Introduction

Carbonate reservoirs comprise more than half of conventional hydrocarbon reservoirs around the world (Dou et al. 2011). The Sarvak carbonate Formation (Middle Cretaceous) has considerable hydrocarbon potential (more than 20% oil-in-place of Iranian oil reserves) in the Zagros Basin of Iran (Hajikazemi et al. 2010; Bordenave and Hegre 2010). These types of reservoirs are highly affected by diagenesis since it causes significant changes in different sediment properties resulting in a higher degree of heterogeneity (Lahann and Swarbrick 2011; Martyushev et al. 2023a, b; Rashid et al. 2022). Since diagenesis plays a significant role in the reservoir quality of carbonate reservoirs (Moore 2001; Qureshi et al. 2023; Bilal et al. 2022; Moforis et al. 2022; Kontakiotis et al. 2020a; Ahmad et al. 2022), its study helps to recognize petrophysical variations and evaluate the reservoir rock quality. In addition, pore systems in carbonate reservoirs tend to be more complicated than clastic reservoirs because of the facies diversity and the combination of several diagenetic processes (Rahim et al. 2022; Bilal et al. 2023; Ahmad et al. 2022; Janjuhah et al. 2021; Kontakiotis et al. 2020b). Therefore, in carbonate reservoirs, it is necessary to consider the control of diagenesis and depositional facies on reservoir characterization.

The main purpose of this study is to construct a 3D geological model indicating the role of diagenesis in reservoir quality. Due to the lack of sufficient cored intervals, the petrophysical logs after calibration with core data are used for the diagenetic modeling because of their continuity and availability in all wells of the area. The diagenetic processes, such as cementation, dissolution, compaction, dolomitization, fracturing, micritization, recrystallization, and bioturbation, were observed based on the petrographic studies. However, among all the above diagenetic processes affecting the reservoir quality of the Sarvak reservoir, dolomitization, dissolution, cementation, and stylolite data were modeled using advanced geostatistics algorithms. Mechanical compaction has reduced the micro-porosity in mud-supported facies, and interparticle porosity in grain-supported facies, due to the intense packing of the grains. Cementation has reduced the porosity by precipitation of authigenic minerals in the pore spaces of Sarvak carbonate. Porosity is considerably enhanced by dissolution through eliminating all or part of earlier existing minerals and reducing the pore spaces in the rocks.

Geological and stratigraphical settings

There are many significant hydrocarbon reservoirs of the Cretaceous age in the Arabian Plate and the Zagros Basin (Hollis 2011). The Zagros Basin includes both carbonate and siliciclastic reservoirs. The late Albian, Cenomanian, and Turonian (89–98.9 Ma) stratigraphic record in the Arabian Plate and the Zagros Basin corresponds to the Sarvak Formation in Iran (Motiei 1993) and is equivalent to Natih Formation in Oman, and Mishrif, Ahmadi, and Rumaila Formations in Saudi Arabia (Van Buchem et al. 2002). It should be noted that the equivalent of the Sarvak Formation is Mishrif Formation in the west of Iran (Iraq) which was investigated by some researchers (Al-Dujaili et al. 2023a, 2023b). Sediments of the Sarvak Formation, a member of the Bangestan Group, were deposited on a platform and within the intrashelf basin on the passive margin of the Arabian Plate (Martin 2001).

The studied field is located in the northern part of the Dezful Embayment (Fig. 1). The Sarvak Formation in the type section (Bangestan anticline) overlies the Kazhdumi Formation and underlies the Gurpi Formation. However, in other parts of the Zagros Basin, particularly in the Dezful Embayment, underlies the Ilam Formation (James and Wynd 1965; Rahimpour-Bonab et al. 2012). The Sarvak Formation has two pelagic (wackestone to packstone with abundant planktonic foraminifera) and neritic (mudstone to packstone with abundant benthic foraminifera) facies (James and Wynd 1965). Reservoir characteristics of the Sarvak Formation were influenced by some local and regional disconformities (Rahimpour-Bonab et al. 2013). The lithology of this formation is mainly made up of carbonate rocks (limestone and argillaceous limestone, with some dolomite and shale, interbeds). Sarvak Formation in the studied field is divided into three main zones including Upper-Sarvak, Ahmadi, and Lower Sarvak (Fig. 2). Both the Upper Sarvak and the Lower Sarvak (as the main target reservoir) are divided into nine reservoir units (Fig. 3). The thickness of the Sarvak reservoir in the studied field is about 600 m based on constructed isochore map.

Fig. 1
figure 1

The main structural zones of the Zagros and the position of the studied zones (After Casini et al. 2011) (the approximate location of the studied field is shown by the black circle)

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Fig. 2
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Generalized chronostratigraphy of the Cretaceous successions in the Zagros region and nearby regions (after Sharland et al. 2001)

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Fig. 3
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Stratigraphic chart and reservoir zonation of the Sarvak Formation in the studied oilfield

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Materials and methods

The first phase of this study began with the thin section study, core description, and core analysis for determining diagenesis features. In addition, the evaluated petrophysical logs were used to construct diagenetic-related logs (such as dissolution and dolomitization) as main input data for the spatial diagenetic model.

Petrographic study

A total of 1350 thin sections of the Sarvak Formation from four wells were used for petrographic studies. Petrographic studies involve identifying microfacies study and diagenetic processes from thin-sections (from cores), discriminating genetic diagenesis types, and evaluating their effects on reservoir quality in 3D geological models. Description of the microfacies was done based on Folk and Dunham (and Embry and Klovan modification) classification schemes (Dunham 1962; Embry and Klovan 1971; Folk 1962). Apart from cored wells, petrophysical logs of 20 drilled wells were used for calibration with petrographic results and creating synthetic diagenesis logs. Four parameters including visible secondary porosity, dolomite volume fraction, cement volume fraction, and existing stylolite, were detected and digitized for spatial modeling. To distinguish dolomite from calcite, all studied samples were stained with alizarin red S solution (Dickson 1965). The percentage of the cement was estimated based on the petrographic studies of thin section.

Petrophysical logs interpretation

Petrophysical interpretation is a process of using petrophysical raw data (such as gamma ray, sonic log, density log, neutron log, photoelectric factor log, and resistivity logs) for obtaining the total and effective porosity, water saturation, and mineral volumes through petrophysical log interpretation. Afterward, petrophysical parameters including, effective porosity, volume of shale, volume of dolomite, velocity deviation log (VDL), secondary porosity, and digenesis electrofacies were populated in a 3D geological grid.

Secondary porosity calculation

Secondary porosity resulting from dissolution was calculated based on the difference between two porosity logs calculated from sonic and neutron-density porosities. The sonic-based porosity is compared with the total porosity obtained from density and neutron logs. Therefore, the total porosity can be subdivided into two “primary porosity” obtained from the sonic log and “secondary porosity” calculated from the difference between the sonic porosity and total porosity (Schlumberger 1974). Although the calculated log is uncertain, it can be used as secondary porosity index.

VDL calculation

The VDL is a synthetic log obtained from applying an average time equation addressed by Wyllie et al. (1956). In this study, the VDL log was calculated for the Sarvak reservoir using the sonic log and calculated petrophysical porosity. In this regard, it can be stated that the synthetic VDL log is dependent on the lithological characteristics, sedimentary textures, diagenetic features, and pore systems of the Sarvak reservoir. For this purpose, the synthetic travel time DTsyn, was derived by calculating through re-ordering the Wyllie formula to calculate synthetic velocity. The difference between the two porosity logs (the real sonic log (DTreal) with the artificial sonic log (DTsyn)) is considered a VDL log (Anselmetti and Eberli 1999). Therefore, the velocity deviation was simply obtained through the calculating difference between Vpreal and Vpsyn.

$$\Phi_{{\text{S}}} = \frac{{{\text{DT}}_{\log } - {\text{DT}}_{{{\text{mat}}}} }}{{{\text{DT}}_{{\text{f}}} - {\text{DT}}_{{{\text{mat}}}} }}$$
(1)

where Φs in secondary porosity, DT log is the sonic log, DTmat, is the sonic value of the matrix, and DTf is the sonic value of the fluid.

$${\text{VDL}} = {\text{Vp}} - {\text{Vp}}_{{{\text{syn}}}}$$
(2)

where VDL is velocity deviation log, Vp, is the real velocity, and Vpsyn is the calculating velocity.

The pore types can be divided into three categories based on the velocity deviation log including positive, zero, and negative deviations (Anselmetti and Eberli 1999; Wang and Nur 1990). Fracturing, caving, anomalies of the borehole, and a high percentage of the free gas can cause a negative VDL value (Nur and Simmons 1969). Positive VDL indicates zones having velocity higher than expected, such as zones in which moldic and vuggy pores are developed. Zero VDL represents intervals having dominant micro-porosity or interparticle porosity.

Diagenetic electrofacies analysis

After petrophysical interpretation and calculating the VDL and secondary porosity, diagenetic electrofacies were calculated. Electrofacies, as introduced by Serra and Abbot, are defined as the set of petrophysical well log responses, which characterizes a stratum that can be distinguished from the adjacent ones (Serra and Abbot 1982). In this regard, various data clustering approaches including multi-resolution graph-based clustering (MRGC), self-organizing maps (SOM), and AHC (agglomerative hierarchical clustering) were employed. Examining the results revealed that the MRGC method outperforms other clustering algorithms for the extraction of diagenetic electrofacies. It is a multi-dimensional algorithm based on the non-parametric and K-nearest neighbor method with graph data representation (Ye and Rabiller 2000). MRGC method gives classes based on the distribution of natural points with various scales (Asgari and Sobhi 2006). It allows the user to gain the ideal cluster numbers for defining electrofacies clusters from conventional petrophysical logs. Several diagenetic-related logs (dolomite volume, secondary porosity, and VDL logs) were chosen for electrofacies analysis as input data. An unsupervised algorithm has been applied after training and normalizing the input data. The optimum number of diagenetic clusters was identified after considering different clusters suggested via the MRGC algorithm and then similar clusters were merged to find the optimum number of clusters. Therefore, after considering the statistical distribution input parameters including secondary porosity, effective porosity, dolomitization, and VDL, a total of 20 electrofacies were extracted for the Sarvak reservoir (Fig. 4). After checking with sedimentological facies and petrophysical properties, 20 clusters were merged until the final number of clusters reached eight electrofacies (Fig. 5). Table 1 outlines the geological/petrophysical properties of the final diagenetic electrofacies.

Fig. 4
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Histograms of normalized input data along with matrix plot showing the relationship between input logs in different clusters

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Fig. 5
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Histograms of the final diagenesis electrofacies

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Table 1 Statistical properties of eight electrofacies clusters in the Sarvak reservoir of the studied oilfield; SPI, dolomite volume, and PHIE units are fractions
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Geological modeling

The 3D geological modeling of the Sarvak reservoir was started with structural modeling. The structural model captures the structural elements such as interpreted horizons, faults, and reservoir zones. Essentially, the construction of the structural model includes importing and defining the depth maps and considering the faults affecting the reservoir. The structural model was created using the corner point approach. A 3D fine geological grid was constructed with 100*100 m cell increments considering the area of the project. The horizon-making is the first step in defining the vertical layering for the 3D grid in the geological model. Afterward, all interpreted horizons in the depth domain were imported into the model. Three main seismic interpreted depth surfaces were used for horizon-making in the model, including Sarvak, Ahmadi, and Kazhdumi surfaces. Isochore maps of each subzone were prepared using well top data. The layering was done as the final step of framework construction. The layering of the constructed model (proportional method) was designed according to the thickness analysis and vertical variogram analysis of reservoir facies. Accordingly, the cell thickness of pay zones was assigned as 0.5–1.5 m. Thus, the vertical changes of the reservoir changes will be captured and the number of whole cells will be optimized. The final layering framework of the model consists of 647 layers with 7,612,602 total cells.

Application of geostatistical modeling methods

Conditional simulation [such as SGS (Sequential Gaussian Simulation) and GRFS (Gaussian Random Function Simulation)] and deterministic algorithms such as ordinary kriging were applied for the porosity modeling. Kriging was originally considered for property estimation based on D.G. Krige’s idea (Krige 1951; Lake et al. 2007). Kriging and cokriging interpolation methods as forms of univariate and multivariate linear regression-based models are usually used for property distribution in static modeling. There are different kriging types such as ordinary kriging, simple kriging, indicator kriging, universal kriging, probability kriging, cokriging, etc. (Basbug and Karpyn 2007). In this study, both simple and ordinary kriging were used for initial property estimation. Gaussian simulation methods such as SGS and SIS are conditional geostatistical methods utilizing the kriging mean and variance to produce a Gaussian distribution of parameters (Evans Annan et al. 2019). All these stochastic methods provide more reliable results, which can improve the quality of the predictions (Zhao et al. 2014). In complex reservoirs such as the Sarvak Formation, the deterministic kriging methods may not represent an accurate level of heterogeneities, while the stochastic simulation methods can provide more reliable results (Sahin and Al-Salem 2001; Zhao et al. 2014).

Results

In this study, after determining the major facies (according to Flügel 2010) and main diagenetic features based on petrographic studies, they were correlated with petrophysical logs to provide necessary diagenetic input data for 3D geological modeling.

Microfacies analysis

The microfacies analysis of the carbonate rocks was defined according to Dunham’s (1962) classification scheme, which was later modified by Flügel (2010). Microfacies analysis of the Sarvak reservoir was done based on the observed sedimentological characteristics during the thin-section study, and through comparison with additional data obtained from the Sarvak reservoir in nearby fields and also from the literature (Kontakiotis et al. 2020a, b; Bilal et al. 2022; Ali et al. 2021; Mehmood et al. 2023). Therefore, a total of 10 facies were distinguished in the Sarvak Formation coded as F1–F10 (Fig. 6). The brief properties of each facies are summarized in Table 2. In classical facies models, a carbonate shelf is separated into an inner shelf, middle shelf, and outer shelf (Burchette and Wright 1992; Kontakiotis et al. 2020a; Flügel and Munnecke 2010). The Sarvak cores in the studied wells contain shallow (inner shelf) to deep water (middle to outer shelf) carbonates. It shows open marine, patch reef, and lagoon sub-environments indicating an extended, carbonate shelf platform. The inner shelf of the Sarvak Formation includes the lagoon sub-environment, while the middle shelf includes the margin platform and reef barrier. The outer shelf environment was recognized in the studied cores of the Sarvak Formation based on abundant planktonic foraminifera (belonging to the lower parts of the upper Sarvak Formation). Based on this study, Biomicrite with abundant benthic foraminifera facies (F6) are the shallowest facies, then toward the lagoon and middle parts of the inner shelf the three facies distinguished including Pel-biomicrite with abundant benthic foraminifera (F1), Pel-biomicrite with abundant benthic foraminifera and rudist (F2), and Biomicrite with abundant foraminifera (F8). Toward the open marine, three facies have been determined as platform margins containing: Bio-pelsparite (F3), Biomicrite with abundant rudist and echinoid (F9,) and Pel-biosparite with abundant rudist debris (F10). Figure 7 indicates histograms of the mentioned ten facies in the Sarvak reservoir from the studied oilfield.

Fig. 6
figure 6

Thin-section photos of the facies in Well-Z8: facies1 (4060.37 m), facies 2 (4076.67 m), facies 3 (4093.94 m), facies 4 (4102.43 m), facies 5 (4106.10 m), facies 6 (4126.63 m.), facies 7 (4312.68 m), facies 8 (4470.15 m), facies 9 (4441.17 m), and facies 10 (4510.83 m)

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Table 2 Properties of ten facies classes in Sarvak reservoir of the studied oilfield
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Fig. 7
figure 7

Histogram of ten facies in Sarvak reservoir of the studied oilfield

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Diagenetic features in the Sarvak reservoir

According to the thin-section studies of four cored wells in this field, a widespread variety of diagenetic processes were determined in the studied Sarvak Formation. However, four diagenetic processes, comprising cementation, compaction, dissolution, and dolomitization show significant impacts on reservoir quality.

Cementation

Various types of cement are developed in the Sarvak carbonate Formation. Equant, drusy mosaic, and blocky cement are the most dominant cement in the studied core samples. Based on the petrographic description, two main types of cement (calcite and dolomite) were observed in this reservoir (Fig. 8).

Fig. 8
figure 8

Partially and complete pore-filling cement (calcite and dolomite) of the Sarvak Formation in Well Z8. A Depth: 4438.70 m, xpl B Depth: 4502.18 m, ppl; C Depth: 4063.11 m, D Depth: 4446.52 m

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Dolomitization

In general, the dolomitization process has dual constructive and destructive effects on the reservoir quality. In the uppermost parts of the upper Sarvak, there is a dolomitic zone showing abundant inter-crystalline porosity and also a lot of the dissolution pores filled by dolomitic cement. Scattered, unimodal, fine-to-medium-grained dolomite rhombs formed within the mud-supported facies (bioclastic wackestones) in both shallow and deep-water environments, and its heterogeneous nature is associated with dissolution seams and stylolite surfaces. Their occurrence along stylolite and solution-seams surfaces indicate a diagenetic origin, particularly during shallow burial diagenesis. In the nearby area, they are laterally equivalent facies, in which dolomitization is related to the late diagenetic and fracture-controlled diagenesis process (Sharp et al. 2010). The dolomite crystals are seen in the form of fine crystalline, subhedral to euhedral dolomite rhombs (Fig. 9). However, the saddle coarse dolomite crystals belonging to the deep-burial diagenesis (Sarg 1988) were not recognized in the studied intervals. The percentage of the dolomite minerals in the thin-section study was estimated visually for generating related logs for spatial modeling.

Fig. 9
figure 9

Physical compaction between bioclastic grains. A Depth: 4474.76 m, ppl; Chemical compaction (stylolite) into the limestone parts of Sarvak Formation. B Depth: 4432.33 m, ppl; Dolomite with abundant inter-crystalline porosity in upper Sarvak Formation of Well Z8 C Depth: 4120.83 m, ppl; and D Depth: 4098.25 m, pp

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Compaction

Chemical compaction was observed in solution seams and stylolites. Most of the solution seams and stylolites were oil-stained. They are observed in both outer-shelf and inner-shelf facies with abundant micrite. In addition, the solution seams and stylolite extend the dolomitization process into the upper and lower Sarvak Formation. It means that in the upper and lower Sarvak Formation, as observed in Well Z8, the dolomitization process is related to the stylolites (Fig. 9). The dolomite crystals formed after stylolitization. The existence of the stylolites was detected and converted to a discrete log for 3D modeling.

Dissolution

The dissolution process is considered the main significant diagenetic phenomenon in this reservoir, improving the reservoir quality. Generally, it is an essential mechanism in developing secondary porosity, including moldic, vuggy, and interparticle porosity (Janjuhah et al. 2021). Dissolution of skeletal grains produced abundant moldic and vuggy pores mostly into the shallow water facies (particularly in rudist-bearing facies) belonging to the lower Sarvak. In the shallow water facies of the upper Sarvak particularly in Well Z8, moldic pores are the common pore type having poor reservoir quality due to the disconnected nature and occurring later cementation (Fig. 9). The best and high porosity belongs to the top of the lower Sarvak (especially related to the rudist-bearing facies) due to developing interparticle, moldic, and vuggy porosities. Moreover, karstification features have also been developed in some intervals. The feature is recognizable over most of the middle Cretaceous carbonate rocks all over the Middle East (Sharland et al. 2001). The percentage of the secondary porosity (moldic and vuggy), which is visible from the thin-section study, was estimated visually for generating diagenetic logs for spatial modeling.

Diagenetic petrophysical logs

As discussed in “Materials and methods” section, VDL and secondary porosity logs were calculated to have complete diagenesis logs for all drilled wells having petrophysical logs. Moreover, diagenesis electrofacies logs were prepared to distinguish the different clusters from, the diagenesis point of view. Those logs, along with effective porosity log (PHIE), shale, and dolomite volume logs from petrophysical interpretation were imported into the 3D geological model.

3D diagenetic parameter modeling

The aim of conventional 3D geological reservoir modeling as an essential stage in field development is to get a 3D spatial distribution of reservoir types, reservoir property, and reservoir anisotropy via integrating all available data and geological concepts (Branets et al. 2009). Generally, 3D geological modeling includes two structural and property modeling. The main purpose of property modeling is to propagate reservoir properties between the wells matching the well data, which can be done after structural modeling. Property modeling was done based on stochastic methods producing more realizations, while deterministic approaches (such as Kriging) resulted in one realization. Generally, property modeling includes facies (discrete) and petrophysical modeling (continuous). Therefore, all the discrete properties were populated using facies modeling and applying “Sequential Indicator Simulation” (SIS). Continuous ones (such as porosity) were propagated using the stochastic approach of “Gaussian Random Function Simulation” (GRFS) via the “petrophysical modeling” module.

Generally, the routine geological reservoir modeling workflow includes integrating seismic data, and geological and petrophysical log data to construct the geological model. Understating the diagenesis phenomena from petrophysical logs and petrographic study has uncertainty which needs some trend maps and secondary variables obtained from seismic cubes. Therefore, due to the uncertainty in the diagenesis modeling, seismic-derived trend maps and secondary variable (AI) with stochastic propagation methods have been applied. Applying geostatistical methods for diagenetic modeling has been investigated by some authors (Doligez et al. 2011; Barbier et al. 2012).

After structural modeling, provided petrophysical diagenetic logs (secondary porosity, effective porosity, VDL, diagenetic electrofacies, dolomite volume, and shale volume), along with petrographic-based index logs were scaled up after detail analyzing for selecting the best methods (Kadkhodaie-Ilkhchi et al. 2019). The “Most of” method was used for scaling up the discrete logs (diagenetic electrofacies and stylolite index), and the “Median” or “Arithmetic” methods were selected for other continuous logs after comparing the resulting histograms. Figure 10 shows the layout of different input diagenetic logs considered for 3D modeling. The data analysis process is the further stage after scaling up, which is used in preparing the data and controlling data quality for geostatistics distribution (Iske and Randen 2005). Therefore, all scaled-up data were analyzed via the “data analysis” module for data transformation (truncating abnormal values and normalizing the distributions) and variography. Data proportion analysis and variography were made by facies and by zones. The variogram analysis is a critical process for geostatistical studies. Data variability between the wells for each zone was considered individually, by the variogram analysis module in three main directions (vertical, major, and minor). The major direction used in variography was obtained from the variogram map created based on the variance of the acoustic impedance. Figure 11 illustrates the workflow for 3D modeling of different diagenetic parameters.

Fig. 10
figure 10

Plot showing the layout of diagenesis logs in the Sarvak reservoir. The tracks from left to right indicate the effective porosity log (PHIE), cement log (based on the petrophysical log), SPI log (secondary porosity based on petrophysical interpretation), SPI-index model (secondary porosity based on petrographic study), lithology (limestone, dolomite, and shale) VDL (velocity deviation log), stylolite index log (based on petrographic study) and diagenesis electrofacies (EFAC)

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Fig. 11
figure 11

Workflow of diagenesis parameters determination, and 3D geological modeling in Sarvak reservoir of the studied field

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PHIE modeling

Effective porosity distribution was obtained after scaling up the effective porosity log by applying the “median” method and variography analysis. After that, it was distributed using the GRFS algorithm and co-kriging with the available acoustic impedance cube. Because of the heterogony effect on porosity distribution (Grader et al. 2009), seismic data is necessary to convert the heterogeneous reservoir into more homogeneous reservoirs. The correlation coefficient between them is 64%. The 3D model of effective porosity in the Sarvak reservoir in cross-section view with a related histogram of the well log, scaled-up log, and model are shown in Fig. 12.

Fig. 12
figure 12

Cross-section view of effective porosity and VDL models with related histograms (C: Histogram of the effective porosity, D: Histogram of the VDL)

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VDL modeling

VDL log was propagated after scaling up and variography analysis. GRFS algorithm was applied for distribution through co-kriging with an effective porosity model as secondary data. Figure 12 indicates a cross-section view of the VDL model and histogram of the original well log, scaled-up log, and model log. After constructing the VDL model, the VDL facies model was constructed using the classification of VDL ranges (code1 (VDL < − 500), code 2 (− 500 < VDL < 0), code 3(0 < VDL < 500), and code4 (VDL > 500)) as shown in Fig. 17.

Cement-volume modeling

The cement model was propagated after scaling up and variography analysis. GRFS algorithm along with PHIE as secondary data was considered for co-kriging and propagation. There is an inverse relationship between porosity and cement logs (Fig. 13). Figure 14 shows a cross-section view of the cement model and related histogram of the original well log, scaled-up log, and model log.

Fig. 13
figure 13

Cross plot between effective porosity and VDL (A), SPI-log (B), dolomite volume (C), and cement index (D)

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Fig. 14
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Cross-section view of shale volume, and cementation models with related histograms (C: Histogram of the shale volume, D: Histogram of the cementation)

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Shale volume modeling

Although shale is supposed to be fine-grained and clastic sediment, it was distributed in the 3D geological model to check the effect of primary depositional factors on the reservoir quality while investigating the impact of diagenesis. GRFS method was used for shale volume distribution by considering the effective porosity model as secondary data through co-kriging. The correlation coefficient between the shale volume and effective porosity is reversed in many zones, indicating the negative impact of the shale volume on reservoir quality (Table 3). Figure 14 shows a cross-section view of the shale volume model and related histogram of the original well log, scaled-up log, and model log.

Table 3 Effective porosity and correlation coefficient between effective porosity and shale volume, dolomite volume, secondary porosity index, and VDL in reservoir zones of Sarvak reservoir (negative correlation coefficient signifies inverse correlation)
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Secondary porosity index (SPI) modeling

Secondary porosity log propagation (from petrophysical interpretation) was done after scaling up and variography analysis. GRFS method along with co-kriging with effective porosity log was used for SPI distribution. The correlation between effective and secondary porosity is 73%, therefore porosity model has been used as secondary data for propagation via co-kriging. In addition, the secondary porosity log (SPI-index) which was provided based on visual petrographic study, was modeled using the same procedure. The correlation coefficient between both SPI data is 43% indicating that the SPI data from petrophysical interpretation has different resolution and accuracy. Figure 15 shows the cross-section view of both secondary porosity models and histograms of the original well logs, scaled-up logs, and model logs.

Fig. 15
figure 15

Cross-section view of A SPI-log model (based on petrophysical interpretation), B SPI-index model (secondary porosity based on petrographic study and related histograms) C Histogram of petrophysical based-SPI model, D Histogram of the petrographic based-SPI-index model)

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Dolomite volume modeling

Two dolomite volume logs derived from the petrophysical interpretation and petrographic study were spatially modeled. VDL model was used as secondary data for propagation through co-kriging and GRFS algorithm. The correlation coefficient between both volumes is about 40%, indicating the different resolutions of both data. Since the dolomite volume from petrophysical interpretation is more accurate and continuous than the petrographic study, it was selected as a final dolomite volume property. Figure 16 shows a cross-section view of both dolomite volume models and related histograms of the original secondary porosity logs, scaled-up logs, and model logs.

Fig. 16
figure 16

Cross-section view of: A dolomite volume model (based on the petrophysical log), B dolomite volume index model (based on petrographic study) with related histograms) C histogram of petrophysical based-dolomite model, D histogram of the petrographic based-dolomite model)

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Stylolite index modeling

The stylolite index, which was provided from a visual petrographic study was distributed using the “SIS” algorithm. Due to the low density of the stylolite index, the model’s accuracy is low. Figure 17 indicates a cross-section view of the stylolite index model and histogram of the original well log, scaled-up log, and model log.

Fig. 17
figure 17

Cross-section view of discrete models, including the stylolite index model (based on petrographic study), and VDL facies model with related histograms (C: Histogram of stylolite index model, D: Histogram of the VDL facies model)

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Diagenetic electrofacies modeling

The diagenetic electrofacies log (EFAC) was distributed in the 3D model after scaling up and variography analysis. It was populated in the geological grid using the “Facies modeling” module and applying the SIS algorithm individually for each facies code. Figure 18 displays the cross-section view of the diagenetic electrofacies model and related histogram of the original well log, scaled-up log, and model log.

Fig. 18
figure 18

A Cross-section view of discrete diagenetic electrofacies model with related histogram (B), C the path of cross section (also for all Figs. 12, 14, 15, 16, 17 and the figure)

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Discussion

After constructing the 3D models for all properties, the average maps of each zone were produced. The relationship between provided maps was investigated in ten pay zones from the diagenetic point of view (Table 3). To understand how diagenetic phenomena control the reservoir quality, all related maps were provided and compared together in all ten reservoir zones.

In the Upper Sarvak zone (USA), according to the effective porosity map (average porosity is 3.7%), the northeast of the field has good reservoir quality (Fig. 19). In poor porosity areas, the shale volume fairly increases. Dissolution is the most effective diagenesis phenomenon, influencing the reservoir quality (correlation coefficient is 0.35). The dolomite and cement volumes are low (less than 10%). However, dolomitization has a positive effect on reservoir quality partially (Table 3). VDL and effective porosity have a high correlation coefficient (0.56) indicating the effect of diagenesis on effective porosity. In the Upper Sarvak-B1 zone (USB1), the western parts have better porosity development (average porosity is 5.4%) that is correlatable with dolomitization and dissolution enhancement. The USB1 zone contains the highest dolomite volume (41.9%) affecting the effective porosity (correlation coefficient is 0.33), particularly in the eastern parts (Fig. 20). Considering the high cementation (10%) and dolomitization with relatively low porosity of this zone, it can be conducted that some dolomites can be assumed as cement reducing the formation porosity. In the USC2b zone, the effective porosity (average porosity is 6.5%) increases from southwest to northeast parts that is correlatable with secondary porosity (correlation coefficient between porosity and secondary porosity is 0.677) and VDL maps (correlation coefficient is 0.6) (Fig. 19). In the high porosity parts, the shale volume is decreased. Because of the low volume of dolomite, it has a low destructive effect on reservoir quality (correlation coefficient is − 0.276).

Fig. 19
figure 19

Average porosity map of pay zones including A USA zone, B USC2b zone, C USC1a zone, D LSC-D zone, E LSF zone, and F LSG zone

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Fig. 20
figure 20

Average porosity map (A) and average dolomite volume map (B) in USB1 zone, increasing dolomitization in central part causes porosity enhancement, high correction coefficient between porosity and volume of dolomite (E); Average porosity map (C) and average secondary porosity map (D) in LSA zone, increasing of porosity in the southeast parts as a result of dissolution with high correction coefficient (0.75) (F)

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The USC1a zone has the highest stylolite index which is correlatable with the relatively low porosity (4%) intervals. In this zone, the porosity improves from the southern parts toward the northern regions (Fig. 19). The porosity trend map is correlatable with the secondary porosity map. The shale volume is decreased in the high porosity parts, especially northwest of the field (Table 3). Dolomite and cement volumes are low and they do not affect the reservoir quality significantly. The porosity of the LSA1 zone is high (0.8%) and increases from west to east, which is correlatable somewhat with the secondary porosity map (Fig. 20). The shale volume decreases in the high porosity parts, particularly in the southeast of the field. Dolomite volume is so low; then, it does not affect reservoir quality. Dissolution is the most effective diagenesis phenomenon of this zone influencing the reservoir quality (correlation coefficient with secondary porosity and VDL are respectively, 0.69 and 0.6). The LSC-D zone, which has the highest effective porosity (9%) among all pay zones, is influenced by diagenesis processes (correlation coefficient with secondary porosity and VDL are respectively, 0.58 and 0.547). The amounts of dolomite and shale volumes are low, and they have low destructive effects on porosity (correlation coefficients are − 0.118 and − 0.144, respectively). The porosity variation in the LSE1 zone is influenced significantly by dissolution and dolomitization (the highest effect of dolomitization, which is approximately 0.48%). Shale volume and cementation have negative relationships with porosity variation (Fig. 21). This zone has the lowest stylolitization. LSE2 has the highest correlation coefficient between effective and secondary porosities (0.75), although the average effective porosity is not over 4.3%. LSE2 has considerable stylolite volume (43%) and was influenced to some extent by dolomitization and shale volume (Fig. 21). The LSF zone has the lowest shale volume (1.68%) and low stylolite (26%). It has a relatively high average porosity (7%). Moreover, dolomitization has the most destructive effect on reservoir quality (the correlation coefficient between porosity and dolomite volume is − 0.456). Since the VDL is negative and the porosity is relatively high (7%), it can be conducted that the fracture also controls the reservoir quality. Apart from diagenesis, some reservoir quality controls from depositional settings are expected. LSG zone has the lowest average porosity among pay zones. However, it increases from west to east (Fig. 19). The shale volume is increased in low porosity areas (correlation coefficient is − 0.3). Although the shale volume is low in all pay zones (less than 5%), it has a destructive effect on effective porosity (Fig. 12). However, dolomitization has both constructive and destructive impacts on reservoir quality. Dolomitization in USC2b, LSC-D, and LSF has a destructive effect on effective porosity, while in other zones, particularly in USB1 and LSE1, it causes an increase in reservoir porosity. As seen in Fig. 22, reservoir quality decreases in the case of developing cementation. In addition, intervals with low porosity are correlatable with developing stylolite and solution seams indicating a negative effect on formation porosity.

Fig. 21
figure 21

Average porosity map (A) and average cementation map (B) in LSE1 zone, showing porosity reduction in the western part as a result of cementation, with inverse correction coefficient (-0.44) (E); Average porosity map (C) and average shale map (D) in LSE2 zone, indicating porosity reduction in the west and northeast parts as a result of high shale content, with inverse correction coefficient (F) (-0.16)

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Fig. 22
figure 22

well section view of upscaled logs (from left to right) including lithology, VDL, VDL facies, SPI index (secondary porosity based on petrographic study), SPI Log (based on petrophysical interpretation), dolomite volume index (based on petrographic study), dolomite volume (based on the petrophysical log), cement, shale volume, stylolite index, diagenetic electrofacies, and effective porosity

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Conclusions

Based on the results of this study, the followings are concluded:

  • ten microfacies were identified in the Sarvak Formation which are influenced by the main diagenetic processes including dissolution, dolomitization, cementation, and compaction

  • Secondary porosity (dissolution) plays a significant role in the porosity enhancement of the reservoir in most pay zones (Such as USA (Upper Sarvak-A), USC2b (Upper Sarvak-C2b), and LSA1 (Lower Sarvak-A1) zones).

  • Among Sarvak zones, the LSE2 (Lower Sarvak-E2) zone has the highest correlation coefficient between effective and secondary porosity (0.75) indicating the significant impact of the dissolution on effective porosity.

  • Dolomitization has the most destructive effect on reservoir quality in the LSF (Lower Sarvak-F) zone and the highest constructive effect in the LSE1 (Lower Sarvak-E1) zone.

  • In some zones, VDL (velocity deviation log) and effective porosity have a high correlation coefficient indicating the effect of diagenesis on effective porosity

  • In most pay zones, the trends of the secondary porosity and VDL maps are correlatable with the corresponding porosity maps

  • Shale volume (as a non-diagenetic parameter) has an inverse relationship with porosity variation.

  • Cementation and stylolitization are dominated in tight intervals.