Introduction

The Gulf of Suez Basin (GSB) province is the oldest and the most productive oil region in Egypt. It represents an intercontinental rift extending for about 325 km northward from Hurghada city in the south (El Nady et al. 2016). Despite the fact that its rifting process began in the Miocene epoch, both post-rift and pre-rift periods contain prospective source rocks and reservoirs (Shahin and Shehab 1984; EGPC, 1996; Atta et al. 2002).

The GSB encompasses more than 80 fields producing oil from Precambrian to Tertiary reservoirs. Due to the large amounts of exploration data as well as the existence of well-exposed syn-rift strata, numerous geological studies covering the evolution of the GSB rifting have been carried out (e.g. Winn et al. 2001; Alsharhan 2003; El Nady et al. 2015; Radwan, et al. 2020; Moustafa and Khalil 2020; Radwan and Sen 2021; Radwan 2021a,b; Radwan et al. 2021a,b,c).

The rifting fault blocks are the main hydrocarbon traps within the GSB oil fields (Sultan 2002; Chowdhary and Taha 1987). The Miocene clastics hold nearly 60% of oil reserves in the GSB, and the residual is frequently existing in the Pre-Cenomanian Nubia sandstones (Peijs et al. 2012).

Rabeh East field is located between longitudes: 33° 39′ 16.8′′ E, 33° 47′ 56.1′′ E and latitudes: 27° 9′ 36.3′′ N, 27° 17′ 0.7′′ N at the southern portion of the GSB (Fig. 1). The sandstones of Nubia and Nukhul formations as well as the carbonates of Rudies Formation exhibit the essential targets for oil production at Rabeh East oil field (Sarhan and Basal 2019; Sarhan 2020, 2021).

Fig. 1
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a Regional map shows the location of Rabeh East Field at the southern GSB. b Study area with well locations

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Consequently, the present work aims to perform geophysical assessment using well log data for the limestone of Thebes Formation and the sandstones of Mutulla Formation in order to add new promising targets to the well-known oil reservoirs in Rabeh East field.

Geological setting

The rifting of the GSB started through the Early Miocene age because of the divergence between the African plate and the Arabian plate, which led to forming a series of extensional faults trending NW–SE to NNW–SSE (Bosworth et al. 2005; Patton et al. 1994). These fault arrays moved to the north-west and affected the Late Miocene sequence beneath the Nile Delta area (Sarhan et al. 2014).

The structural and depositional setting of the GSB is complex due to the superimposing of the rifting-related faults with the pre-rift structures (Abul Karamat and Meshref 2002). The faulted blocks of the GSB are bounded principally by NW extensional faults, which are linked to each other by WNW-, NNE- and NE-oriented faults (Abd-Allah et al. 2014).

The lithostratigraphy of the GSB including Rabeh East Field starts with the clastics of Nubia Formation, which are overlain by the Matulla, Duwi and Sudr formations. These units are topped by Esna Shale Formation (Palaeocene) and then the Thebes Formation (Eocene). The Miocene stratigraphy comprises: Nukhul, Rudeis, Kareem, Belayim, South Gharib and Zeit formations, respectively, from base to top (Fig. 2).

Fig. 2
figure 2

Stratigraphic column at West Hurghada region comprising Rabeh East field (after Abd El Hafez et al. 2016). Note the stratigraphic position for the examined formations in the present study, which outlined by dotted red polygons

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Based on the available wells in Rabeh East Field, the Eocene Thebes Formation is mainly composed of limestones (Fig. 3), whereas the Matulla Formation consists principally of sandstones and shale interbeds (Fig. 4).

Fig. 3
figure 3

Mud log displays the Thebes Formation in RE-25 Well. Note the green rectangle outlines the most promising zone within the Thebes Formation (Zone A) between depths 5084 and 5100 ft

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Fig. 4
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Mud log shows the Mutulla Formation in RE-25 Well. Note the green rectangles outline the most promising oil-bearing zones between depths: 5403.5 to 5413.5 ft (Zone B), 5425.5 to 5436 ft (Zone C), 5488 to 5498 ft (Zone D) and 5558.5 to 5563.5 ft (Zone E)

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The limestone of Thebes Formation was deposited during the Tethyan major transgression over the north-east of Africa in the Eocene times. This limestone characterises a potential source rock with TOC equal to 3.2% of type I/II kerogens; however, the generated hydrocarbon has low API gravity, high sulphur content and high HI and low OI values (Alsharhan 2003). The fractured limestones of the Thebes Formation provide around 1.1% of oil production in the GSB with 13% average porosity, and net pay thickness varies between 15 and 17 m. Numerous fields, such as Sudr, Asal, Kareem, Ras Matarma, Bakr, West Bakr, Ali, Issaran, Shoab and Rahmi, produce oil from the entire carbonates of Thebes Formation (Alsharhan 2003).

The Matulla Formation is separated between the overlain Brown limestone Formation and the underlain Wata Formation by two unconformity surfaces. The entire clastics of the Matulla Formation were deposited throughout the Coniacian–Santonian time span. A diverse planktonic foraminiferal content including Dicarinella concavata and D. asymetrica zones revealing the Coniacian–Santonian age characterizes the Matulla Formation (Alsharhan 2003).

The Matulla Formation represents a complete third-order depositional sequence that embraces the Coniacian–Santonian interval and is subdivided into LST, TST and HST system tracts. This sequence was deposited through a reduction in the accommodation space towards the inner shelf water depth, resulting in the sedimentation of the lowest part of Matulla Formation as lowstand system tracts (LSTs). This step was followed by a transgressive stage within a relatively deeper marine setting (outer shelf conditions), resulting in the deposition of the middle part of the Matulla Formation as transgressive system tracts (TSTs). The deposition of the uppermost parts of the Matulla Formation as highstand system tracts (HSTs) was due to a significant decline in the holding accommodation space at the final basin filling stage (Elhossainy et al. 2021).

Data and methods

The available geophysical data in this paper comprise the conventional wireline logs from three examined wells drilled in Rabeh East oil field. These wells are: Rabeh East-8 (RE-8), Rabeh East-22 (RE-22) and Rabeh East-25 (RE-25) as presented in Fig. 1b. The mud logs for the three wells are also accessible.

The current work appraises the mud logs with the electric well logs data for the Thebes and Mutulla formations in the three studied wells at Rabeh East field. The three wells’ mud logs were initially evaluated qualitatively to identify the prospective hydrocarbon yielding zones within the Thebes and Mutulla formations. After that, the wireline logs for the three wells were analysed using Techlog software to determine the most essential petrophysical parameters for the zones of interest. These parameters contain shale volume (VShale), total porosity (ΦT), effective porosity (ΦE), water saturation (Sw) and bulk volume of water (BVW).

Shale volume

The amount of shale (Vsh) in the studied intervals has been determined using the following equation:

$${\mathbf{Vsh}}_{{({\mathbf{N}} - {\mathbf{D}})}} = \left( {{{\varvec{\Phi}}}_{{\mathbf{N}}} - {{\varvec{\Phi}}}_{{\mathbf{D}}} } \right) \, / \, \left( {{{\varvec{\Phi}}}_{{{\mathbf{N}} \, \left( {{\mathbf{shale}}} \right)}} - {{\varvec{\Phi}}}_{{{\mathbf{D}} \, \left( {{\mathbf{shale}}} \right)}} } \right)$$
(1)

where Vsh (N-D) is the calculated shale volume from neutron and density logs; ΦN is the neutron porosity; ΦD is the density porosity; ΦN (shale) is the neutron porosity of shale; ΦD (shale) is the density porosity of shale.

Total porosity

Following Asquith and Gibson (1982), total porosity (ϕT) was determined from neutron–density logs using the following formula:

$${{\varvec{\Phi}}}_{{\mathbf{T}}} = \, ({{\varvec{\Phi}}}_{{\mathbf{N}}} + {{\varvec{\Phi}}}_{{\mathbf{D}}} ) \, / \, {\mathbf{2}}$$
(2)

where ΦT is the total porosity; ΦN is the neutron porosity; ΦD is the density porosity.

Effective porosity

The effective porosity (ϕe) has been measured by the following equation of (Asquith and Gibson 1982):

$$\phi_{{{\mathbf{e}} \, = }} \phi_{{{\mathbf{T}} \, *}} \left( {{\mathbf{1}} - \, {\mathbf{Vsh}}} \right)$$
(3)

where ϕe is the effective porosity; ϕT is the total porosity; Vsh is the shale volume.

Water saturation

The water saturation (Sw) for the examined zones has been calculated by the Indonesia model (Poupon and Leveaux 1971) from the following equation:

$$S_{w} = \left\{ {\left[ {\left( {\frac{{V_{sh}^{2 - Vsh} }}{{R_{sh} }}} \right)^{{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$2$}}}} + \left( {\frac{{\phi_{e}^{m} }}{{R_{w} }}} \right)^{{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$2$}}}} } \right]^{2} R_{t} } \right\}^{{{\raise0.7ex\hbox{${ - 1}$} \!\mathord{\left/ {\vphantom {{ - 1} n}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$n$}}}}$$
(4)

where Sw is the water saturation; Vsh is the shale volume; ϕe is the effective porosity; Rsh is the shale resistivity; Rt is the deep resistivity; Rw is the connate water resistivity (set equal to 0.025 Ω \({\mathrm{m}}^{2}\)/m according to Ganoub El-Wadi Petroleum Company); m is the cementation exponent (set equal to 2); n is the saturation exponent (set equal to 2); a is the tortuosity factor (set equal to 1).

Bulk volume of water

The bulk volume of water (BVW) has been estimated by applying the following equation of Buckles (1965):

$${\mathbf{BVW}} = \phi_{{{\mathbf{e}}*}} {\mathbf{S}}_{{\mathbf{w}}}$$
(5)

where BVW is the bulk volume of water; ϕe is the effective porosity; Sw is the water saturation.

Results

The qualitative examination for Thebes and Mutulla formations in the studied wells (RE-8, RE-22 and RE-25) exposed that RE-25 Well is the only well exhibiting optimistic criteria in five zones for being potential oil reservoirs. The first zone (A) locates between depths 5084 and 5100 ft in the limestone of Thebes Formation (Fig. 5). However, the sandstones of Mutulla Formation have four promising oil-bearing zones (B, C, D and E). These intervals situate between depths: 5403.5–5413.5 ft (Zone B), 5425.5–5436 ft (Zone C), 5488–5498 ft (Zone D) and 5558.5–5563.5 ft (Zone E) as shown in Figs. 6, 7 and 8.

Fig. 5
figure 5

Petrophysical data with interpretation for the Thebes Formation in RE-25 Well representing the favourable characteristics for oil production in Zone A

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Fig. 6
figure 6

Petrophysical data with interpretation for the Mutulla Formation in RE-25 Well displaying the positive characteristics for Zones B and C for being oil-bearing intervals

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Fig. 7
figure 7

Petrophysical data with interpretation for the Mutulla Formation in RE-25 Well displaying the optimistic characteristics for oil production in Zone D

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The favourable signals for the recommended five zones comprise the existence of oil shows as well as the high values of the ditch gas analysis opposite to the five examined intervals (Figs. 3 and 4). Also, these intervals display high deep resistivity, which confirm the occurrence of the non-conducive oil in addition to the relatively low gamma-ray approving the little shale content (Figs. 5–8). The sandstones of the examined zones in Mutulla Formation have been defined in the mud log as: colourless, white, greyish white, yellowish white, fine-grained graded to siltstones, occasionally medium-grained, sub-rounded to sub-angular, moderately sorted with calcareous cement, glauconitic and pyritic, brown spotty-patchy oil stain with pale-yellow to yellow fluorescence, moderate fast yellowish white stream-cut (Fig. 4).

Fig. 8
figure 8

Petrophysical data with interpretation for the Mutulla Formation in RE-25 Well displaying the bright characteristics of Zone E for being oil-bearing interval

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Consequently, the wireline log suites for the motivating zones (A, B, C, D and E) have been quantifiable appraised. This assessment encompasses the calculations of the vital petrophysical parameters obligatory for judging the potentiality for hydrocarbon reservoirs. These calculations include: shale volume, total porosity, effective porosity, water saturation and bulk volume of water. The results of these parameters for zone A within Thebes Formation in Rabeh East-25 Well are displayed in Table 1, while the calculations for zones B, C, D and E in have been shown in Mutulla Formation, as given in Table 2.

Table 1 Log evaluation table for zone A within Thebes Formation in Rabeh East-25 Well
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Table 2 Log evaluation table for zones B, C, D and E within Mutulla Formation in Rabeh East-25 Well
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The neutron–density cross-plot (Schlumberger 1972) for the studied zones shows clearly higher porosity values for zones B, C, D and E within Mutulla Formation (between 20 and 30%) rather than Zone A in Thebes Formation (only between 10 and 20%) as shown in Fig. 9.

Fig. 9
figure 9

Neutron–density cross-plot for Zone A in Thebes Formation and Zones B, C, D, E within Mutulla Formation in RE-25 Well

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Fig. 10
figure 10

Pickett cross-plot for the promising Zones A, B, C, D, E in RE-25 Well. Note that the all points locate less than Sw = 75% line confirming the oil potentiality of these zones

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The calculated amount of shale in the inspected zones as demonstrated in Tables 1 and 2 reveals that the maximum shale volume (27%) was documented in Zone D and the minimum value (7.0%) was noted in Zone A. However, the estimated total porosity shows that the lowest average value (16%) was noted in Zone A and the highest total porosity (28%) was recorded in Zone E as given in Tables 1 and 2. The measured effective porosity reaches the highest value (23%) that was recorded in Zone C, whereas the lowest value (14%) was noted in Zone A.

It is worth mentioning that the total and effective porosities for the entire limestone of Zone A have been also calculated using sonic log in order to examine the existence of secondary type of porosity (e.g. fractures, vugs, etc.). This is because the sonic measures only the primary porosity; however, the neutron–density porosity estimates both primary and secondary porosities. The results show that the calculated sonic total porosity (PHIT_S) is 11% and sonic effective porosity (PHIE_S) is 9%. Whereas the neutron–density total porosity (PHIT_ND) is 16%, the neutron–density effective porosity (PHIE_ND) is 14% (Table 1). This notable variance between sonic and neutron–density porosities reflects the existence of a specific type of secondary porosity within Zone A, which increase the efficiency of Zone A to be a favourable potential oil reservoir in Rabeh East Field.

The calculated water saturation has been displayed in track twelve in Fig. 5 and track ten in Figs. 6–8, shading with blue colour, while the green colour in the same track refers to the hydrocarbon saturation. The highest average water saturation of 50% (i.e. the hydrocarbon saturation equals 50%) was recorded in Zone D, while water saturation was low in Zone A (23%) (Tables 1 and 2).

The constructed Pickett plot (Pickett, 1972) for the studied zones shows that most of the plotted points are clustered below line of Sw = 50% confirming the hydrocarbon potentiality of these intervals. This reflects that the hydrocarbon saturation in the examined zones expected to be more than 50% as shown in Fig. 10. This result demonstrates the correctness of the mathematical calculations for the calculated water saturation values as well as the significance of these zones as oil-bearing zones.

The calculated BVW values have been presented in the last track in Figs. 5–8 shading with blue colour. The maximum bulk volume of water (0.10) was documented in Zone E, and the minimum value (0.03) was noted in Zone A (Tables 1 and 2).

The bulk volume of water at the irreducible case in sandstone reservoirs (i.e. expectable to yield water-free oil) depends on the grain size. If sand grains are fine-grained and graded to siltstones as the sand grains in the examined zones within the Mutulla Formation, the BVW values should vary between 0.035 and 0.09 (Asquith and Gibson 1982; Fertl and Vercellino 1978; Asquith 1985). Accordingly, since the BVW values in Zones; B, C and D vary between 0.06 and 0.09 (Table 2), it is expected that these zones will produce oil without water. However, Zone E that exhibits the highest BVW of 0.10 will produce oil with water.

Conclusions

The explanation of the well log data for the sandstone of the Mutulla Formation as well as the limestone of the Thebes Formation in Rabeh East Field at Gulf of Suez Basin exposed that these formations are superior oil reservoirs. The comprehensive petrophysical assessment for the well log data of RE-25 Well revealed five oil-bearing zones (A, B, C, D and E). These promising intervals represent total net pay thickness of 51.5 ft and display relatively low shale volume (0.07–0.27), high effective porosity (0.14–0.23), low water saturation (0.23–0.50) and low bulk volume of water (0.03–0.10). Zone A represents the promising limestone interval of Thebes Formation with 16 ft thick. This zone includes primary and secondary porosity types supporting the effectiveness of this limestone to be a valuable oil reservoir in the Rabeh East Field. However, the sandstone reservoirs within the Mutulla Formation in RE-25 Well represented by zones B (10 ft thick), C (10.5 ft thick), D (10 ft thick) and E (5 ft thick). Consequently, drilling new wells close to the RE-25 Well in Rabeh East Field is highly indorsed to examine the Mutulla and the Thebes formations as supplementary oil reservoirs beside the main targets including the Nubia, Rudies and Nukhul formations.