3D Reservoir Rock Type Model Based on Cluster Analysis Technique for Rumaila Formation in the Ahdeb Oil Field, Central Iraq

This study presents is a classification of reservoir properties (porosity and shale volume) into rock types for carbonate Rumaila reservoir in Central Iraq (Ahdeb Field). The Cluster analysis method is used to identify rock types and to recognize well log clusters of similar characteristics. For most subsurface research, the determination of the rock type (lithofacies and petrofacies) is not adequate enough because of a lack of cores and cuttings. An interactive petrophysics software program was used to get the results of a cluster analysis technique, in order to determine the rock typing (log facies) in Rumaila formation units in the Ahdeb oil field. Initially, petrophysical parameters such as porosity, shale volume and quantity of various reservoir minerals were determined using the probabilistic evaluation process. In the second stage, the multiresolution graphic clustering method was employed to separate the sequential electrofacies which resulted in the identification of four electrofacies with different geological reservoir properties. The vertical variations of the rock type for Rumaila formation are based on four log facial groups. These log groups are categorized according to porosity and shale volume of formation based on responses to well logs after division of Rumaila formation into four units (Ru-1, Ru-2, Ru-3, and Ru-4).A 3D rock type model for Rumaila Formation was performed using Petrel software in order to illustrate the horizontal distribution of rock type along the Ahdeb field and showing the best characterized of reservoir rock type in any unit of Rumaila Formation. Cluster analysis technique classified porosity and shale volume, which were calculated for Rumaila Formation using well logs, into four similar characteristics rock types: rock This work is licensed under a Creative Commons Attribution 4.0 International License. Journal of Petroleum Research and Studies PISSN: 2220-5381 EISSN: 2710-1096 Open Access No. 31, June 2021, pp.49-73 50 type-1, rock type-2, rock type-3 and rock type-4. A 3D Petrel model of rock type shows that rock type-2 has better reservoir quality than other rock types in Rumaila Formation which is characterized by high porosity and low shale volume. The model clarifies the distribution of rock type-2 in the Ahdeb field at units Ru-1 and Ru-3 of Rumaila Formation.

type-1, rock type-2, rock type-3 and rock type-4. A 3D Petrel model of rock type shows that rock type-2 has better reservoir quality than other rock types in Rumaila Formation which is characterized by high porosity and low shale volume. The model clarifies the distribution of rock type-2 in the Ahdeb field at units Ru-1 and Ru-3 of Rumaila Formation.
identified. The sedimentary units identified on this basis and characterized by cable logs are known in the literature as electrofacies or logfacies [1].
The most important tools for research on crude oil, depositional basin are the rock type and log facies analysis, particularly when accurate information is only available on wireline logs. Rock type analysis can be carried out manually or automatically using mathematical methods. One of the most reliable and affective approaches to oil storage in a reservoir is a multi-varian cluster analysis (as the best data grouping method). This technique is used with both detrital and carbonate rocks [2].
The determination of the kind of reservoir rock type is the most important activity in the oil industry and relies mainly on the essential characteristics of rocks. Specific rock properties are usually known in a detailed field definition (lithofacies evaluation) and in the laboratory (petrofacies study) [3].
The purpose of well log cluster analysis is to look for similarities/dissimilarities between data points in the multivariate space of logs, in order to group them into classes also called electrofacies.
The clusters analysis defines electrofacies on the basis of the unique characteristics of well log measurements reflecting minerals and lithofacies within the logged interval [4].
The classification of well logs not includes a synthetic division of the set of data, but it follows normally the specific characteristics of log-based measurement data representing minerals and lithofacies within the logged interval.  [5].
In this study, Interactive Petrophysics program V4.4 made this classification.
Furthermore, the horizontal and vertical distributions of rock types in Ahdeb Oil Field for Rumaila Formation are carried out on the basis that these clusters are classified into four classes of rock type. Rumaila Formation has been selected from the ten Ahdeb Area (AD-1, AD-2, AD-3, AD-5, AD-9, AD-11, AD-12, AD-13, AD-14, and AD-15) as a carbonate reservoir penetrating and uniformly distributing it in a carbonate reservoir for units of rock type. In order to obtain presence and distributed rock types based on cluster analysis, Petrel software is used to implement the 3D rock type model per area of Rumaila Formation.

Geological and Structural Background:
The Ahdeb field is located between Nomina and Wasit cities, in central Iraq, 180 kilometers South-East of Baghdad [6] in Figure (1). The petroleum field is located in the river plain between the Euphrates and the Tigris. The field is situated in the central region of Mesopotamia according to Iraq's tectonic zones. It is situated on the northeast edge of the Arab plate, on the Arabian platform inside an intra-platform basin. The Ahdeb oil field is the NWW-SEE anticlinal structure. It is distinguished by two small, low-amplitude NW-SE rising crests (the south dome, with a wide spread) and three structural crests along its length referred to as the AD-1 at the north dome and divided into the two AD-2 crests and the AD-4 crests separated by the saddles. There is no fault in this area above Mauddud Formation. The dip angle from the south side of the anticline is 0.7 to -0.9 to the south, the dip angle from the north side is 2 to the south side, and the north limb is more moving than the south limb [8].
The Ahdeb oil field consists of several reservoir formations comprising major oil- The Rumaila formation is the most common Cenomanian group in middle and southern Iraq. It was initially identified from the Zubair wells of the Mesopotamian region [10].
In the area of type, the formation includes fine, marly, oligosteginal limestone with marbles, which fall into fine grain, limestone calystone below [11]. The formation in the type area usually is 90 m -120 m thick. The top portion of the Ahdeb oil field rumaila formation primarily consists of red, brown, brownish white, soft-hard calestone, interspersed with thin clay calestone. The middle and bottom parts are brownish gray, porous calcareous sediments off-white to red [12].

Clustering Procedure:
Different log responses can arise because of several factors affecting the logs. Data are clustered into a minimum distance and maximum homogeneity during the clustering stage since the use of statistical processes is compulsory. It is evident that a collection of data, such as rock type, can be used by geologists to further examine various geological parameters. Both log readings for this calculation are known as "observations" and logs used as the "values of observations" [13].
The smallest distances are linked to a pair in cluster analysis. The number of rock type is normally less than the number of readings, since vector pairs (log readings couples) have been combined to form a cluster. In order to build higher classes, the lower classes are related. This procedure goes on until a single cluster has been generated (which represents the entire data). Two clusters are related by different methods. Any of these are related by the minimum distance of the components of the clusters. The two-stage clustering module used in interactive petrophysics software (IP) is divided into handling data clusters. First, information (porosity and shale volume). The number of clusters should be sufficient enough to cover the various data sets in the logs. In most data sets, 15 to 20 clusters tend to be a decent number. The second and more manual step is to group these 15-20 clusters into a number of geological faces that are achievable. This may involve reducing the data to four groups identified by four rock types.

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The important data used in the clustering model is porosity and shale volumes which are measured based on data from well logs imported into software Interactive Petrophysics. Estimate of the gamma ray index is the first stage in evaluating the shale volume of a gamma ray log; [14] is used for old rocks: …………… (1) The shale volume was computed by using the following [15] formula -1) ……… (2) Where IGR = gamma ray index.
The neutron and density calculation combination is the most common This provides a more precise porosity, commonly used for the calculation of the mean neutron density porosity ND. This combination is called the total porosity (total porosity), which is the overall volume of voids [16,17]. The combination formula is …………………….. (3) Φe can be computed by the following equation [18] that used in the current study. The clustering module carried out in two stages using Interactive Petrophysics software (IP): Firstly, the data (effective porosity and shale volume) are divided up into manageable data clusters. The number of clusters should be enough to cover all the different data ranges seen on the logs. Fifteen to 20 clusters would appear to be a reasonable number for most data sets. The second step, which is more manual, is to take these 15 to 20 clusters and group them into a manageable number of geological facies.
This may involve reducing the data to four clusters A first step of 'rock clustering' is using K-mean statistical techniques to cluster data into a known number of clusters attempted to enter by using comprehensive logs to determine porosity and shale thickness. Initially, for each input log, the average value of each cluster must be determined. Original measurement influences outcomes. For reasonable results, the initial values should cover the entire log range. K-mean clustering works by assigning a cluster to each input level. This approach aims to reduce the internal cluster square gap from data point to cluster mean [19]. This loop continues until the mean values between loops do not change. Such are the outcomes.
Before beginning, all log data is standardized and each log input has the same dynamic range. Normalization is done by measuring the log's average and standard deviation and then normalizing the data by extracting the mean and separating it into the standard deviation.

Cluster Consolidation:
Cluster aggregation can be achieved entirely by using the results for group data from the cross plot and log plot using the hierarchy technique of data grouping. Hierarchical clustering operates by calculating distances between all clusters and fusing them closely. The next two clusters combine. The current cluster distance has been republished. The loop continues until there is one cluster. Prüfungen can be represented as a dendrogram. The dendrogram indicates how clusters were grouped and merged. The top numbers of each branch give the order of merge. Initial K-mean is checking. IP has five different approaches to clustering to assess whether clusters have merged which are:

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1. Minimum distance between all objects in clusters-the distance from Z to C is the minimum of the distances (A to C and B to C as shown in Figure (3)) 2. Maximum distance between all objects in clusters-the distance from Z to C is the maximum of the distances (A to C and B to C).
3. Average distance between merged clusters-the distance from Z to C is the average distance of all objects that would be within the cluster formed by merging clusters and C.
4. Average distance between all objects in clusters-the distance from Z to C is the average distance of objects within cluster Z to objects within cluster C.
5. Minimize the within-cluster sum of squares distance-clusters are formed so as to minimize the increase in the within-cluster sums of squares. The distance between the two clusters is the increase in these sums of squares if the two clusters were merged.

Fig. (3) Dendrogram plot shows distance between clusters (A, B, and C).
The default method 'Limit the in-cluster square distance number' produces good results in separating the different types of log rock from clusters as shown in Figure (4).
The clusters are grouped into a known number of groups by stopping the grouping at a Editing and quality control of input data (Q.C).
Make horizons, make horizons.

4-Modeling of properties, which includes:
Scale logs up well.
Modeling of facies (model type of rock).

3D rock types (log-facies) model
One of the most critical tasks of reservoir design is the protection of the key geological features and heterogeneities in the reservoir. In certain cases the modeling of facies of reservoirs is the most critical aspect of reservoir modeling as the rock type can be the main control factor of reservoir heterogeneity. If rock modeling technology has been used, the geometry and distribution of key facies and petrophysical properties in the facies must also be generated and populated.
Modeling rock type is a way of spreading distinct rock form around the model grid.
Typically, by analyzing this data in the process data analysis phase, the processor would have up-scaled logs with discreet properties in the model grid and theoretically identified patterns within the reservoir (Fig.6). In this study, the 3D rock type model of Rumaila Formation is constructed from study of main rock types which are deduced using well logs data by cluster analysis technique.
After making layering for reservoir units for Rumaila Formation, the layers for each reservoir unit is recognized with specific Rock type. Petrel provides several algorithms for modeling rock type distribution in a reservoir environment Sequential indicator Simulation Algorithm is used as a statistical tool for creating a model type that suits the

Results and Discussions
The Each cluster is characterized by average shale volume and porosity measurements. Training has been divided into four groups. The group of logfacies has a well-log answer, and each group can contain one or more clusters. Figure (6) shows histograms and cross-plots for the Rumaila Formation groups between the wells used as generated by a k-means cluster analysis. Researchers in [20] were built four rock types and groups which are identified in the Yamama formation depending on the FZI method but in the current study, four rock types were defined and distributed vertically and horizontally among the 10 wells examined depending on Cluster Analysis Technique as shown in Figures (8) and (9).Each rock type is characterized by response of porosity and shale volume as well as microfacies type:    The units of Rumaila Formation are characterized by the following:

Unit Ru-1
It is the highest oil-bearing unit. This unit consists of packstone and grainstone facies due to consists mainly of rock type -2 that represents the highest percent about 95% from this unit as well as 5% of wackstone to packstone of rock type-3 distributed near to well AD-15 at northern dome, Figure (10).

Unit Ru-2
The unit is characterized by major differences and variations in Facies which consists mainly of rock type-2 about 38% and change to rock type-1 about 28% with 28% mudstone facies of rock type-4 as well as 5% of rock type -3. This unit represents morally bad facies in all domes of Ahdeb field, Figure (11).

Unit Ru-3
Represents the second good unit in Rumaila Formation which consists mainly of packstone and grainstone of rock type-2 with a small percentage of rock type -1 and rock type-3 especially near the well AD-5 at northern dome. According to distribution of rock type, this unit is oil bearing unit in Rumaila Formation especially at southern dome, Figure (12).

Unit Ru-4
This unit is fair oil bearing unit which becomes moderate rock type towards southern dome but becomes bad facies towards northern dome. It is characterized by wackestone to packstone facies which range from rock type-2 about 56% to rock type -1 about 42% and 2% of rock type-3, Figure (13).

Conclusions:
The function of multivariate cluster analysis based on response well logs determination has been documented in this study by comparing with thin section examination. Based on different cutoff levels, a desirable number of logfacies for any given formation has been achieved. Rock type construction represents the essential method to deduce the log-facies based on well logs data when the core and cutting is absent in drilled wells. The Cluster Analysis technique is a useful method to classify the