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Article

Matching of Water Breakthroughs in a Low-Resistivity Oil Reservoir Using Permeability Anisotropy

by
Svetlana Rudyk
1,
Majid Al-Musalhi
2,
Usman Taura
1 and
Pavel Spirov
3,*
1
Oil and Gas Research Center, Sultan Qaboos University, Muscat 123, Oman
2
Earth Science Department, Sultan Qaboos University, Muscat 123, Oman
3
Geology Department, Faculty of Science, Palacky University, 779 00 Olomouc, Czech Republic
*
Author to whom correspondence should be addressed.
Appl. Sci. 2024, 14(11), 4618; https://doi.org/10.3390/app14114618
Submission received: 28 April 2024 / Revised: 18 May 2024 / Accepted: 22 May 2024 / Published: 27 May 2024
(This article belongs to the Special Issue Petroleum Exploration and Structural Geology)
Browse Figures
Versions Notes

Abstract

:
In a mature middle and lower Gharif field in Oman, uncertainties surrounding initial water saturation and early water breakthroughs of unknown sources and paths suggest the presence of significant bypassed oil. In order to determine the areas with remaining oil, petrophysical and logging data of seven wells were processed using Techlog software and imported into Petrel software for modelling and simulation. Porosity was calculated using the Electric Propagation Time log and was utilized to evaluate the presence of oil, particularly in the upper tight zone of the formation. Despite the low resistivity readings in the highly porous layers, caused by good network connectivity and high formation water salinity, the resistivity contrast was sufficient to differentiate them from the oil zone. However, the calculated water saturation (Sw) in the tight top oil zone was high, consistent with the observed water production in the field. To improve the match between production data and simulation results, sensitivity analyses were conducted on various permeability anisotropy and relative permeability values within the model. The analyses showed that core-derived permeability anisotropy (vertical to horizontal ratio of 1:1) yielded a better history match for water production compared to the conventionally used value of 1:10. Water saturation maps were generated at the start and the end of production to highlight saturation distribution within the reservoirs. The maps revealed that in the lower porous part, the oil was fully depleted around the wells but remained trapped in the undrilled areas.

1. Introduction

1.1. Low Resistivity Reservoirs

Low resistivity in oil-bearing zones can lead to low contrast with water-bearing zones, resulting in water saturation above 50%, due to which they can be overlooked and bypassed [1]. For example, no resistivity contrast between oil and water zones was observed for the reservoirs in Sudan which were bypassed in the past [2]. Low resistivity and low contrasts can be associated with water salinity, clay type, micro-porosity, the presence of conductive minerals, anisotropy, bed thickness, bed dip, drilling mud invasion, and logging tool resolution [1,2,3,4,5]. High-salinity interstitial water causes low resistivity within the pay zone, while low-salinity water can cause low contrast in the pay zone.
The main features of a low-resistivity pay zone are abundant microporosity and high irreducible brine saturation resulting from cementation, clay coating, or clay bridging within pores and in fine-grained sandstones [1,3]. Due to the lack of vertical resolution, the tools provide an average resistivity measurement over the bedded sequences with laminar shales. With dispersed clay, the irreducible water saturation increases, which can dramatically reduce resistivity. The actual water saturation can be high but water-free hydrocarbons are produced due to micro-porosity [4]. In the presence of conductive minerals such as metal sulfides, the calculated water saturation can be overestimated compared to the amount of water produced during hydrocarbon production. However, the causes of low resistivity can differ from reservoir to reservoir or between particular depositional environments and may not be directly applicable to other reservoirs where conditions initially appear to be similar [5]. Thus, uncertainty in low-resistivity pay zones can arise at the initial phase of the evaluation of water saturation before the start of production.

1.2. Difficulties in Reservoir Simulation of Mature Fields

The revision of existing data accumulated over a long period of production from mature oil fields is required for the evaluation of remaining oil reserves to plan future operations such as the drilling of new wells, water injection, pump settings, as well as the repair and maintenance of existing wells. Reservoir simulation is used to model and reproduce the original state in the field using history matching to predict future well and field performances. A good history match serves as a means for verifying the accuracy of the dynamic model to adequately present the field performances and their appropriateness for the predictions of future field characteristics such as oil production, water production, and pressure. The static and dynamic models undergo a series of revisions to obtain a match between the measured field data and the calculated data from the model. However, a prolonged production history with field operations overlapping in time and space complicates the simulation. Additionally, production from multiple reservoirs can occur simultaneously, which could lead to uncertainties regarding the individual performances of the reservoirs and wells. The original data are often missed, which makes it impossible to compare with the base case that occurred before the start of production. New wells are often drilled in the areas already under previous water injections. In this regard, the following wireline logging cannot provide reliable data for the water saturation. All of the above-mentioned issues contribute to inconsistency and a lack of robust evidence supporting the explanations of observed anomalies. In addition, the use of different parameters during history matching by various investigators often requires rescaling. The segmentation and isolation of various formation intervals can also be required through the introduction of baffles or barriers vertically and horizontally. As a result, models and predictions vary largely from investigator to investigator, leading to contradictory conclusions.
Early water breakthrough during water injection may lead to the bypassing of oil reserves, especially in heterogeneous formations. Other sources of water breakthroughs such as those resulting from borehole cementing integrity issues, water encroachments along the high permeable streaks, fractures, or underlying aquifers of unclear sources and paths make the history matching especially complicated. In the zone of active aquifers and dependent on the structure of the traps, tilted OWC can be formed. This can lead to early water breakthroughs in the areas of the uplifted plane of OWC [6].
Fluid flows within the formation are controlled by the mobility ratio and permeability anisotropy. The mobility ratio (M), which describes the stability of a displacement process, is defined as the ratio of the mobility (λ) of the displacing fluid to the mobility of the displaced fluid:
M = λ w a t e r λ o i l = K r w a t e r K r o i l ⋅ μ o i l μ w a t e r
where Kr is the relative permeability, μ (cP) is the viscosity, crude oil is the displaced fluid, and water is the displacing fluid.
Efficient piston-like frontal displacement of oil occurs at M ≤ 1. A significant contrast between relative permeabilities and/or viscosities creates a high mobility ratio indicative of an unstable displacement front and fingering [7]. Notwithstanding, reservoir engineers widely use relative permeability curves as a parameter in history matching because of the inherent uncertainties in these flow curves. By varying relative permeability curves, reservoir engineers can adjust the fluid flow behavior in the model to match the observed production data. Therefore, uncertainty in relative permeability is an important consideration in history matching and reservoir engineering.

1.3. Permeability Anisotropy

Permeability anisotropy is mathematically described as the ratio of vertical to horizontal permeability (Kv/Kh) within a formation. Rock permeability is influenced by the size, shape, and orientation of the grains that make up the reservoir rock. When these grains are not uniformly distributed or have a preferred orientation (anisotropy), they can cause permeability variations measured in different directions. This phenomenon is known as permeability anisotropy [8]. The permeability anisotropy established during deposition may be further modified by burial diagenetic processes including the compaction, dissolution, and cementation of grains. The packing and shape of grains change due to the compaction, leading to higher permeability in the horizontal than in the vertical direction. Clark (1969) indicated that the horizontal permeability (Kh) is higher than the vertical permeability (Kv) for both large and flat rock grains and concluded that generally, vertical permeability is lower than horizontal permeability, especially if the sand grains are small and have irregular shapes [9].
Moreover, laminar heterogeneities are very common in sandstone reservoirs, resulting in successive layers that may differ in permeability by several orders of magnitude [10]. In such layering structures, the permeability measured parallel to the layers is higher than in the perpendicular direction. However, Kv can be bigger than Kh if measured along fractures [11].
Anisotropy is also a scale-dependent property. Smaller volumes tend to be isotropic, as can be seen in core plugs. In contrast, at the formation scale, bedding fabric can lead to significant differences between Kv and Kh. In fluvial systems, the arrangement of channel and inter-channel elements can have a substantial effect on anisotropy. For example, well-intercalated channel systems have a higher tendency to be isotropic, whilst the preservation of more discrete channels will exhibit a more anisotropic behavior.
The permeability anisotropy controls single-phase fluid flow as well as two-phase effective mobility of immiscible phases such as oil–water, and provides a framework to upscale the effects of such structures to field-scale grids for reservoir models [11,12].
A more homogeneous permeability distribution has important consequences for the efficiency of fluid flow, and hence, the implication is made that fluid displacement processes commonly applied in the industry (as in a waterflood project) will be more efficient in a sub-vertical direction. In contrast, displacement fronts are expected to be more highly fingered in a horizontal direction, subparallel to bedding or laminae.
The ratio of vertical to horizontal permeability (Kv/Kh) represents the contrast in permeability between the vertical and horizontal planes within a formation, and it is used in simulation. Therefore, the derivation of relevant Kv/Kh ratios is of great importance to predict and guide hydrocarbon recovery at the time scale of a few decades typical of subsurface exploitation schemes, but also to model secondary migration processes leading to the location and filling of hydrocarbon reservoirs over geologic time.
In the present study, the effects of permeability anisotropy and relative permeabilities are studied on reservoir simulation results to find an explanation for early water breakthroughs and subsequent high water production in the oil reservoirs. The water breakthroughs from the production wells occurred before the start of water injection in the field; it is therefore believed that a decent volume of unrecovered oil could have been bypassed. Petrophysical and logging data of seven wells were processed using Techlog software and further imported into Petrel software for modelling and simulation. Various reasons for the early water breakthroughs and mismatches in water production were investigated. The maps of the remaining oil are presented.

2. Geologic and Production Overview

2.1. Geologic Setting of the Oil Field

The oil field under investigation is located in the west-central part of the Sultanate of Oman on the eastern flank of the Rub Al Khali Basin, near the international border with Saudi Arabia. The field was discovered in 1978. Since then, a total of 32 wells have been drilled in the Haushi reservoirs of the Middle and Lower Gharif. The Haushi Group, deposited during the Late Carboniferous to Early Permian period, consists of the glaciogenic Al Khlata Formation and the marginal marine to fluvial Gharif Formation overlaid by the Khuff Formation [13]. As the deposits are located close to the marine basin, the facies are transitional from marine to the west to basinal to the east. The Gharif Formation exhibits complex lithological architecture due to these reasons. The Lower Haushi reservoir of the Lower Gharif (LHS), which represents the first post-glacial Permian transgression, is the most prolific of the reservoirs, producing 45° API oil. The sands are mostly of glacio-lacustrine or deltaic origin, almost entirely composed of silica with intensive quartz cementation, which increases with the depth and degrades permeability. Porosity is up to 23%. Fissures were detected in core samples, resulting in permeabilities of up to 200 mD. More details about the Gharif Formation and the Haushi reservoirs in this field can be found in [14,15].

2.2. History of LHS Reservoir Production and Modelling

At the start of production in 1980, the first eight wells produced from the Lower Haushi Sand (LHS) reservoir comingled with the overlying reservoirs of the Middle Gharif, which comprise the following from top to bottom: Upper Haushi Sandstone (UHS), Dolomite Drain (DD), Sandstone Drain (SD), and Basal Gharif Sand (BS). The dates of comingled production from the reservoirs are given in Table 1.
The wells are characterized by high initial oil rates with varying degrees of water encroachment. In 1996, Well D was converted to an injector and was the only injector for the next 11 years. Water breakthroughs, however, were recorded before the water injection started. The sources and paths of water inflow remain uncertain.
The comingled production significantly complicated the interpretation and simulation of the production results. The biggest challenge in the simulation was matching the Lower Haushi water breakthroughs, specifically, the timing of the breakthroughs and the magnitude of the influx. Different explanations for the water breakthroughs and several static and dynamic reservoir properties have been considered to improve the matching in the past [16].
In the early wells drilled, the Lower Haushi appeared to have an oil-down-to (ODT). This suggests the presence of the oil–water contact (OWC) in the underlying Al-Khlata Formation. However, the OWC remained uncertain due to the complexity of the mineralogy, uncertainty around the formation water resistivity at that time, potential changes in the contact, and saturation changes due to production.
The additional water observed was believed to be a result of failure in the plug and wellbore integrity issues, which led to the influx from either the overlaying Khuff Formation or the underlying Al-Khlata Formation. The step change in the water–oil ratio (WOR) was indicative of sudden failure more than likely associated with wellbore integrity as opposed to water coning or water channeling through the wellbore [16,17].
Thus, the high water influx is attributed to a combination of aquifer influx and water encroachment through defective wellbores, most likely due to poor well cementing [16]. If a significant amount of water is attributed to wellbore issues and not the reservoir, then there is potential for additional oil recovery from the Lower Haushi.

3. Materials and Methods

The objective of this study was to evaluate the remaining oil reserves by comparing the oil reserves before and after production. Core data from LHS formation, including porosity, permeability, Kv, and Kh, were obtained from four wells. Log data from seven wells, which were drilled before 1998, were used for the static modeling. Zonation and well correlation were performed using a gamma ray (GR) log. Clay volume (Vsh) was calculated using GR. A Juhasz plot was imported in Techlog to determine the clay type, adjust the baselines for calculations of clay volume, and choose the appropriate water saturation model [18]. Porosity (Phi) was calculated using a density log, which provided a good match with the core data, and permeability was calculated using correlations with porosity, as described in [14]. Water saturation was calculated using the Archie and Simandoux equations for comparison. Petrophysical and logging data were processed using Techlog software (2017) and further imported into Petrel software (2019).
A fine-scale 3D grid consisting of 660,192 cells (69 × 104 × 92) oriented SW–NE at an angle of 50 degrees was generated to create 3D models of thickness. Petrophysical properties were populated using sequential Gaussian simulation. Each cell had a size of 100 m × 100 m × 1.6 m (max) and the model was optimized for computational efficiency through cell cut-off, the utilization of theoretical aquifers, grid size refinement, etc. Sensitivity analyses for porosity and permeability cut-offs and other main uncertainties such as the oil–water contact were also conducted. Details of the modelling and simulation procedures can be found in [14,15].
Dynamic simulation was carried out using Intersect software to history match the production data from the above-mentioned wells of LHS up to the year 1999 and to further evaluate the remaining oil reserves. The history match philosophy adopted was that a simple model capable of a general match is preferable to a complex model requiring heavy “tuning” to individual wells. The history-matched data in order of importance were the oil production rate (OPR) and the cumulative water cuts and water production rate (WPR), RFT pressures, GOR, productivity index, bottom-hole shut-in, and flowing pressures. To investigate the influence of permeability anisotropy, the model was history-matched by varying the Kv/Kh ratio from 1:10 to 20:1. This was followed by analyzing the sensitivity of relative permeability curves. Previous coreflood data indicated that the maximum water relative permeability (Krwmax) in the presence of irreducible oil saturation was 0.8. Therefore, five different relative permeability curves were generated by shifting both curves (Krw and Kro) to the left or right or by shifting a single curve at a time. The maps of initial water saturation and at the end of production are presented. The percentage of remaining reserves to the initial oil in place is also presented for all of the sensitized cases.

4. Results and Discussion

4.1. Vertical Permeability as a Function of Horizontal Permeability and Porosity

Conventionally, core measurements are the primary source for horizontal permeability (Kh) data, while vertical permeability (Kv) measurements are often scarce. Therefore, correlations based on Kh or the Kh/porosity (Φ) ratio are commonly used to estimate Kv. Generally, the equation used for Kv is given in Equation (2) [19]:
Kv = (Kh/Phi)0.5
However, we have found that the power coefficient of 0.5 does not match the correlation line when plotting Kv vs. (Kh/Phi)0.5. The datasets of individual wells required a substantially higher slope than 0.5. To clarify the power coefficient, Kv was plotted vs. Kh/Phi for four wells in Figure 1. The highest slope of 2 was required for Well J, which is located outside of the considered area. The lowest slope of 0.7 was obtained for Well C. The analyses on Wells B and G indicate that most of the data have a slope of 1.2.
The line which intercepts most of the data is described using the following equation:
Kv = 0.05·(Kh/Phi)1.2
where the y-intercept is 0.05 and the power coefficient which regulates the slope of the line is 1.2.
It could be assumed that the large data scattering is caused by the porosity. For the given datasets, porosity was measured in both horizontal (Phi_h) and vertical (Phi_v) directions and showed significant differences. For example, although the porosities in the horizontal and vertical directions of Well G are concentrated around a 1/1 line, the majority of the data are scattered (Figure 2a). These deviations are caused by fissures, as mentioned in the core description.
It can be expected that the data scattering in Figure 1 can be decreased if we use the Kv/Phi_v ratio instead of Kv; however, the effect is the opposite. The scattering of data increased dramatically on the plot of Kv/Phi_v vs. Kh/Phi_h in Figure 2b compared to Kv vs. Kh/Phi_h in Figure 1, which shows data from Well G, as an example. Consequently, the Kv/Kh ratio was further analyzed to understand its significance in modelling the displacement.

4.2. Permeability Anisotropy (Kv/Kh)

Permeability anisotropy (Kv/Kh), which is often represented as an integer ratio (Widarsono et al. 2006) [19], is an essential parameter that controls fluid production rates, OPR, and WPR. If the fractured samples with Kv/Kh above 1000/1 are excluded, the data of all wells converge between the upper line of Kv/Kh = 1/1 and the lower line of Kv/Kh = 2/3 (Figure 3). Most of the data follow the line of Kv/Kh = 1/1. Well G data are more widely scattered, while some of the deviating points belonged to Well C. Most of the data were below 10 mD, which may mean that Kv/Kh has little significance in terms of recovery because such low permeabilities affect flow rate and the fluids are diverted almost exclusively through the more permeable cells (Lishman 1970) [20].
Despite the absence of fissures in Well G, certain intervals within the very tight formation exhibited Kh up to 200 mD. However, irrespective of the high values of the permeabilities, ranging up to 10,000 mD, the data of Well B closely followed a 1/1 line. The data deviating above the 1/1 line indicate secondary fabrics with increased Kv, while the data below indicate a depositional pore structure. In [21], it can also be seen that a group of data followed a 1/1 line, with other data below it indicating a higher Kh.
Simulations often employ a default Kv/Kh ratio of 0.1, which indicates a laminar (layered) rock structure, as suggested by Meyer and Krause [22]. For example, a Kv/Kh ratio of 0.19 was used for the Arbuckle Formation, which is a laminar rock structure without fractures [11]. In contradiction with the commonly held notion that laminated sandstones have a low Kv/Kh, it was found that the values for the laminated sandstones of the Virgelle Member varied between 0.5 and 0.8, while it was 0.7 for the homogeneous sandstone [12], which is close to the 2/3 that we found for the Gharif Formation [14].
A Kv/Kh value of 1/1 indicates that the LHS sandstone is very homogeneous, through which the water flow can be equally diverted in all directions, with the upward water inflow into the upper layers controlled only by gravity. The relatively higher vertical water mobility can be a substantial factor for the early breakthrough observed in LHS.

4.3. Water Saturation Calculation

Water saturation was calculated using Archie’s equation:
Sw = [(aRw/RtPhim]1/n
where m is the cementation exponent, n is the saturation exponent, aRw is the formation water resistivity (Rw) multiplied by tortuosity (a), Rt is the Formation resistivity, and Phi is porosity.
Applsci 14 04618 g003
Figure 3. Permeability anisotropy (Kv/Kh) derived from core data from four wells in LHS.
Figure 3. Permeability anisotropy (Kv/Kh) derived from core data from four wells in LHS.
Applsci 14 04618 g003
A Pickett plot was used to derive Archie’s parameters, as shown for two wells in Figure 4. The slope of the line across the water zone is 1/m, while the resistivity on the x-axis corresponding to the y-intercept at Phi = 1 indicates Rw = 0.025 Ohmm, with a = 1. The lines across oil zones are parallel to that of the water zone, implying similar m in both zones. Pickett plot can also be used to determine n-m for the oil zone. Red lines indicate n–m = 0.4, which implies that n = 2. The data more clearly follow the lines with slopes of 0.4 in the plot of Well E.
Two field water samples with total dissolved solids of 166 and 183 g/L collected in the year 2005 (although water injection started in 1997) were considered to determine the formation water salinity. At a reservoir temperature of 90 °C, such salinity results in the resistivity close to the Rw determined using the Pickett plot, which can indicate that the Rw reflects the actual formation water resistivity.
The cementation exponent can vary laterally as well as vertically with the depth [23,24]. The m decreases with a decrease in porosity and salinity [25]. Experiments using a porosity greater than 65% showed that an increase in m is universally correlated with the volume fraction of pore throats for all of the samples, regardless of their particle shapes, particle size range, and porosities [26]. On the other hand, m decreases with the increase in clay volume due to the large amount of interconnected clays combined with the formation water effect [24]. As a result, m = 1.3 can be obtained in unconsolidated sand, as well as in shaly sand [27,28]. A cementation exponent of 1.5 represents the analytical solution for the case where the rock is composed of perfect spheres [25].
Based on that, it can be concluded that the cementation exponent of the LHS reservoir, which is uniformly close to 1.6 in all wells, indicates a high degree of connectivity in the pore network and poor cementation if such a low value is not associated with the shaliness. The parameters m and n are often close in magnitude; however, n = 2 was used in the Sw calculations, since most of the data clearly followed two lines of n-m = 0.4 in Figure 4b.
Thus, the obtained Archie’s parameters are as follows: aRw = 0.025, m = 1.6, and n = 2. In the previous calculations, the parameters used were aRw = 0.035, m = 1.66, and n = 2 and aRw = 0.054, m = 1.8 or 1.95, and n = 2 [16]. It is important to highlight that small differences in Archie’s parameters can cause big differences in the Sw. Therefore, the sensitivity of the Sw to Archie’s parameters was studied using our values (revised) and previous datasets. The decrease in aRw by 0.1 decreased the Sw by about 5%, while a decrease in m by 0.06 decreased Sw by about 2%. In general, the Sw calculated using the revised parameters is about 7–8% lower than the previous dataset, thus increasing oil saturation to values higher than 60%. Regardless of the specific Archie’s parameter set used, the calculated oil saturation remains above 50% in both cases, indicating a significant oil presence in the formation. In this regard, previous evaluations of Sw can be considered conservative, and, hence, high water production cannot be associated with underestimations of Sw.

4.4. Clay Type Using a Juhasz Plot

The logging curves of GR, porosity, and water saturation are shown for two wells in Figure 5 and Figure 6. The LHS reservoir is divided into two sections, the upper section (LHS-UD) and the lower section (LHS-LD), by a shale layer. The uppermost section (approximately 4 m) of the LHS-UD reservoir consists of tight sandstone with porosity values significantly below 6%. Below this zone, thin layers have even lower porosities, measuring less than 2%. This upper layer of LHS-UD can be characterized as a tight oil reservoir due to its low porosity and permeability. Such tight oil sandstone reservoirs attract much attention in many countries, and especially in China, they present huge oil resource potential [29].
Due to the very low porosity, and despite resistivity in the range of 10–50 Ohmm, the Sw at the top of LHS-UD results in values close to unity. Figure 5 and Figure 6 depict the water-bearing low-porosity zones (shown in blue) in the uppermost 4 m of LHS-UD. This observation suggests a potential re-evaluation of the initial assumption that oil is located above the water in the reservoir. Figure 7 depicts the zonation scheme used in the model.
Shale volume (Vsh) and clay type can significantly affect the values of water saturation derived from resistivity logs. To account for shaliness in the calculations of Sw, numerous water saturation models have been derived, which can be found elsewhere [25,27]. The Juhasz plot was used to evaluate the clay type distribution, as shown for Wells G and E in Figure 5 and Figure 6. The shale lines were adjusted to make sure that the shale in the middle of LHS was indicated as shale. Along the depth, clay types were distributed differently, as indicated by the different colors. In the tight oil section, the clay is pore-filling, with Vsh between 20 and 25%. In the cleanest part of the sandstone with the highest porosity, the dispersed clay is below 7%. In other parts also with high porosity, the Vsh of dispersed clay varies between 7 and 15%.
In Well E, the lowest 8 m of LHS-LD have resistivity below 1 Ohmm, resulting in Sw > 80%, which indicates a water zone and oil–water contact (OWC). This can be explained by the fact that this well was drilled 7 years later than Well G, and this water zone at the bottom shows a rise in OWC rather than water breakthroughs. This also shows that in the porous part, the contrast between oil and water is sufficient to separate them even at such low resistivity, implying that the oil zone in Well G reaches to the base of the reservoir. However, this water influx from the aquifer and the logging response of the invading water may not be the same as the connate water saturation.
Hence, the lower parts of LHS-UD and LHS-LD sandstone are mostly clean homogeneous sandstone with porosities of up to 23% on average, with a low fraction of dispersed shale, which should not noticeably affect the water saturation. A sufficient contrast between oil and water zones is generated irrespective of the low resistivity. However, in the tight part of LHS-UD, low porosity with a shale volume of about 20–25%, even at higher resistivity, results in high water saturation due to a low contrast between oil and water.

4.5. Well Logging Profile for LHS Reservoir

Gamma ray logs, porosity, resistivity, water saturation, and perforation intervals in the LHS reservoir are shown for Wells G, D, C, B, H and E in Figure 7. Well A was not included because well logging was not performed in this well. Instead, Well H was shown for correlation purposes, but it did not produce from LHS.
Core porosity closely followed the calculated log-derived porosity in Well G. In Well C, the core porosity also closely followed the log-derived porosity in the tight section of LHS-UD, but log-derived porosity was higher in LHS-LD.
In the lower part of the LHS-UD and over the entire LHS-LD, the porosity is up to 23% and the resistivity is below 5 Ohmm. The resistivity in the porous layers can be less than 1 Ohmm. Porosity does not vary significantly across the LHS-LD section in Wells G and C. However, the porosity noticeably decreased from top to bottom in Well D accompanied by a resistivity increase, which can indicate a decrease in grain size with depth in LHS-UD.
The resistivity decrease is often associated with an increase in grain size, since resistivity is inverse to average grain diameter when other parameters are kept constant. For example, quartz sandstones composed of big grains formed in the continental crust in the rift zones of Western Siberia and the Dnieper-Donetsk depression have a resistivity of 1–5 Ohmm at Rw = 0.01 Ohmm [30].
The uppermost tight layer on top of LHS-UD has a Sw value close to unity in all wells in the oil zone, which can be due to the low contrast between oil and water caused by very low porosity. Except for this layer, the water saturation is consistently about 40–45%, indicating that the oil zone covers the entire LHS reservoir. Consequently, the OWC was set in the underlying Al-Khlata Formation in the previous model and was maintained in this study.
Although it was assumed that the oil zone included both the LHS and UHS reservoirs, low resistivity or low contrast may mask the difference between oil and water, leading to misinterpretation of OWC. For example, 59 oil pools were recently discovered in Sudan in low-resistivity reservoirs, which were bypassed in the past because they did not exhibit any contrasts with the water zones [2].
Among all of the wells, only Well D, which produced solely from LHS, did not experience early water breakthroughs. Other wells, produced in comingled mode with the reservoirs of Upper Haushi, as shown in Table 1, experienced early water breakthroughs. In Wells C, B, and E, perforations also covered the overlying shale and reservoirs of the Upper Haushi Formation. Perforations in Well C extended down to the Al-Khlata Formation. Hence, water can influx from the upper or the lower formations if the contrast between water and oil is not captured by the logging methods. For example, well testing performed in the uppermost tight oil zone of UHS showed only water.

4.6. Porosity Derived from Electric Propagation Time Method

Well E, drilled later than the others, exhibits a distinct resistivity contrast between oil and water zones in the LHS-LD reservoir, as evident in Figure 5, Figure 6 and Figure 7. The electric propagation time (EPT) log, which is only available in this well, was used to investigate the viability of the method in capturing the oil–water contrast. The gamma ray log, deep and shallow induction logs, electric propagation time (EPT) log and Sw calculated using Archie and Simandoux equations in Well E are compared in Figure 8. Porosity calculated using EPT (PhiTPL) was compared with Phi calculated using the neutron and density methods (mean porosity of neutron and density porosities (PhiND), density total porosity (PHIT) and neutron porosity (NPHI)). The brown colour indicates water, which can be seen in the shale.
In the LHS-UD, bigger separations between PhiTPL and the three other curves indicate oil (green) in the tight as well as the porous zones. Therefore, EPT certainly indicates oil in the upper tight part of the reservoir despite the Sw value being close to 1 when calculated using the Archie equation and above 1 using the Simandoux equation.
However, the porosity curves are so close in the LHS-LD that the result is inconclusive regarding whether this is oil or water. The separation of PHIT_TPL with NPHI is indicative of water in the entire LHS-LD section, while the water zone is distinguishable in the Sw curves.
The separation of PHIT_TPL with PHIT_ND and PHIT is too small to provide a confirmative conclusion regarding the type of saturation. Low contrast can be caused by water influx due to the rise of OWC. Accordingly, EPT and ILD methods can have different sensitivity to the presence of water according to the conditions of the reservoir.
Other methods may be required to determine water saturation such as the pulsed neutron–neutron method, which has shown good results in a low-resistivity depleted oil reservoir [31].
Additionally, the perforations in this well cover the upper shale (K-member), which has sandstone layers, for which the EPT and both water saturation curves indicate water that can be mobile in these layers. Initially, UHS and LHS were considered as single reservoirs with a single OWC. Later, they were separated into two different reservoirs with unclear and undetermined OWC contacts [16].

4.7. Factors Leading to Low Resistivity

To discuss the reasons for the low resistivity in the LHS reservoir, various factors were considered. The factor of additional conductivity can be excluded, since Vsh is very low and conducting minerals have not been mentioned in the mineralogical description of the reservoir. The factor of a high irreducible water saturation can also be excluded. Although the microbially induced calcium carbonate precipitation (MICP) data were unavailable for LHS, they were available for the Upper Haushi sandstone (UHS) reservoir, which also has similar low resistivity with a tight section at the top. The irreducible water saturation (Swir) in UHS according to capillary curve analysis was below 20% in the measured range of pressure. For comparison, in another tight sandstone sample, Swir was 18% at a porosity of 5.7% and a permeability of 5.6 mD [32,33].
The resistivity of the formation is influenced by both the resistivity of the fluid and the rock itself. Fluids with high salinity typically demonstrate lower resistivity. Additionally, a well-developed porous system combined with fissures can contribute to lower resistivity by reducing resistance to electrical current flow.
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Figure 8. Gamma ray (GR) logs, resistivity logs (ILD, LLS), density porosity (POR), plots in reverse scale of porosity (PHI) calculated using EPT (TPL), neutron (NPHI) and density (PHIT) logs, average of neutron and density porosity (PHIT_ND), water saturation (Sw) calculated using Archie and Simandoux equations, and perforations in Well E of LHS reservoir.
Figure 8. Gamma ray (GR) logs, resistivity logs (ILD, LLS), density porosity (POR), plots in reverse scale of porosity (PHI) calculated using EPT (TPL), neutron (NPHI) and density (PHIT) logs, average of neutron and density porosity (PHIT_ND), water saturation (Sw) calculated using Archie and Simandoux equations, and perforations in Well E of LHS reservoir.
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When combined with high-salinity formation water, this porous system results in low resistivity readings overall. The cementation factor of 1.6, the Kv/Kh of 1, the dispersed clay type, and the high porosity of LHS indicate homogeneous sandstone with even grain packing and good connectivity. The fact that the resistivity is high in the oil-producing Dolomite Drain of the Upper Haushi reservoir despite its differing pore geometry supports this conclusion [14].

4.8. Influence of Kv/Kh on the Production Curves

The factor of similar horizontal and vertical permeabilities can play a substantial role in causing early water breakthrough. In this study, we focused on the influence of permeability anisotropy on the simulation results. The details of the simulation procedure can be found in [14,15].
In the base-case simulation, a Kv/Kh of 1/10 was used by default in the history matching of OPR and WPR. Several Kv/Kh ratios were attempted in our simulations, such as 1:100, 1/1, 2/3, 10/1 and 20/1 for the comparison with the base-case. For some wells, slight differences between the results were observed for cases with 1/1 and 2/3, but the simulation appeared to be insensible to higher ratios when a Kv/Kh of 10/1 was compared to 20/1. In addition, there was no difference between the results of 1/10 and 1/100. Therefore, only the results for the cases with 1/10 and 1/1 were compared.
Well D was perforated in the lower porous part of the LHS-UD and the upper part of LHS-LD (Figure 8) and no water breakthroughs were observed in the well. In the simulation case with Kv/Kh = 1/1, WPR with a value close to zero was predicted, which better matches the actual WPR below 20 STB/d. On the contrary, the case with Kv/Kh = 1/10 predicted a higher WPR.
Moreover, Well G was perforated in LHS-UD and LHS-LD, but the production has also occurred from Gharif Basal Sandstone. In this well, the water breakthroughs began in 1983 and ended in 1985, with a maximum of 2200 STB/d. The case with Kv/Kh = 1/1 predicted WPR of about 900 STB/d on average, but one month earlier than the actual date.
The case with Kv/Kh = 1/10 predicted significantly lower WPR but matched more accurately the start of the water breakthrough. The end of the water breakthrough was predicted by both cases on the same date, matching the observed data (Figure 9a). In Well C, WPR predicted by the case with a 1/1 ratio is two times higher than that predicted by the case with 1/10 during the first year of production. In the following three years, the WPR for the case with 1/10 gradually increased to the same WPR of 1000 STB/d on average and became similar to the WPR of the 1/1 case between 1986 and 1987. Water production rate (WPR) using Kv/Kh of 1 and 0.1: (a) Well G, (b) Well B. Kv/Kh = 1 scenario better match to WPR than 0.1 The field-observed WPR between 1983 and 1987 was higher, varying between 3000 and 4000 STB/d. The comingled production started on the same date from LHS and Basal Gharif, which indicates that the water could be from Basal Gharif.
In Well B, the comingled production started with LHS and DD in 1982 and the water breakthrough started at the end of June 1983, reaching a maximum of 2700 STB/day at the end of 1987. WPR of 650 STB/d on average was predicted using 1/1, while WPR below 100 STB/d was predicted using 1/10 (Figure 9b). In Well E, the WPR was below 300 STB/day, which is much lower than in Wells C and B. From 1986 to 1993, Kv/Kh = 1/10 predicted the beginning of water inflow 3 months earlier, close to the WPR in 1988–1990, but about two times higher than in 1990–1994. Similar to Well D, 1/1 predicted a WPR near zero, which indicates that the water inflow was lateral (Figure 10a).
In Well A, the WPR predicted by Kv/Kh = 1/10 is higher by 500 STB/day than the actual 1000 STB/day on average. The match provided by 1/10 indicates that the water inflow was in the lateral direction. The case using the 1/1 ratio predicted significantly higher WPR, illustrating the severity of the Kv/Kh effect. However, this scenario is not unrealistic considering that Well A is located at the edge of the structure. Unfortunately, logging data are absent for this well to compare the petrophysical properties with those from other wells (Figure 10b).
Thus, in Wells G, C and B, Kv/Kh = 1/1 provides a better match to the observed WPR because of the higher WPR than predicted using 1/10, while using 1/1 predicted a better match in Well G, because of lower WPR. Conversely, Kv/Kh = 1/1 indicates water inflow in both the lateral and the vertical directions. However, the case using 1/10, which indicates lateral direction, was a better predictor for Wells E and A because the WPR predicted by 1/1 was too low in Well E and too high in Well A. In conclusion, a comparison of observed WPR with the simulated WPR using two Kv/Kh ratios of 1/10 and 1/1 can help in evaluating whether the water inflow is vertical or lateral.
For all the Kv/Kh scenarios, a higher WPR was predicted at the beginning and a lower WPR was predicted at the end of the assumed water breakthrough periods. However, WPR increased while OPR decreased, often linearly, e.g., in Well B, during the first 4–5 years. Such a consistent decline in OPR and increase in WPR can be attributed to the depletion of the reservoir rather than water breakthroughs due to the borehole’s poor integrity. Moreover, the repairs of the borehole cementing carried out later during the many years of production often did not lead to a reduction in WPR.
It can be assumed that water intervened in the porous intervals of LHS due to the good hydrodynamic conductivity of the reservoir in all directions, leading to earlier waterflooding than expected. The vertical water inflow may show that the mostly wet underlying Al Khlata Formation or the overlying Upper Haushi reservoirs are hydrodynamically connected with the LHS reservoir. A bottom and edge water Carter–Tracy aquifer model for the Lower Haushi was implemented in the model previously and showed that influx can be attributed to the aquifers from the north and west [16].
However, the volumes of water produced from the Lower Haushi wells are much higher and could not be justified from a material balance standpoint using any of the attempted models. Although a full match of WPR was not obtained by changing Kv/Kh values only, a substantially better match for WPR was obtained using Kv/Kh = 1. For comparison, primarily to facilitate the pressure match in the simulation, the previous investigators reduced Kv globally in all of the reservoirs by a factor of 0.01, which led to a significant WPR mismatch [16].

4.9. Influence of Relative Permeability on Water Production

Wettability can significantly influence oil recovery. The position of relative permeability curves on the plot of water saturation indicates wettability: lower Sw—oil-wet; higher Sw—water-wet. Reliable relative permeability data to be used in the simulation were not available for the LHS reservoir. For the simulations of OPR and WPR shown in Figure 9 and Figure 10, a pair of relative permeability curves called Case 1 (Base case) were used with Kv/Kh = 0.1 (Figure 11). To test the sensitivity of the simulation results to the changes in relative permeabilities, six additional pairs of curves were generated. The curves were shifted relative to the curves of base Case 1, as follows: Case 2—shifting both curves to the right; Case 3—shifting both curves to the left; Case 4—shifting Krw only to the left; Case 5—shifting Krw only to the right; Case 6—shifting Kro only to the right; and Case 7—modifying the curvature by changing the curvature and reducing the Krw max (Figure 11). Shifting to the left indicates more water-wet and shifting to the right indicates more oil-wet contact between the rock and fluid. In the result, the following pairs of Kr with the specific crossing points were used to build the cases: Case 1 with Sw = 0.58 for (1, 2); Case 2 with Sw = 0.68 for (3, 4); Case 3 with Sw = 0.48 for (5, 6); Case 4 with Sw = 0.51 for (5, 2); Case 5 with Sw = 0.63 for (3, 2); Case 6 with Sw = 0.61 for (1, 4); and Case 7 with Sw = 0.6 for (7, 8). Crossing points and intervals of Sw are shown in Table 2. Thus, of all these cases, Case 3 indicates the most oil-wet and Case 2 indicates the most water-wet conditions, while Case 7 covers the widest Sw range.
Changes in WPR due to variations in relative permeabilities were investigated using simulation, as shown in Figure 12 for two wells. In Well D, no increase in water production was predicted using any of the pairs, which corresponds to the observed small WPR in this well. The most oil-wet scenario, Case 3, with the lowest Sw intersection of 0.48, predicted the highest WPR in all wells, excluding Well C.
Except for the modified Case 7, crossing Sw increased in the following order of cases: 3, 4, 1, 6, 5, and 2. However, WPR does not strictly follow the same order. In all wells, the highest WPR indeed decreased in the following order of cases: 3, 4, and 6. The lowest WPR was predicted by Cases 2, 5, and 7 distributed in random order from well to well. WPR predicted by Case 1 varies randomly in a broad range, predicting the maximum WPR in Well C and the minimum in Well B.
With the decrease in Sw, the start of water breakthrough shifted to much earlier dates, which did not correspond to the start of water breakthrough in Wells G, B, and E.
The simulated WPR matched the observed WPR in Wells G and C, although the prediction in WPR was substantially lower. In Wells B, E, and A, the prediction of WPR was higher in the first part of the considered period and lower in the second part, while it was the opposite for the observed WPR.
Case 3 was a better predictor of the high WPR in the second period starting from 1992 in Well A and between 1985 and 1986 in Well B (Figure 12). This shows that the contact between rock and oil changed to more oil-wet from Case 1 to Case 3, indicating lower water inflow during that production period. Case 1 predicted a better match for Wells E and A during the first 2–5 years of production. Because the decrease in crossing Sw resulted in the shifting of the water breakthrough to an earlier date compared to the observed situation, the simulation was carried out using the relative permeability curves of Case 1, which predicted the onset of water breakthrough correctly (Figure 12).

4.10. Petrophysical Property Modelling

Reservoir modelling begins with the classification and zonation of the reservoir, structural construction and petrophysical models, followed by a 3D static model and mapping of porosity, permeability, and water saturation [34].
The initial high oil saturation and fast water breakthrough imply that some oil was bypassed and remained unrecovered in LHS. Property modelling using reservoir simulation was employed to build models of porosity and water saturation at the start and the end of production using Kv/Kh = 0.1 and Kv/Kh = 1 for comparison (Figure 13, Figure 14 and Figure 15).
The highest porosity is related to the dome in the vicinity of Well E. Wells G and H also fall into the area with a high porosity of above 16% (Figure 13). Other wells with lower porosity in LHS surrounded this dome.
In LHS-UD, the highest initial oil saturation was to the NW of Wells C and F and between Wells A and B (Figure 14). In these areas, the oil saturation decreased after production but still had significant oil saturation remaining. Although the difference was insignificant, Kv/Kh = 1 indicates a larger area of the remaining oil saturation.
Another area with high initial oil saturation was to the SE of Wells E and G. With Kv/Kh of both 0.1 and 1, these areas remained unrecovered. The area around Well D with Kv/Kh = 1 was more depleted compared to Kv/Kh = 0.1.
In LHS-LD, the highest initial oil saturation was also in the dome close to Wells E and G, with even higher oil saturation to the south where wells were yet to be drilled (Figure 15). Another undrilled area of high oil saturation is located to the NW of Wells F, C, and A. After years of production, this reservoir is almost fully depleted. Oil was recovered in Wells A, D, C, and F. The drainage areas around Wells B, E, G, and H were significantly reduced. However, oil remains at the top of the dome to the SE of Wells E and G in the undrilled part. When the ratio of Kv/Kh was equal to 1, there was an increase in oil saturation not only in the dome area but also towards the northwest of Well C, as compared to when the Kv/Kh ratio was 0.1. Therefore, two areas remained unswept in the LHS reservoir due to the absence of wells: to the NW of Wells C and F and to the SE of Wells E and G.

5. Conclusions

1. The Lower Haushi Sandstone (LHS) oil reservoir has a complex lithological architecture that is transitional from marine to basinal due to its position on the continental slope. The LHS reservoir is divided into two parts by a shale layer. The uppermost part of the upper layer is tight across almost the entire thickness, with high water saturation confirmed by a well test. The reservoir was waterflooded early, which could be due to uncertainties in water saturation and fluid contact caused by low resistivity, presenting unclear vertical and lateral hydrology.
2. The analysis of all factors showed that the low resistivity was caused by the high salinity of the Formation water in combination with the well-connected porous system of the homogeneous sandstone that is characterized by a cementation factor of 1.6, permeability anisotropy with a Kv/Kh = 1, and the presence of fissures, indicating that such a porous system can be highly electrically conductive. In contrast, the Dolomite Drain oil reservoir above the LHS with a different porous system demonstrated high resistivity.
3. Using Petrel software, simulation was performed to test varying Kv/Kh ratios and relative permeability curves to understand the reason for the early water breakthrough and obtain a better history match with production data. An increase in Kv/Kh from 0.1 used by default in the simulation to 1 increased the WPR substantially in Well G and Well B throughout the production period, and about two times higher in Well C during the first 2 years. This provided a better match to the observed data and is indicative of vertical water inflow. However, Kv/Kh = 0.1 provided a better match in Well A and Well E, which can be explained by their location on the edges of the structures and lateral water inflow from the adjacent areas. The high water influx can be attributed to the faster-than-expected water encroachment due to the high hydrodynamic connectivity in all directions leading to the fast depletion of the reservoir. The shift of the relative permeability ratio to more oil-wet in some production periods shows the wettability changes and can help in history matching.
4. The depletion of the reservoir is confirmed by the two areas remaining unswept in the LHS reservoir due to the absence of wells: to the NW of Wells C and F and to the SE of Wells E and G. With Kv/Kh = 1, the areal size and the oil saturation in the potentially unswept areas were greater. The remaining oil in the tight upper part of LHS-UD requires unconventional methods of oil extraction.

Author Contributions

Methodology, S.R., U.T.; software, M.A.-M., U.T.; validation, S.R., M.A.-M. and U.T.; formal analysis, P.S.; investigation, S.R., P.S. and U.T.; data curation, S.R., U.T., and M.A.-M.; writing—original draft preparation, S.R.; writing—review and editing, S.R., U.T. and P.S.; visualization, S.R., U.T., M.A.-M. and P.S.; supervision, S.R.; project administration, S.R., U.T.; funding acquisition, P.S. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

Data is contained within the article.

Acknowledgments

The authors would like to express their sincere gratitude to the company that provided the field data used in this study. Their valuable contribution and support played a critical role in the success of this research project. Additionally, the authors would like to thank Schlumberger for granting us academic licenses for Petrel, Intersect, and Techlog, which were instrumental in the analysis and interpretation of the data. Without the generous support and collaboration from these organizations, this study would not have been possible.

Conflicts of Interest

The authors declare no conflict of interests.

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Figure 1. Kv vs. Kh/Phi obtained using core data of four wells of the Lower Haushi sandstone (LHS) reservoir. The resulting mean function is described by the equation Kv = 0.05·Kh1.2.
Figure 1. Kv vs. Kh/Phi obtained using core data of four wells of the Lower Haushi sandstone (LHS) reservoir. The resulting mean function is described by the equation Kv = 0.05·Kh1.2.
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Figure 2. Data of Well G measured in horizontal (h) and vertical (v) directions: (a) porosity (Phi); (b) ratio Kv/Phi_v vs. ratio Kh/Phi_h.
Figure 2. Data of Well G measured in horizontal (h) and vertical (v) directions: (a) porosity (Phi); (b) ratio Kv/Phi_v vs. ratio Kh/Phi_h.
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Figure 4. Pickett plots for (a) Well G; (b) Well E. Rw—resistivity of formation water; m—cementation factor; n—saturation exponent.
Figure 4. Pickett plots for (a) Well G; (b) Well E. Rw—resistivity of formation water; m—cementation factor; n—saturation exponent.
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Figure 5. Logging data profiles of Well G (left): gamma ray log (GR), porosity determined using density log and water saturation. The Juhasz plot (right) shows the distribution of different clay types at respective depths in different colors in the LHS reservoir. Colors indicate layers.
Figure 5. Logging data profiles of Well G (left): gamma ray log (GR), porosity determined using density log and water saturation. The Juhasz plot (right) shows the distribution of different clay types at respective depths in different colors in the LHS reservoir. Colors indicate layers.
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Figure 6. Logging data profiles of Well E (left): gamma ray log (GR), porosity determined using density log and water saturation. The Juhasz plot (right) shows the distribution of different clay types at respective depths in different colors in the LHS reservoir. Colors indicate layers.
Figure 6. Logging data profiles of Well E (left): gamma ray log (GR), porosity determined using density log and water saturation. The Juhasz plot (right) shows the distribution of different clay types at respective depths in different colors in the LHS reservoir. Colors indicate layers.
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Figure 7. Well logging profile of 6 wells in the following order from left to right (G, D, C, B, H, E): gamma ray (GR), resistivity logs, porosity, water saturation and perforation intervals. Well E was drilled 7 years after Well G, which explains the appearance of water at the base of LHS-LD as a result of OWC rise. Well H is shown for correlation purposes only, as it did not produce from LHS.
Figure 7. Well logging profile of 6 wells in the following order from left to right (G, D, C, B, H, E): gamma ray (GR), resistivity logs, porosity, water saturation and perforation intervals. Well E was drilled 7 years after Well G, which explains the appearance of water at the base of LHS-LD as a result of OWC rise. Well H is shown for correlation purposes only, as it did not produce from LHS.
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Figure 9. Comparison of observed and simulated oil production rate (OPR) and water (WPR) productions designated as historical and simulated values using a Kv/Kh of 1 and 0.1: (a) Well G, (b) Well B. The Kv/Kh = 1 scenario better matched the WPR than the 0.1 scenario, indicating vertical water inflow.
Figure 9. Comparison of observed and simulated oil production rate (OPR) and water (WPR) productions designated as historical and simulated values using a Kv/Kh of 1 and 0.1: (a) Well G, (b) Well B. The Kv/Kh = 1 scenario better matched the WPR than the 0.1 scenario, indicating vertical water inflow.
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Figure 10. Observed and simulated oil production rate (OPR) and water production rate (WPR) designated as historical and simulated values using a Kv/Kh of 1 and 0.1: (a) Well E, (b) Well A. The Kv/Kh = 0.1 scenario better matches the WPR, indicating lateral water inflow.
Figure 10. Observed and simulated oil production rate (OPR) and water production rate (WPR) designated as historical and simulated values using a Kv/Kh of 1 and 0.1: (a) Well E, (b) Well A. The Kv/Kh = 0.1 scenario better matches the WPR, indicating lateral water inflow.
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Figure 11. Relative permeability curves (Kr) for water and oil used to build various simulation cases.
Figure 11. Relative permeability curves (Kr) for water and oil used to build various simulation cases.
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Figure 12. Actual (historical data) and simulated water production using different pairs of relative permeability curves that are plotted for different cases as shown in Figure 11: (a) Well-A, (b) Well-B.
Figure 12. Actual (historical data) and simulated water production using different pairs of relative permeability curves that are plotted for different cases as shown in Figure 11: (a) Well-A, (b) Well-B.
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Figure 13. Petrophysical model of porosity of LHS reservoir.
Figure 13. Petrophysical model of porosity of LHS reservoir.
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Figure 14. Petrophysical models of water saturation of porous LHS-LD reservoir: before the start of production (a) and at the end of production with (b) Kv/Kh = 0.1 and (c) Kv/Kh = 1. Red, orange, and yellow colors indicate the areas of remaining oil.
Figure 14. Petrophysical models of water saturation of porous LHS-LD reservoir: before the start of production (a) and at the end of production with (b) Kv/Kh = 0.1 and (c) Kv/Kh = 1. Red, orange, and yellow colors indicate the areas of remaining oil.
Applsci 14 04618 g014
Applsci 14 04618 g015
Figure 15. Petrophysical models of water saturation of porous LHS-UD reservoir: before the start of production (a) and at the end of production with (b) Kv/Kh = 0.1 and (c) Kv/Kh = 1. Red, orange, and yellow colors indicate the areas of remaining oil.
Figure 15. Petrophysical models of water saturation of porous LHS-UD reservoir: before the start of production (a) and at the end of production with (b) Kv/Kh = 0.1 and (c) Kv/Kh = 1. Red, orange, and yellow colors indicate the areas of remaining oil.
Applsci 14 04618 g015
Table 1. Comingled production from the Upper Haushi and Lower Haushi reservoirs.
Table 1. Comingled production from the Upper Haushi and Lower Haushi reservoirs.
Well NameProduction
Start Date		Commingled
Production		Reservoir
Well G11/1/1980Lower Haushi
Dolomite Drain
Gharif Basal 		LHS
UHS-DD
UHS-GB
Well D11/1/1980Lower Haushi LHS
Well C9/1/1982Lower Haushi
Gharif Basal 		LHS
UHS-GB
Well B10/1/1982Lower Haushi
Dolomite Drain		LHS
UHS-DD
Well E3/1/1987Lower Haushi
Dolomite Drain		LHS
UHS-DD
Well A3/1/1988Lower Haushi
Upper Haushi
Dolomite Drain 		LHS
UHS
UHS-DD
Table 2. Relative permeability curves and their parameters used for the simulation. The parameters are shown for Case 3 (green curves) in Figure 11 for example.
Table 2. Relative permeability curves and their parameters used for the simulation. The parameters are shown for Case 3 (green curves) in Figure 11 for example.
Case NKr OilKr WaterCrossingSw MinSw Max
1210.580.30.8
2430.680.370.8
3650.480.20.7
4250.510.20.8
5230.630.370.8
6410.610.250.9
7870.60.20.9
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Rudyk, S.; Al-Musalhi, M.; Taura, U.; Spirov, P. Matching of Water Breakthroughs in a Low-Resistivity Oil Reservoir Using Permeability Anisotropy. Appl. Sci. 2024, 14, 4618. https://doi.org/10.3390/app14114618

AMA Style

Rudyk S, Al-Musalhi M, Taura U, Spirov P. Matching of Water Breakthroughs in a Low-Resistivity Oil Reservoir Using Permeability Anisotropy. Applied Sciences. 2024; 14(11):4618. https://doi.org/10.3390/app14114618

Chicago/Turabian Style

Rudyk, Svetlana, Majid Al-Musalhi, Usman Taura, and Pavel Spirov. 2024. "Matching of Water Breakthroughs in a Low-Resistivity Oil Reservoir Using Permeability Anisotropy" Applied Sciences 14, no. 11: 4618. https://doi.org/10.3390/app14114618

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