Calculating heterogeneity of Majnoon Field/Hartha reservoir using Dykstra Parsons method

One of the principle concepts for understanding the hydrocarbon field is the heterogeneity scale; this becomes particularly challenging in supergiant oil fields with medium to low lateral connectivity in carbonate reservoir rocks. The main objective of this study is to quantify the value of the heterogeneity for any well, and propagate it to the full reservoir. This is quite useful specifically prior conducting detailed water flooding or full field development studies and work, in order to be prepared for a proper design and exploitation requirements, which fits with the level of heterogeneity of this formation. The main tool used for these purposes is the application of the famous Lorenz coefficient method, in conjunction with the Dykstra Parsons technique for calculating the degree of heterogeneity for any well. The starting point for this kind of complicated studies needs to start from the basics. In order to understand the big picture and be able to plan properly for the scope to be delivered. Utilizing analytical tools like the ones mentioned above becomes quite necessary, if not crucial, to the success of full field modelling and choosing an optimum water flood pattern and design. This work covers the methodology for quantifying and calculating the level of heterogeneity in a given reservoir. The Dykstra-Parsons Coefficient or the variation of Dykstra Parsons (VDP) is commonly used in calculating permeability variation. The method of calculating begins by sorting the property of interest and make the other property fixed value (to calculate No.23(6) 2019 Journal of Petroleum Research & Studies (JPR&S) E55 permeability you have to make porosity a fixed value for all calculations) and make permeability in order of decreasing magnitude. For each of the values calculate the percentage of values greater or the ‘cumulative probability’, so that the probability of X is P(x≤X). Then plot the original permeability values on a log probability graph with the cumulative probability values. The slope value and the intercept of the line of the best fit, for all data are used to calculate the 50th and 84th probability values or by variation layering system to calculate the variation of P10, P50 and P90, which are used to find VDP. This methodology has been tested successfully in the stated super giant oil field, in which the reservoir is a carbonate rock formation. The reservoir is areally extensive reservoir and not of a great thickness. The importance of this step is to conclude a utilizing heterogeneity calculation method before conducting any detailed reservoir simulation study. It can save a lot of time and effort by providing guidance to the path, which needs to be followed, and sheds light on the critical elements to be looked after. This also can help to uncover many insights on the reservoir itself, hence allowing the engineer to plan for the necessary voidage replacement and water injection rates to sustain the reservoir pressure and pattern development based on the magnitude of heterogeneity those results from this procedure. The suggested method, in combination with geological and petrophysical information available, can be applied to majority of the reservoirs. This combination is paramount to ensure optimum time and planning is followed for each reservoir development study that involves for example water flooding.


No.23-(6) 2019 Journal of Petroleum Research & Studies (JPR&S)
permeability you have to make porosity a fixed value for all calculations) and make permeability in order of decreasing magnitude.
For each of the values calculate the percentage of values greater or the 'cumulative probability', so that the probability of X is P(x≤X). Then plot the original permeability values on a log probability graph with the cumulative probability values. The slope value and the intercept of the line of the best fit, for all data are used to calculate the 50th and 84th probability values or by variation layering system to calculate the variation of P10, P50 and P90, which are used to find VDP. This methodology has been tested successfully in the stated super giant oil field, in which the reservoir is a carbonate rock formation. The reservoir is areally extensive reservoir and not of a great thickness.
The importance of this step is to conclude a utilizing heterogeneity calculation method before conducting any detailed reservoir simulation study. It can save a lot of time and effort by providing guidance to the path, which needs to be followed, and sheds light on the critical elements to be looked after. This also can help to uncover many insights on the reservoir itself, hence allowing the engineer to plan for the necessary voidage replacement and water injection rates to sustain the reservoir pressure and pattern development based on the magnitude of heterogeneity those results from this procedure.
The suggested method, in combination with geological and petrophysical information available, can be applied to majority of the reservoirs. This combination is paramount to ensure optimum time and planning is followed for each reservoir development study that involves for example water flooding.

Introduction:
Heterogeneity is a very important factor in determining the recovery from petroleum reservoirs. Thus; heterogeneity calculations can be classified into static and dynamic techniques.
Heterogeneity is the quality and situation of being heterogeneous. It was first defined in 1898 as the difference or diversity in kind from other kinds. Other definition is consisting of parts or things that are very different from each other [1]. In petroleum studies, it is

No.23-(6) 2019 Journal of Petroleum Research & Studies (JPR&S)
E57 referred to as the isotropy and anisotropy. Heterogeneity can be named as; complexity, deviation from norm, difference, discontinuity, randomness, and variability. [2] A number of scholars noted that the difference between homogeneous and heterogeneous was relative, and it was based on the economic considerations [3]. This shows how heterogeneity has a variable concept which can be changed and re-defined to describe any situations arises during production from a reservoir, based on the researchers` experiences and expectations [4].
The disparity between heterogeneous and homogeneous was relative, and economical.
Nurmi et al. suggested the previous highlights, which indicates that heterogeneity has a variable meaning which can be defined in other words to depict situations that emerge while the reservoir is under production. The heterogeneity is very tendentious to the researcher`s experience and anticipations [7]. The heterogeneity was defined by some researchers as the variability and complexity of the system characterization in 3D space.
All these definitions proposed that the heterogeneity is not necessarily refer to an individual rock unit or an overall system. However, it deals with measurement types, properties, individual units and parameters [3].
These mentioned definitions clarify that heterogeneity does not refer to the overall system, or individual rock or reservoir unit, but instead it deals separately for each individual unit, properties, parameters and measurement types [5].

Dykstra Parsons method
The Dykstra-Parsons Coefficient or the variation of Dykstra Parsons (VDP) is commonly used in calculating permeability variation. The method of calculating begins by sorting the property of interest and make the other property fixed value (to calculate permeability you have to make porosity a fixed value for all calculations) and make permeability in order of decreasing magnitude [6].
For each of the values calculate the percentage of values greater or the 'cumulative probability', so that the probability of X is P(x≤X). Then, plot the original permeability values on a log probability graph with the cumulative probability values. The slope value and the intercept of the line of the best fit, for all data are used to calculate the 50th and 84th probability values, which are used to find VDP [7].

No.23-(6) 2019 Journal of Petroleum Research & Studies (JPR&S)
E58 This methodology has been tested successfully in the stated super giant oil field, in which the reservoir is a carbonate rock formation. An important note is that the reservoir is areally extensive reservoir and not of a great thickness. It was concluded that utilizing a heterogeneity calculation method before conducting a detailed reservoir simulation study can save a lot of time and effort by providing guidance to the path which needs to be followed, and sheds light on the critical elements to be looked after. This has also helped to uncover many insights on the reservoir itself, hence allowing the engineer to plan for the necessary voidage replacement and water injection rates to sustain the reservoir pressure and pattern development.
The suggested method, in combination with geological and petrophysical information available, can be applied to majority of the reservoirs. This combination is paramount to ensure optimum time and planning followed for each reservoir development study that involves water flooding.
This method also called the stratified method or the permeability averaging method.

Results:
The procedure and results of this method can be clarified in Table (1) and Table (2   The results are: where; x Heterogeneity parameter Hp = k effective / K average = (1+ sum v^2 /h) ^ -1 x v^2 = (1 -K i /K average ) ^2 x K average = 212.000 , k effective 88.104 , HP 0.416 (1 for homo, 0 hetero)

Fig. (1) (A, B) Permeability variation of layers of Dykstra parson's method
It can be found that the value of the Dykstra Parsons` coefficient = 0.799 which indicates a very heterogeneous reservoir (0 homo -1 hetero). That proves that Hartha reservoir / Majnoon field is a very heterogeneous reservoir.

Discussion:
Although, it is the first time for calculation the heterogeneity for Majnoon Field / Hartha reservoir, but it is somehow expected that all the Iraqi reservoir have heterogeneous nature.
The degree of heterogeneity which can be only calculated by such methods it what matters, so the researcher can have a full idea about the field or the reservoir.
The higher heterogeneity is more preparations and considerations, must be taken during any later work especially when planning to water flooding and choosing the most proper design. The creating reservoir or geological model because these models cannot be undetailed or else all the importance of heterogeneity will be lost and thus the authenticity of the model will be lost as well.
The main model or design of Hartha reservoir must be detailed and with the fine gridding system. 1-Dykstra Parsons is a straight forward method to calculate heterogeneity efficiently and accurately.
2-Hartha reservoir -Majnoon Field is a very heterogenous reservoir with a complicated nature.
3-Any further work on tis reservoir must be taken into consideration the detailed properties, and the authenticity of the model would be lost.