Distribution of Petrophysical Properties Based on Conceptual Facies Model, Mishrif Reservoir/South of Iraq

A 3D geological model is an essential step to reveal reservoir heterogeneity and reservoir properties distribution. In the present study, a three-dimensional geological model for the Mishrif reservoir was set-up based on data obtained from seven wells and core data. The methodology includes setting up a 3D grid and preparing it with petrophysical properties such as (facies, porosity, water saturation, and net to gross ratio). The structural model was built based on a base contour map obtained from 2D seismic interpretation along with well tops from seven wells. A simple grid method was used to build the structural framework with 234x278x91 grid cells in the X, Y, and Z directions, respectively, with lengths equal to 150 meters. The total number of grids is (5919732) in the geological model. CPI (computer-processed interpretation) for 7 wells contain (facies, porosity, water saturation, and NTG) was imported to Petrel 2016 software. Facies log was upscaled and distributed along the 3D grid. Truncated Gaussian with trend method was used to distribute the facies taking into account the conceptual facies model of the Mishrif formation. The result shows that the trend of sedimentation suggests a retrogradation the 3D geological model, which reflects the geological knowledge used to distribute the reservoir properties (porosity and water saturation) correctly.

the 3D geological model, which reflects the geological knowledge used to distribute the reservoir properties (porosity and water saturation) correctly.

Introduction
One of the standard tools currently used to generate production forecasts of any oil and gas field is three-dimensional reservoir modeling and flow-simulation studies. A significant challenge has been facing geologists in constructing 3D geological modeling. Facies distribution in lateral and vertical directions and between different flow units in the defined 3D grid is one of these challenges [1]. Also, the proper and acceptable mapping of reservoir characterization is one of the significant challenges. Therefore, integration and incorporation of all quantitative field studies with all available data are required. Building 3D stochastic models based on the conceptual geological model had great benefit to reflect the geological knowledge and proper distribution of reservoir properties [2]. The main objective of conceptual geological model is its using as a guide to build the 3D reservoir model, and representing the geological knowledge based on real and or conceptual geological objects [3].
Porosity, water saturation, and permeability have an essential impact on hydrocarbon reservoir and reservoir modelling. The petrophysical properties and reservoir characterization are used to generate petrophysical models. The petrophysical model predicts future performance and estimates reserves [4]. The Mishrif formation in X-field is the main hydrocarbon reservoir, which is the subject of our study. The Mishrif formation is a heterogeneous reservoir.
Consequently, a critical petrophysical analysis and model development is required to ensure optimal enhancement of oil recovery using a 3D petrophysical model. The Mishrif Formation in central and southern Iraq was a subject for many studies [5][6][7][8][9][10]. It is considered one of the important reservoirs in the south Iraq region; approximately 30% of the total Iraqi oil reserves were found in this formation [8,11].
The Mishrif Formation was first described by [12] in southern Iraq. The formation consists of sub basinal, shelf limestone, and restricted shelf facies [5]. Mishrif formation belongs to the middle Cenomanianearly Turonian age and is deposited on a basin-wide shallow-water platform [13].
Few studies have been carried out on the Mishrif formation to distribute petrophysical properties using the facies model as a guide for distributions. Therefore, the primary purpose of this paper is to build a 3D static geological model for Mishrif Formation in X-field, south Iraq, and build the 3D petrophysical model based on the conceptual facies model. The study also aims to understand better the lateral and vertical distribution of petrophysical properties (Porosity, water saturation, and NTG) of the Mishrif reservoir.

The study area
The X-field is situated in the south-eastern part of Iraq. It is located above the suture structure at the junction of the inner part of the Arabian plate and the western part of the Mesopotamian The super sequence Albianlower Turonian represents a transition from onlap margin to the basin [14]. This super sequence consists of Wara, Ahmadi, Rumaila, and Mishrif formation.
Mishrif formation belongs to the middle Cenomanian -Early Turonian age, and it is considered one of the important reservoirs in this sequence. The formation consists of two third-order sequences [8], consisting of bioclastic limestone rock and chalky Limestone.
The Mishrif formation in X-field consists of upper Mishrif (MA) and lower Mishrif (MB), which differ one from another by reservoir properties of sediments, and are separated by shale (CR-II) and marls. The average thickness of the formation is about 186 m.

Data set and Methods
The data used in this paper consists of CPI (computer-processed interpretation) for 7 wells. The CPI contains (Facies, Porosity, Water saturation, and NTG), base contour map for Mishrif Formation from the last interpretation of 2D seismic. Collecting and quality check of the data and preliminary information from the final geological reports and previous reservoir studies is the first step in the workflow of geological modeling.
Schlumberger's Petrel 2016 software was used for 3D geological modeling. Modeling software presents a 3D view for all reservoir properties and helps geologists distribute the petrophysical properties models and design new wells [15].  The second step is constructing the conceptual facies model from seismic interpretation and core study. This conceptual model will be used as a guide for the final 3D facies model.
 The last step is upscaling and distributing the petrophysical properties over geological model cell using facies model as a guide for the distribution. The sequential Gaussian Simulation (SGS) method was used in petrophysical model distribution.
In the following, the workflow of geological model construction is discussed in more detail.  seismic interpretation, and these maps have been adapted to well tops.
A simple grid method was used to build the structural framework of X-field with 234x278x91 grid cells in the X, Y, and Z directions, respectively. The grid was depicted as a square; its side length is equal to 150 meters. The grid dimensions were relatively large to preventing grid upscaling problem when exported into the simulation model. Figure (4) shows the skeleton of the geological model. After grids construction, layering and zoning is the final step in constructing the structural framework. It is essential to define the thickness and orientation of the layers between horizons of the 3D grid. To ensure the best upscaling values for petrophysical properties in the geological model cell, we should define the grid thickness properly. It is normal to modify the layering after upscaling is done to compare input data and upscaled data better.
Each Mishrif unit in X-field has been divided into many layers depending on petrophysical properties. CR11 zone consists of one layer in the uppermost of the formation because it represents the seal rock of Mishrif formation. Table (1) illustrates the number of layers of each unit in Mishrif formation.

Table (1) Mishrif unit and number of layers in each unit
The scale-up well logs are making averages for the values to the cells in the 3D grid penetrated by the wells. An excessively large considerable model will cause PETREL's simulation to take more significant amounts of time. During the process of upscaling well data into the model, we have to ensure that once in the model; the data is representative of the original well data. Too few layers will result in data loss, and too many layers will result in slow modeling in the future.
Comparison between well data and upscaled data is a primary process in static modeling and needs to be thorough [17]. In geological models, facies and petrophysical properties (porosity (Ø), permeability (K), and water saturation (Sw)) have been scaled up. Many statistical methods are used to scale up, such as (arithmetic, harmonic, and geometric method). The facies log was upscaled using most methods, while the current model's porosity, water saturation, and permeability values were scaled up using the arithmetic average. Figure 5 showing the Scale-up of facies, porosity, and water saturation logs for well-B.

Property Modelling
Property modeling is the process of filling the grid cells with discrete (facies) or continuous properties (porosity and water saturation). It is used to distribute petrophysical properties laterally and vertically in the 3D grid cells.

Petrophysical model
The distribution of the petrophysical properties on a 3D grid is the primary purpose of this paper. The reservoir petrophysical modelling can be done by deterministic and stochastic methods. Sequential Gaussian simulation is a stochastic method, and it was widely used in petrophysical modeling because of the flexibility of this method (Deutsch, 2014[18]).
The porosity, water saturation, and net to gross logs from Computer Processed Interpretation results (CPI) for seven wells were scaled up into a cellular model using the arithmetic method.
The porosity model was built using the Sequential Gaussian Simulation (SGS) method and the facies model as a guide for distribution. The same geostatistical method used in the porosity models was also used in the water saturation and NTG model.

Results and Discussion
Well, correlations (lateral and longitudinal) were made for Mishrif Formation in X-field to take an initial idea about the subsurface geological layers and check the thickness of subunit of Mishrif formation ( Figure (7 and 8)). Figure (8) shows that well-D stratigraphically higher than other wells. The thickness of the Mishrif unit is slightly decreasing toward the southeast of the field, and a decrease in petrophysical properties is observed in the west of the field (well-E).
The petrophysical properties are very good with high net pay and NE-SW direction, which presents the reef environment in X-field (Figure 7).  study.
The NTG model shows that unit Mishrif B has the highest NTG with a range from (1-0.6), then gradually decreasing toward the SE direction of the field. The unit Mishrif B3 has high NTG along the reef area. Figures (18, 19) show the NTG model in each reservoir unit of Mishrif formation.

Conclusions
The study aimed to distribute the reservoir properties in the framework of 3D geological modelling for Mishrif Formation using Petrel software. It can be concluded that: 1-The stratigraphic model shows that the SE part of the field is stratigraphically more arisen than the NW part, with the thickness of the Mishrif unit slightly decreasing toward the southeast of the field. The Mishrif reservoir was subdivided into four units according to logs and petrophysical interpretation. 6-The NTG model shows that unit Mishrif B has the largest NTG with a range from (1-0.6), and then gradually decreases toward the SE direction of the field.