Uncertainty Analysis of Reservoir Static Modelling: A Case Study of KMJ Oil Field

: This case study explains the uncertainty of Original Oil in Place (OOIP) calculations in reservoir static modeling of KMJ Oil Field. This field consists of 4 (four) wells in an area of ± 600 acres with high heterogeneity, so in building a 3D Model, it is necessary to analyze the sensitivity and uncertainty of geological concepts, calculations of petrophysical properties, and fluid contact. The OOIP calculation uses a probabilistic method and determines reserves related to field development. The uncertainty analysis study begins by identifying the parameters with the most significant influence (Sensitivity Analysis) in calculating OOIP in the static reservoir model. To determine the ranking of reservoir uncertainty parameters, several geological, geophysical


Introduction
Three-dimensional (3D) geological static models of oil reservoirs at present are very sophisticated, namely by using computer software processing so that it will get representative 3D model results close to actual conditions with accurate modeling results.In geological and geophysical modeling (geological concepts), the existing model conditions are often unknown, and 3D modeling uses geological interpretation/assumptions [1][2][3][4][5].Each input data used to build a static 3D model has uncertainty, so the model building cannot be realized in a deterministic model [6][7][8].
The combination of the depositional environment facies uncertainty, porosity-water saturation, net-to-gross (NTG), and fluid contact determination contribute significantly to the estimation of volumetric hydrocarbon calculations [8][9][10][11][12].In terms of the distribution of rock properties, using unrealistic variogram parameters (nuggets, sills, and correlation ranges) can result in calculations of Original Oil in Place (OOIP) that are too high or too low so that reserves cannot be calculated correctly [13][14][15].
This work describes the problems encountered in constructing geological 3D models and OOIP calculations with probabilistic methods to achieve mutually acceptable results toward the transition to dynamic models.
Production of the KMJ Oil Field started in 1992 until now and is still in production in the primary production phase.The total number of wells in the KMJ Oil Field until 2021 is 4 (four) wells.As of November 2021, the number of wells still actively producing is 1 well.Cumulative oil production in the KMJ Oil Field until November 2021 is 3.36 MMSTB, which comes from the sandstones of the Bekasap Formation.Geology 3D modeling in the KMJ Oil Field is done using the software.The reservoir layer in the KMJ Oil Field for which 3D modeling will be carried out consists of 9 (nine) sand reservoir units included in the Bekasap Formation, namely Sand Units A, B, C, D, E, F, G, and H.In the KMJ Oil Field, 8 (eight) units of sand are proven to produce hydrocarbons, based on the results of fluid contact analysis.The total results of STOIIP in KMJ Oil Field using deterministic volumetric calculation is 10.98 MMSTB [16], as shown in Table 1.

Unit Sand
Net Volume (ft

Research Methodology
This study consists of several steps, from creating a static model through calculating OOIP (Step 1 to Step 4) as shows in Figure 1.Determining the research methodology is made by modification of the previous studies conducted by Bueno et al. 2011 [9], and also based on guidance of SKK Migas, 2018 [17].

Mapping
Mapping aims to make a subsurface map from well markers that result from correlations between wells.Marker mapping is carried out on sand units (layers) A through H, in the form of top and bottom.

Fault Modeling
The fault pattern to be modeled is derived from seismic interpretation results, integrated with production and pressure data, and also supported by local geological concepts.

Pillar Gridding
The gridding process carried out in the KMJ Field is in the form of depth units (x and y: meters and z: ft).The grid size used is (50x50) meters.

Segmentation
Segmentation is a division of the 3D Grid, which is bounded by faults that intersect, intersect, or faults that exceed the boundary model boundaries.

Make Horizon and Make Zone
The Make Horizon stage creates a 3-dimensional (3D) depth structure map controlled by well-marker data and fault modeling results.
Make Zones stage, this is done to create horizons that cannot be mapped based on seismic interpretation due to the limited resolution of seismic data.

Make Fluid Contact
Analysis of the determination of fluid contact in the KMJ Field begins with a review of the analysis results of previous studies.The review results are then carried out in an integrated analysis of the data from the petrophysical analysis and production tests.

Layering
Layering is done to create thinner and more complex layers in each reservoir zone.This layering will be the thickness of the cells in the well properties to be modelled.Layering validation makes scale-up well logs of petrophysical properties by comparing the histogram data with the layered histograms.

Scale up Well Logs
Scale Up is the process of averaging the log values from the well, which initially had a high vertical resolution, to one value for each cell penetrated by the well.

Data Analysis
Data analysis is the data analysis stage resulting from the scale-up of well logs before distribution throughout the 3D Grid model.The data analysis process uses variogram geostatistics by analyzing the trend toward the spatial distribution of data, both laterally and vertically.

Facies Modeling
Facies modeling begins with defining facies both vertically and laterally.Defining vertically is by using well data such as log data and core/petrographic data while defining laterally using seismic analysis results in the form of seismic attributes and validated with production data.

Step 4: Calculate STOIIP Volumes (Deterministic)
Volume calculations in the KMJ Oil Field were carried out using the volumetric method and based on the 2001 SPE regarding the classification of reserves [2,6].

Iteration 1: Sensitivity Analysis
At this stage, the aim is to identify the variables that influence the size of the calculation results of the KMJ Oil Field OOIP.Sensitivity analysis was carried out for 100 samples using the Equal Spacing Sampler method as shown in Figure 2.

Iteration 2: Uncertainty Analysis
At this stage, the aim is to analyze the uncertainty of multi-scenario OOIP calculations (P10) low estimate, (P50) base estimate and (P90) high estimation with the 3D model input variables that have been obtained from sensitivity analysis.Uncertainty analysis was carried out for 700 samples using the Monte-Carlo Sampler method as shown in Figure 3.

A. Sensitivity Cut-off
The determination of the cut-off used in the sensitivity analysis is divided into 3 (three) value scenarios, namely the minimum, base, and maximum values.The size of this value is determined based on petrophysical analysis, namely plots between rock property data (Vshale and PHIE) vs. test data (oil rate), as show in Figure 4.
Figure 4 shows that the minimum limit for the Vshale cut-off is 0.4, the base value is 0.5, and the maximum value is 0.6; while the minimum limit for the porosity cut-off is 0.11, the base value is 0.13, and the maximum cut-off porosity value is 0.15.Tabulation of the use of minimum, base, and maximum values can be seen in Table 2.

B. Fluid Contact Sensitivity
Determination of the depth of fluid contact in the KMJ Oil Field is divided into 3 (three), namely LTO (Lowest Tested Oil), OWC (Oil Water Contact), and LKO (Lowest Known Oil).LTO depth is determined based on the outermost well with oil test results at the lowest perforation interval (bottom perforation).OWC depth is determined by integrating test data and log data to determine the maximum contact depth in each sand unit.LKO value is obtained from the integration of test data and log data, and then the contact withdrawal is determined based on the cut-off resistivity for each sand unit.
There is still a possibility of decreasing the LKO depth if the unit sand below the LKO depth still has good rock properties (Vsh value below the Vsh cut-off and PHIE value above the PHIE cut-off).From these three types of fluid contact, we can determine the minimum -maximum values that will be used in the contact uncertainty analysis.Tabulation of minimum -maximum uncertainty of fluid contact is shown in Table 3.

C. Sensitivity Property Modeling (Seed)
The realization of the KMJ Oil Field model properties used in sensitivity analysis is Vsh and PHIE property models.The seed value in the property model is used randomly to get different OOIP values for each model.An example of using petrophysical modeling (seed) variables can be seen in Figure 5.

D. Sensitivity Property Modeling (Variogram)
Variogram variables include major direction, minor direction, vertical, and azimuth.These four directions will be used in the uncertainty analysis at the KMJ Oil Field.In the KMJ Oil Field, 3 (three) scenario models are used, namely Low Case, Base Case, and High Case, hence each model has different variogram direction values.
Determination of the minimum -maximum value based on the largest difference in each sand unit and each direction.After sorting from the smallest value to the largest value, this value is used as a subtracting or adding factor to produce a minimum -maximum value in each direction, as shows in Table 4. While, examples variogram of sensitivity analysis in the KMJ Oil Field is shows in Figure 6.

Uncertainty Analysis
The KMJ Oil Field uncertainty analysis consists of 7 (seven) categories, namely fluid contact, Vsh cut-off, PHIE cut-off, seed PHIE model, seed Vsh model, PHIE variogram, and Vsh variogram.In these 7 (seven) categories, there are a total of 99 variables used in the analysis as shown in Table 5.
As an example, it can be seen in Figure 7, which shows that variable No. 1 through No. 15 is a fluid contact uncertainty category.The sensitivity results for each category of uncertainty which has the greatest to the least influence on the results of OOIP KMJ Oil Field calculations.The uncertainty category that has the most significant effect on the OOIP calculation is the Vsh cut-off, as shows in Figure 8.
KMJ Oil Field Uncertainty Analysis using the Monte-Carlo Sampler method with 700x running samples.The uncertainty analysis results of KMJ Oil Field have a low OOIP estimate (P10) of 10.86 MMSTB, a base estimate (P50) of 11.49 MMSTB, and a high estimate (P90) of 12.01 MMSTB as shown in Figure 9.In comparison, the detailed results for each sand unit can be seen in Table 6 through Table 8.Furthermore, the static model uncertainty results used for reservoir simulation modeling (dynamic model) of the KMJ Oil Field is the base estimate model (P50) of 11.49 MMSTB.

Conclusion
Based on the results of the analysis and discussion, can be concluded as follows: The combination of determining facies (shale volume) porosity, fluid contact, and the cut-off is a variable/parameter that is very influential in volumetric multi-scenario calculations in the KMJ Oil Field, with the most significant parameter being the cut-off volume of shale.
The results of OOIP multi-scenario calculations for the KMJ Oil Field are based on a low estimate (P10) category of 10.86 MMSTB, a base estimate (P50) of 11.49 MMSTB and a high estimate (P90) of 12.01 MMSTB.
The static model used for reservoir simulation modeling (dynamic model) of the KMJ Oil Field is the base estimate model (P50) of 11.49 MMSTB.

Figure 4 .
Figure 4. Determination of minimum, base, and maximum values on sensitivity cut-off.

Figure 5 .
Figure 5. Usage of seed values on uncertainty analysis.

Figure 6 .
Figure 6.Examples of using variogram on uncertainty analysis.

Figure 7 .
Figure 7. Examples of variogram on uncertainty analysis, where variable no. 1 through no.15 is uncertainty category of fluid contact.

Table 2 .
Tabulation of minimum, base, maximum values of sensitivity cut-off.

Table 3 .
Minimum -maximum values tablation on fluid contact sensitivity.

Table 5 .
KMJ oil field uncertainty category.