Three-Dimensional Integrated Geo-Static Modeling for Prospect Identification and Reserve Estimation in the Middle Miocene Multi-Reservoirs: A Case Study from Amal Field, Southern Gulf of Suez Province

Middle Miocene reservoirs in the southern part of the Gulf of Suez province are characterized by geometrical uncertainties due to their structural settings, lateral facies change, different lithologies, and diverse reservoir quality. Therefore, in this study, detailed 3D geo-static models were constructed by integrating multiple datasets, including 2D seismic sections and digital well-logs. The 3D models were constructed for the Belayim Formation (Hammam Faraun Member), Kareem Formation (Markha Member), and Rudies Formation (Upper Rudies Member) with detailed structuration, zonation, and layering for Amal Field in the southern Gulf of Suez province to assess the hydrocarbon potential, calculate accurate reserves, recommend development and exploration plans, and propose locations for future drilling. The resultant structural model exhibited a compartmentalized area of major and minor normal faults trending NW–SE, forming structurally high potential hydrocarbon trapping locations in the study area. The petrophysical models indicated the good potentiality of Hammam Faraun as a reservoir with porosity values of 15–23%, increasing towards the central part of the area, volume of shale (Vsh) of 21–31%, water saturation (Sw) of 34–49%, and sand thickness increasing toward the northeastern part of the area. The Markha Member was also interpreted as a good reservoir, with porosity values of 15–22%, increasing towards the southeastern part of the area, Vsh of 13–29%, Sw of 16–38%, and sandy facies accumulating in the central horst block. Upper Rudies exhibits good reservoir properties with porosity values of 16–23%, Vsh of 29–37%, Sw of 35–40%, and good sandy facies in the central horst block of the area. The study results showed hydrocarbon potential in the central horst block of the study area for the Middle Miocene multi-reservoirs.


INTRODUCTION
The 3D static modeling of producing reservoirs is very important to control the proper evaluation for the exploration and development phases.A variety of geoscience platforms can be used to model hydrocarbon reservoirs (Abdel-Fattah et al., 2010, 2018;Noureldin et al., 2023aNoureldin et al., , 2023bNoureldin et al., , 2023cNoureldin et al., , 2023d)).However, the accuracy of the modeling process is still a major challenge that can affect the development of reservoirs (Bryant & Flint, 1992;Bilodeau et al., 2002;Noureldin et al., 2023aNoureldin et al., , 2023bNoureldin et al., , 2023cNoureldin et al., , 2023d)).
A 3D structural model is obtained based on seismic interpretation outputs (Abdelmaksoud et al., 2019a(Abdelmaksoud et al., , 2022;;Radwan et al. 2022), which include depth maps and associated fault sticks/planes.The ability to construct complex structures is a main advantage of a 3D structural model.Moreover, it enables the interpreter to inspect and analyze the static model (Fagin, 1991) by showing a variety of geological cross-sections of the model in any direction (Cosentino, 2005), and the seismic world is linked to other branches of structural geology via the structural model (De Jager & Raymond, 2006).The advantage of modeling complex hydrocarbon reservoirs with varying formations and reservoir heterogeneity is the fundamental benefit of 3D modeling methodologies (Radwan et al., 2022).Therefore, correct parameters and the integration of the best data are necessary for superior reservoir modeling (Noureldin et al., 2023a(Noureldin et al., , 2023b(Noureldin et al., , 2023c(Noureldin et al., , 2023d)).
There should be some caution when determining rock and petrophysical properties from electrical well logs (Radwan et al., 2020;Noureldin et al., 2023aNoureldin et al., , 2023bNoureldin et al., , 2023cNoureldin et al., , 2023d)).There may be uncertainties associated with geological, seismic, and petrophysical interpretations in the geo-evaluation processes.Therefore, the best-fit parameters were used in the reservoir static modeling to decrease the final geological model uncertainties.The ability to model complex structures is a primary benefit of 3D modeling approaches.By displaying cross sections across a built-in model in any direction, this technique enables the interpreter to assess the model.The 3D facies/petrophysical modeling is also essential for linking wellbore parameters to a 3D geostatic model (De Jager and Pols, 2006;Abdel-Fattah et al., 2010;Abdelmaksoud et al., 2019b).
Middle Miocene sediments have excellent hydrocarbon potentiality as a source, reservoir, and seal rocks (Attia et al., 2015;Radwan et al., 2019).The Middle Miocene succession in the Gulf of Suez province is composed of six formations, namely, from base to top: Nukhul, Rudeis, Kareem, Belayim, South Gharib, and Zeit Formations.The sandstones of these formations have good quality and good history of hydrocarbon accumulation.The Nukhul Formation is composed of marine calcareous conglomerates, sandstones, and marl.The Rudies Formation is composed of deep marine shale and marl sedimentation with siliciclastic sandstones.The Kareem Formation is subdivided into two members: the lower one is the Markha Member, which is composed of interbedded shale, carbonates and anhydrite with sandstone in the lower part; the upper member is the Shagar, which is composed of shale and marl with thin beds of limestone and sandstone.The Belayim Formation is composed of four members: Hammam Faraun (top), Feiran, Sidri, and Baba (bottom).The Hammam Faraun Member consists of sandstone with shale intercalations.The Feiran, Sidri, and Baba Members consist of evaporite deposits (Bosworth & McClay, 2001;Alsharhan, 2003;Nabawy and Barakat, 2017;Radwan et al., 2021).
The goal of this study was to construct a detailed 3D geo-static model for the Middle Miocene reservoirs in the Amal Field in the southern Gulf of Suez province, as these reservoirs exhibit different connectivity and geometry, which, in turn, affect the production performance behavior through the life of the field, and are characterized by uncertainties due to their structural settings, lateral facies change, and different lithologies.A 3D model can help to solve these reservoirs problems.

GEOLOGICAL SETTING
The Gulf of Suez rift basin was formed in the late Oligocene -early Miocene (Hempton, 1987;Bosworth et al., 2005).The Gulf of Suez is composed of three major half-grabens that have reversed dip polarity from north to south (Kassem et al., 2020).The major faults of the half-grabens in the north and south dip toward the northeast (Radwan et al., 2021), and the layers within the tilted fault block dip toward the southwest.The major faults of the central half-graben dip toward the southwest, which is the opposite direction relative to the other grabens, and the layers dip toward the northeast (Patton et al., 1994).Two accommodation zones separate the three half-grabens (Moustafa, 1976) (Fig. 1).
Stratigraphically, the Gulf of Suez comprises rocks ranging from Precambrian to Holocene (Said, 1990); these rocks were classified based on tectonic rifting into three stratigraphic phases (Moustafa, 1976) (Fig. 2).The pre-rift stratigraphic phase (pre-Miocene units) rests unconformably on basement rocks with ages ranging from Paleozoic to Eocene (Alsharahn, 2003).The syn-rift stratigraphic phase (Miocene units) is composed of sedimentary clastic units (Colletta et al., 1988) at the base of the section and evaporitic facies at the top.The post-rift stratigraphic phase (post-Miocene units) includes clastic rock units (Afifi, 2016).
Middle Miocene reservoirs represent approximately 20% of the Gulf of Suez's production (Patton et al., 1994).Source rocks in the study area may be from the Lower Miocene Rudeis and Kareem Formations and pre-rift units such as the shale of the Thebes Formation, the brown limestone of the Sudr Formation, and the shale of the Matulla Formation (Alsharahn, 2003).The Rudeis Formation may be an oil-prone source rock or an oil and gas-prone source rock (Afifi, 2016).Vertical and lateral evaporites and mudstone represent the cap rocks in the study area.The mode of migration in the study area is hydrocarbon migration along faults or migration vertically from shale/carbonate source rocks.The trapping mechanism in the study area is faultbounded horst, and a three-way dip-closed faultbounded trap (Alsharahn, 2003).
The study area is located between latitudes 28°0 2¢ N and 28°05¢ N and between longitudes 33°33¢ E and 33°36¢ E (Fig. 1).This study focused mainly on Middle Miocene reservoirs, namely, the Belayim Formation, with more focus on the Hammam Faraun zone, the Markha Member of the Kareem Formation (Patton et al., 1994), and the Upper Rudies Formation.The Hammam Faraun is composed of sandstone, shale intercalations, carbonate, and thin beds of anhydrite.The Markha Member is composed of shales and sandstone intercalations.The Upper Rudies Formation in composed mainly of shales with sandstone units (Alsharahn, 2003;Shehata et al., 2021).

MATERIAL AND METHODOLOGY
Ten 2D seismic lines in the depth domain along with logging data from five wells (Well #1, #2, #3, #4, and #5), including gamma ray (GR), density, neutron, sonic, and resistivity, were combined for the 3D geo-static modeling of the Belayim Formation (Hammam Faraun Member/zone), Kareem Formation (Markha Member/zone), and Rudies Formation (Upper Rudies Member/zone).Throughout the 3D modeling procedures, several simulation ap-proaches, such as the sequential Gaussian simulation technique (Hu & Le Ravalec-Dupin, 2005), were proposed to comprehend and model the reservoirs of interest.
The lithology identification of the three main formations was constructed based on four wireline logs: (GR, density, neutron, and sonic).Three sand isolith maps were constructed for the three formations based on the sand net thickness of each reservoir in all the wells, which is constructed based on the interpretation of the log responses.The GR  (Mostafa et al., 2015).log was used to differentiate between the shale and non-shale zones, and the other logs were used for the lithology identification of non-shale zones.Sandstone was interpreted based on the low GR and density-neutron crossover.Anhydrite was interpreted mainly based on the high density and high sonic velocity, and salt was interpreted based on low density and low sonic values (Fig. 4).
The procedures undertaken in this study were subdivided into various stages, starting with well correlations, seismic interpretation, structural, facies, and petrophysical analysis, then modeling, and ending with the final interpreted model (Radwan et al., 2022).The seismic interpretation outputs were used as input data in fault modeling, pillar gridding, and horizon modeling.The fault modeling step represents the basis for 3D grid generation, followed by the creation of pillar grids, which represent a structural grid created based on fault modeling concerning the horizons of interest.The seismic data were the container for the 3D geologic modeling (facies and their petrophysical characteristics).Facies modeling is significant during the exploration and development phases because it helps to understand facies distribution and reservoir parameters away from known well locations (Radwan et al., 2022).Reservoir variability and hydrocarbon flow can be identified using 3D facies modeling and reservoir geometry (Cressie, 1990).Also, the connectivity of reservoirs represents an important role (Zhang et al., 2019).Gaussian distribution algorithms were used to create simulations of geological properties or to create interpolation that is based on geostatistical techniques (Goovaerts, 1997).
Petrophysical analysis was performed to estimate the key parameters that are used for the evaluation of reservoir characteristics.Wireline logs were used to evaluate the petrophysical properties of the reservoirs.The key parameters of formations (shale volume (V sh ) total porosity, effective porosity, and water saturation (S w )) were estimated using standard techniques.
The V sh was calculated from GR logs, thus (Asquith and Gibson, 1982): where V sh is clay or shale volume, GR log is log value of GR, GR min is minimum value of GR, and GR max is maximum value of GR.The V sh was calculated using GR logs for the Hammam Faraun, Markha, and Upper Rudies zones.V sh log curves were scaled up using arithmetic computation.A sequential Gaussian simulation algorithm was used to distribute V sh among and around the wells.
where [ T is total porosity, [ N is neutron porosity, [ D is density porosity, [ eff is effective porosity, and [ sh is shale porosity.The S w was calculated based on the Indonesian formula because of the presence of shale, thus (Poupon & Leveaux, 1971): where R t is true resistivity, V cl is clay or shale volume, a is tortuosity factor, R w is formation water resistivity, and R cl is resistivity of shale.The S w was calculated for Hammam Faraun, Markha, and Upper Rudies zones.Using the arithmetic computation, the S w log was scaled up into the geo-cellular grid of the model.A sequential Gaussian simulation algorithm was used to populate S w among and around the wells.The outputs of petrophysical analysis are used as inputs into the modeling process for the petrophysical parameters of reservoirs.

Well Correlation and Sand Isolith Maps
The correlation was conducted for all the wells based on wireline logs.The correlation chart exhibits three major reservoir intervals with variable thickness throughout the formations of Belayim, Kareem, and Rudies (Fig. 4).The three formations were recorded in all the drilled wells.Three sand isolith maps were constructed for the three formations based on the net thickness of the sand of each reservoir in all the wells.
The Belayim Formation is subdivided into four zones: Hammam Faraun, Feiran, Sidri, and Baba members.The Baba is composed of anhydrite and shale.The Sidri is composed of salt, anhydrite, and shale.The Feiran is composed of anhydrite and shale.The Hammam Faraun is composed mainly of sand and shale intercalations.Sandstone facies are concentrated in the southeastern part of the area with thickness reaching 34 m (Fig. 5).The thickness distribution varied may be due to the unconformity/ erosional surface.
Variable thicknesses of the Kareem Formation were recorded over the study area may be due to unconformity/erosional surface, which is composed of two members, the Markha and Shagar Members.The Shagar Member is composed mainly of shale with minor sand strikes.The Markha is composed of sandstone with shale and streaks of anhydrite.The sandstone thickness of the Markha Member in the southern part of the area is about 60 m (Fig. 6).
The Upper Rudies is composed mainly of shale and sandstone.Sandstones and shales of the Upper Rudeis Member extended over the entire area laterally with thickness variations with 70 m average thickness, ranging from 30 to 120 m thick due to structuration during the deposition that is related to the Kareem-Rudeis unconformity (Okeil et al., 2019).In the southern part of the study area, sandstone thickness reaches about 30 m, according to the sand-isolith map (Fig. 7).The correlation results are in agreement with those of Okeil et al. (2019).

Petrophysical Analysis
The logging data were analyzed to estimate the petrophysical parameters of wells.Wireline logging data of neutron, density, resistivity, sonic, and GR were used to estimate total porosity, effective porosity, V sh , S w , hydrocarbon saturation, gross thickness, and net thickness of the target zone.GR logs were used to differentiate between the shale and non-shale zones then based on the density, neutron, and sonic logs the lithological type of the non-shale zones were identified.
V sh values distribution exhibits several variations.The Hammam Faraun zone has V sh range of 0.21-0.30,Markha 0.13-0.29,and Upper Rudies 0.29-0.37.These variations may be due to the heterogeneity of the study area.Porosity values exhibit several variations.The Hammam Faraun zone has porosity range of 0.2-0.26,Markha 0.18-0.24,and Upper Rudies 0.20-0.26.The S w values distribution exhibits several varieties of increasing and decreasing.The Hammam Faraun zone has S w ranges of 0.34-0.49,Markha 0.16-0.38,and Upper Rudies 0.35-0.4.These may be due to the heterogeneity of the facies in the study area.Table 1 represents the petrophysical analysis of the Hammam Faraun, Markha, and Upper Rudies reservoirs in the five studied wells.All the obtained petrophysical parameters show good agreement with previous researches (Ata et al., 2012;Ramadan et al., 2019;Farouk et al., 2022).

Seismic Data Interpretation
Faults were interpreted and tracked in all the seismic sections.The interpreted seismic section exhibited a main crest structure bounded by two major faults and affected by minor faults (Fig. 8).All major and minor faults affect the three picked reflectors.The reflector of the Belayim Formation is represented by a peak as the wells have encountered shale after sand, also Kareem and Upper Rudies Formations are marked by peak amplitude for the same reason.The interpreted structures are in agreement with previous work (Ata et al., 2012;Okeil et al., 2019) Depth structure contour maps were created for areas near the Belayim, Kareem, and Rudies Formation tops.The reflectivity of the three formation tops is moderate to low due to the presence of salt.Surfaces were constructed near the top of the three formations.The depth values of the Belayim Formation were in the range of 155-2540 m, the depth values of the Kareem surface map were in the range of 1700-2700 m, and the Rudies surface has a depth range of 1800-2820 m (Figs. 9, 10, and 11, respec-tively).These depth variations reflect the effect of structural features in the study area.
All the depth structure contour maps showed a main fault block bounded by two major faults extending along the area trending NW-SE.Most of the major faults throwing northeast with large displacement are branched in the northern direction into smaller faults; faults throwing southwest with smaller displacement relative to the northeast fault were noticed (Figs. 9, 10, and 11).All the seismic data and the constructed maps were in the depth domain.Eight normal faults were picked in the area of study and named F1, F2, F3, F4, F5, F6, F7, and F8, and they affect the studied stratigraphic units (Fig. 8).The study area is subdivided structurally by the two main bounding faults into three blocks: eastern, western, and central blocks and the central horst block is subdivided into subblocks.According to the study, additional prospect areas can be identified that offer a good location for hydrocarbon accumulation (Fig. 9, 10, 11).

3D Geo-Static Modeling
Structural modeling starts by picking and interpreting geological surfaces (horizons and faults) and then modeling contacts between geological surfaces (e.g., fault and fault, horizon and horizon, fault and horizon) (Euler et al., 1999).The property model exhibits the distribution of the facies and petrophysical parameters (sand to shale ratio, porosity, and fluid distribution) as estimated from petrophysical analysis (Yan-lin et al., 2011).It is important to differentiate and execute an accurate structural model according to geologic information because research in the energy industry (Wu & Xu, 2004) focuses on enhancing subsurface resource utilization via enhanced resource evaluation with production efficiency (Radwan et al., 2022).
A structural model is constructed in three main steps: geometry definition, fault framework modeling, and horizon modeling.Geometry is defined by defining the x-y coverage for the area of interest from the seismic survey automatically.Faults are modeled from interpreted faults in seismic sections in the depth domain.A crucial step in creating a structural model is to accurately represent the fault relationships.Time will be saved later in the workflow if the fault models are accurate and geologically reasoned, faults relationships can be edited (Fig. 12).
Figure 13 represents the fault modeling of the study area.Horizons were modeled using interpreted horizons, thickness maps, and the well-defined tops of the study area (Fig. 13).This model was subdivided into zones (Figs. 18a,19a).The Belayim Formation is subdivided into four zones (Hammam Faraun, Fieran, Sidri, and Baba), the Kareem Formation into two zones (Markha and Shagar), and the Rudies Formation into two zones (Upper and Lower Rudies).This model was finely layered; the Hammam Faraun Member was subdivided into 25 layers, the Markha Member into 40 layers, and the Rudies 2619 Three-Dimensional Integrated Geo-Static Modeling Member into 60 layers.This model had relatively small xyz cell dimensions to capture important flow units.This model was constructed for three main formations (Belayim, Kareem, and Rudies) in the depth domain about the structural elements (Fig. 13).The structural model showed the main crest structure bounded by two major faults trending NE-SW.The main horst structure is affected by synthetic and antithetic faults that form small horst and small graben.One of the major faults throws large displacement northeast and it is branched into smaller faults in the northern part of the study area, and the other throws a smaller displacement relative to the northeast fault.The property modeling represents the filling process of the cellular grid of the model with specific properties by assigning the well log data to grid cells (scaling up well logs).A single log value will be generated for each grid cell by averaging all the log values that fall inside that cell using the chosen algorithm.Interpolation methods were used to dis- tribute the reservoir properties between and around the wells (Fig. 13).
The facies model was constructed for the Hammam Faraun, Markha, and Upper Rudies Members using different algorithms to distribute facies randomly.The three main reservoirs are composed mainly of sand and shale.Lithological log curves were constructed based on the wireline logs for each well, then scaled up using arithmetic computation, then distributed into geo-cellular grids by the sequential gaussian simulation algorithm method to track sand facies in the three main reservoirs.The Hammam Faraun exhibits good sandy facies in the northeastern part of the area.The Markha and Upper Rudies exhibit good sandy facies in the cen- tral part of the area, which is the horst block (Fig. 14a, b).
Figure 14a shows that all the wells encountered the Hammam Faraun zone but with different lithologies.Only very good sandy facies are in well #1, marked by yellow color, compared to the shale facies in the other wells.Figure 14b shows that all the wells encountered the Markha Zone with good sandy facies, marked by yellow areas, except Well #2, which has a shaley facies.
The petrophysical properties modeling for each cell passing through the trajectory of a well can be extracted between the wells in the 3D grid once the log data have been scaled up to the 3D geo-cellular grid.Therefore, each cell in a grid has a value for the selected property.Porosity, V sh and S w were distributed on the 3D grid using algorithms for the Hammam Faraun Member, the Markha Member, and the Upper Rudies Formation.Porosity models show lateral variations in porosity because of lateral facies change.The Hammam Faraun porosity models show good porosity values in the range of 0.15-0.23 (Fig. 15a), with porosity increasing toward the central part of the area.
Figure 15a shows that all the wells that encountered the Hammam Faraun zone have very good porosity values, marked by red and yellow areas.The Markha porosity model shows that the porosity increases toward the southwestern part of the area, with values in the range of 0.15-0.22 (Fig. 15b).Figure 15b shows that all the wells that encountered the Markha zone have varieties in the porosity values, which are good at Well #2, Well #3, and Well #4 marked by red to green areas compared to well #1 and Well #5, which have low porosity values marked by blue color.Figures 18a and 19a represent structural traps in the area.All these models were used to evaluate reservoir properties in the area.Figures 18c and 19c exhibit the porosity distribution.
The V sh was calculated using GR logs for the Hammam Faraun, Markha, and Upper Rudies zones.V sh log curves were scaled up using arithmetic computation.The sequential Gaussian simulation algorithm method was used to distribute V sh among and around the wells.The V sh models exhibited several variations (Fig. 16a, b).In the Hammam Faraun zone, V sh ranged 0.21-0.31,explained as 0.21 in Well #1, 0.27 in Well #2, 0.25 in Well #3, 0.31 in Well #4, and 0.3 in Well #5.In the Markha zone, V sh ranged 0.13-0.29,explained as 0.13 in Well #1, 0.25 in Well #2, 0.28 in Well #3, 0.29 in Well #4, and 0.26 in Well #5.In the Upper Rudies zone, V sh ranged 0.29-0.37,explained as 0.34 in Well #1, 0.29 in Well #2, 0.33 in Well #3, 0.37 in Well #4, and 0.34 in Well #5.These variations may be due to the heterogeneity of facies of the study area.Figures 18b and 19b represent the structural cross section with V sh distribution of the study area.
The S w was calculated for Hammam Faraun, Markha, and Upper Rudies zones using the Indonesian formula (Eq. 1) because of shale presence.Using the arithmetic computation, the S w log was scaled up into the geo-cellular grid of the model.
The sequential Gaussian simulation algorithm method was used to populate water saturation among and around the wells.The S w models exhibited several varieties from increasing and decreasing (Fig. 17a, b).The Hammam Faraun zone has S w range of 0.34-0.49,Markha 0.16-0.38,and Upper Rudies 0.35-0.4.These may be due to the heterogeneity of facies of the study area.Figures 18d and  19d represent the structural cross section with S w distribution of the study area.

Modeling Uncertainties and Quality Control
Modeling is impacted by interpretation uncertainties.Due to limited data availability, poor data quality, difficulties of the reservoir design in estimating flow in a particular reservoir, and modeling process errors, reservoir modeling is commonly plagued by uncertainty (Radwan, 2022).Therefore, it is crucial to assess the input data for quality, quantity, and complexity at different scales, as well as to review fundamental assumptions about the suitability of a modeling workflow in the context of static reservoir uncertainty.We made an effort to carry out precise interpretations and extract the best-fit input parameters in this work.
To fill up the gaps, general geologic knowledge, local geology, and some prior work experience from Avoid having twisted cells that are always close to faults.Observe good match between the scaled-up logs and the electrical well logs (Fig. 13).Review a reasonable facies distribution.The main sources of uncertainty in lithofacies modeling are constrained data and reservoir geological information.Therefore, there is a great deal of uncertainty in the 3D structural system's facies or flow unit distribution.In this study, we employed integrated facies analysis and well-log interpretation across the examined wells to try and reduce uncertainty in the facies model.

Prospect Estimation and Reserve Estimation
Prospects are subsurface locations composed of traps, cap rock, reservoir rock, and source rock that can expel hydrocarbon into the trap where the economic conditions are suitable for drilling new wells.Prospects have the potential to produce hydrocarbons but need to be proven (Gluyas and 10, 11).Table 2 shows the deterministic reserve estimations of the three main reservoirs in the southern Gulf of Suez.The volumetric technique was used to estimate the original oil in place based on the following equation: where

CONCLUSIONS
The main focus of the current study was on the interpretation of geological and geophysical data to assess the structure, lithofacies, and petrophysical characteristics of Middle Miocene reservoirs in the southern Gulf of Suez province, as well as their 3D distribution.To estimate the distribution and quality of the intricate Middle Miocene reservoirs and to lessen uncertainty during oilfield development in the research area, we employed integrated datasets in this work.The modeling procedures applied in this work can be used to understand similar reservoirs.The primary results of this investigation were as follows: The structural models shows that the area was affected by normal faults trending NW-SE with downthrown side directed to the southwest and northeast, forming step, horst, and graben rotated fault blocks that provide good structural traps, which can hold good amounts of hydrocarbon.The study areaÕs structural framework is a big compartmentalized horst block.The depth values of the Belayim Formation range 155-2540 m, those of the Kareem 1700-2700 m, and those of Rudies 1800-2820 m.The sand thickness of the Hammam Faraun Member ranges from null to 50 m, that of Markha Member null to 60 m, and that of Upper Rudies null to 45 m.Property and facies modeling showed that the central part of the area is a potential area with good reservoir properties.The modeling results of the study area show that the Hammam Faraun zone is a good reservoir, with porosity values ranging 0.15-0.23, the porosity increasing toward the central part of the area, V sh ranging 0.21-0.31,S w ranging 0.34-0.49,net pay thickness ranging 10-35 m, and sandy facies increasing toward the northeastern part of the area according to the facies model.The Markha zone also is a good reservoir, with porosity increasing toward the southeastern part of the area with values ranging 0.15-0.22,V sh ranging 0.13-0.29,S w ranging 0.16-0.38,net pay thickness ranging 3-51 m, and very good sandy facies at the horst block, which is the central part of the area.The Upper Rudies exhibit good reservoir properties with porosity values ranging 0.16-0.23,V sh ranging 0.29-0.37,S w ranging 0.35-0.4,net pay thickness ranging 3-33 m, and good sandy facies at the central part of the area.We merged numerous datasets to improve the modeling of the complex Middle Miocene reservoirs and lower the typical uncertainties related to the static modeling procedure.

Figure 1 .
Figure 1.Location map of the study area.(a) Gulf of Suez rift tectonic map (modified after Khalil, 1998).(b) Base map showing the available seismic lines and the five used well locations over the Amal field.

Figure 2 .
Figure 2. Stratigraphic column of the southern part of the Gulf of Suez(Mostafa et al., 2015).
Figure 3 represents the flowchart for the modeling process.

Figure 4 .
Figure 4. Well correlation showing log responses.The upper zone of Belayiem is sand with shale intercalations, and the lower zones are anhydrite with salt and shale.Kareem's upper zone is mainly shale, while the lower zone is sand with shale intercalations.The upper zone of Upper Rudies is composed of sand and shale intercalations.

Figure 5 .
Figure 5. Sand isolith map of net sand of Hammam Faraun Member from all the wells.

Figure 6 .
Figure 6.Sand isolith map of net sand of Markha Member from all the wells.

Figure 7 .
Figure 7. Sand isolith map of net sand of Upper Rudies Member from all the wells.

Figure 8 .
Figure 8. Seismic section from the southern part of Amal area: (a) un-interpreted and (b) interpreted sections showing the extensional faults and horizons of interest.

Figure 9 .
Figure 9. Depth structure contour map of near the top of the Belayim Formation with prospect location highlighted in the white dashed polygon.Grey polygon represents fault heaves.

Figure 10 .
Figure 10.Depth structure contour map near the top of the Kareem Formation with prospect location highlighted in the white dashed polygon.Grey polygons represent fault heaves.

Figure 11 .
Figure 11.Depth structure contour map of the Rudies Formation with prospect location highlighted in the white dashed polygon.Grey polygons represent fault heaves.

Figure 12 .
Figure 12. 3D structural model across the study area with zones.

Figure 14 .
Figure 14.(a) Facies modeling for the Hammam Faraun zone showing sandy facies in well #1 marked by yellow color compared to the shaly facies in the other wells.(b) Facies modeling for the Markha zone showing that all the wells encountered sandy facies marked by yellow areas except Well #2.

Figure 15 .
Figure 15.Porosity models of (a) the Hammam Faraun zone and (b) the Markha zone.

b
Figure 19.NE-SW integrated C-D Cross section through all formations.(a) Structural cross section with zones.(b) Structural cross section with shale content (V sh ).(c) Structural cross section with porosity (NPHI).(d) Structural cross section with S w .

Table 1 .
Petrophysical analysis of the study area N(t)is original oil in place (STB, stock tank barrel) at time t; V b = 7758 Ah is bulk reservoir volume (bbl, barrels), where 7758 is bbl/acre-ft, A is area (acres 1 ), h is reservoir thickness (ft 2 ); U (p(t)) is porosity at reservoir pressure p at time t; S w (t) is water saturation at time t; Bo(p(t)) is oil formation volume factor (bbl/STB 3 ) at reservoir pressure p; P(t) is reservoir pressure (psia) at time t.

Table 2 .
Deterministic reserve estimates for the identified prospects of the Hammam Faraun, Markha, and Upper Rudies reservoirs