioned that the technique can be used to correlate any reservoir property, such as information extracted from well logs. In this aspect, we used the following reservoir properties: core porosity (Ф), rock density (rb), interval transit time (DT), acoustic impedance (AI) and reflection coefficient expressed in term of energy ('R). We begin with helium core porosity and follow the same previous steps as mentioned. Two zones were also obtained, but at different depths (Tables 4 and 5). Using such reservoir property, it was found that only zone II in wells A and B is continuous and the other zones are discontinuous
(Fig. 6). By using the reservoir properties extracted from well logs, the two wells X1 and X2 can be used. Applying the Testerman technique for rb also yielded two zones with continuity of zone II in wells B, C and X2 with zone I in wells A and X1 (Fig. 7 and Table 6). Using interval transit time (DT) and acoustic impedance (AI) yielded discontinuity for all resulted zones (Tables 7 and 8). On the other hand, reflection coefficient expressed in term of energy ('R) yielded continuity of all zones except for the zone I in well B (Fig. 8 and Table 9). 2.1. Reservoir zonation based on SML plot Gunter et al. (1997) used the stratigraphic modified Lorenz (SML) plot to identify reservoir flow units based on statistical calculations of cumulative storage capacity and the cumulative flow capacity. The former is a function of core porosity and thickness and the later is a function of core permeability and thickness. Plotting of the two parameters as described in equations (5) and (6) yielded a curve. Any change in its slope means a new flow unit. The horizontal change can be treated as a barrier. According to this method,
M.S. El Sharawy, G.R. Gaafar / Journal of African Earth Sciences 124 (2016) 199e210
10750 Well X2 10800
Well B Zone I
10700
Zone II
206
10350 10400
Zone II
10450 10500 10550 10600
10650
10650
Well X1
10750 10800 10850 10900
9800 9850 9900 9950
Zone II
10700
Zone II
10600
Zone I
Well A
10000 10050 10450
Well C
10550
Zone I
10500
10600
Zone II
10650
Fig. 7. Results of reservoir zonation based on Testerman (1962) technique using bulk density (rb).
the cored interval in the studied cored wells ranged from 9 to 11 flow units (Fig. 9). As shown in this figure, the lowest microscopic heterogeneity was found in well A, which has the lowest Parson e Dykstra coefficient (0.74). Petrophysical reservoir zonation based on principal component and cluster analyses: Petrophyscists introduced several approaches to divide the reservoir into zones, namely hydraulic flow unit (HFU), as well as
multivariate statistical methods, such as principal component analysis (PCA) and cluster analysis. These methods were explained with details in several papers by Amaefule et al., 1993; Chekani and Kharat, 2009 and Doveton, 1994, 2014. The first technique uses core permeability and porosity data, while the statistical methods use data derived from geophysical well logs. Due to the limitation and high cost of core data, well log data can be used to divide the whole reservoir into electrofacies or zones.
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207
Table 6 Results of examination of continuity and discontinuity of zones based on bulk density (rb). Abbreviations as in Table 3. Zone
Mean
Number of data
p
z
Fp
(1,a2a)
(2,a3b)
(2,a9a)
(1,a3b)
(1,a9a)
(1,a2a) (2,a3b) (2,a9a) (1,a3b) (1,a9a) (2,a2a)
2.44 2.43 2.42 2.38 2.36 2.33
6 49 151 430 76 392
2 3 4 5 6
2.77 2.92 3.02 3.09 3.15
0.10 0.10 0.11 0.11 0.11
0.03 0.07 0.21 0.27 0.38
0.09 0.47 0.54 0.93
0.6 0.6 1.3
0.2 1.0
0.3
Table 7 Results of examination of continuity and discontinuity of zones based on interval transit time (DT). Abbreviations as in Table 3. Zone
Mean
Number of data
p
z
Fp
(1,a9a)
(2,a3b)
(1,a2a)
(2,a9a)
(2,a2a)
(1,a9a) (1,a2a) (2,a9a) (2,a2a) (2,a3b) (1,a3b)
95.18 92.45 77.7 76 69.5 67.9
14 135 213 263 158 321
2 3 4 5 6
2.77 2.92 3.02 3.09 3.15
9.0 9.5 9.8 10.0 10.2
13.8 89.6 98.9 130.2 141.3
189.6 219.7 276.9 338.5
26.1 110.4 156.8
91.3 137.7
23.3
Table 8 Results of examination of continuity and discontinuity of zones based on acoustic impedance (AI). Abbreviations as in Table 3. Zone
Mean
Number of data
p
z
Fp
(1,a9a)
(2,a3b)
(1,a2a)
(2,a9a)
(2,a2a)
(1,a3b) (2,a3b) (2,a9a) (2,a2a) (1,a2a) (1,a9a)
35673.3 34680 32307.7 30938.1 28337.7 27844.7
129 350 149 251 147 78
2 3 4 5 6
2.77 2.92 3.02 3.09 3.15
3816.7 4023.4 4161.2 4257.7 4340.3
13638.2 39577.0 61814.9 85990.3 77189.1
34297.4 63979.5 91259.1 77202.6
18728.7 48296.0 45161.6
35408.6 33747.2
4977.1
In PCA, gamma-ray, density, sonic and neutron logs for all six studied wells were used as inputs. The aim of PCA is summarizing the data without losing too much information, in which it reduces the dimensionality of the problem by introducing principal components. Training PCA showed that the first three logs form about 92.2% of the variability. This percentage indicates the success of PCA in reducing the dimensionality of diverse datasets and providing the optimal representation of the data. Therefore, gamma-ray, density and sonic logs represent the PCA input data. The outputs are referred as PC1, PC2, PC3 which were used as inputs in the cluster analysis, in which processing started by assuming the presence of 15 rock types. By using the dendrogram chart, the optimum number of rock types can be determined. In cluster analysis, minimizing the within e cluster sum of squares distance method was used. According to this method and based on the dendrogram chart, at least four electrofacies can be considered to represent the studied reservoir (Fig. 10). Correlating with permeability, it can be noted that yellow and red colours represent the lowest reservoir quality in which permeability is usually less than 1 md (Fig. 11). This rock type can be considered as a non reservoir. On the other hand, the blue color is associated with the highest reservoir quality; usually, permeability is more than 100 md. Between these two extreme rock types, there is a moderate rock reservoir quality represented by green color. The results of the cluster analysis can be used to confirm the statistical zonation reservoir technique, in which the lower part in both wells B and C are continuous. This lower part is dominated by poor reservoir quality. In well A, most of the reservoir is of high quality with the decreasing quality of the uppermost part. It can be inferred also that well C ranges from poor reservoir quality in the lower zone to moderate reservoir quality in the upper zone. In well B, the reservoir quality increased upward from low to high in the uppermost part (Fig. 11). In light of these results, the uncored well X1 is considered to be dominated by high reservoir quality (blue
color) bounded by poor reservoir quality (yellow color). Well X2 showed that the reservoir quality is the best between 10400 and 10,522 ft in depth. 3. Conclusions From the previous discussions and results, it can be concluded that: Reservoir zonation using the Testerman statistical analysis technique is a good technique for determining the continuity of the reservoir zones. However, the dependence of this technique on core permeability limited its applicability. The studied reservoir was divided into two zones. The boundary between them may coincide with an unconformity. Using reservoir properties other than permeability results in the same number of zones with variation in the depth at which the separation occurred. However, the continuity or discontinuity of the resulting zones showed a great deviation from that obtained by using core permeability. Stratigraphic Modified Lorenz (SML) plot indicated the presence of more than 9 flow units, indicating a high degree of microscopic heterogeneity. Petrophysical reservoir zonation based on principal component and cluster analyses produces more details about the interior rock structure and texture, which translated into reservoir quality. Correlation with the cored interval, zones of high and low reservoir qualities can be determined based on the results of principal component and cluster analyses. Limitation of the core data and their high cost advocate the use of statistical reservoir zonation techniques based on well logging data such as principal component and cluster analyses.
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10700
Well B
Zone II
10750 Zone I
Well X2 10350
10800
10400
Zone II
10450 10500 10550 Zone I
Well A 10600
10600
10650
10650 Zone II
Well X1
10750
Zone I
10700
9800
10800
9850
10850
Zone II
9900
10900
9950 10000 10050
10450
Well C
10500 Zone I
10550 10600 10650
Fig. 8. Results of reservoir zonation based on Testerman (1962) technique using reflectance coefficient in terms of energy (‘R).
Table 9 Results of examination of continuity and discontinuity of zones based on reflectance coefficient in terms of energy (‘R). Abbreviations as in Table 3. Zone
Mean
Number of data
p
z
Fp
(1,a9a)
(2,a3b)
(1,a2a)
(2,a9a)
(2,a2a)
(1,a9a) (2,a3b) (1,a2a) (2,a9a) (2,a2a) (1,a3b)
0.00459 0.00046 0.000398 0.000162 0.000096 0.000046
7 2 47 219 350 467
2 3 4 5 6
2.77 2.92 3.02 3.09 3.15
0.00167 0.00176 0.00182 0.00186 0.00190
0.0073 0.0146 0.0163 0.0166 0.0169
0.0001 0.0006 0.0007 0.0008
0.002 0.003 0.003
0.001 0.08
0.001
Fig. 9. Stratigraphic modified Lorenz (SML) plot for the cored interval for the studied wells. The numbers indicate the flow units and the blue horizontal lines indicate barriers. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 10. Dendrogram randomness plot and the dendrogram cluster tree showing the optimum number of cluster.
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Fig. 11. Association of principal component and cluster analyses resulted in classifying the studied reservoir into four electrofacies. Note that yellow and red colours are associated with poor reservoir quality. Meanwhile green and blue colours are associated with high reservoir quality. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Acknowledgement The authors would like to thank the Egyptian General Petroleum Corporation ‘EGPC’ and the Gulf of Suez Petroleum Company ‘GUPCO’ for releasing the data. Thanks also are for Dr Joseph Clay Hilton for grammatically reviewing the manuscript. We thank warmly the reviewers and the Editor e in e Chief of the Journal of African Earth Science for their valuable comments which improved the original manuscript. References Amaefule, J., Altunbay, M., Tiab, D., Kersey, D.G., Keelan, D.K., 1993. Enhanced reservoir description using core and log data to identify hydraulic flow units and predict permeability in uncored intervals/wells. In: SPE Annual Technical Conference and Exhibition, Houston, Texas, pp. 205e220. SPE 26436. Barakat, M.G., Darwish, M., El Barkooky, A.N., 1986. Lithostratigraphy of the post carboniferous e pre cenomanian clastics in west central sinai and Gulf of Suez, Egypt. In: 8th EGPC Exploration Conference, pp. 380e405. Beghtol, L.A., 1958. A Statistical Approach to the Zonation of a Petroleum Reservoir. MSc Theses. University of Missouri, 70 p. Chekani, M., Kharat, R., 2009. Reservoir Rock Typing in a Carbonate Reservoir e Cooperation of Core and Log Data: Case Study. SPE 123703, 22 p. Dorfman, M.H., Newey, J.J., Coats, G.R., 1990. New techniques in lithofacies determination and permeability prediction in carbonates using well logs. In: Hurst, A., Lovell, M.A., Morton, A.C. (Eds.), Geological Applications of Wireline Logs. Geological Society, London, Special Publ., No. 48, pp. 113e120. Doveton, J.H., 1994. Geologic Log Analysis Using Computer Methods. AAPG, Computer applications in geology, Tulsa no. 2, 169 p. Doveton, J.H., 2014. Principles of Mathematical Petrophysics. Oxford University Press, 288 p. Ebanks, W., Scheihing, M., Atkinson, C., 1992. Flow units for reservoir characterization. In: Morton-Thompson, D., Woods, A.M. (Eds.), Development Geology Reference Manual, Amer. Assoc. Petrol. Geol. Methods in Exploration Series 10, pp. 282e284. El Heiny, I., Enani, N., Abdou, I., 1998. Structural and stratigraphic interpretation of a new Nubian sandstone oil reservoir, Gulf of Suez, Egypt. In: 14th EGPC Exploration and Production Conference 1, pp. 466e491. Gunter, G., Finneran, J., Hartmann, D., Miller, J., 1997. Early Determination of Reservoir Flow Units Using an Integrated Petrophysical Method. SPE 38679, 8 p.
Harter, H.L., 1960. Critical values for Duncan's new multiple range test. Biometrics 16 (4), 671e685. Hawkins, D.M., Merriam, D.F., 1974. Zonation of multivariate sequences of digitized geologic data. Math. Geol. 6 (3), 263e269. Hermina, M., Klitzsch, E., List, F.R., 1989. Stratigraphic Lexicon and Explanatory Notes to the Geological Map of Egypt 1: 500 000. Conoco Inc., Cairo, Egypt. Kadkhodaie-Ilkhchi, R., Rezaee, R., Moussavi-Harami, R., Kadkhodaie -Ilkhchi, A., 2013. Analysis of the reservoir electrofacies in the framework of hydraulic flow units in the whicher range field, perth Basin, Western Australia. J. Pet. Sci. Eng. 111, 106e120. Lee, S.H., Datta-Gupta, A., 1999. Electrofacies Characterization and Permeability Predictions in Carbonate Reservoirs: Role of Multivariate Analysis and NonparaMetric Regression. SPE-56658-MS, 13 p. Li, D., Beckner, B., 2000. Optimal Uplayering for Scaleup of Multimillion-cell Geologic Models. SPE Paper Number 62927, 16 p. Li, D., Cullick, A.S., Lake, L.W., 1995. Global scale-up of reservoir model permeability with local grid refinement. J. Pet. Sci. Eng. 14, 1e13. Maglio-Johnson, T., 2000. Flow Unit Definition Using Petrophysics in a Deep Water Turbidite Deposit. Unpubl. M.S. thesis. Colorado School of Mines, Lewis Shale, Carbon County, Wyoming, 121 p. Omran, M.A., El Sharawy, M.S., 2014. Tectonic evolution of the Southern Gulf of Suez, Egypt: a comparison between depocenter and near peripheral basins. Arab. J. Geosci. 7 (1), 87e107. Patton, T.L., Moustafa, A.R., Nelson, R.A., Abdine, A.S., 1994. Tectonic evolution and structural setting of the Suez rift. In: Landon, S.M. (Ed.), Interior rift Basins: AAPG Memoir 59, pp. 9e55. Perez, H.H., Datta-Gupta, A., Mishra, S., 2005. The Role of Electrofacies, Lithofacies, and Hydraulic Flow Units in Permeability Predictions from Well Logs: a Comparative Analysis Using Classification Trees. SPE-84301-PA, 13p. Porras, J.C., Barbato, R., and Khazen, L., 1999. Reservoir Flow Units: A Comparison Between Three Different Models in the Santa Barbara and Pirital Fields, North Monagas Area, Eastern Venezuela Basin,” paper SPE 53671 presented at the SPE Latin American and Caribbean Petroleum Engineering Conference, Caracas, Venezuela, April 21e23. Reading, H.G., 1978. Facies. In: Reading, H.G. (Ed.), Sedimentary Environments and Facies. Elsevier, New York, pp. 4e14. Rushing, J.A., Newsham, K.E., Blasingame, T.A., 2008. Rock Typing - Keys to Understanding Productivity in Tight Gas Sands. SPE 114164, 31 p. Serra, O., Abbott, H.T., 1980. The Contribution of Logging Data to Sedimentology and Stratigraphy. SPE 9270-PA, 19 p. Stinco, L.P., 2006. Core and log data integration; the key for determining electrofacies. In: SPWLA 47th Annual Logging Symposium, 7p. Testerman, J.D., 1962. A statistical reservoir-zonation technique. JPT 889e893.
Contents lists available at ScienceDirect
Journal of African Earth Sciences journal homepage: www.elsevier.com/locate/jafrearsci
Reservoir zonation based on statistical analyses: A case study of the Nubian sandstone, Gulf of Suez, Egypt Mohamed S. El Sharawy a, *, Gamal R. Gaafar b a b
Geophysical Sciences Department, National Research Centre, Cairo, Egypt PETRONAS Carigali Sdn Bhd, Kuala Lumpur, Malaysia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 April 2016 Received in revised form 20 September 2016 Accepted 21 September 2016 Available online 21 September 2016
Both reservoir engineers and petrophysicists have been concerned about dividing a reservoir into zones for engineering and petrophysics purposes. Through decades, several techniques and approaches were introduced. Out of them, statistical reservoir zonation, stratigraphic modified Lorenz (SML) plot and the principal component and clustering analyses techniques were chosen to apply on the Nubian sandstone reservoir of Palaeozoic e Lower Cretaceous age, Gulf of Suez, Egypt, by using five adjacent wells. The studied reservoir consists mainly of sandstone with some intercalation of shale layers with varying thickness from one well to another. The permeability ranged from less than 1 md to more than 1000 md. The statistical reservoir zonation technique, depending on core permeability, indicated that the cored interval of the studied reservoir can be divided into two zones. Using reservoir properties such as porosity, bulk density, acoustic impedance and interval transit time indicated also two zones with an obvious variation in separation depth and zones continuity. The stratigraphic modified Lorenz (SML) plot indicated the presence of more than 9 flow units in the cored interval as well as a high degree of microscopic heterogeneity. On the other hand, principal component and cluster analyses, depending on well logging data (gamma ray, sonic, density and neutron), indicated that the whole reservoir can be divided at least into four electrofacies having a noticeable variation in reservoir quality, as correlated with the measured permeability. Furthermore, continuity or discontinuity of the reservoir zones can be determined using this analysis. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Reservoir zonation Statistical analysis Permeability Electrofacies
1. Introduction Studying of the reservoir rocks has been associated with some terms such as facies, lithofacies, petrofacies, rock types, hydraulic flow units and electrofacies. The most widely used definition of facies was introduced by Reading (1978): facies should ideally be a distinctive rock which forms under certain conditions of sedimentation reflecting a particular process or environment. Lithofacies were defined by Dorfman et al. (1990) as “mappable stratigraphic units, laterally distinguishable from the adjacent intervals based upon lithologic characteristics, such as mineralogical, petrographical, and paleontological signatures that are related to the appearance, texture, or composition of the rock”. Similar rock types have also been defined as geological facies or simply facies. Petrofacies are defined as intervals of rocks with similar average
* Corresponding author. E-mail address: [email protected] (M.S. El Sharawy). http://dx.doi.org/10.1016/j.jafrearsci.2016.09.021 1464-343X/© 2016 Elsevier Ltd. All rights reserved.
values in pore throat radius, thus having similar fluid flow characteristics (Porras et al., 1999). Other similar definitions have been referred to as petrophysical rock types, reservoir rock types, and static rock types. Rock type is defined 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 (Gunter et al., 1997). This definition also indicates that rocks should be grouped according to physical properties controlling fluid storage, flow, and distribution (Rushing et al., 2008). They further differentiated rock types into depositional, petrographic and hydraulic units. The hydraulic flow unit (HFU) is defined as a mappable portion of the total reservoir, within which geological and petrophysical properties that affect the flow of fluids, are consistent and predictably different from the properties of other reservoir rock volumes (Ebanks et al., 1992). The term electrofacies was introduced by Serra and Abbott (1980) to define a set of log responses that characterizes a bed and permits it to be distinguished from the others. The aim of electrofacies
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Table 1 Statistics of the routine core data in the studied wells. Well
Well Well Well Well
No. of samples
A B C #Ref#
158 94 80 514
Core permeability
Core porosity
Min
Max
Avg.
Min
Max
Avg.
0.07 0.46 0.07 0.01
1568 1610 177 1050
425.5 198 13.7 68.7
8 6.8 1.2 2.7
24 22 17.2 20.4
16.2 16.3 9.13 13.4
2 L X mi 2 1 4X W¼ Kij Ki N L i¼1 j¼1
R¼
BW B
Khi Ki > identification is to correlate them with lithofacies that are identified from core or outcrop (Doveton, 2014). Electrofacies can be used also to assign relationships for each rock type such as porosity/ permeability equations (Stinco, 2006). Lee and Datta-Gupta (1999) and Perez et al. (2005) used electrofacies in predicting permeability. Kadhodaie-Ikhchi et al. (2013) integrated electrofacies and hydraulic flow unit concept to identify reservoir characterization. In 1958, Beghtol applied a modification of variance statistical analysis to zonation of the petroleum reservoir to determine the fluid flow pattern. In order to achieve his goal, he used core permeability data for eight closely spaced wells. After four years, Testerman (1962) published his statistical reservoir zonation study. He used variance technique and core permeability data to drive zonation in four adjacent wells. The technique was based on the premises that the variation is minimized within the zones and maximized between the zones. He introduced the following four equations to prove continuity or discontinuity in the zones across the studied wells:
" # L 2 X 1 B¼ mi Ki: K:: L 1 i¼1
(1)
(2)
(3) sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 1 þ szðv; pÞ 2 nh ni
(4)
where B ¼ the variance between zones, L ¼ the number of zones, i ¼ the summation index for the number of zones, j ¼ the summation index for the number of data within the zone, mi ¼ the number of data in the ith zone, Ki: ¼ the mean of the permeability data in the ith zone, K:: ¼ the over-all mean of the data in the well, W ¼ the pooled variance within zones, N ¼ the total number of data, the kij's ¼ the permeability data, R ¼ the zonation index. Khi ¼ the arithmetic average of the permeability data of the hth zone in one well, Ki: ¼ the arithmetic average of the permeability data of the ith zone in an adjoining well, nh and n, ¼ the number of data in the hth and ith zones, s ¼ the standard deviation S of all the permeability data from the reservoir, z ¼ a constant tabulated as a function of the number of data, the number of zones and a probability level. v and p are used to identify z-values as functions of the probability level. Harter (1960) provided a table of z-values. Hawkins and Merriam (1974) used gamma ray, conductivity and
Fig. 1. Well e to e well correlation of the studied reservoir. It can be noted that the lowermost part is occurred in all wells except for well X1. Meanwhile the upper part in well # Ref# is absent in other wells. This may be attributed to non deposition.
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Dip angle and direction 0
10
20
30
Rock Unit
201
this study, the main purpose is using a variety of statistical analyses techniques to zone the Nubian sandstone reservoir in the Southern Gulf of Suez, Egypt.
Rudeis
1.1. Data and methods
Nukhul
10612
10695
Nubia Sandstone
Fault
Unconformity
10808 Fig. 2. Dipmeter of well B showing the following: 1) Drag fault zone associated with normal fault in which the pre e rift sequence except for the lower part of the Nubia sandstone interval was missed. 2) Possible unconformity between zone I and zone II.
resistivity logs for zonation of the stratigraphic sequences based on multivariate techniques. Recently, Li et al. (1995) and Li and Beckner (2000) extended Testerman's approach to global upscaling in which they used three-dimensional unequal spaced grid cells to capture reservoir heterogeneities residing in geologic models. In
Three adjacent wells, A, B, and C, are used in this study. The average distance between the wells is 1.29 km. Well A encountered about 366 ft thick of the Nubia sandstone. About 180 ft have undergone routine core analyses, including air permeability, porosity, fluid saturation and grain density. Well B encountered about 90 ft thick in which most of the interval has undergone routinely cored analyses. Well C encountered about 229 ft thick, in which only the lowermost 80 ft were cored and analyzed (Table 1). Beside the routine core analysis data, geophysical well logging data was available. This data includes gamma ray, density, neutron, and sonic logs. Two additional uncored wells in the same field (X1 and X2) were used to test the validity of the applied techniques. Another cored well, located north of the studied field, was chosen to verify the obtained results. The methodology used in the current work includes the following steps: the first step is an environmental correction of the well logs data. The environmentally corrected data was then depth matched with the core data. For Testerman technique, the permeability data in original order were divided into two possible two zones using Equations (1)e(3) for a single well. The index of zonation “R” is the criterion used to indicate the best division. According to Testerman (1962), R index, which ranges between 0 and 1.0, indicates how closely the division corresponds to homogeneous zones. The closer the index is to 1.0, the more homogeneous the zones are. Therefore, the larger index denotes the best division into two zones and is retained for comparison with other indices. Repeating Equations (1)e(3) is done for the further division until reaching either two cases. The First case is when the new R is less than the previous one. The second case is when the difference between the two alternating indices is less than 0.06. In these two cases, no further division must be applied. After dividing each well into zones, Equation (4) is used to identify continuity or discontinuity of the zones. Other reservoir properties were used to zone, such as porosity, density, interval transit time, acoustic impedance (AI) and reflection coefficient (RC). The second method used principal component and cluster analyses to petrophysically zone the reservoir into electrofacies based on well logging data. The third method was based on classifying the reservoir into flow units using the Modified Stratigraphic Lorenz (MSL) plot as described by Gunter et al. (1997). The method depends on using core porosity and permeability, in which cumulative storage capacity “(Fh)cum” and cumulative flow capacity “(kh)cum” can be determined. The following equations were used for this purpose (Maglio-Johnson, 2000):
ðFhÞcum ¼ F1ðh1h0Þ þ F2ðh2h1Þ þ … þ Fkiðhi hi 1Þ Fkiðhi hi 1Þ
Table 2 Final zonation of reservoir permeability data. Zone
Zone mean, md
Number of data
(2,A) (1,A) (1,B) (1,C) (2,B) (2,C) (1,# Ref.#) (2, #Ref.#)
539.7 295.8 295.3 177 48 11.8 88.6 16.2
84 74 57 1 37 78 373 141
Note that (2, A) means well A and zone 2, and so on. In other words letter refers to well and number refers to zone.
(5)
where Ф is fractional porosity. h is a thickness of the sample interval.
ðkhÞcum ¼ k1ðh1h0Þ þ k2ðh2h1Þ þ … þ kiðhi hi 1Þ kiðh1 hi 1Þ
(6)
where k is permeability in md, 2. Results and discussions The studied Nubia sandstone reservoir represented one of the
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Table 3 Results of examination of continuity and discontinuity of zones based on core permeability data. Zone
Mean
Number of data
p
z
Fp
(2,A)
(1,A)
(1,B)
(1,C)
(2,B)
(2,A) (1,A) (1,B) (1,C) (2,B) (2,C)
539.7 295.8 295.3 177 48 11.8
84 74 57 1 37 78
2 3 4 5 6 7
2.77 2.92 3.02 3.09 3.15 3.19
722.9 762.1 788.2 806.4 822.1 832.5
2163.5 2014.1 509.9 3524.2 4747.8
4.0 166.9 1740.5 2475.0
165.85 1656.58 2300.84
180.02 232.14
256.46
Legend: p ¼ is used to identify z-values as functions of the probability level. z ¼ a constant tabulated as a function of the number of data, the number of zones and a probability level. Fp ¼ is the product of z- values times standard deviation (s).
Well A
1.25 Km
Well B 10700
10750
Zone I
Zone I 10750 10800 Zone II 10800
Well C
1.125 K m
1.5 K
m
10850
10650 Zone II
Fig. 3. Results of reservoir zonation based on Testerman (1962) technique using core permeability.
most important reservoirs in the prolific Gulf of Suez Province, Egypt. The geologic age extended from Cambrian to Lower Cretaceous deposited in continental to fluvial braided systems. The Nubia sandstone is resting unconformably on Precambrian basement rocks and overlain unconformably by Upper Cretaceous deposits. Due to the reservoir sediments being usually unfossiliferous, its age is under debate. Several classifications were adopted for the Nubia sequence (Hermina et al., 1989). The thickness of the Nubia sequence generally decreased from north to south as a response to the southward regression phase as well as the prevailing tectonic regime. Several tectonic activities and unconformities occurred during deposition of the Nubia sandstone sequence (Barakat et al., 1986; Patton et al., 1994; El Heiny et al., 1998 and Omran and El Sharawy, 2014). Generally, three factors can be considered to control the encountered thicknesses in the drilled wells in the southern Gulf of Suez. The first one is the normal decrease in thickness towards the south. The second is the erosion processes and the third factor is the location of the drilled well relative to the tilted fault
blocks, which formed as a response to the Oligocene e Miocene Gulf of Suez rifting. Therefore, the drilled well may be encountered the only lowermost part of the reservoir due to faulting effect rather than erosion process. This situation can be observed in the studied wells, especially in well B (Figs. 1 and 2). Well e to e well correlation using gamma ray and sonic logs shows that the lowermost part is correlated in the studied wells except for well X1 (Fig. 1). It can be noted also that the upper part reference well is not correlated in the other wells, almost due to non deposition. As a response to the Tertiary Gulf of Suez rifting, the pre- rift stratigraphic sequence is highly affected by the complicated tectonic activities that were dominant during the Suez rift stages which resulted in tilt e fault blocks with different sizes. So, missing parts are expected in the pre- rift sequence in response to fault cutting rather than facies changes or erosion processes. The main part of the reservoir is faulted out in well B as well as the uppermost part in well C. Applying the first three equations of Testerman technique for
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203
Fig. 4. Dipmeter of wells C, X1 and X2 showing the possible unconformity within the Nubia sandstone.
well A yielded two zones (1, A) and (2, A), with zonation index (R) ¼ 0.95. Such zonation occurred at depth 10,795 ft. The value of the zonation index indicated that further zonation is meaningless in which the difference between this value and the new one will be less than 0.06. Well B has divided also into two zones (1, B) and (2, B), with R ¼ 0.96. Such separation of zones occurred at 10,766 ft depth. For well C, the separation into two zones has occurred just after the first data point with R ¼ 0.97, at 10,608 ft depth, which means no further zonation is necessary. After zonation of the individual reservoir into possible zones, the next step is to identify if these zones are continuous or not. In order to do that Equation (4) is used with the following steps: 1. Rank the means of well zones in descending order (Table 2). 2. Calculate Equation (2) using all permeability data in the three wells yielding W ¼ 68110.75.
3. Calculate the standard deviation for W value in step two, pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi yielding s ¼ 68110:75 ¼ 260:98 4. Select z e values from Harter (1960) for 95% probability level. 5. Multiply z e values by the standard deviation to get F'p ¼ sz,p 6. Examine the significant differences among the well e zone means (Table 3). This Table indicated that the comparison is significant until zone (2, B). Therefore, the first four zones represented a continuous zone (zone I) while the last two zones represented another continuous zone (zone II). This means that zones (1, A) and (2, A) are merged in one zone. Therefore, the cored interval of well A represented one zone while the cored interval in the other two wells represented two zones (Fig. 3). Geologically, zones I and II seem to be separated by an unconformity, as indicated by dipmeter data (Figs. 2 and 4). The cored interval in well C represented only the lowermost part
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Fig. 5. Dipmeter, well logs response, cored interval and electrofacies in well # Ref.#. The sequence is divided into two zones based on core permeability. The same result was obtained by using reflectance coefficient in term of energy ('R). The two zones seem to be separated by unconformity. High permeability is associated with blue and green colours, while low permeability is associated with red and yellow colours. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Table 4 Two zones are the result with each reservoir property but the separation is always occurred at different depth. Reservoir properties
Core permeability, K Core Porosity, Ф Bulk Density, rb Interval transit time, Dt Acoustic impedance, AI reflectance coefficient expressed in term of energy, R0
Depth of separation for the identified two zones Well A
Well B
Well C
Ref# well
Well X1
Well X2
10,795 10,768 10,576 10,705 10,717 10,617
10,757 10,733 10,732 10,701 10,733 10,698
10,608 10,658 10,662 10,608 10,512 10,686
11,074 10,874 10,595 10,585 10,594 11,072
Not cored Not cored 9814 9963 9967 9877
Not cored Not cored 10,333 10,330 10,330 10,364
of the Nubia sandstone sequence as shown in Fig. 1. On the other hand, the core plugs in well A covered an interval within the middle part. As shown, the reservoir thickness increases gradually from well B to well A with a medium thickness in well C. The question now is whether there are other zones if the whole interval was
tested in well A, which represented the thickest reservoir amongst studied wells. The answer can be obtained through two ways. The first way is achieved through permeability prediction of the uncored interval using empirical models, multiple regression analysis and/or artificial intelligence methods such as fuzzy logic
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205
Table 5 Results of examination of continuity and discontinuity of zones based on core porosity data (Ф). Abbreviations as in Table 3. Zone
Mean
Number of data
p
z
Fp
(1,a9a)
(1,a2a)
(2,a2a)
(2,a9a)
(1,a3b)
(1,a9a) (1,a2a) (2,a2a) (2,a9a) (1,a3b) (2,a3b)
17.92 16.8 15.86 15.62 11.66 4.57
37 51 107 57 51 30
2 3 4 5 6
2.77 2.92 3.02 3.09 3.15
6.7 7.0 7.3 7.4 7.6
7.3 15.3 15.4 41.0 76.8
7.8 8.7 36.7 75.2
2.07 34.91 77.29
29.05 69.28
43.58
Well A
1.25 Km
Well B 10700
Zone I 10750
Zone I 10750 10800 Zone II 10800
Zone II
1.5 K
m
10850
Well C
1.1 25 Km
Zone I 10650 Zone II
Fig. 6. Results of reservoir zonation based on Testerman (1962) technique using core porosity.
and neural network. In this way, uncertainty will be presented depending on the strength of the prediction. The second way is using a reference well that contains cored interval covering the whole thickness in the studied wells. This reference well #Ref# is located about 11 km north well A (Fig. 1). This well encountered about 707 ft thick of the Nubia sandstone reservoir, in which about 600 ft thick were cored (Fig. 5). Applying the Testerman technique in this well also yielded two zones. As shown in Fig. 5, the two zones are separated by a possible unconformity. Therefore, two zones are the optimal division for this reservoir. In his approach, Testerman mentioned that the technique can be used to correlate any reservoir property, such as information extracted from well logs. In this aspect, we used the following reservoir properties: core porosity (Ф), rock density (rb), interval transit time (DT), acoustic impedance (AI) and reflection coefficient expressed in term of energy ('R). We begin with helium core porosity and follow the same previous steps as mentioned. Two zones were also obtained, but at different depths (Tables 4 and 5). Using such reservoir property, it was found that only zone II in wells A and B is continuous and the other zones are discontinuous
(Fig. 6). By using the reservoir properties extracted from well logs, the two wells X1 and X2 can be used. Applying the Testerman technique for rb also yielded two zones with continuity of zone II in wells B, C and X2 with zone I in wells A and X1 (Fig. 7 and Table 6). Using interval transit time (DT) and acoustic impedance (AI) yielded discontinuity for all resulted zones (Tables 7 and 8). On the other hand, reflection coefficient expressed in term of energy ('R) yielded continuity of all zones except for the zone I in well B (Fig. 8 and Table 9). 2.1. Reservoir zonation based on SML plot Gunter et al. (1997) used the stratigraphic modified Lorenz (SML) plot to identify reservoir flow units based on statistical calculations of cumulative storage capacity and the cumulative flow capacity. The former is a function of core porosity and thickness and the later is a function of core permeability and thickness. Plotting of the two parameters as described in equations (5) and (6) yielded a curve. Any change in its slope means a new flow unit. The horizontal change can be treated as a barrier. According to this method,
M.S. El Sharawy, G.R. Gaafar / Journal of African Earth Sciences 124 (2016) 199e210
10750 Well X2 10800
Well B Zone I
10700
Zone II
206
10350 10400
Zone II
10450 10500 10550 10600
10650
10650
Well X1
10750 10800 10850 10900
9800 9850 9900 9950
Zone II
10700
Zone II
10600
Zone I
Well A
10000 10050 10450
Well C
10550
Zone I
10500
10600
Zone II
10650
Fig. 7. Results of reservoir zonation based on Testerman (1962) technique using bulk density (rb).
the cored interval in the studied cored wells ranged from 9 to 11 flow units (Fig. 9). As shown in this figure, the lowest microscopic heterogeneity was found in well A, which has the lowest Parson e Dykstra coefficient (0.74). Petrophysical reservoir zonation based on principal component and cluster analyses: Petrophyscists introduced several approaches to divide the reservoir into zones, namely hydraulic flow unit (HFU), as well as
multivariate statistical methods, such as principal component analysis (PCA) and cluster analysis. These methods were explained with details in several papers by Amaefule et al., 1993; Chekani and Kharat, 2009 and Doveton, 1994, 2014. The first technique uses core permeability and porosity data, while the statistical methods use data derived from geophysical well logs. Due to the limitation and high cost of core data, well log data can be used to divide the whole reservoir into electrofacies or zones.
M.S. El Sharawy, G.R. Gaafar / Journal of African Earth Sciences 124 (2016) 199e210
207
Table 6 Results of examination of continuity and discontinuity of zones based on bulk density (rb). Abbreviations as in Table 3. Zone
Mean
Number of data
p
z
Fp
(1,a2a)
(2,a3b)
(2,a9a)
(1,a3b)
(1,a9a)
(1,a2a) (2,a3b) (2,a9a) (1,a3b) (1,a9a) (2,a2a)
2.44 2.43 2.42 2.38 2.36 2.33
6 49 151 430 76 392
2 3 4 5 6
2.77 2.92 3.02 3.09 3.15
0.10 0.10 0.11 0.11 0.11
0.03 0.07 0.21 0.27 0.38
0.09 0.47 0.54 0.93
0.6 0.6 1.3
0.2 1.0
0.3
Table 7 Results of examination of continuity and discontinuity of zones based on interval transit time (DT). Abbreviations as in Table 3. Zone
Mean
Number of data
p
z
Fp
(1,a9a)
(2,a3b)
(1,a2a)
(2,a9a)
(2,a2a)
(1,a9a) (1,a2a) (2,a9a) (2,a2a) (2,a3b) (1,a3b)
95.18 92.45 77.7 76 69.5 67.9
14 135 213 263 158 321
2 3 4 5 6
2.77 2.92 3.02 3.09 3.15
9.0 9.5 9.8 10.0 10.2
13.8 89.6 98.9 130.2 141.3
189.6 219.7 276.9 338.5
26.1 110.4 156.8
91.3 137.7
23.3
Table 8 Results of examination of continuity and discontinuity of zones based on acoustic impedance (AI). Abbreviations as in Table 3. Zone
Mean
Number of data
p
z
Fp
(1,a9a)
(2,a3b)
(1,a2a)
(2,a9a)
(2,a2a)
(1,a3b) (2,a3b) (2,a9a) (2,a2a) (1,a2a) (1,a9a)
35673.3 34680 32307.7 30938.1 28337.7 27844.7
129 350 149 251 147 78
2 3 4 5 6
2.77 2.92 3.02 3.09 3.15
3816.7 4023.4 4161.2 4257.7 4340.3
13638.2 39577.0 61814.9 85990.3 77189.1
34297.4 63979.5 91259.1 77202.6
18728.7 48296.0 45161.6
35408.6 33747.2
4977.1
In PCA, gamma-ray, density, sonic and neutron logs for all six studied wells were used as inputs. The aim of PCA is summarizing the data without losing too much information, in which it reduces the dimensionality of the problem by introducing principal components. Training PCA showed that the first three logs form about 92.2% of the variability. This percentage indicates the success of PCA in reducing the dimensionality of diverse datasets and providing the optimal representation of the data. Therefore, gamma-ray, density and sonic logs represent the PCA input data. The outputs are referred as PC1, PC2, PC3 which were used as inputs in the cluster analysis, in which processing started by assuming the presence of 15 rock types. By using the dendrogram chart, the optimum number of rock types can be determined. In cluster analysis, minimizing the within e cluster sum of squares distance method was used. According to this method and based on the dendrogram chart, at least four electrofacies can be considered to represent the studied reservoir (Fig. 10). Correlating with permeability, it can be noted that yellow and red colours represent the lowest reservoir quality in which permeability is usually less than 1 md (Fig. 11). This rock type can be considered as a non reservoir. On the other hand, the blue color is associated with the highest reservoir quality; usually, permeability is more than 100 md. Between these two extreme rock types, there is a moderate rock reservoir quality represented by green color. The results of the cluster analysis can be used to confirm the statistical zonation reservoir technique, in which the lower part in both wells B and C are continuous. This lower part is dominated by poor reservoir quality. In well A, most of the reservoir is of high quality with the decreasing quality of the uppermost part. It can be inferred also that well C ranges from poor reservoir quality in the lower zone to moderate reservoir quality in the upper zone. In well B, the reservoir quality increased upward from low to high in the uppermost part (Fig. 11). In light of these results, the uncored well X1 is considered to be dominated by high reservoir quality (blue
color) bounded by poor reservoir quality (yellow color). Well X2 showed that the reservoir quality is the best between 10400 and 10,522 ft in depth. 3. Conclusions From the previous discussions and results, it can be concluded that: Reservoir zonation using the Testerman statistical analysis technique is a good technique for determining the continuity of the reservoir zones. However, the dependence of this technique on core permeability limited its applicability. The studied reservoir was divided into two zones. The boundary between them may coincide with an unconformity. Using reservoir properties other than permeability results in the same number of zones with variation in the depth at which the separation occurred. However, the continuity or discontinuity of the resulting zones showed a great deviation from that obtained by using core permeability. Stratigraphic Modified Lorenz (SML) plot indicated the presence of more than 9 flow units, indicating a high degree of microscopic heterogeneity. Petrophysical reservoir zonation based on principal component and cluster analyses produces more details about the interior rock structure and texture, which translated into reservoir quality. Correlation with the cored interval, zones of high and low reservoir qualities can be determined based on the results of principal component and cluster analyses. Limitation of the core data and their high cost advocate the use of statistical reservoir zonation techniques based on well logging data such as principal component and cluster analyses.
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10700
Well B
Zone II
10750 Zone I
Well X2 10350
10800
10400
Zone II
10450 10500 10550 Zone I
Well A 10600
10600
10650
10650 Zone II
Well X1
10750
Zone I
10700
9800
10800
9850
10850
Zone II
9900
10900
9950 10000 10050
10450
Well C
10500 Zone I
10550 10600 10650
Fig. 8. Results of reservoir zonation based on Testerman (1962) technique using reflectance coefficient in terms of energy (‘R).
Table 9 Results of examination of continuity and discontinuity of zones based on reflectance coefficient in terms of energy (‘R). Abbreviations as in Table 3. Zone
Mean
Number of data
p
z
Fp
(1,a9a)
(2,a3b)
(1,a2a)
(2,a9a)
(2,a2a)
(1,a9a) (2,a3b) (1,a2a) (2,a9a) (2,a2a) (1,a3b)
0.00459 0.00046 0.000398 0.000162 0.000096 0.000046
7 2 47 219 350 467
2 3 4 5 6
2.77 2.92 3.02 3.09 3.15
0.00167 0.00176 0.00182 0.00186 0.00190
0.0073 0.0146 0.0163 0.0166 0.0169
0.0001 0.0006 0.0007 0.0008
0.002 0.003 0.003
0.001 0.08
0.001
Fig. 9. Stratigraphic modified Lorenz (SML) plot for the cored interval for the studied wells. The numbers indicate the flow units and the blue horizontal lines indicate barriers. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 10. Dendrogram randomness plot and the dendrogram cluster tree showing the optimum number of cluster.
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Fig. 11. Association of principal component and cluster analyses resulted in classifying the studied reservoir into four electrofacies. Note that yellow and red colours are associated with poor reservoir quality. Meanwhile green and blue colours are associated with high reservoir quality. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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