4.2.1 Hydraulic Flow Unit
The concept of the hydraulic flow unit was initially proposed from the Kozeny-Carmen equation of a capillary tube model for rock pore spaces, with a key parameter in the method as the reservoir quality index (RQI), which is the average hydraulic radius in a rock 45–48. The input parameters for reservoir quality index (RQI) and flow Zone indicator (FZI) are core porosity (Phi) and permeability (K) data that present the relationship below:
Rock quality index (RQI) = 0.0314 x Sqrt( K / Phi ) …………. ( 1)
Pore-Grain volume ratio (PhiZ) = Phi / (1 – Phi)……………… (2)
Flow Zone Indicator ( FZI) = RQI / PhiZ ……………………. (3)
From a log-log plot of RQI against PhiZ, we can determine points of similar FZI characteristics of value because they plot on a similar line with identical flow characteristics and identify flow zone boundaries. Therefore, we first select flow unit boundaries based on points positioned on 450 lines with similar FZI values in the analysis. Then, we create hydraulic flow units using the FZI boundaries. This method has been successfully applied and documented by researchers in carbonate and clastic reservoirs9,24,49.
Results present five flow units vertical boundary lines shown in the histogram of Fig. 5a, and the flow units are calculated using the boundaries set in the flow units statistical table 2, which resulted in five hydraulic flow units HFU1, HFU2, HFU3, HFU4, and HFU5 shown in Fig 5b. The boundaries using FZI indicate that HFU1 range from 0 to 1 micron, HFU 2 from 1 to 2 microns, HFU3 from 2 to 3 microns, and HFU 4 from 3 to 5 HFU 5 from 5 to 10 microns. HFU5 presents the best reservoir rock quality with RQI ranging from 0.5 to 2.1 microns, and the least reservoir rock flow unit is HFU with an RQI value ranging from 0.02 to 0.2 microns.
4.2.2 Winland r35 Rock Typing Model
Winland (1972)50 created a method for determining pore throat radius from core data using core measurements of porosity and permeability data, published by 51. From the Winland r35 method,the pore throat radius (r35), corresponding to the 35th percentile of mercury saturation (µm) could be calculated on different data such as well logs and core provided they have porosity and permeability data 15,51,52. From that concept, Winland noted that large pores connected large crystals, and small pores connected small crystals. Therefore, Winland indicated that if the intercrystalline pore system is filled by intergranular and solution pore, the one that controls outflow and inflow into large pore is the smallest pore system 53. Winland's correlation equation between pore sizes, porosity, and permeability published by 51 is shown in Eq. 4.
Winland r35 = Log( 0.732 + 0.588 Log(K) – 0.864 Log(Phi) ) …………………….(4)
Where Phi is porosity (%) and K is air permeability in mD. From Eq. 4, rock typing can be done by calculating the r35 value for each sample, classifying the sample with the same r35 value, and making an iso-pore throat line in a graph. In this study, rock typing has been done for 371 plug samples from routine core analysis with Winland r35 method. Our result was superimposed on the standard Winland r35 plot shown in Fig. 6a. From the plot, we obtained distribution pore spaces, porosity, and permeability at iso-pore throat line that presents five hydraulic flow units (HFU5 as mega pores ranging between 10 to 20 µm, HFU4 as macropores between 4 to 10 µm, HFU3 as mesopore between 2 to 4 µm, HFU2 as micropores ranges between 1 to 2 µm, and HFU1 as nanopores less than 1 µm). The porosity/permeability function (K/Phi) was also introduced in e Fig. 6b to understand better the influence of porosity and permeability on pore throat size distribution and connectivity. Applying the (K/Phi) plot indicates that higher reservoir quality is assigned to the mega pore rocks, whereas the lowest is assigned to the nanopore rocks (Fig. 6b). Though the plot may successfully group the rocks, the influence of diagenesis and the lithology must be considered 20,54,55. Several empirical relationships were established from the Winland r35 pore throat method to estimate permeability from porosity.
4.2.3 Hydraulic Conductivity (HFU) Method
From HFU and in reference to 56, reservoir quality index method, the hydraulic conductivity method was developed 57 for sandstone reservoirs. This method was applied in this study because we are working on sandstone reservoirs. The technique was developed by 58 to obtain a capillary model for a porous medium from the relationship between permeability and porosity from Eq. 6: In this study, the method developed by Scheidegger, 1957 was modified and called hydraulic reservoir unit (HRU) to replace conductivity that best fits the purpose of the study.
Hydraulic Reservoir Unit (HRU)= { Permeability/ (1014* (Porosity) ^3) } * 0.1………..(5)
In applying the hydraulic conductivity method, we first calculate HRU from each core sample using Eq. 5, then cross plot of hydraulic conductivity against (Permeability/Porosity)0.5 and establish five different HRU's (Fig. 7). HRU5 ranges from 50 to 120; HRU4 from 20 to 50; HFU3 from 5 to 20; HRU2 from 1 to 5; and HRU1 less than 1. The best reservoir quality is HRU5, and the least reservoir rock quality is HRU1. An empirical power relation was established to estimate hydraulic conductivity as follows:
Hydraulic Conductivity = 0.56 * Log ((Permeability/Porosity)0.5)^ 2.39 R2 = 0.91 ….(6)
4.2.4 SMLP Method
Stratigraphic Modified Lorenz Plot (SMLP), a petrophysical-based method, was also used in this study to identify hydraulic flow units within a sequence-stratigraphic framework 59–61. This method is applied through analysis of porosity and permeability to establish the vertical variation of flow (permeability with the thickness, kh) and storage capacity (porosity with the thickness, Ph). The SMLP utilizes the cross plot of cumulative flow and storage capacity values to determine flow units within a stratigraphic framework from base to top of reservoir 61,62. Significant inflection points on the SMLP are interpreted to represent changes in flow and storage capacity flow unit. The interval of cumulative flow and storage capacity that slopes higher than 450 lines on the plot is used to indicate high flow and low storage capacity; interval with a slope lower than the 450 lines on the plot represents higher storage and low flow capacity, while those that plot around the 450 lines represents an interval of equal flow and storage capacity.
SMLP was generated for our study using porosity and permeability values (Fig. 8). According to SMLP, four flow units (FU1 to FU4) are recognized in well OW1(red line), OW2 (black line), OW3 (green line), and five flow units (FU1 to FU5) are recognized for well OW4 (blue line) respectively. As seen in Fig. 8, FU1 presents the best reservoir quality with a high flow unit in all the wells, whereas FU2 represents the least reservoir quality and poor flow unit which are a barrier to flow.
4.3 Reservoir Zonation Model
Integrating the lithofacies, Lucia's Petrophysical rock classification model with different reservoir characterization methods developed culminated into a new applicable reservoir zonation scheme for the oil field presented in Table 2. We used an average value of the different reservoir zonation methods to produce four distinct flow zones as high flow zone (HFZ), moderate flow zone (MFZ), low flow zone (LFZ), and tight flow zone (TFZ), respectively. The HFZ porosity and permeability values range from 18–22% and permeability from 200mD to 1000mD, with Winand r35 values ≥ l0µm; FZI between 5 to 10 µm, HC between 50 to 120, which corresponds to HFU5, where the highest and the best reservoir quality is detected. Therefore, it is ranked as very good (Table 2). MFZ porosity and permeability values range from 12% to 18% and permeability from 50mD to 200mD, with Winand r35 values ranging from 4 to l0µm; FZI between 3 to 5 µm, HC between 20 to 50, which corresponds to HFU4, ranked as good reservoir quality. LFZ porosity and permeability values range from 14% to 18% and permeability from 10mD to 50mD, with Winand r35 values ranging from 2 to 4µm; FZI between 2 to 3 µm, HC between 5 to 20, which corresponds to HFU3, ranked as fair reservoir quality. TFZ is classified as an impervious reservoir rock with porosity and permeability values less than 10% and 1.0 mD, respectively. Winand r35, FZI, and HC values are ≤ 1 µm for TFZ, which corresponds to HFU1, with the least reservoir quality. We observed permeability variations at similar porosities in some flow zones, attributed to pore type control on fluid flow. It has been reported previously that sandstone samples with similar porosities can have different permeability resulting from the impact of diagenetic overprints on the pore throat radius of sandstones 63,64. Consequently, we used quantitative point-count mineralogy results of well OW3 and OW4 (Table 3) to determine mineral types and abundances in different zones that affect reservoir quality, resulting in diagenetic effects on the pore throat radius.
The results indicated quartz as the dominant framework grain ranging in abundance from 62% to 82 weight % (Table 3). Feldspar, lithics, and glauconite were all identified in varying proportions in the studied samples. According to 65,66, the main factors that influence the permeability and porosity of sandstone reservoirs are the clay type and distribution, cementation, sandstone composition, hydrocarbon saturation, and compaction. Quartz overgrowth and siderite are the predominant types of cement in the samples ranging from 7.9 % to 18.8 % and 0.9% to 6.2 weight %, respectively. Dolomite is variable and minor pyrite is present in some samples as an alteration and replacement product. Samples of high siderite content ≥ 2% belong to the tight flow zone, while samples with low siderite content ≤ 2% belong to the low, moderate, and high flow zones. The most abundant clay mineral is the kaolinite ranging from 1% to 4.1%, and illite ranging from traces to 2.6%. The amount of cement (siderite) and clay minerals (kaolinite and illite) increases in the tight flow zone compared to other zones. Due to the coarse nature of kaolinite and its position on the pore spaces and not in the pore throat, kaolinite is less destructive of permeability than other clay minerals 65,67. However, there appears to be a slight increase of illite, which could affect permeability. This may be attributed to why illite correlates better with the flow zones, where samples with illite of 2% to 2.6% belong to the tight flow zones,1.3% belong to the low flow zone, and moderate and high flow zones have illite ≤ 0.7%.
The results of integrating the four different methods (FZI, Winland r35, HC, SMLP) with lithofacies alongside each other are presented in Figures 9 to 12 for each well. In addition, detailed analyses of all rock types in a zone are described in the following sections.
Table 2
Calculated average values of petrophysical parameters and ranges used to group rock types into five petrophysical categories modified after26
Well
|
Top
Depth (m)
|
Bottom Depth (m)
|
Thickness
(m)
|
Porosity
%
|
Permeability
mD
|
Zone/
Unit
|
r35 (µm)
|
HFU
|
Rock Type
|
FZI (µm)
|
Ranking
|
Hydraulic
Conductivity
mD/v3
|
|
|
|
|
18–22
|
200–1000
|
High
|
> 10
|
5
|
Megaporous
|
5–10
|
Very Good
|
50–120
|
|
|
|
|
12–18
10–18
10–14
< 10
|
50–200
10–50
1–10
< 1.0
|
Moderate
Low
Very Low
Tight
|
4–10
2–4
1–2
< 1
|
4
3
2
1
|
Macroporous
Mesoporous
Microporous
Nanoporous
|
3–5
2–3
1–2
< 1
|
Good
Fair
Poor
Impervious
|
20–50
5–20
1–5
≤ 1
|
EB1
|
2624.0
|
2634.7
|
10.7
|
17.7
|
332.0
|
High
|
14.0
|
5
|
Megaporous
|
6.4
|
Very Good
|
62.3
|
|
2634.7
2635.8
2640.0
2648.7
|
2635.8
2640.0
2648.7
2652.2
|
1.1
4.2
8.7
3.5
|
11.3
15.8
15.5
15.0
|
10.0
216.0
104.4
60.0
|
Low
High
Moderate
Moderate
|
2.3
13.1
8.0
6.9
|
3
5
4
4
|
Mesoporous
Megaporous
Macroporous
Macroporous
|
2.1
6.5
4.5
3.9
|
Fair
Very Good
Good
Good
|
6.0
66.6
30.0
26.0
|
EB2
|
2579.4
|
2584.4
|
5.0
|
18.1
|
333.0
|
High
|
14.7
|
5
|
Megaporous
|
6.4
|
Very Good
|
66.5
|
|
2584.4
|
2589.0
|
4.6
|
17.8
|
245.0
|
High
|
12.4
|
5
|
Megaporous
|
5.6
|
Very Good
|
51.0
|
EB3
|
2589.0
2616.6
2620.5
2622.7
2636.0
2637.3
|
2596.1
2620.5
2622.7
2636.5
2637.3
2642.5
|
7.1
3.9
2.2
13.8
1.3
5.2
|
16.7
16.2
7.0
17.1
6.4
16.7
|
164.0
275.0
0.4
304.0
0.9
110.0
|
Moderate
High
Tight
High
Tight
Moderate
|
9.6
14.6
0.8
14.0
0.9
8.3
|
4
5
1
5
1
4
|
Macroporous
Megaporous
Nanoporous
Megaporous
Nanooporous
Macroporous
|
4.7
7.5
0.8
6.4
1.1
4.2
|
Good
Very Good
Impervious
Very Good
Impervious
Good
|
35.7
64.7
1.0
70.0
1.2
31.0
|
EB4
|
2609.4
|
2612.6
|
3.2
|
17.7
|
221.0
|
High
|
11.5
|
5
|
Megaporous
|
5.3
|
Very Good
|
49.5
|
|
2612.6
|
2616.4
|
3.8
|
17.7
|
167.0
|
Moderate
|
10.1
|
4
|
Macroporous
|
4.7
|
Good
|
39.5
|
|
2616.4
2618.0
2619.8
2623.0
2630.0
|
2618.0
2619.8
2623.0
2630.0
2642.0
|
1.6
1.8
3.2
7.0
12.0
|
7.2
10.2
4.2
15.8
16.6
|
0.3
10.0
0.2
109.0
123.0
|
Tight
Low
Tight
Moderate
Moderate
|
0.4
3.5
0.5
4.7
6.9
|
1
3
1
4
4
|
Nanoporous
Mesoporous
Nanoporous
Macroporous
Macroporous
|
0.5
2.4
0.9
3.2
3.6
|
Impervious
Fair
Impervious
Good
Good
|
0.3
14.2
0.7
22.0
23.4
|
Table 3
Result of quantitative mineralogical analysis of wells OW3 and OW4 indicating the dominant cement and clay that affects flow zones
|
|
|
Framework Grain
|
Cements
|
Clay
|
Well
|
Zone
|
Sample
Depth
m
|
Quartz
%
|
Feldspar
%
|
Lithics
%
|
Glauconite
%
|
Carbonaceous
%
|
Quartz
Overgrowth
%
|
Dolomite
%
|
Siderite
%
|
Pyrite
%
|
Kaolinite
%
|
Illite
%
|
OW3
|
High
|
2613.0
|
79.8
|
3.0
|
3.1
|
1.3
|
-
|
7.9
|
-
|
1.3
|
-
|
1.6
|
-
|
OW3
|
High
|
2620.2
|
80.2
|
2.0
|
2.5
|
0.3
|
-
|
11.4
|
-
|
1.0
|
-
|
1.8
|
0.5
|
OW3
|
Moderate
|
2625.7
|
80.4
|
2.0
|
1.5
|
1.0
|
-
|
10.9
|
-
|
1.4
|
0.5
|
2.0
|
0.2
|
OW3
|
Moderate
|
2634.8
|
76.6
|
2.5
|
2.0
|
1.7
|
-
|
12.1
|
-
|
0.7
|
|
2.5
|
0.7
|
OW4
|
High
|
2615.4
|
79.8
|
2.3
|
2.8
|
1.8
|
traces
|
10.6
|
1
|
1
|
0.5
|
traces
|
0.3
|
OW4
|
Moderate
|
2615.7
|
79.7
|
2.9
|
6.2
|
1.3
|
traces
|
7.9
|
0.3
|
0.3
|
|
1.3
|
|
OW4
|
Moderate
|
2616
|
77.1
|
3
|
3
|
2
|
0.3
|
10.3
|
1
|
1
|
0.5
|
1
|
0.3
|
OW4
|
Tight
|
2617.3
|
62.4
|
3.2
|
1.1
|
2.2
|
5.8
|
18.8
|
1.1
|
6.2
|
2.6
|
4.1
|
2.6
|
OW4
|
Tight
|
2622.7
|
64.1
|
3.7
|
3.5
|
1
|
1.3
|
17.1
|
0.9
|
2.2
|
0.4
|
1.7
|
2
|
OW4
|
Low
|
2624.9
|
72.1
|
0.8
|
3
|
1
|
1
|
16.8
|
0.5
|
1.8
|
0.3
|
1.5
|
1.3
|
OW4
|
Low
|
2625.4
|
76.5
|
0.9
|
2.3
|
|
1.2
|
14.9
|
0.7
|
0.9
|
0.5
|
1.4
|
0.5
|
OW4
|
Moderate
|
2641.8
|
82
|
2.4
|
0.5
|
|
|
14.6
|
0.5
|
-
|
-
|
traces
|
traces
|
4.3.1 HFZ
The rocks are mainly coarse-grained sandstone (lithofacies A), and samples are, on average, moderately to poorly sorted and belong to class 1 of Lucia's Petrophysical classification. The HFZ's have very good petrophysical properties with porosity and permeability ranging from 18–22% and 200mD to 1000mD, respectively (Table 2). The pore throat size is the best, with Winland r 35 greater than 10 µm and FZI in the range between 5 to 10 µm, and HC between 50 to 120 mD/v3. The HFZ is composed of HFU5 and ranked as a very good reservoir quality rock. The HFZ appears at the upper part of the reservoirs in the studied wells (Fig. 9 to 12) track 2. The content of framework grain is high (80% on average), and the average content of quartz overgrowth is (10%), and siderite cement(≤ 1.3%) and illite clay mineral(≤ 0.5%) are low (Table 3). Seven HFZ's are identified in the wells. The best HFZ is found in well OW1(Fig. 9) with a thickness of 10 m and has strong flow capacity, FU1 (60%), and storage capacity of 42%.
4.3.2 MFZ
The rocks are generally composed of lithofacies A (coarse-grained sandstone) and B (fine to medium-grained sandstone) and belong to classes 1 and 2 of Lucia's Petrophysical classification. The MFZ's have good petrophysical properties with porosity ranging from 12–18% and permeability from 50mD to 200mD, respectively (Table 2). The pore throat size is good with calculated Winland r 35 values range between 4 to10 µm, FZI in the range between 3 to 5 µm, and HC between 20 to 50 mD/v3. The MFZ is of HFU4 and ranked as a good reservoir quality rock. Seven MFZ's are observed in the studied wells (Fig. 9 to 12) track 2. The best HFZ is found in well OW2 (Fig. 10) with a thickness of 7.1m, average porosity, and permeability of 16.7% and 16mD, respectively. The content of framework grain is high (79% on average), and the average content of quartz overgrowth is (11.2%) and siderite cement (≤ 1.4%) and illite clay minerals (≤ 0.7%) are low (Table 3). Seven MFZ's contribute more than 26 % flow and 58% storage capacities, FU3.
4.3.3 LFZ
The grain size of the LFZ is mainly composed of lithofacies B (fine to medium sandstone) of class 2 of Lucia's classification. Fair petrophysical properties are observed, with porosity ranging from 10–18% and permeability from 20 mD to 50 mD, respectively. The calculated Winland r35 pore throat size values range between 2 to 4 µm, FZI between 2 to 3 µm, and HC between 5 to 20 mD/v3. The LFZ is of HFU3 and ranked as a fair reservoir quality rock. Two LFZ's are observed in well OWI (Fig. 9 ) and OW4 (Fig. 12) track 2. The LFZ of well OW1 is bounded vertically at the top and bottom by HFZ. The LZF is interpreted to provide a lithofacies A and lithofacies B contact that allows fluid flow between the high flow zones 24,68, implying that the HFZs are in communication. The LFZs identified to have the same average permeability of 10mD but differ in their average porosity values of 11.3 % for well OW1 and 10.2% for well OW4, respectively. Comparison of calculated petrophysical properties between the two wells showed that OW4 has better pore throat size values (r35 of 3.5 µm, an average FZI of 2.4 µm, and HC of 14 mD/v3) than that of well OW1 (r35 of 2.3 µm, an average FZI of 2.1 µm, and HC of 6.0 mD/v3). The LZF is found in well OW2 (Fig. 10) with a thickness of 7.1m, average porosity, and permeability of 16.7% and 16mD, respectively. According to 1,69, pore throat radius is related to grain diameter, which explains why rocks of the same average permeability values may have different pore throat radius due to differences in pore volume. An average quartz framework grain of 74% and the average content of quartz overgrowth is (15.8%), and siderite cement (1.35%) and illite clay mineral( 0.9%) are presented for LFZ (Table 3). LFZ contributes about 15 % flow and 20 % storage capacities, FU3 (well OW4 in Fig. 12).
4.3.4 TFZ
The essential characteristic of TFZ is that it is predominantly composed of lithofacies C ( claystone, finely laminated with siltstone) and corresponds to class 3 of Lucia's classification. The petrophysical properties (porosity, permeability, Winland r35, FZI, and HC) of the TFZ are ≤ 1, as shown in Table 2. An average of 63% quartz framework grain with a slight increase (1.3 to 5.8%) of carbonaceous material is indicated in this rock type. The highest amount of cement (quartz overgrowth,18.8%, siderite,6.2%, pyrite, 2.6%) and clay minerals (Kaolinite,4.1% and illite,2.6%) are indicated in the TFZ samples (Table 3). The high amounts of cement and clay minerals ultimately fill the pores, block the pores, and constrict the sandstone's pore-throat, making the throat small, leading to poor reservoir properties observed in TFZ 70. According to 70, lower permeability values, as in our case (≤ 1mD), indicate that tiny pore throats play a dominant role in tight reservoirs. The pore throat is the primary physical property controlling the reservoir properties. Hence the lower the permeability, the smaller the pore throat radius.
TFZ has the most reduced reservoir property, and it is ranked as an impervious rock that acts as a barrier to flow, found in well OW3 (Fig. 11) and OW4 (Fig. 12), respectively. As a result, the TFZ has zero contribution to flow in both wells (OW3 and OW4) but has about 7% and 16% contributions to storage capacities (FU2) presented in Fig. 8 for both wells.