Introduction

The Western Desert represents one of the greatest productive hydrocarbon's provinces in the Egyptian territory. The Shushan Basin has a significant exploration potential in northern Western Desert (EGPC 1992). Safir Oil Field is located in the Shushan Basin between latitudes 30°35′–30°37′ N and longitudes 26º53′–26º55′ E as shown in Fig. 1. It represents one of the numerous hydrocarbon discoveries situated in this extremely faulted sedimentary basin. It is distinguished by high oil and gas accumulations which attracted the concern of the researchers and oil companies for hydrocarbons exploration. Khalda Petroleum Company was the main producer company since the discovery of Safir Oil Field in 1986.

The Alam El-Bueib Formation (Early Cretaceous; Barremian to Aptian) represents the main producing horizon in Safir Oil Field addition to the Kharita and Upper Bahariya formations (EGPC 1992).

This article aims at evaluating the petrophysical parameters for AEB-3A reservoir in Safir-03 well, Safir Field, Western Desert in Egypt. The available data include a suite of well log and number of seismic lines. The petrophysical parameters include shale volume (Vsh), porosity (Φ), water saturation (Sw), critical water saturation (Scw), bulk volume of water (BVW), minimum bulk volume water (BVWmin), irreducible water saturation (Swirr) and absolute permeability (K).

Fig. 1
figure 1

Location map of Safir-03 well in Safir Field within Shushan Basin and seismic lines. The maps enlarged upper left and below show the main Mesozoic basins in the Western Desert and main structural elements and major faults in Shushan Basin, respectively (EGPC, 1992; Shalaby et al. 2012, 2014)

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Geological setting

Moustafa (2008) concluded that the sedimentary basins of the northern Western Desert including Shushan Basin were subjected to tectonic inversion during the Upper Cretaceous. Moustafa 2008; Sarhan 2017; Sarhan et al. 2017a and b; Sarhan and Collier 2018; Sarhan 2019 attributed the NE-SW trending anticlines which were produced in northern Western Desert to the NW movement of the African Plate relative to Laurasian Plate.

Shushan Basin is a half-graben basin (El Shazly 1977; Hantar 1990). It was developed as a result of the initial origin of the Neo-Tethys Sea and continued as a depocenter throughout most Cretaceous (Metwalli and Pigott 2005). It lies within the unstable shelf tectonic zone in Egypt (Said 1962) and bounded by the Umbarka Platform to the north and by the Qattara Ridge to the south (Alsharhan and Abd El-Gawad 2008).

In the North Western Desert, the lithostratigraphic section comprising Shushan Basin contains thick sedimentary succession that ranges from Paleozoic to Paleogene (Fig. 2). This sequence comprises of clastics depositional cycles alternating with carbonates (EGPC 1992).

The Lower Cretaceous period witnessed the sedimentation of a regressive phase and marginal marine clastics of Alam El Bueib (AEB) Formation. The transgressive phase represents a shallow sea over the north Western Desert, where the carbonate unit of the Alamein Formation was deposited during the Aptian age. The Albian is represented by another regressive phase, when the North Western Desert received the fluvial input (mainly coarse sands) of the Kharita Formation which coming from the south (Said 1990).

The main reservoir of Shushan Basin is the Lower Cretaceous (AEB Formation) which represents one of the generality productive formations in the Western Desert, predominantly in the concession of Khalda Oil Company (Schlumberger 1995). The AEB Formation is composed of fine to coarse grains clastics that conformably overly the Masajed Formation (Upper Jurassic carbonates) and underlay the Alamein Dolomite (Fig. 2). The AEB Formation was subdivided into six units based on the lithological variation, these units arrange from top to base; AEB-1, AEB-2, AEB-3, AEB-4, AEB-5 and AEB-6. Also, AEB-3 unit is further subdivided into six sub-units from top to base: A, C, D, E, F and G (Hantar 1990).

Data and techniques

The available data include (20) two-dimensional reflection vertical seismic sections that cover the study area in addition to the well logging dataset for Safir-03 well (Fig. 1). The accessible well log data in Safir-03 well include bit size (BIT), caliper (CALX), gamma ray (GR), spontaneous potential (SPDH), resistivity (M2R9, M2R3 and RMSL), neutron porosity (CNCF), density (ZDEN), density correction (ZCOR) and photoelectric factor (PE). The logging analysis was carried out using Senergy Software Interactive Petrophysics program (IP) (version 3.6). The whole abbreviations stated in this study are listed at the begning of the paper.

Fig. 2
figure 2

modified from Schlumberger 1995)

General lithostratigraphic column of the Western Desert of Egypt (

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The structural setting of AEB-3A Member has been deducted from the interpretation of the available 2D seismic lines. However, the formation evaluation for the sandstone of the AEB-3A Member to be a potential hydrocarbon reservoir in Safir Field was based on qualitatively and quantitatively interpretation.

Results

Seismic data interpretation

The seismic reflector (horizon) that represents Alam El-Bueib 3A Member has been easily detected on the existing seismic profiles because it is characterized by strong amplitude and high continuity (Fig. 3). The traced horizon on the seismic sections exhibits a clear raised fault block relative to their surroundings bounded by two normal faults. This horst has been clearly notable in Fig. 3.

Fig. 3
figure 3

The picked horizon of AEB-3A Member (yellow color) as tied to Safir-03 well. (a) S–N Xline 14499 seismic profiles. (b) NE-SW composite line 1 seismic profiles

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Well-log interpretation (qualitative and quantitative)

Qualitative interpretation

The interpretation of the well log curve shapes and their relative positions to each other represent the key for judging the existence of any possible reservoir and for discrimination between hydrocarbon and wet productive intervals.

Figure (4) represents a complete set of log data for AEB-3A Member in Safir-03 well in the form of Triple Compo format as one option of the Interactive Petrophysics (IP) software. The visual examination of the available well log data for the AEB-3A Member in the Safir-03 well indicates that the interval from 8108 to 8133 ft has very interesting log characters and optimistic log curve shapes (Fig. 4). This interval reflects good hole conditions as indicated by the caliper log (CALX) (blue color, track number 1) that reads borehole diameter values that are equal to the bit size (BIT) or even less than it.

Fig. 4
figure 4

Well log data Triple Compo as displayed on the IP Software for AEB-3A Member, Safir-03 well, Safir Field, North Western Desert

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Neutron curve (CNCF) is displayed on the right side to the density curve (ZDEN) on track number (5) and PE reading of about 2 b/e confirms the sandstone matrix. Low gamma ray reading (Track 1) reflects a clean sandstone interval. The plotted points of this interval are clustered around the sandstone line that has porosity ranging between 21 and 25 PU based on the neutron—density cross-plot (Fig. 5). Also, the grain size in the examined AEB-3A reservoir indicates that the majority of the sand grains within this interval are coarse grains based on the analysis of the cross-plot of the porosity against water saturation (Fig. 6).

Fig. 5
figure 5

Neutron—density cross-plot (Schlumberger, 1972) of AEB-3A Member, Safir-03 borehole displaying that the reservoir interval is predominated by sandstone matrix

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Fig. 6
figure 6

Porosity—water saturation cross-plot (Asquith and Gibson, 1982) displays the distribution of the grain size of the AEB-3A sandstone reservoir

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The former interpretation of the well logging data indicates that the uppermost interval of AEB-3A Member (between 8108 and 8133 ft) displays certain signs of movable hydrocarbons. The resistivity curves of this interval also display clear positive separation (M2R9 > M2R3 > RMSL) (as shown in Track 4) indicating the presence of invasion profile, which reflects good porosity and permeability. The porosity logs (CNCF and ZDEN) show high porosity values that range from 21 to 25%. The minimum content of shale is indicated by the lowest gamma ray reading.

Quantitative interpretation

Based on these prior diagnoses, furthermore calculations were done for the expected pay interval of AEB-3A Member between 8108 and 8133 ft. These calculations include the following petrophysical parameters: shale volume (Vsh), total porosity (PHIT), effective porosity (PHIE), water saturation in the un-invaded zone (Sw), bulk volume of water (BVW), irreducible water saturation (Swirr), absolute permeability (K), critical water saturation (Scw) and minimum bulk volume of water (BVWmin). The quantitative evaluations of the examined interval were calculated based on Archie model (Archie 1942), and the gained results were displayed in Table (1).

Water Saturation (SW)

Water saturation of the virgin zone (Sw) is fundamental parameter for any further quantitative interpretation and reservoir evaluation. As the reservoir is clean inter-granular porosity sandstone, Archie model (1942) is used as follows:

$$\left( {S_{w} } \right)^{n} = \frac{{aRw}}{{\Phi ^{m} \times Rt}}$$
(1)

The resistivity of the formation water (Rw), resistivity of the virgin zone (true resistivity, Rt) and porosity (Ф) represent the fundamental parameters needed for calculating the reservoir water saturation (Sw). While the true resistivity (Rt) and porosity (Φ) are easily obtained directly from the log curve as described above, the formation water resistivity (Rw) cannot be directly picked on the logs.

The 100% water saturated zone is located directly below about depth equals 8133 feet where Rt suddenly lowered to 0.3 Ωm2/m (Fig. 4). This value will be considered to represent Ro. The water zone has the same matrix as that of the reservoir with average porosity equals 19%. The connate water resistivity (Rw) can then be obtained by applying Archie equation (Ro = F × Rw) with F = 1/Φ2. In this case, Rw is calculated to be equals 0.01 Ωm2/m. This value matched well with 0.019 Ωm2/m obtained through the analysis of formation water samples under the same reservoir conditions in the majority of fields of Khalda Petroleum Company.

According to the above discussion, the average reservoir water saturation (Sw) can then be calculated with average effective porosity of 0.21 and resistivity (Rt) equals 14 Ω.m2/m. The calculated average water saturation equals 13%. In addition, the flushed zone water saturation (Sxo) can also be calculated using Archie equation by replacing Rt and Rw with Rxo and Rmf, respectively, as:

$$\left( {S_{{xo}} } \right)^{n} = \frac{{aRmf}}{{\Phi _{m} \times Rxo}}$$
(2)

The mud filtrate resistivity (Rmf) can be determined for zone which have Sw equals 100% (Rmf = \({\Phi 2}\) × Rxo). The shallow resistivity (Rxo) opposite 100% wet zone equals 1 Ω.m2/m with (0.19) porosity. Applying this technique gives Rmf value of about 0.036 Ω.m2/m. It is interesting to notice that this value 0.036 is very close to 0.034 that obtained from well header (0.1 Ω.m2/m @ 60 °F) after adjusting to formation temperature (Tf = 190°F). In Fig. 7 by locating the resistivity value, 1 Ω.m2/m, on the scale to the left of the graph and move horizontally to the right along the 1 Ω.m2/m line until the vertical line representing a temperature of 60 °F (from the bottom of the graph) is met (point A on the chart). Then move parallel to the constant salinity line (diagonal) to the point where it intersects the vertical line representing a temperature value of 190 °F (point B on the graph). From point B, follow the horizontal line to the left to determine the resistivity of the mud filtrate at the desired temperature (0.034 Ω.m2/m @ 190°F). Consequently, the average water saturation in flushed zone (Sxo) has been calculated in the pay zone using average effective porosity of 0.21 and average shallow resistivity (Rxo) of 2 Ω.m2/m. The results show that Sxo equals 64% (i.e., the movable hydrocarbon is 64% and the residual hydrocarbon is 36%) (Table 1).

Fig. 7
figure 7

Chart for adjusting the mud filtrate resistivity (Rmf) for formation temperature (Schlumberger, 1986, Figure Gen-9)

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Table 1 Well logging data and their output analysis of AEB-3A reservoir, Safir-03 borehole
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The water saturation can be calculated by means of ratio method (Swr) as (Asquith et al. 2004) is:

$$S_{wr} = \left( {\frac{{{\text{Rxo}}/{\text{Rt}}}}{{{\text{Rmf}}/{\text{Rw}}}}} \right)^{0.625}$$
(3)

where Swr = water saturation ratio, Rxo = shallow resistivity, Rt = true formation resistivity, Rmf = resistivity of mud filtrate, Rw = connate water resistivity.

It is important here to notice that the calculated water saturations using Archie (Swa) and ratio (Swr) are about equal each other (Table 1) which mean that all values determined (Sw, Rt and Rxo) are correct (Asquith et al. 2004).

Pickett cross-plot

The Pickett cross-plot, introduced by Pickett (1972), represents a graphical representation of Archie’s model. It is constructed by representing the deep resistivity (Rt) on the horizontal axis and the porosity (Φ) at the vertical axis on a logarithmic Plot. This results in a linear equation as:

$$y \, = \, mx \, + \, b$$
(4)
$$\log \, \Phi \, = \, - \frac{1}{m}\log \, \left( {R_{t} } \right) \, - \, n \, \log \, \left( {S_{w} } \right) \, + \, \log \, \left( {aR_{w} } \right)$$
(5)

Using logarithmic scales for both axes, plotting the true resistivity (RT) on the horizontal axis and porosity (Φ) on vertical axis, the parallel lines that represent the water saturation (Sw) can be drawn. The SW for any plotted point can be read directly. This technique depends on the perception that the true resistivity is dependent on porosity (Φ), water saturation (Sw) and the factor of cementation (m). The 100% water saturation line represents the wet resistivity (RO). The line has a slop of (-1/m) and intercepts the vertical scale, at porosity equals unity, where a (Rw) can be read on the resistivity scale.

The plotted points representing AEB-3A reservoir in Safir-03 well (Fig. 8) are clustered below 25% Sw line indicating oil production and matches very well with the calculated water saturation values above.

Fig. 8
figure 8

Pickett plot for AEB-3A sandstone reservoir in Safir-03 borehole. The red points that are plotted below the 25% Sw line represent the pay interval

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Bulk Volume of Water and Irreducible Water Saturation

Buckles (1965) represented a graphical technique depending on plotting porosity (Φ) versus water saturation (Sw). When the bulk volume of water (ΦxSW) is constant (or almost constant), the plotted points will follow specific hyperbolic curve through this graph. In this case, the reservoir is said to be at irreducible state and the water in the virgin zone will not move and caught on the grain's surfaces by the capillary force. Consequently, the reservoir will produce only oil. The irreducible water saturation (Swirr) is of supreme importance for evaluating the performance of the reservoir and its quality. This parameter is needed for applying any model for calculating permeability from well log data. It can be read directly from Buckles plot.

Figure 9 represents Buckles plot for AEB-3A reservoir in Safir-03 well. The majority of the plotted points followed 0.025 BVW hyperbolic curve. As this reservoir described as sandstone, it can be concluded that it is at irreducible state (Table 1). The irreducible status in this reservoir may be also affected by the presence of amount of shale matrix which lead to the increase in capillary pressure. This capillary pressure holds the water molecules and prevent water to flow through the production process.

Fig. 9
figure 9

Porosity versus water saturation (Buckles plot) for AEB-3A reservoir. The plot shows that the points follow the 0.035 hyperbola of the bulk volume of water (BVW), which indicates that the reservoir is producing free-water oil

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Asquith and Gibson (1982) presented the most popular relation to calculate the Swirr for a particular zone using the formation factor (F) as:

$$S_{wirr} = \sqrt {\frac{F}{2000}}$$
(6)

It is important here to mention that this relation calculates the approximate and theoretical values and is valid only for constructing cross-plots to qualitatively evaluate the relative permeabilities (Kr) and water cut (WC).

Relative permeability (Kr) and water cut (WC)

The main concern for any log analyst is the amount and type of fluid which will be produced. Accordingly, it is of prime importance to compare relative permeabilities to both oil and water (Kro and Krw, respectively), and the accompanying water cut (WC). As stated above, the irreducible water saturation (SWirr) is the cornerstone for evaluating these parameters. In this article, Eq. (6) will be applied. In this concern, Schlumberger (1986) presented a number of charts representing graphically the relation between SWirr versus SW. The following section represents application of such technique for AEB-3A reservoir in Safir-03 well.

Figure 10 represents relative permeabilities to water (Krw) for each zone. The plotted points are clustered below 0.01 relative permeability to water. In addition, there are many points plotted on and even below zero Krw. This very low relative permeability to water reflects free water-producing reservoir (i.e., at irreducible state).

Fig. 10
figure 10

Water saturation (Sw) against irreducible water saturation (Swirr) plot (Asquith and Gibson, 1982) to determine relative permeability to water (Krw) of the AEB-3A reservoir, Safir-03 well

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Figure 11 represents the different relative permeability to oil (Kro) lines based on plotting SWirr versus SW. The plotted points on this plot are clustered around 1 (Kro = 100%) line. This indicates that AEB-3A reservoir in Safir-03 well is expected to produce 100% oil. Points plotted with increasing distance from 1Kro line indicate zones which will produce some water.

Fig. 11
figure 11

Water saturation (Sw) versus irreducible water saturation (Swirr) plot (Asquith and Gibson, 1982) to determine relative permeability to oil (Kro) for AEB-3A reservoir, Safir-03 well

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The water cut (WC) cross-plot for the study reservoir (Fig. 12) shows that the plotted points clustered between 0 and 20% WC. This means that this reservoir has zones which will produce only oil in addition to another zones which will produce oil and water (less than 20%).

Fig. 12
figure 12

Irreducible water saturation against water saturation plot (Asquith and Gibson, 1982) for estimating the percentage of water cut for the AEB-3A reservoir, Safir-03 well

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Absolute permeability (K)

All log-derived permeability models are only valid for estimating permeability (K) in the reservoirs under irreducible state conditions (i.e., Sw = Swirr). Absolute permeability (K) of the pay zone in AEB-3A reservoir was estimated using the following formula (Timur 1968):

$$K^{{1/2}} = 100\left( {\frac{{\Phi ^{{2.25}} }}{{S_{{{\text{wirr}}}} }}} \right)$$
(7)

Table 1 summarizes the obtained permeability values for AEB-3A reservoir in Safir-03 well. It is clear that this reservoir possesses excellent permeability which ranged between 393 and 1339.5 MD with 845MD as average. This confirms good quality for AEB-3A reservoir in Safir-03 well.

Critical water saturation (SCW)

Critical water saturation (Scw) is a percent of water above which the reservoir will begin to produce water in addition to oil. The ability of zones to produce oil depends on their relative permeability to oil and saturation (So). If the relative permeability to water (Krw) is higher than that to oil (Kro) as well as the water saturation (Sw) higher than the critical limit (Scw), the capability of the reservoir to conduct hydrocarbon will decrease quickly and the rock's ability to produce water will increase rapidly. This indicate the importance of evaluating the critical water saturation (SCW).

In case of sandstone reservoirs, as in the case of AEB-3A reservoir, Scw is a function of permeability (K) and effective porosity (Φe) (Fig. 13). Since the average permeability is 845 MD and the average effective porosity is 21%, the critical water saturation (Scw) in this case is 29.5%. This means that AEB-3A reservoir in the study well will produce clean oil as the average Sw is 13%, which is much less than critical saturation (Table 2). Drill stem test (DST) results (Table 3) confirm this conclusion.

Fig. 13
figure 13

Comparison of critical water saturation (Scw) with the porosity and permeability of tertiary's sand in the Gulf Coast (Granberry and Keelan, 1977; Bassiouni, 1994)

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Table 2 BVWmin, Rtmin, Scw for the AEB-3A pay zone, Safir-03 well, Safir Field, North Western Desert
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Table 3 Drill stem test (DST) data for the AEB-3A pay zone, Safir-N07and Safir-03 wells, Safir Field, North Western Desert (Khalda, Pet. Co.)
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Minimum Bulk Volume of Water (BVWmin)

The term minimum bulk volume water (BVWmin) refers to the minimum BVW value, at or below which the reservoir is expected to produce water-free hydrocarbons. Water-free production is required, because it costs money to extract and dispose the accompanied water.

BVWmin varies with lithology. For carbonate, it is about 3.5% and 5% for clean sandstone to as high as 14% for slightly shaly sandstone (Johnson and Kathryne 2006). Since Sw and Φ are the main parameters used for calculating water saturation, BVWmin can be calculated through rearrangement of Archie model as follows:

$$S_{w} ^{2} = \frac{{Rw}}{{\Phi ^{2} \times {\text{ }}Rt}}$$

Rearrange this equation in terms of BVW yield

$$S_{w} ^{2} x\Phi ^{2} = \left( {S_{w} x\Phi } \right)^{2} = \left( {{\text{BVW}}} \right)^{2} = \frac{{{\text{Rw}}}}{{{\text{Rt}}}}$$
$$\left( {{\text{BVW}}_{{{\text{min}}}} } \right)^{2} = \frac{{{\text{Rw}}}}{{{\text{Rtmin}}}}$$
(8)
$${\text{Rt}}_{{{\text{min}}}} = \frac{{{\text{Rw}}}}{{\left( {{\text{BVWmin}}} \right)^{2} }}$$

The minimum true resistivity (RTmin) required for free-water production can be approximated according to matrix. In case of carbonate, it equals 800 × Rw. In case of clean sandstone, it equals 400 × Rw and 200 × Rw for slightly shaly sandstone. (Johnson and Kathryne 2006).

Applying this technique for AEB-3A pay interval, Rtmin equals 4 Ω.m2/m (400 × 0.01) and BVWmin 0.05 (Eq. 8). The average values of the true resistivity (Rt) and BVW for this interval are 14 Ω.m2/m and 0.03, respectively. Comparing these values with Rtmin and BVWmin (Table 2) clearly indicates water-free production as confirmed through the DST (Table 3).

Conclusions

Alam El Bueib Formation of the Lower Cretaceous age represents the major oil reservoir in Safir Field at Shushan Basin, northern Western Desert. Therefore, the current work aims to evaluate the quality of the sandstone reservoir of AEB-3A Member in Safir-03 well.

The formation evaluation of the Alam El Bueib 3A member from well logging data analysis indicates the presence of an oil-producing reservoir that has good quality between depths 8108–8133 ft. This reflects the net pay thickness of the AEB-3A sandstone reservoir in the studied borehole (well) amounts to 25 ft as indicated in Fig. 14. This reservoir characteristics show that the shale volume is less than or equal to 9%, which reflects a clean sandstone interval. It also displays low water saturation values (10–23%), interconnected porosity (19% to 23%), low BVW (≤ 0.04), irreducible water saturation (10–12%) and permeability 393–1339 MD, which reflects excellent reservoir quality. The calculated BVWmin of clean sandstone reservoir is 0.05, by comparing it with BVW values (BVWmin > BVW) clearly indicating hydrocarbon production will be water free as confirmed through the DST. The relative permeabilities for water and oil (Krw and Kro,, respectively), which have been calculated based on Sw and Swirr cross-plots, clearly indicate good reservoir quality because the plurality of points is situated between 0.01 and 0 Krw and located between 1.0 and 0.5 Kro for AEB-3A sandstone reservoir. Also, the zero points of Krw are plotted on and below 1.0 Kro line, which reflects 100% and 0% relative permeabilities to oil and water, respectively. On the other hand, the water cut of water production of the AEB-3A Member is quite low (0–20%).

Fig. 14
figure 14

Interpretation of the well-logging data of AEB-3A reservoir in Safir-03 well

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The critical water saturation (Scw) for net pay AEB-3A sandstone reservoir is 29.5%, while the average of the calculated water saturation values for this pay is 13% (i.e., Sw < Scw). So, it is reflected that the total net pay will flow oil, whereas the water phase will remain immobile. This is confirmed with reservoir engineering through the DST.