Petrophysical characterization, microfacies analysis, and diagenetic attributes of the Lower Jurassic surface analog sequence in Gebel El-Maghara area, north Sinai, Egypt

This study concerns with the petrophysical characteristics of the Lower Jurassic surface analog in Gebel El-Maghara area (from base to top Mashaba, Rajabia, and Shusha formations), north Sinai, Egypt and implementation of the mineral components and diagenetic controls on reservoir characteristics. A full set of petrophysical measurements including porosity ( ∅ He ), permeability (k), grain and bulk densities (σ g and σ b , respectively), and true formation resistivity factor was applied. The Lower Jurassic sequence is subdivided into ve hydraulic ow units (HFUs) that consist of three reservoir rock types (RRTs). These RRTs are composed of three microfacies association (MFAs). The RRT1 plug samples consist of the mostly clastic MFA1; they are porous, permeable, and have good reservoir quality that is using the ow zone indicator (FZI), and the reservoir quality index (RQI). The lowest reservoir quality is assigned to the RRT samples which are mostly composed tight carbonates. Based on the petrographical studies, SEM imaging, and the XRD analysis, dissolution and fracturing slightly enhanced the reservoir potentiality of the RRT1 samples, whereas physical compaction, tight cementation, and authigenic clay content (kaolinite, hematite, and goethite) are responsible for deterioration of the reservoir properties of RRT3 samples and reduction of the RRT2 samples. obliterated ( cementation. are and HFU-4, respectively. These two prospective units are mostly composed of the rst and second microfacies association (MFA1 and MFA-2, respectively). The HFU-2 of the RRT1 samples which are characterized by ∅ He in the range with higher values for the lower carbonate part. Selective and partial dolomitization enhanced and supported the prospective petrophysical properties of this sequence which is composed mostly of ferruginous dolomitic packstone microfacies. The upper parts of Rajabia (top of HFU2), and the HFU4 in Shusha formations are consists of the siliceous quartz arenite and the ferruginous kaolinitic siliceous quartz arenite microfacies (RRT1) which are porous and permeable microfacies. Due to lling pores and cementation with sparite and pseudo sparite the reservoir prospectivity of the top parts of HFU4 (ferruginous kaolinitic and sparitic quartz arenite microfacies, MFA2, RRT2) is slightly reduced. Separation the

Rajabia Formation outcrop is located at Wadi Rajabia and Wadi Sad El-Mashaba areas; its lithostratigraphic sequence is similar to the Mashaba Formation. Its basal and upper parts are composed of interbedded sequence of brownish sandstones and yellow marl; whereas its middle parts are composed of dolomitic limestone rocks intercalated with few thin sandstone and sandy limestone beds. However, the upper and middle part of Rajabia Formation contains more claystone and shales intercalations than its basal parts and the Mashaba Formation (Fig. 2).

Shusha Formation (272 m, Pliensbachian-Toarcian)
The type section of Shusha Formation is in the midway between Shushat El-Maghara and Wadi Mahl in Gebel El-Maghara area. It mostly consists of clastic sedimentary intercalations of cross-bedded continental sandstones, clays and shales, which are intercalated with some shallow marine limestones interbeds, especially at its lowermost parts. Its shale interbeds contains some sideritic concretions vary in thickness from few cm to 2 mm giving them their dark brown appearance. The top parts of this formation are characterized by yellowish brown hard sandstones interbedded with some shale intercalations.

Methodology
Some eld trips were conducted to study the lithostratigraphy and geologic setting of the Lower Jurassic sequence at Gebel El Maghara area, where 100 representative surface block samples were collected and oriented horizontally parallel to the bedding plane.
To perform the petrophysical measurements, 56 representative plugs were obtained representing the different levels and lithologies of the collected blocks samples (21 plugs for Rajabia, 18 for Shusha, and 17 plugs for Mashaba formations). The studied plugs were cleaned with ushing water under vacuum to remove the ne cuttings and the soluble materials, and then dried at a temperature not more than 60° C for 48 hours in an electric oven.
The cleaned and dried plugs were weighed (w dry , in g) and their bulk volume (v b , in cm 3 ) was then estimated using a digital micrometer to estimate bulk density (σ b ). σ b (g/cm 3 ) = w dry / v b Porosity was measured using helium injection and water saturation techniques. The water porosity is measured by evacuating the different samples using vacuum pump then injecting them by water and weight of the saturated samples was measured (w sat , in g).
∅ W = 100 x v p / v b = 100 x (w sat -w dry ) / v b Where, v p is the total volume of pore spaces The grain volume (v g ) is then measured using a pycnometer technique by injecting helium at 19 psi and the grain density (σ g ) and helium porosity (∅ He ) are calculated as follows. σ g (g/cm 3 ) = w dry / v g Water has less ability than helium to invade into the micro and nano pore spaces, so the helium porosity (∅ He ) is always more than or rarely equals to the water porosity (∅ He ). The difference between ∅ He and ∅ W represents the inaccessible pores that water can invade them (Nabawy, 2018). It can be estimated as follows: ∅ inacc = 100 x (∅ He -∅ W ) / ∅ He Permeability (k) was estimated using air permeameter, as samples were plugged in a Hassler-type core holder and k was estimated using the following equation. where; Q is the ow rate, µ is the air viscosity, A is its cross sectional area, L is the plug length, and ΔP is the applied differential pressure.
For reservoir quality ranking, the concept of Amaefule et al. (1993) on the hydraulic ow unit (HFU) was applied, where the HFU quality is based on the normalized porosity index (NPI), reservoir quality index (RQI), and the ow zone indicator (FZI). Each HFU is the sum up of group of samples having the same range of porosity (∅), permeability (k), RQI and FZI values. These HFU quality parameters can be estimated as follows.
More details on the applied reservoir quality parameters were published by Nabawy and ElHariri (2008) and .
The predominant diagenetic factors and mineralogy were checked petrographically; where 100 thin sections were prepared representing the collected block samples. These were impregnated with Araldite dyed blue to enable visual porosity estimation. To discriminate between calcite and dolomite, thin sections were stained Red using Alizarin Red S. Dyed and stained thin section were then studied using polarized microscope supported with a PC monitor to enable monitoring the different components, detailed studies, and precise imaging.
To image the pore spaces in details, to reveal the predominant digenetic factors, and to check clay types and distribution, 15 representative rock fragments were coated by gold and scanned using scanning electron microscopy (SEM). The SEM Model QUANTA FEG250 was applied with accelerating voltage 200v-30kV, and magni cation 30X-300kX. Finally, to estimate the different mineral components of the studied rock types in semi-quantitative way, ten representative samples were selected form the studied samples and prepared as very ne powder for X-ray diffraction analysis (XRD). Analysis was applied using a Philips X-ray diffractometer supported with Ni-ltered Cu radiation at 40 KV and 30 MA, in the range 2θ = 5-80° and scanning speed of 0.01°/sec. The X-ray data analysis was performed using ASTM cards and compared with the data published by Brown (1961), where a semi-quantitative estimation of the different mineral components of the studied rock types has been assigned.

Reservoir Rock Types (RRTs)
Based on the discrete rock type (DRT) values and the other petrophysical parameters, the Lower Jurassic sequence in north Sinai at Gebel El-Maghara area is subdivided into three reservoir rock types (RRTs). The RRT is highly porous and permeable with good reservoir quality; it has very good average helium porosity (2.3 %), good water porosity (16.4 %), very good permeability (129.9), fair reservoir quality index (0.68 µm), poor ow zone indicator (2.31 µm), relatively high DRT values (12.2), and meso effective pore radius R 35 (5.72 µm, Table 1). Its average RQI and FZI values are fair and poor values with fair reservoir rank.  where; FRT is the true formation resistivity factor; a is the lithology factor, m is the xed porosity exponent, and m' is the variable porosity exponent. RRT and MFA are the reservoir rock type and microfacies association, respectively. The FR T classi cation ranks are following Nabawy (2018).

Microfacies Analysis
To reveal the mineral composition of the available Lower Jurassic samples and to reveal the dominant diagenetic factors that control the reservoir quality of this sequence in its surface type section, a detailed microfacies analysis was applied. Also, discriminating the samples into some microfacies association (MFA) will explain the variation in the petrophysical properties of the assigned RRTs. Following rock typing, three microfacies associations (MFAs) were assigned for the studied samples. Each is characterized by some distinctive visible aspects that are identi able by the petrographical studies, and represents the mineral composition and microfacies of each corresponding RRT.

Microfacies Association MFA1 (RRT1)
This microfacies association represents the mineral composition, and pore types of the RRT1 samples. It is mostly represented through the Shusha and Rajabia formations.

Siliceous Quartz Arenite
It represents the top parts of Shusha and Rajabia formations; it consists of very ne to ne, well-sorted, and sub-rounded to sub-angular quartz grains and feldspars cemented together by meniscus silica cement and quartz overgrowth with very good visual porosity (∅≥ 20 %). Pore spaces are mostly described as: 1) intergranular pore spaces, slightly reduced by iron oxide patches (Fig. 3a), 2) micro to meso vugs, and 3) microfractures (Fig. 3a).

Ferruginous Kaolinitic Siliceous Quartz Arenite
It also represents the top parts of Rajabia Formation; it consists of medium-sorted ne to very ne angular monocrystalline quartz grains with some feldspars cemented by silica cement (Fig. 3b). Compaction is indicated by concave-convex, suture and point grain contacts, and wavy extinction ( Fig. 3b). The quartz grains are commonly corroded by the cement increasing the grain angularity. A noticeable amount of silt sized-grained iron oxides, and kaolinite patches are disseminated in between quartz grains to support the microsparite cement in reducing the total connected pore volume. This iron content gives the samples their diagnostic brownish yellow colour. The interstitial pore spaces are described as: 1) intergranular pores, frequently reduced by kaolinite, silica and iron oxides (Fig. 3b), 2) micro vugs (Fig. 3b), and 3) microfractures. The estimated visual porosity is good to fair and varies between 10 and 20%.

Ferruginous Dolomitic Packstone
It represents the middle parts of both Shusha and Rajabia formations. It is composed of highly porous micrite with some sparite, pseudo sparite, dolomicrite and dolomicrosparite (Fig. 3c). Few clastic components and allochems are assigned in the groundmass, besides to many sparite-lled fossil molds are assigned. Iron oxide and clay patches are scattered within the groundmass. Though invading this microfacies by Ca-bearing solution and lling many pore spaces, it has good to very good visual porosity (15-20%). Pores are described as: 1) micro intercrystalline pores, 2) meso to micro vugs, sometimes lled by sparite and pseudo sparite, 3) sparite-reduced moldic porosity, 4) microfractures, partially reduced by microsparite, and 5) meso to micro channels partially lled by microsparite (Fig. 3d).

Microfacies Association MFA2 (RRT2)
This association is composed of only one clastic microfacies, ferruginous kaolinitic and sparitic quartz arenite, forming the top parts of Shusha Formation.

Ferruginous Kaolinitic and Sparitic Quartz Arenite
It consists of medium to ne-grained, moderately sorted, and sub-angular to sub-rounded quartz grains cemented by sparite cement (stained red, Fig. 3e). The quartz grains are slightly compacted together and corroded by the sparitic cement with many dull spots of iron oxides and clay patches.

Microfacies Association MFA3 (RRT3)
It is relatively compacted and tight MFA composed of many clastic and non-clastic microfacies representing the basal parts of Shusha and Rajabia formations, and most parts of Mashaba Formation.

Highly Ferruginous and Sparitic Quartz Arenite
This tight microfacies consists of very ne to ne, well sorted, sub-rounded to sub-angular quartz grains cemented by pseudo sparite to microsparite.

Highly Compacted Siliceous Lithic Arenite
It represents the topmost parts of Mashaba Formation; it consists of poorly sorted, pebbly sized to ne grains, angular to sub-angular highly compacted quartz grains cemented by silica cement (Fig. 3f). It is characterized by many lithic/rock fragments aligned in streaks in alternation with ne to very ne quartz grains. Compaction is indicated by point, straight, and suture contacts, wavy extinction, with some fractured quartz grains.

Fractured Bioclastic Packstone
This microfacies is similar to the highly fractured bioclastic wackestone microfacies but with less sealed fractures and more developed crystals with some dull clay, sparite and pseudo sparite patches. Some allochems are disseminated within the groundmass; sometimes are replaced by welldeveloped sparite crystals with some preserved brous micritization at the borders (Fig. 3k). Besides, some channels are assigned lled with welldeveloped drusy sparite crystals (Fig. 3l). Visual porosity is highly obliterated (∅ < 5 %) due to a prolonged phase of cementation by sparite. It is characterized by: 1) micro intercrystalline pores, 2) macro to meso sparite-lled molds (Fig.

Authigenic Minerals
Authigenic minerals including types and distribution of clay minerals and iron oxides can be studied in details using the scanning electron microscopy (Nabawy and Abd El Aal, 2019b). These accessory minerals and their distribution are the main diagenetic control for the reservoir quality ).

MFA1
The siliceous quartz arenite and ferruginous kaolinitic siliceous quartz arenite microfacies of MFA1 are affected by kaolinite clay content which is assigned lling the pore channels which slightly reduced the pore volume of the siliceous quartz arenite and moderately affected the ferruginous kaolinitic siliceous quartz arenite microfacies (Fig. 4a). It is aligned lling the pore spaces and attached to their walls. Also, presence of few illite clay patches (Fig. 4b), and some patches of rose and sea star-shaped iron oxides stained the samples with its brownish colour and slightly reduced the pore volume (Fig. 4c). The SEM studied indicated dissolution of some sparite crystals of the ferruginous dolomitic packstone microfacies of Shusha which helped in enhancing its reservoir quality. This phenomenon is represented by pitted surface and hollow crystals (Fig. 4d).
However, due to their low swellability, implementation of the present kaolinite and iron oxide content is not enough to reduce visual porosity which varies between 15 and 30 % (Fig. 4a-d).

MFA2
As the case of the MFA1 microfacies, the ferruginous kaolinitic and sparitic quartz arenite samples of Shusha Formation is affected by the kaolinite clay content which lled the pore channels and affected the total pore volume of this microfacies (Fig. 4e). Also, the pore spaces are lled with some iron oxides in the form of star shape (Fig. 4f), which accumulated with the kaolinite booklets to reduce the pore connectivity (Fig. 4g). Filling the pore spaces with patches of the iron oxides helped the diagenetic cementation by sparite to reduce the visual porosity of the studied microfacies (Fig. 4h).

MFA3
The last microfacies association is mostly composed of tight, compacted, and well cemented microfacies. This due to quartz overgrowth and lling the pore spaces by well-developed dolomite and sparite crystals (Highly Compacted Siliceous Lithic Arenite, Fig. 4i). Beside to the tight cementation, presence of illite bers and kaolinite booklets highly reduced the connected pore spaces of the highly ferruginous and sparitic quartz arenite microfacies (Fig. 4j). The illite bers and star-like iron oxides are embedded within the cement indicating that forming of these authigenic minerals is prior to the nal stage of cementation by sparite (Fig. 4k, l).

X-ray Diffraction Studies
Samples of the Lower Jurassic Mashaba, Rajabia, and Shusha formations are composed of carbonate and sandstone intercalations, represented by quartz (SiO 2 ), and calcite (CaCO 3 ) with few dolomite (Mg.Ca(CO 3 ) 2 ) and kaolinite (Al 2 Si 2 O 5 (OH 4 )) content (Table 3). Also, few iron contents of goethite (FeO(OH)) and hematite (Fe 2 O 3 ) are present with traces of Gypsum (CaSO 4 .2(H 2 O)). The analyzed Mashaba samples are mostly composed of calcite mineral assigned (2θ = 29.42°, Fig. 5a) Upwards through Rajabia and some intercalations in Shusha formations, the non-clastic composition is replaced by sandstones that composed of quartz (2θ = 26.65°) with few plagioclase (Fig. 5b, c). Some ferruginous (12.4 ≤ hematite ≤ 29.5%) sandy limestone and calcareous sandstone are assigned in Rajabia and Shusha formations, respectively. Some goethite and kaolinite contents are also present in the studied two formations (Table 3). Table 3 Relative proportions of the different mineral components of the Lower Jurassic formations in Gebel El-Maghara area obtained from the XRD analysis.

MFA1 (RRT1)
Dominance of the reservoir quality-enhancing diagenetic controls including dissolution of cement and allochems (Fig. 3a), and fracturing ( Fig. 3d) increased the storage and ow capacities of the RRT1 samples with fair to excellent porosity and permeability (Table 1). Also, impacts of the reservoir quality-reducing diagenetic controls are limited. These are represented by slight compaction leads to some grain fracturing and point contact grain to grain relationship (Fig. 3a). Cementation by the intercrystalline pore spaces and vugs by sparite, invading and lling the pore channels by micro and pseudo sparite partially reduced the pore volume, but still there is a 15-20% visual porosity (Fig. 3c, d). Even though, presence of some iron oxides and authigenic clay minerals (Fig. 4a-c), their impact is also limited to block few vugs and to line some pore walls.

MFA2 (RRT2)
The reducing impact of diagenetic factors on reservoir parameters of the ferruginous dolomitic packstone samples is effective, where cementation by sparite and dolomite is dominant and more implemented than that for the MFA1 samples. Accumulation of high amount of kaolinite and iron oxides in the pore spaces blocked some pore throats and reduced the pore connectivity (Figs. 3e-g, 4e-h). In comparison to the MFA1 (RRT1) and MFA3 (RRT3), implementation of the reservoir quality-reducing factors is moderate, so the MFA2 (RRT2) samples are a transitional group between the RRT1 and RRT3 samples.

MFA3 (RRT3)
This group of samples has the lowest reservoir quality in the studied Lower Jurassic samples in Gebel El-Maghara area. It is highly cemented by sparite and dolosparite (Fig. 4i). Impacts of the reservoir quality-enhancing factors including fracturing and dissolution are obliterated by cementation ( Fig. 3i-l). It is also suffered from severe compaction which supported cementation in reducing the total pore volume. The authigenic minerals lled and blocked the pore channels in between the cement and matrix which seem to be supported by later phase of calcite cementation that tightly blocked some pore spaces (Fig. 4l).

Porosity-density relationships
Two types of densities are assigned, the grain density (σ g ) which is a function of the mineral composition and the bulk density (σ b ) which is controlled by the grain density and porosity. Plotting the grain and bulk densities on X-Y plot indicates that most of RRT1 plugs have grain densities between 2.65 g/cm 3 (quartz line) and 2.71 g/cm 3 (calcite line, Fig. 6a). The siliceous quartz arenite and the ferruginous kaolinitic siliceous quartz arenite RRT1 samples are characterized by grain density around the quartz line at 2.65 g/cm 3 . Shifting the grain density to values higher than the quartz line is due to the calcitic composition of the carbonate microfacies in the MFA3 and the ferruginous dolomitic packstone of the MFA1 samples, whereas increasing the grain density of the clastic microfacies (the ferruginous kaolinitic siliceous quartz arenite of MFA1, ferruginous kaolinitic and sparitic quartz arenite of MFA2, and the highly compacted siliceous lithic arenite of MFA3) is attributed to increasing their sparite, dolomite and iron oxides content 4c,g,i). The 2.71 g/cm 3 bulk density line separates the RRT1 samples from that of the other two RRTs which is attributed to their fair to excellent porosity values (Fig. 6a). This plot is supported by plotting the helium porosity (∅ He ) as a function of the bulk density which indicates that porosity values of the RRT1 samples is higher than that of the other two RRTs. Porosity of the RRT1 samples is mostly higher than 15 %, whereas porosity of the RRT2 and RRT3 are less than 10 % (Fig. 6b). The high reliability of the obtained best-t line for the different rock types (R 2 ≥ 0.921, Fig. 6b) is a good proof for quality of the petrophysical measurements. Due to the similar multiplication factors and constants of the obtained RRTs' porosity-density models (Fig. 6b), a model can be applied to estimate the helium porosity of all plugs in terms of their bulk densities as follows.
∅ He = -35.2 σ b + 95.0 (R² = 0.995) For the electric measurements, samples were saturated with saline and water porosity was estimated for the samples. Data of the ∅ W -σ b plot are scattered (R 2 < 0.73, Fig. 6c) and less reliable than that of the ∅ He -σ b (R 2 > 0.92, Fig. 6b), i.e., its indication for the bulk density is less than that of the helium porosity and. This can be attributed to the fact that, water has less ability than helium to invade the micro and nano pores, so the water porosity (∅ W ) is mostly less than that of the helium porosity ( Fig. 7m Table 1). The more shifts toward the helium porosity Y-axis on the ∅ He -∅ W plot indicates presence of more micro and nano pores that the water cannot invade. A set of reliable mathematical equations (0.641 ≤ R 2 ≤ 0.742) were introduced to estimate the ∅ He and ∅ W in terms of each other (Fig. 7).

Contribution of porosity to permeability
Permeability and porosity are the main controls for reservoir quality; they de ne the reservoir storage and ow capacities. Plotting permeability versus helium porosity indicates three different petrophysical behaviors; RRT1 samples have the highest storage and ow capacities (very good to good permeability, and excellent to fair permeability values), whereas RRT3 samples are tight to poor (tight to poor porosity and permeability values). A set of reliable models were introduced to estimate permeability as a function of the helium porosity (Fig. 8). Similarity in the porosity exponent of the k-∅ He is due their dominant clastic composition, whereas the RRT3 are mostly composed of carbonate microfacies.

Reservoir quality controlling factors
The reservoir quality concept, including the RQI and FZI parameters, has been introduced by Amaefule et al. (1993) and checked for ranking the clastic and non-clastic reservoirs by many researchers (e.g., Tiab and Donaldson, 1996;Corbett and Potter, 2004;Al-Dhafeeri and Nasr-El-Din, 2007;Teh et al., 2012;Abed, 2014;Nabawy andEl Sharawy, 2015, 2018;. These reservoir quality parameters are estimated as a function of porosity and permeability, so they are reasonable are factors of these two parameters (∅ and k). Plotting the RQI versus permeability ( Fig. 9a) indicates that the RQI is mostly controlled by the permeability as an indicator for the ow capacity of the reservoir. Factors and exponents of the RQI-k models of the RRT1 and RRT2 groups are similar with tight quality for RRT2 plugs and poor to good reservoir quality for RRT1 plugs (Fig. 9a). This should be attributed to the fact that cementation and lling pores with authigenic clay and iron oxides are more effective for the RRT2 than the RRT1. Tightness, well cementation, and blocking the pore channels by calcite cement are the main reason for the tight RQI values of the RRT3 samples (Figs. 3i-l, 4k-l, Fig. 9a). Due to the high reliability of the obtained RQI-k mathematical models and similarity in the multiplication factors and exponents, a general model is applied to estimate permeability in terms of their RQI values as follows. RQI = 0.11 k 0.39 (R² = 0.994) Dependence of the RQI on porosity values is less than its dependence on permeability, where the reservoir quality is a direct measure of how much the reservoir porosity contributes to its permeability, i.e., it is a measure for the most effective and permeable porosity not all the connected pore spaces. So, its dependence on porosity is based on the amount of connected pore spaces, where reliability of the RQI-∅ He model is higher for the more porous RRT samples (Fig. 9b). No reliable models can be obtained for the RQI with the ∅ He values of the tight RRT3 samples. This may be explained by the higher complexity and the lower connectedness of its pores than the other two RRTs.
On the other side, due to the effect of the normalized porosity index (NPI) values on the ow zone indicator (FZI) values, the relationship between the FZI values and the reservoir parameters are less consistent than those relationships with the RQI. No relationships can be established between the FZI and ∅ He values for the different RRTs, whereas two moderately reliable models were established between the FZI and k for the RRT1 and RRT2 samples (R 2 ≤ 0.559) with scattered samples for the RRT3. This also can be attributed to more tightness and complexity of pore throats of the RRT3 samples.

Rock typing based on FZI
Rock typing of the present study is based on the discrete rock types (DRT) which in turns based on the FZI values which is also used as a main key factor for rock typing process. Plotting permeability versus porosity is also applied as a common technique for subdividing the rock samples into some RRTs. So, the FZI values is superimposed on the k-∅ He plot as intersecting lines separating the studied samples into clusters of similar porosity and permeability trends (Fig. 11). This plot indicates that, the RRT1 is limited by FZI lines = 1.582 and 3.011 µm, which is considered as poor to fair reservoir quality, whereas the RRT2 samples are situated between FZI lines 1.00 and 1.582 µm indicating samples of poor reservoir quality. This is due to their very good to poor permeability values, and their very good to poor porosity values. The tight RRT3 samples are characterized by FZI values less than 1.00 µm (Fig. 11).
On the other side, superimposing the FZI lines on the RQI-NPI plot supports this achievement, and indicates that only the RQI values of the RRT1 samples are accepted for poor to good reservoir quality (0.33 ≤ RQI ≤ 1.18 µm, Fig. 12a Fig. 13). Therefore, due to its tightness and pore fabric complexity, the RRT3 samples are characterized by high average FR T value = 473.1 (300 < high FR T ≤ 500, Nabawy, 2018), whereas due to the pore connectedness the RRT1 samples are characterized by medium average FR T value = 169.8 (150 < medium FR T ≤ 300, Nabawy, 2018). It is indicated that, increasing the water porosity is accompanied by decreasing the FRT, i.e., they are inversely related to each other (Fig. 13). To check Archie's parameters, m and a (porosity exponent, and lithology/tortuosity factor, respectively), two methods of statistical processing are applied: 1) free regression with a constant m value, and 2) xed regression with variable m values (m') . For the rst method, FR T values of each RRT are plotted versus their corresponding ∅ W and are processed as one set of samples to get its diagnostic tortuosity factor (a), and its porosity exponent (m) (Fig. 13) Fig. 13). To get more detailed information about the porosity exponent, the second method ( xed regression) is applied to the studied samples assuming a = 1 to get variable m (m') which changes from sample to sample with the highest m' samples are assigned to the highly porous RRT1 samples and the lowest m' values for the tight and compacted RRT3 samples (Table 2). Plotting the m' values for the different RRT samples indicate that m' is directly proportional of the water porosity. A set of mathematical models can be obtained to calculate the m' using the water porosity ( Fig. 14). This achievement is corresponding with that obtained by Nabawy (2018), where m is directly proportional to ∅ W .
Due to differences pore connectivity, and variation in the electric effectiveness and sharing of the iron oxides and clay content (based on their amounts and type of distribution), no model can be obtained to estimate the FR T of all RRTs in terms of their ∅ W .

Reservoir Zonation and Hydraulic Flow Units (HFUs)
Subdividing the reservoir sequence into some HFUs is required for getting a precise reservoir modeling, each HFU with its diagnostic model. The HFU is a common concept referring to a cumulative sequence of similar ow capacity and petrophysical properties in a given reservoir. Its petrophysical properties are internally consistent, but easily recognized from that of the overlying and underlying units. The reservoir rock typing is based on some X-Y plots and the depth is not taken into consideration, but the HFU concept is based on plotting the different petrophysical parameters versus depth Abuamarah et al., 2019). It has been tested and applied by many authors (e.g., Ebanks et al., 1987;Ti et al., 1995;Martin et al., 1997;Aminian et al., 2003;Orodu et al., 2009;Abde, 2014;Kassab et al., 2016Kassab et al., , 2017Abdulelah et al., 2018).
Plotting porosity (∅ He , ∅ W ), inaccessible porosity (∅ Inacc ), permeability, FR T , RQI, FZI, and the R 35 of Winland (1972) as a function of depth, enabled assigning ve HFUs in the studied Lower Jurassic sequence. Each unit is characterized by its internal consistent petrophysical properties and is easily predicted from the surrounded units (Fig. 15). As shown in Fig. 15, and based on arbitrary cutoff values (∅ cutoff = 10 %, k cutoff = 1.0 md, RQI cutoff = 0.25 µm, FZI cutoff = 1.0 µm, R 35, cutoff = 1.0 µm), it is indicated that the whole sequence of Rajabia Formation, and middle parts of Shusha Formation are prospective units represented by HFU-2 and HFU-4, respectively. These two prospective units are mostly composed of the rst and second microfacies association (MFA1 and MFA-2, respectively). The HFU-2 consists of the RRT1 samples which are characterized by ∅ He in the range 20-30%, with higher values for the lower carbonate part. Selective and partial dolomitization enhanced and supported the prospective petrophysical properties of this sequence which is composed mostly of ferruginous dolomitic packstone microfacies. The upper parts of Rajabia (top of HFU2), and the HFU4 in Shusha formations are consists of the siliceous quartz arenite and the ferruginous kaolinitic siliceous quartz arenite microfacies (RRT1) which are porous and permeable microfacies. Due to lling pores and cementation with sparite and pseudo sparite the reservoir prospectivity of the top parts of HFU4 (ferruginous kaolinitic and sparitic quartz arenite microfacies, MFA2, RRT2) is slightly reduced. Separation between the water and helium porosities (track-1, Fig. 15) is due to presence of some micro and nano pores that water cannot invade, i.e., the high separation indicates higher inaccessible pore percentage (Track-2). Due to the high effective porosity of these two HFUs, permeability values are mostly higher than 10md (Track-3), the RQI and FZI values are higher than their cutoff values (Track-5) with the effective pore radius R 35 more than 1.0 µm (meso pores, Track-6, Fig. 15).
Due to complexity of the pore throat distribution and diagenesis, and the bad pore connectivity, the basal parts of the section, Mashaba Formation (HFU-1), basal and top parts of Shusha Formation (HFU-3, HFU-5) an intensive uctuation of the inaccessible pore percentages is assigned with very low porosity, permeability, RQI and FZI, and micro pore sizes (R 35 < 1.0 µm).
Increasing the FR T values (Track-4) of the Mashaba Formation is due to its tight cementation, very low porosity values, and complexity of pore throats. Fluctuation of these electric values is comparable to their corresponding water porosity and effective pore radius (Fig. 15).
For subsurface exploration of the area in vicinity (offshore marine exploration in the Mediterranean Sea), it is recommended to follow up the Rajabia Formation and top parts of Shusha Formation. On the other side, due to the very low porosity values of Mashaba Formation, tightness, fossil content, and beauty appearance, it can be used as building stones and marble tiles.

Conclusions
Based on their petrophysical properties, the Lower Jurassic Mashaba, Rajabia and Shusha formations in their type sections in Gebel EL-Maghara area were subdivided into ve hydraulic ow units (HFUs) that consist of three reservoir rock types (RRTs). Each ow unit has its diagnostic petrophysical properties. HFU2 of Rajabia Formation is the best ow units; it consists mostly of RRT1 samples, whereas the HFU1 of Mashaba Formation is the tightest unit that is built of RRT3 plugs.