Gas Saturated Sandstone Reservoir Modeling Using Bayesian Stochastic

This study has been done to map the distribution of gas saturated sandstone reservoir by using stochastic seismic inversion i Bonaparte basin. Bayesian stochastic inversion seismic method is an inversion method that utilizes the principle of geostatistics so th will get a better subsurface picture with high resolution. The stages in conducting this stochastic inversion techniqu analysis, (ii) well to seismic tie, (iii) picking horizon, (iv) picking fault, (v) fault modeling, (vi) pillar gridding, ( vi (viii) scale up well logs, (ix) trend modeling, (x) variogram anal statistical wavelets are used because they can produce good correlation values. Then, the stochastic seismic inversion result reservoir in the study area is a reservoir with tight sandstone lithology which has a low porosity value and a value of High acoustic impedance ranging from 30,000 to 40,000 ft /s*g/cc.


Introduction
The Bonaparte Basin is mostly located off the coast of the Arafura Sea and has an area of about 270,000 km2. This basin is known as one of the basins that produces hydrocarbons in Indonesia, especially hydrocarbons in the form of gases and condensates. The Bonaparte Basin is generally dominated by extensional fractures and very few fractures or compressional structures are found. (O'brien et al, 1993 According to Barber et al (2003), lithological characters based on biostratigraphic data indicate that the depositional pattern in the Bonaparte Basin Plover Formation is domina by the deposition of braided fluvial types in the south of the study area to the coastal environment which is influenced by waves (wave dominated shoreline) and in the wave dominated shoreline the northern part is formed in a shallow marine environment. The direction of deposition in the braided fluvial environment is relatively northwest-southeast.
In the oil and gas exploration stage, the seismic method is one of the top choice geophysical methods that can provide better subsurface information by utilizing the seismic wave propagation properties. There is a technique commonly used in this seismic method, namely seismic inversion technique.
Seismic inversion is a method that can describe and estimate the physical properties of subsurface in the form of acoustic impedance values by utilizing seismic data as input and well data as control. Well data here has detailed resolution on thin layer thickness. Meanwhile, seismic data is strongly influenced by bandwidth which for thin layer thicknesses under tunning thickness cannot be resolved properly so as to cause high ambiguity problems in conducting inversions. Therefore, to overcome these problems, an inversion technique with a geostatistical approach can be used which will result in high resolution inversion results.
Journal of Geoscience, Engineering, Environment, and Technology This study has been done to map the distribution of gas saturated sandstone reservoir by using stochastic seismic inversion i basin. Bayesian stochastic inversion seismic method is an inversion method that utilizes the principle of geostatistics so th will get a better subsurface picture with high resolution. The stages in conducting this stochastic inversion techniqu analysis, (ii) well to seismic tie, (iii) picking horizon, (iv) picking fault, (v) fault modeling, (vi) pillar gridding, ( vi (viii) scale up well logs, (ix) trend modeling, (x) variogram analysis, (xi) stochastic seismic inversion (SSI). In the process of well to seismic tie, statistical wavelets are used because they can produce good correlation values. Then, the stochastic seismic inversion result s a reservoir with tight sandstone lithology which has a low porosity value and a value of High acoustic impedance seismic, geostatistic, stochastic inversion, Bonaparte basin The Bonaparte Basin is mostly located off the coast of the and has an area of about 270,000 km2. This basin is known as one of the basins that produces hydrocarbons in Indonesia, especially hydrocarbons in the form of gases and condensates. The Bonaparte Basin is generally dominated by ry few fractures or compressional O'brien et al, 1993). According to Barber et al (2003), lithological characters based on biostratigraphic data indicate that the depositional pattern in the Bonaparte Basin Plover Formation is dominated by the deposition of braided fluvial types in the south of the study area to the coastal environment which is influenced by waves (wave dominated shoreline) and in the wave dominated shoreline the northern part is formed in a shallow marine . The direction of deposition in the braided fluvial southeast. In the oil and gas exploration stage, the seismic method is one of the top choice geophysical methods that can provide izing the seismic wave propagation properties. There is a technique commonly used in this seismic method, namely seismic inversion technique.
Seismic inversion is a method that can describe and estimate the physical properties of subsurface in the form of acoustic impedance values by utilizing seismic data as input and well data as control. Well data here has detailed resolution on thin layer thickness. Meanwhile, seismic data is strongly influenced by bandwidth which for thin layer thicknesses g thickness cannot be resolved properly so as to cause high ambiguity problems in conducting inversions. Therefore, to overcome these problems, an inversion technique with a geostatistical approach can be used which results.
Bayesian stochastic inversion seismic method is an inversion method that uses a geostatistical algorithm to obtain property models that have detailed resolution such as well data.
In this study a mapping of sandstone reservoirs saturated with plover formation gas using stochastic inversion seismic methods in the "X" field in the Bonaparte

Methodology
In this research 3D post-stack time migration seismic data which is equipped with inline in the east totaling 300 lines (1100 -1400) and xline in the north direction totaling 800 lines (1000 between the lines which is 18.75 m. Well data used in this study amounted to 4 wells named AR AR-4. There are also data markers, namely t and base reservoir and checkshot data on each well.
Data processing conducted in this study consisted of qualitative and quantitative data processing for obtaining hydrocarbon prospect zones, log data sensitivity analysis, wavelet extraction, well seismic tie, picking horizon, picking fault, fault modeling, pillar gridding, time structure map and depth structure map, isopatch map creation, AI scale-up log and trend modeling so that later stochastic inversion results will be obtained.
Stochastic seismic inversion is an inversion technique whose basic principle uses a random simulation algorithm and produces more than one acoustic impedance model that fills observational seismic data. More than one solution can overcome the problem of non-uniqueness and uncertainty in deterministic inversion, especially in the case of thin films. Another advantage is that this method does not depend on the bandwidth of the seismic data used, but on the block size This study has been done to map the distribution of gas saturated sandstone reservoir by using stochastic seismic inversion in the "X" field, basin. Bayesian stochastic inversion seismic method is an inversion method that utilizes the principle of geostatistics so that later it will get a better subsurface picture with high resolution. The stages in conducting this stochastic inversion technique are as follows, (i) sensitivity analysis, (ii) well to seismic tie, (iii) picking horizon, (iv) picking fault, (v) fault modeling, (vi) pillar gridding, ( vii) making time structure maps, ysis, (xi) stochastic seismic inversion (SSI). In the process of well to seismic tie, statistical wavelets are used because they can produce good correlation values. Then, the stochastic seismic inversion results show that the s a reservoir with tight sandstone lithology which has a low porosity value and a value of High acoustic impedance Bayesian stochastic inversion seismic method is an inversion method that uses a geostatistical algorithm to obtain property models that have detailed resolution such as well In this study a mapping of sandstone reservoirs saturated ver formation gas using stochastic inversion seismic Bonaparte Basin.
stack time migration seismic data which is equipped with inline in the east-west direction 1400) and xline in the north-south direction totaling 800 lines (1000 -1800) with the distance between the lines which is 18.75 m. Well data used in this study amounted to 4 wells named AR-1, AR-2, AR-3, and 4. There are also data markers, namely the top reservoir and base reservoir and checkshot data on each well.
Data processing conducted in this study consisted of qualitative and quantitative data processing for obtaining hydrocarbon prospect zones, log data sensitivity analysis, on, well seismic tie, picking horizon, picking fault, fault modeling, pillar gridding, time-map mapping structure map and depth structure map, isopatch map creation, up log and trend modeling so that later stochastic ined. Stochastic seismic inversion is an inversion technique whose basic principle uses a random simulation algorithm and produces more than one acoustic impedance model that fills observational seismic data. More than one solution can uniqueness and uncertainty in deterministic inversion, especially in the case of thin films. Another advantage is that this method does not depend on the bandwidth of the seismic data used, but on the block size W when simulating the impedance model so that the results of this stochastic inversion are less smooth than the deterministic inversion results.
The basic principle of this stochastic seismic inversion is the Bayesian principle. This principle uses the concept of probability which is interpreted as "a measure of a state of knowledge". This principle is a probability principle, where there is a prior probability model, which is then formulated with a likelihood probability function so as to obtain the output of the posterior probability model. This output model is the realization of the impedance model. The formulation of the Bayesian principle is as follows (H.Anders, 1998 σ : likelihood function k : constant Bayes' theorem is the result of a combination of probability theory and conditional probability. Probability theory states the likelihood of an event occurring with real numbers 0 to 1. Meanwhile, conditional probability is an event A that occurs when it is known that event B has already occurred (Wapole, 2000).

Qualitative Analysis
In this study four data wells were used, namely AR AR-2 well, AR-3 well, and AR-4 well. Qualitative analysis is the first step in determining the hydrocarbon prospect zone. This qualitative analysis is performed by the quick look method where by looking at the response from the gamma ray log, resistivity log, neutron porosity log, and density log. This quick look method aims to interpret zones that are permeable, impermeable, lithological types, and hydrocarbon fluid content.  The basic principle of this stochastic seismic inversion is the Bayesian principle. This principle uses the concept of ed as "a measure of a state of knowledge". This principle is a probability principle, where there is a prior probability model, which is then formulated with a likelihood probability function so as to obtain the his output model is the realization of the impedance model. The formulation of the H.Anders, 1998).
Bayes' theorem is the result of a combination of probability theory and conditional probability. Probability theory states the likelihood of an event occurring with real numbers 0 to 1. Meanwhile, conditional probability is an event when it is known that event B has already In this study four data wells were used, namely AR-1 well, 4 well. Qualitative analysis is the first step in determining the hydrocarbon prospect zone. This qualitative analysis is performed by the quick look oking at the response from the gamma ray log, resistivity log, neutron porosity log, and density log. This quick look method aims to interpret zones that are permeable, impermeable, lithological types, and hydrocarbon fluid d in the study Well Name In the AR-1 well contained in Figure 1 it can be seen that the depth of the reservoir layer containing hydrocarbons is 3955 ft to 4275 ft which is marked with a dark blue box. In this layer it is known that the response of the gamma ray log curve shows a low response which ranges from 10 gAPI to 60 gAPI so that the layer can be said to be a permeable layer and has a sandstone or sandstone lithology type. Then, the resistivity log curve response, the log LLD, shows a very high response of more than 80 ohms. So the layer can have a gas hydrocarbon fluid content. In addition, the separation of the log density and neutron porosity log also indicates that the layer is a hydrocarbon prospect zone.
Furthermore, the AR-2 well did not show any reservoir layers containing hydrocarbons. This is because in AR there is no separation between log density and log neutron porosity and is also dominated by high gamma ray log response. In addition, if seen from the response of the log resistivity curve, there is no contrast of high resistivity values. The qualitative analysis on AR-2 wells can be seen in Figure  2.  Figure 3 it can be seen that the depth of the reservoir layer conta hydrocarbons is 4185 ft to 4492 ft which is marked with a dark blue box. In this layer it is known that the response of the gamma ray log curve shows a low response which ranges from 10 gAPI to 60 gAPI so that the layer can be said to be a permeable layer and has a sandstone or sandstone lithology type. Then, the resistivity log curve response, the log LLD, shows a high response of more than 80 ohms. So that the layer can be said to have a gas hydrocarbon fluid content. In addition, the separation of the log density and neutron porosity log also indicates that the layer is a hydrocarbon prospect zone.
Then, in the AR-4 well contained in Figure 4 it can be seen that the depth of the reservoir layer containing hydrocarbons is 4220 ft to 4541 ft marked w box. In this layer it is known that the response of the gamma ray log curve shows a low response which ranges from 10 gAPI to 60 gAPI so that the layer can be said to be a permeable layer and has a sandstone or sandstone lithology type. Then, the resistivity log curve response, the log LLD, shows a high response of more than 80 ohms. So that the layer can be said to have a gas hydrocarbon fluid content. In addition, the separation of the log density and neutron porosity log also indicates that the layer is a hydrocarbon prospect zone. 1 well contained in Figure 1 it can be seen that the depth of the reservoir layer containing hydrocarbons is 3955 ft to 4275 ft which is marked with a dark blue box. In this layer it is known that the response of the gamma ray log ow response which ranges from 10 gAPI to 60 gAPI so that the layer can be said to be a permeable layer and has a sandstone or sandstone lithology type. Then, the resistivity log curve response, the log LLD, shows a very high So the layer can be said to have a gas hydrocarbon fluid content. In addition, the separation of the log density and neutron porosity log also indicates that the layer is a hydrocarbon prospect zone.
2 well did not show any reservoir layers containing hydrocarbons. This is because in AR-2 well there is no separation between log density and log neutron porosity and is also dominated by high gamma ray log response. In addition, if seen from the response of the log e is no contrast of high resistivity values. 2 wells can be seen in Figure   Qualitative analysis of AR-2 wells 3 well contained in Figure 3 it can be seen that the depth of the reservoir layer containing hydrocarbons is 4185 ft to 4492 ft which is marked with a dark blue box. In this layer it is known that the response of the gamma ray log curve shows a low response which ranges from 10 gAPI to 60 gAPI so that the layer can be said to be a layer and has a sandstone or sandstone lithology type. Then, the resistivity log curve response, the log LLD, shows a high response of more than 80 ohms. So that the layer can be said to have a gas hydrocarbon fluid content. In the log density and neutron porosity log also indicates that the layer is a hydrocarbon prospect 4 well contained in Figure 4 it can be seen that the depth of the reservoir layer containing hydrocarbons is 4220 ft to 4541 ft marked with a dark blue box. In this layer it is known that the response of the gamma ray log curve shows a low response which ranges from 10 gAPI to 60 gAPI so that the layer can be said to be a permeable layer and has a sandstone or sandstone lithology n, the resistivity log curve response, the log LLD, shows a high response of more than 80 ohms. So that the layer can be said to have a gas hydrocarbon fluid content. In addition, the separation of the log density and neutron porosity at the layer is a hydrocarbon prospect

Sensitivity Analysis
In the sensitivity analysis in the research, a cross between the P-Impedance and log porosity (PHIT) logs is used with a color scale of values in the form of a gamma ray log. This is done to see the sensitivity of these parameters in separating shale and sand lithology. In this research, sensitivity analysis is divided into two zones, name marked in yellow is identified as sandstone lithology or sandstone while the zone marked in blue is identified as shale lithology.
Based on the results of cross plots on each well it can be seen that the separation of lithology (sandstone) and shale is considered sensitive because it can separate the boundary between sand and shale contained in the reservoir zone. Lithology of sandstone or sandstone is indicated by an acoustic impedance value of 27.500 ft/s* /cc to 50.000 ft/s*g/cc where this is also indicated by a low gamma ray log value and a low porosity value caused by the study area consisting the reservoir with lithology in the form of tight sand. Meanwhile, shale lithology is indicated by acoustic impedance values of 17.000 ft/s*g/cc to 25.000 ft/s*g/cc In the sensitivity analysis in the research, a cross-plot porosity (PHIT) logs is used with a color scale of values in the form of a gamma ray log. This is done to see the sensitivity of these parameters in separating shale and sand lithology. In this research, sensitivity analysis is divided into two zones, namely the zone marked in yellow is identified as sandstone lithology or sandstone while the zone marked in blue is identified as shale Based on the results of cross plots on each well it can be seen that the separation of lithologybetween sandstone (sandstone) and shale is considered sensitive because it can separate the boundary between sand and shale contained in the reservoir zone. Lithology of sandstone or sandstone is indicated by an acoustic impedance value of 27.500 ft/s* /cc to /cc where this is also indicated by a low gamma ray log value and a low porosity value caused by the study area consisting the reservoir with lithology in the form of tight sand. Meanwhile, shale lithology is indicated by acoustic 0 ft/s*g/cc to 25.000 ft/s*g/cc where this is also indicated by high gamma ray log values and relatively high porosity values as well.

Time Structure Map
Time structure map making is done to see trends in the research area which will be used in making trend modeling in the stochastic inversion process. Time structure map is obtained from the results of picking top reservoir and base reservoir so that it produces a map of the depth of the reservoir zone in the time domain.
Based on the results of the time structure map on the top reservoir and base reservoir, it is known that the area marked in red has shallow depth or the highest elevation area. Meanwhile, the blue area has a fairly deep depth. On the structure map the top reservoir tim dominant time range of -1100 ms to base reservoir time structure map is known to have a range of -1200 ms to -2100 ms.
From the two time structure maps above, it can be identified that the location of the four peak and it can be identified that the hydrocarbons in the study area migrated from the southeast to the northwest. This is indicated by the contour that represents the lowlands in the southeast and contours that represent the heig northwest. where this is also indicated by high gamma ray log values and relatively high porosity values as well.
Time structure map making is done to see trends in the research area which will be used in making trend models or trend modeling in the stochastic inversion process. Time structure map is obtained from the results of picking top reservoir and base reservoir so that it produces a map of the depth of the reservoir zone in the time domain. results of the time structure map on the top reservoir and base reservoir, it is known that the area marked in red has shallow depth or the highest elevation area. Meanwhile, the blue area has a fairly deep depth. On the structure map the top reservoir time is known to have a 1100 ms to -2100 ms. Meanwhile, the base reservoir time structure map is known to have a range of From the two time structure maps above, it can be identified that the location of the four wells ison the anticline peak and it can be identified that the hydrocarbons in the study area migrated from the southeast to the northwest. This is indicated by the contour that represents the lowlands in the southeast and contours that represent the height in the

Upscaling
Based on the results of acoustic impedance log scale up that has been done on AR-1 wells, AR-2 wells, AR and AR-4 wells it is known thatthere are similarities from the acoustic impedance log data with the acoustic impedance log data that has been done upscaling. This is evident from the results of the histogram that shows similarities to each other so that it can be said that the upscaling process is correct. The acoustic impedance scale up log process is useful to assist in spreading the acoustic impedance values during a stochastic inversion process.

Trend Modeling
Making trend modeling is done by using input in the form of acoustic impedance scale up log data and time structure map. The making of this trend model is done to describe the spatial distribution based on the value of the acoustic impedance scale up log with the trend direction based on the time structure map. The results of the modeling trend are shown in Figure 9. Based on the results of acoustic impedance log scale up 2 wells, AR-3 wells, there are similarities from the acoustic impedance log data with the acoustic impedance log data that has been done upscaling. This is evident from the results of the histogram that shows similarities to each other so upscaling process is correct. The acoustic impedance scale up log process is useful to assist in spreading the acoustic impedance values during a stochastic Histogram analysis scale up the acoustic impedance log Making trend modeling is done by using input in the form of acoustic impedance scale up log data and time structure map. The making of this trend model is done to describe the spatial distribution based on the value of the acoustic up log with the trend direction based on the time structure map. The results of the modeling trend are Based on the results of the trend modeling conducted, it is known that the acoustic impedance value in the a range of values of 10,000 ft / s * g / cc to 50,000 ft / s * g / cc where the high acoustic impedance values are marked with red to green in around the AR-3 well and AR while the low acoustic impedance values are marked in pur to blue around the AR-1 well and AR

Stochastic Inversion
In this study, stochastic inversion was carried out using the Bayesian method approach with a total of 20. Meanwhile, the variogram used was the cubic model. In doing this stoch inversion seismic method is done by using input in the form of acoustic impedance scale up log data and trend models. The results of this stochastic inversion are in Figure 10. Based on the acoustic impedance distribution map using stochastic seismic inversion it is known that the area marked in red is an area that has a high acoustic impedance value with a range of values of 30,000 ft / s * g / cc to 40,000 ft / s * g / cc and is identified as reservoir with lithology in the form of tight sand saturated with hydrocarbons in the form of gas which is also supported by the results of interpretation of data wells that have been carried out in the previous process on AR-1 wells, AR-3 wells, and AR-4 wells that are identified as having a gaseous hydridarbon content.

Depth Structure Map
Depth structure map is obtained from the conversion of time structure map into depth domain. In doing time to depth Based on the results of the trend modeling conducted, it is known that the acoustic impedance value in the study area has a range of values of 10,000 ft / s * g / cc to 50,000 ft / s * g / cc where the high acoustic impedance values are marked with 3 well and AR-4 well area, while the low acoustic impedance values are marked in purple 1 well and AR-2 well area.
In this study, stochastic inversion was carried out using the Bayesian method approach with a total of 20. Meanwhile, the variogram used was the cubic model. In doing this stochastic inversion seismic method is done by using input in the form of acoustic impedance scale up log data and trend models. The results of this stochastic inversion are in Figure 10.
Map of acoustic impedance acoustic impedance distribution on the acoustic impedance distribution map using stochastic seismic inversion it is known that the area marked in red is an area that has a high acoustic impedance value with a range of values of 30,000 ft / s * g / cc to 40,000 ft / s * g / ntified as reservoir with lithology in the form of tight sand saturated with hydrocarbons in the form of gas which is also supported by the results of interpretation of data wells that have been carried out in the previous process on 4 wells that are identified as having a gaseous hydridarbon content.

section of stochastic seismic inversion results
Depth structure map is obtained from the conversion of in. In doing time to depth conversion the stacking velocity method is used which is a method that can convert from time domain to depth domain using the speed model. Making this depth structure map is very important because there are differences between th domains that can cause ambiguity when interpreted where in fact conditions are domain depth, but seismic data has a time domain (TWT). Based on the map of the depth structure of the top reservoir and base reservoir it is known that the prospect area of the four wells is identified to be in the height area in the southeast where it has a depth of 4000 ft to 4500 ft. In the prospect area there are two areas of height in the form of anticline which are in the southeast and northwest. This structure was formed because there is a fault that separates the two height areas. In the research area, there are three main Based on the map of the depth structure of the top reservoir and base reservoir it is known that the prospect area of the four wells is identified to be in the height area in the southeast where it has a depth of 4000 ft to 4500 ft. In the ere are two areas of height in the form of anticline which are in the southeast and northwest. This structure was formed because there is a fault that separates the two height areas. In the research area, there are three main faults namely faults that are southwest are east-west, and faults that are southeast these three faults are identified as normal faults or normal faults. These faults can act as structural traps where hydrocarbons will migrate and are trapped in t traps so that hydrocarbons can accumulate in them.

Isopach Map
Isopach map making is done to describe the thickness of the reservoir layer where this map is made by depth of the top reservoir from the base reservoir. Based on the isopatch map that has been made it is known that in AR wells, AR-3 wells, and AR-4 wells have a thick reservoir layer which is around 300 ft to 450 ft. Meanwhile, the AR has a thinner reservoir layer which is arou isopach map found in Figure 14 it can be said that there was a depletion of the reservoir from the southeast to the northwest.

Conclusion
This study showed that the Bayesian can produce better results than the 27 southwest-northeast, faults that west, and faults that are southeast-northwest where these three faults are identified as normal faults or normal faults. These faults can act as structural traps where hydrocarbons will migrate and are trapped in these structural traps so that hydrocarbons can accumulate in them.
3D map of the structure of the top reservoir depth ch map making is done to describe the thickness of the reservoir layer where this map is made by subtracting the depth of the top reservoir from the base reservoir. Based on the isopatch map that has been made it is known that in AR-1 4 wells have a thick reservoir layer which is around 300 ft to 450 ft. Meanwhile, the AR-2 well has a thinner reservoir layer which is around 210 ft. On the ch map found in Figure 14 it can be said that there was a depletion of the reservoir from the southeast to the northwest.

Isopach Map
Bayesian stochastic inversion can produce better results than the deterministic inversion.
W Because of the smoothness and average, the deterministic inversion was unsuitable for constraining reservoir models when this model was used for volumetric calculati estimation of connectivity, and individualization of sand bodies or fluid flow simulation Based on the results, it is known that the hydrocarbon prospect zone has a high acoustic impedance value ranging from 30,000 ft/s * g/cc to 40,000 ft/s * g/cc wh of 4,000 ft to 4,500 ft. This is due to the reservoir of the study area which is dominated by tight sandstone lithology which contains gas and has a low porosity value.
Finally, the Bayesian stochastic inversion efficiently improved the reservoir characterization process by not only producing accurate estimation of the low heterogeneities but also generating outcomes that help study the uncertainty analysis.