Spatial Distribution of Heterogeneity of the AB Reservoir Unit of Zubair Formation in the South Rumaila Oilfield, Southern Iraq

Reservoir heterogeneity, a critical factor in fluid flow and recovery processes, manifests at various scales and is influenced by depositional facies, diagenesis, and structural features. This study aims to quantify and map the spatial heterogeneity within Unit AB of Zubair Formation, south Rumaila oilfield, utilizing the Lorenz coefficient (Lk ) for vertical heterogeneity and ordinary kriging for spatial interpolation. Analyzing porosity and permeability data from 44 boreholes using the Lk coefficient revealed that the AB reservoir unit is primarily homogeneous, with 65% of boreholes exhibiting homogeneity. However, heterogeneity is present in the central and southeastern portions of the oilfield. Without considering the reservoir’s heterogeneity, placing injection wells along the eastern flank could lead to increased water production and reduced volumetric sweep efficiency.


Introduction
Heterogeneity in petroleum reservoir studies refers to the variability of petrophysical properties within a specific space and/or time, at a given scale [1].It is a fundamental concept that greatly influences fluid flow, recovery processes, and overall reservoir performance.The degree of heterogeneity is highly dependent on observational scales and measurement methods employed, making it an intrinsic and critical property to consider.Reservoir heterogeneity manifests at various levels, spanning from micrometers to hundreds of meters, and is commonly attributed to differences in depositional facies, diagenesis, and structural features such as fractures and faults [2].These variations impact the spatial distribution of petrophysical properties, ultimately shaping fluid flow behavior and recovery processes [3].Two primary types of heterogeneity exist: vertical and horizontal heterogeneity [4].Vertical heterogeneity refers to variations in properties with depth, while horizontal heterogeneity encompasses lateral variations.Both types hold equal significance in reservoir characterization and require comprehensive analysis.
One of the most important reservoir management strategies is waterflooding.Waterflooding is a secondary recovery method that involves injecting water into the reservoir to displace oil towards producing wells [4].Reservoir heterogeneity can have a significant impact on the performance of waterfloods [5].If the reservoir is highly heterogeneous, the injected water may preferentially flow through high-permeability zones, leaving behind significant amounts of oil in low-permeability zones.This can lead to low oil recovery and premature water breakthrough.There are a number of ways to address the challenges posed by reservoir heterogeneity in waterflooding.One approach is to use reservoir characterization techniques to identify and map the heterogeneities in the reservoir.This 1300 (2024) 012034 IOP Publishing doi:10.1088/1755-1315/1300/1/012034 2 information can then be used to design waterflood patterns and injection strategies that are more effective at displacing oil from all parts of the reservoir.
Zubair Formation in the South Rumaila oilfield in southern Iraq is an important formation due to its large amounts of recoverable oil reserves.Unit AB, which is located within the main pay zone of the formation, is an important unit for oil production due to its high porosity and permeability.This unit, along with other units within the main pay zone, has been developed for oil production, which has led to a decrease in reservoir pressure and production.As a result, the operating companies of this field have implemented water injection to recover reservoir pressure and sustain oil production.The study of spatial heterogeneity of this unit and other units is very important for reservoir management under current and future operating conditions, as it provides a better understanding of flow paths within the reservoir.This allows the operator to select locations for injection and production wells that are consistent with the spatial distribution of heterogeneity in the reservoir.This study aims to evaluate the vertical heterogeneity of the reservoir unit and map its lateral heterogeneity across the oilfield.The goal is to identify suitable locations for water injection wells that are compatible with reservoir and production conditions.The Lorenz coefficient (Lk) was used to quantify vertical heterogeneity, and ordinary kriging was employed to interpolate and map heterogeneity distribution across the oilfield.

The study area
The Rumaila oilfield is one of the largest in the world, with estimated reserves of over 17 billion barrels [6].It is located in southern Iraq, near the city of Basrah, and was discovered in 1953.The field is operated by the Rumaila Operating Organization, a joint venture between Iraq's state-owned South Oil Company, BP, PetroChina, and SOMO.The field comprises three domes, Rumaila South, Rumaila North, and West Qurna, that stretch from the Kuwaiti borders in the south to the Hamar Marshes in the north.These three domes combine to create a continuous oil accumulation that is more than 15 km wide in some places and more than 100 km long.The dimensions of South Rumaila oilfield can be characterized by a length of around 38 km and a crest width of approximately 12 km.The fold structure itself is a simple fold that is asymmetrical, with an eastern side inclination of 30 [7].As it extends in a NNW-SSE direction, its longitudinal axis gradually descends to form the Saddle region and moves northward toward the Rumaila North field [8].Fig. (1) depicts the geographical location of the South Rumaila oilfield and the depth at which the target AB unit is situated.
In Iraq, the Zubair Formation is the most important formation for oil production.A prograding delta originating from the Arabian Shield characterizes the depositional environment of the formation.The formation can be dated to the Hauterivian to Early Aptian period [9].A sequence of shale, siltstone, and sandstone layers comprise the Zubair Formation.The formation in the south Rumaila oilfield has been classified into five units consisting of sand and shale, which are frequently utilized in reservoir research [10] (Fig. 2) [3]: the upper shale member, the upper sandstone member (the main reservoir or main pay), the middle shale member, the lower sandstone member, and the lower shale member.The main pay of Zubair Formation at South Rumaila oilfield primarily comprises sandstones with some interbedded shales.The reservoir has a total thickness of approximately 145 m and is composed of three reservoir units, namely AB, DJ, and LN, in descending order.These units are separated by two isolating units, C and K. AB Unit, which is the focus of this study, consists mainly of sandstone with thin layers of silt and shale occasionally present.Based on the examination of conventional log data and core data from 44 wells, the AB unit thickness ranges from 3.51 to 13.87 m with an average of 9.37 m [11], Table 1.As a result, it appears that the unit is marginally thinner than other units within the main pay zone of the Zubair Formation.The porosity () values range 0.03 -0.18 with an average of 0.13, while the permeability (k) values have a mean value of 227.8 md, with values ranging from 1.6 to 624.3 m.The average values of ( and k) indicate that this reservoir unit holds fluid well and thus represents a good reservoir unit.Contrary, the volume of shale has a mean value of 0.19, with values ranging from 0.03 to 0.57.In terms of spatial distribution of these petrophysical properties (Fig. 3 a-d), the reservoir unit's thickness, , and k have a consistent pattern of distribution that is opposite that of the shale volume.The northern, middle, and southwestern parts of the area have high values for these three characteristics, while the remaining areas have low values.In contrast, high shale volume values correspond to low values of the aforementioned characteristics, and vice versa.It is well known that shale volume reduces the porosity and permeability of rocks, thereby impeding fluid flow within the reservoir unit.Therefore, petrophysical properties ( and k) are inversely related to shale volume distribution.

Data and methods used
The  and k data from 44 boreholes were used in this study to calculate the degree of vertical heterogeneity of the AB reservoir unit using the Lk coefficient.The conventional well logs such as density (RHOB), sonic (t), and neutron (PHIN) were used to estimate , while core data and NMR log were used to calculate k.Lk is a statistical measure of heterogeneity calculated by plotting the cumulative flow capacity on the y-axis against the cumulative storage capacity on the x-axis [3] If Lk = 0, then the reservoir will have an entirely homogeneous distribution, but if Lk = 1, then the reservoir will have a completely heterogeneous distribution [12].In order to map the horizontal heterogeneity, the ordinary kriging stochastic interpolation technique was used.The OK technique is a geostatistical technique based on the spatial autocorrelation principle, which states that data points close to each other are more likely to be similar than those farther apart [13].It employs a mathematical framework to estimate unknown values at unobserved locations by taking the weighted average of neighboring data points into account.The weights are determined based on the spatial distribution and correlation of data points, making Ordinary Kriging an adaptive interpolation method [14].The idea of spatial autocorrelation, which is frequently represented by a semivariogram, is the basis of OK.By quantifying the degree of spatial dependence between data points at various distances, the semivariogram offers crucial information on the spatial organization of the dataset.In order to interpolate the unknown values, this information is needed to calculate the spatial continuity and uncertainty [15].The process of "kriging weights" is used to determine the weights for each surrounding point when performing OK.These weights are determined to provide the best possible interpolation by minimizing the estimation variance.Greater weights are given to points near the target location, while less weight is given to points farther away.One of the most significant advantages of OK is its ability to estimate the interpolation uncertainty [16].By employing the kriging variance, users can assess the reliability of the interpolation at any given location.This valuable information enables decision-makers to understand the spatial variability and make well-informed choices based on the interpolation results.

Results and Discussion
The calculated Lk values for the 43 wells are shown in Table (2).The Lk values were calculated using a Microsoft Excel template.Examples of calculated Lk from north to south of the oilfield are shown in Fig. (4a).The Lk values range 0.24 -0.69 with an average of 0.45.The AB unit was considered to be homogeneous if the Lk at the well location is < 0.5, and heterogeneous if the Lk is > 0.5.Overall, 0.35% (15 wells) were considered heterogeneous, while 0.65% (28%) were considered homogeneous.In other words, homogeneity dominates the reservoir unit.The spatial distribution of heterogeneity was shown after interpolation using ordinary kriging stochastic interpolation technique, Fig. (4a).The results indicate that significant regions of the reservoir unit, particularly in the northern, southwestern, and southern areas, exhibit a state of homogeneity.On the other hand, the central portion of the oilfield and southeastern parts exhibit a condition of heterogeneity.
Effective waterflooding in the AB reservoir demands a comprehensive approach that acknowledges the varying reservoir properties and optimizes injection well placement to maximize oil recovery and minimize potential production disruptions.Strategically positioning injection wells in the northern, west-middle, and westsouth regions, surrounding production wells as they approach their economic limit due to oil depletion, is essential for efficient reservoir management and enhanced oil production.A comparison of the 2020 annual average interpolated water-cut surface [17], (Fig. 4b) with the interpolated heterogeneity surface reveals a marked increase in water-cut values in the southern portion of the oilfield relative to the northern region.This surge in water-cut indicates that a substantial number of oil production wells are likely to cease production in the future due to hydrocarbon depletion.The indiscriminate placement of injection wells along the eastern flank of the oilfield, without considering the reservoir unit's areal heterogeneity, could inadvertently increase the number of oil production wells that transition into water-producing wells.This could result in suboptimal volumetric sweep efficiency, stemming from a failure to account for the reservoir's heterogeneous nature.

Conclusion
The following conclusions were drawn from this study: (1) The AB reservoir unit exhibits a state of homogeneity (2) Heterogeneity is primarily concentrated in the central and southeastern portions of the oilfield, while homogeneity dominates the northern, southwestern, and southern regions.(3) Strategically positioning injection wells in the northern, west-middle, and west-south regions, surrounding production wells as they approach their economic limit, is crucial for efficient reservoir management and enhanced oil production.(4) The disproportionate increase in water-cut values in the southern portion of the oilfield suggests that a substantial number of oil production wells in this region are likely to cease production in the future due to hydrocarbon depletion.( 5) Indiscriminate placement of injection wells along the eastern flank of the oilfield, without accounting for the reservoir's heterogeneity, could lead to an increase in water production and suboptimal volumetric sweep efficiency.

Figure 1 Figure 2
Figure 1 Location of South Rumaila oilfield and depth to the top of AB unit

Figure 4
Figure 4 (a) spatial distribution of heterogeneity of AB unit (b) spatial distribution of annual average of water-cut of the same unit for the 2002.

Table 1
Petrophysical properties of the AB unit (well log and core data analysis)

Table 2
Lk coefficients for the used wells