Determining the Difference in Homogeneity between the Euphrates and Jeribi Formations in the Qayyarah Oil Field Based on Vertical and Horizontal Core Samples

Abstract


Introduction
Coring represents an important procedure to calibrate the petrophysical model and obtain additional information about the reservoir not obtainable by well logs.Several types of cores can be recovered from a well, including horizontal and vertical oriented cores.The two main considerations that influence reservoir quality and estimate hydrocarbon reserves are porosity and permeability.As a result, the changing trend of porosity and permeability in the reservoir zone must be investigated.Vertical permeability (Kv) is important in reservoir management and development, such as determining the optimal well placement and rate of production (Zahaf and Tiab, 2002).The difference in permeability between the vertical and horizontal directions inside a formation is represented by the vertical to horizontal permeability ratio (Kv/Kh) (called anisotropic permeability).(Kv/Kh) ratio is significant in reservoir modeling studies since it applies to vertical wells and is especially relevant in partially penetrated or horizontal wells.The vertical permeability of each bed in a bedded reservoir differs from that of the surrounding beds.As a result, these reservoirs are classified into layers based on the (Kv/Kh) relations (Shedid, 2019).The porosity and permeability of carbonate rocks in several Iraqi oil reservoirs have been investigated by many researchers (Sadeq and Yusoff, 2015;Mamaseni et al., 2018;Mohammed, 2018;Al-Jaberi and Al-Mayyahi, 2018;Abdulrahman et al., 2020;Mamaseni, 2020;Al-Baldawi, 2021;Albeyati et al., 2021;and Al-Majid, 2021).The permeability-porosity equations were derived by Gamage et al. (2011) based on sediment type and particle size distribution.Variations in permeabilityporosity correlations were evaluated using the influence of interlayer water and the overall compaction history.According to Lucia (2007), permeability (K) is a function of porosity (φ) and pore size.Iheanacho et al. (2012) investigated many vertical and horizontal permeability relations for sandstone and shaly sandstone reservoirs and concluded that vertical permeability reduces with depth.As indicated in Table 1.Fazelalav (2013) discovered many equations for predicting vertical permeability for Arbuckle Formation.However, these relationships are hampered by weak correlating coefficients.The impact of kv/kh anisotropy was investigated by producing reservoirs with kv/kh values of 0.1, 0.2, 0.4, and 0.55.As the vertical to horizontal permeability ratio rises, cumulative oil production rises constantly.This is because a high (Kv/Kh) ratio enhances hydrocarbon vertical cross-flow between reservoir strata (Abraham et al., 2019).The aim of this study is to use the directed porosity and permeability measurements taken from the core samples of the Jeribi and Euphrates formations to identify the difference in homogeneity between the two formations.

Location and Geology
Qayyarah oil field (study area) is located about 50 km to the southwest of Mosul city on the western side of the Tigris River (Fig. 1).According to the tectonic framework of Iraq (Dunnington, 2005), the study area lies within the low folded zone (Fig. 1).The region is delineated low structures with NW-SE direction, such as the folds of Najmah, Jawan, and Qaiyarah.These structures are accompanied by low synclines, which feature multiple sinkholes of varying widths.(Fig. 2).Stratigraphically, the lower Miocene Euphrates, and Middle Miocene Jeribe formations are regarded as the primary targets of the Tertiary petroleum system in the western section of the Zagros Basin.The formations are the important oil reservoirs in the Qayyarah field, which is characterized by their good permeability and porosity.Below is a brief description of each of the two formations, based on National Oil Company (NOC) reports.
The Jeribe Formation consists mainly of grey limestone with thin overlaps of chalky limestone.The thickness of formation in well QY39 is about 45 m.The Euphrates Formation is mostly made of limestone and dolomite, with anhydrite nodules.Because the Dhiban Formation is primarily formed of anhydrite, it is considered the cap rocks for the Euphrates reservoir.Its thickness in the studied well is about 62 m, while its cap rock (Dhiban Formation) is about 22 m (Fig. 3).In this study, routine core data for analysis was used to develop new correlations and characterization of limestone reservoirs by measuring the permeability and porosity on a set of sedimentary rock samples from Jeribi and Euphrates formations in the Qayyara oil field.The paper investigates the relationship between permeability and porosity for these samples.

Materials and Methods
At different depths in well QY39, 123 vertical core samples and 108 horizontal core samples were collected and prepared for performing various tests (Tables 2, and 3).Porosity and permeability values for all samples were measured by using Corelab Helium porosimeter and Core lab Micropermeameter respectively.Many relationships among measured parameters were performed to evaluate the studied formations.These relationships are: • Log permeability (LogK) -Porosity(ɸ) • Vertical permeability (Kv) -Horizontal Permeability (Kh) • Vertical porosity(ɸv) -Horizontal Porosity(ɸh) In addition, the ratios of Kv/Kh and ɸv/ɸh were used to explain the heterogeneity between the two formations.Also, the subtraction between these two ratios (Kv/Kh minus ɸv/ɸh) may give important information about the type of pores and the percentage of shale.

Results
Initially, it is necessary to draw a relationship between both porosity and permeability, which measured from core samples, with the depth for both formations (Jeribi and Euphrates) to see the compatibility between the two parameters with depth (Fig. 4).The relationship between permeability (K) and porosity (φ) explains the difference between interconnected pores (effective porosity or permeability) and total porosity, which may be resulted from the ratio of shale and clay materials that fill some voids of rocks and lead to their separation.A relationship between the porosity and logarithmic permeability was established.Figs. 5, and 6 shows logK -φ linear relationships for Jeribi and Euphrates Formations in the study area.the left end of the descending curve, which indicates the porosity value when the permeability approaches zero, differs in the two formations.It equals 15.5 in the Jeribe Formation and increases to 17 in the Euphrates Formation.It is also noted that there is a stronger correlation (R 2 ) between the two variables in the Euphrates Formation.Exponential relationships between (Log K and φ) for the two formations were drawn to establish new equations (Figs. 7 and 8).The R 2 values for the equations that appeared in Fig. 5 confirm the difference in homogeneity in the two formations.In addition, an increase in R 2 values may indicate a decrease in the shale size.The permeability of the Euphrates Formation has a larger exponential connection with porosity than that of the Jeribe Formation, suggesting that the Euphrates Formation is permeable and porous, with a high potential for hydrocarbon accumulation and production.Figs. 9 and 10 displays a Log-Log plot of vertical permeability (Log Kv) vs horizontal permeability (Log Kh) based on 102 core data points, yielding an equation for determining vertical permeability.From the lines slope and R2 values appeared in Fig. 6 it is clear that the horizontal permeability is more effective than the vertical one in the Jeribe Formation, while there is a great convergence in their values in the Euphrates Formation, which can be explained based on homogeneity in the vertical and horizontal directions.The high R2-value (0.989) produced from Log Kv -Log Kh relationship for the Euphrates Formation is closely matched the high R2-value found by Fazelalav (2013) in formations with Kv much greater than Kh In Figs.11 and 12 below, a vertical porosity (φv) -horizontal porosity (φh)) relationship shows a greater correlation in the Euphrates Formation than the Jeribe Formation.The ratio Kv/Kh is very important in petroleum studies, especially in the horizontal wells, where the amount of oil production of these wells is estimated by knowing this ratio.This is due to the fact that a high Kv/Kh anisotropy ratio enhances the vertical cross flow of hydrocarbon across reservoir beds.A relationship between Kv/Kh and depth was drawn to understand the rate of oil production at different depths (Fig. 13).The mean value of Kv/Kh in the Jeribe and Euphrates Formations was 0.97 and 0.93, respectively, indicating the great homogeneity in the distribution of pores in both formations.Despite this homogeneity, there are significant increases to the ratio of Kv/Kh in some depths of both formations, which may mean an increase in the number of vertical joints and vugs in those depths (Fig. 13).The ratio (ɸv/ɸh) can be used to understand the joints system and their distribution in the two studied formations by comparing it with the ratio (Kv/Kh).Despite the variation in the values of the two ratios, there is a great agreement in the directions of their increase and decrease in both formations (Fig. 13).The great agreement between the values of the two ratios greatly confirms the increase in vertical joints at a certain depth, while incompatibility may give other evidence related to the closing of some pores in the vertical direction or the increase of pores ratio in the horizontal direction.
The difference between the two ratios (Kv/Kh minus ɸv/ɸh) is very important to explain the closing of some horizontal pores, which increases Kv/Kh while keeping ɸv/ɸh constant.This closing in the pores increased the difference between the two ratios in the Jeribe Formation, while the difference between them appears slightly in the Euphrates Formation (Fig. 9).The greater difference between Kv/Kh and ɸv/ɸh appears clearly in the lower part of the Jeribe Formation, which may indicate a closure in some of the horizontal pores in the formation at this depth.The slight difference between the two ratios indicates that there is a great homogeneity between permeability and porosity in the horizontal and vertical directions.This appears to be evident in the Euphrates Formation, such as shown in Fig. 14.

Discussion
The R 2 value is an important indicator in all relationships drawn up in this paper but with different interpretations and meanings.Porosity and permeability in the Jeribe and Euphrates Formations depend on the ratio of fractures and vugs in them.Φ-logK relationship of Euphrates Formation shows stronger R 2 than in the Jeribe Formation, which may indicate an increase in effective porosity.The relationships (φv-φh) and (Kv-Kh) showed a large and strong R 2 in the Euphrates Formation, in contrast to the Jeribe Formation, which may give a clear idea of the great homogeneity in the distribution of joints and vugs in the Euphrates Formation.These strong relationships can be used to calculate any of the parameters in terms of the other.Kv/Kh ratio in this study clarified the homogeneity at different depths, which may give a good idea about the location of vertical joints, while Kv/Kh minus ɸv/ɸh explains the effect of separate voids on both formations.

Conclusions
• Determine the difference in the compaction between the two formations by relying on the linear relationship between the logarithm of permeability and porosity, which can be expressed by the porosity value at permeability close to zero.• Depending on the exponential relationship between the permeability logarithm and porosity, it was found that there was a near-strong correlation between their values in the Euphrates Formation compared to the Jeribe Formation.This may indicate an increase in the volume of interconnected pores in the Euphrates Formation.• The strong correlation between vertical and horizontal permeability in the Euphrates Formation gave a clear idea of the great uniformity in the distribution of fractures and vugs in both directions, which makes the formation a typical oil reservoir.• The coefficient of determination was used successfully in this study to explain the difference in petrophysical properties between the two formations.• This study concluded the great homogeneity in the distribution of interconnected pores and vugs by the mean ratio of vertical to horizontal permeability that approached one in both formations.

Fig. 4 .
Fig. 4. The agreement between φ and K curves with the depth for; a) Jeriby Formation and b) Euphrates Formation in well QY39

Fig. 9 .
Fig. 9. Relationship between Log Kv and Log Kh for Jeribe in well QY39

Fig. 13 .
Fig. 13.The relationships between the ratio Kv/Kh and ɸv/ɸh with the depth for both formations

Table 2 .
The horizontal (H) and vertical (V) permeability values for Jeribe and Euphrates Formations at each core sample depth.The Red one is Jeribe, while the black is Euphrates

Table 3 .
The horizontal and vertical porosity values for Jeribi and Euphrates Formations at each core sample depth The Red one is Jeribi, while the black is Euphrates