Estimation of Reservoir Properties by Monte Carlo Simulation

The shallow gas zone in the Pantai Pakam Timur (PPT) field, located in Northern Sumatra, Indonesia, has recently become an important target for development. However, only two wells were drilled in peripheral part of the field. In this situation the method of Geostatistics is hardly applied because of less control points, but there is a new suitable method to estimate reservoir properties under the condition of such few control points (GDI: Geology Driven Integration Tool). To compensate few controls, GDI creates pseudo-wells by Monte Carlo Simulation method with regional geological constraints in its regulation, and generates theoretical seismic traces from them. Then the suitable seismic attributes are selected after checking the proportionality with the given reservoir property. Finally the artificial neural network (ANN) is applied to detect the weighting factors, which relate the selected seismic attributes to the given physical reservoir properties. We apply this method to the 2-D seismic records in the PPT field to extract successfully the distribution of porosity and thickness of the gas sandstone reservoir. The most prospected area is figured out in the southern part of the field, where the net thickness of gas zone is estimated to increase 27 meters with fairly higher porosity of 28%, which can be fairly confirmed by the well proposed and drilled by this study. Once getting the distribution, it is easier to calculate the total rock volume of the target reservoir under non-homogenized situation, and hence to progress on estimating more precise volume of reserves in place. Thus this method has an advantage in estimating reservoir characters from a few well data in the early development stage, or even in the late exploration stage. It is certainly important for asset managing that new idea should save the cost even in the stage of exploration. Introduction The Pantai Pakam Timur (PPT) gas field is located about 17 km to the Northwest of Medan, Northern Sumatra (Fig. 1), and was discovered in 1979 where two main reservoir horizons were recognized. It was under development mainly for the deep reservoirs for which some economical difficulties have been found in the later stage. The total of 6 wells have been drilled since 1979 in the study area,. In recent years, the shallow gas zone (called here as 1275 m zone) becomes important as a developmental target, even though the reserve may be critical. The wells PPT-5 and PPT6 were drilled at the almost same locations as PPT-2 and PPT1, respectively, for developing the shallow gas reservoir as a target. These wells were successful in finding gas columns of 5 m+ at PPT-5 and 19 m at PPT-6. However, we need more development wells to be drilled for efficient recovery. This is the most suitable setting to apply Monte Carlo Simulation for estimating the reservoir characteristics over the field, where the usual geostatistics method cannot be applied because of too small number of known data points. The objective of this study is to estimate lateral distribution of reservoir properties, using seismic data as useful guide in interpretation under this condition. Reservoir characterization software (de Groot et al., 1996) was applied for this purpose, and the reserves will be re-evaluated. Geological Background of PPT Field Seismic facies of the target gas reservoir has to be characterized and correlated over the field with consideration of the regional litho-facies in mind. To do this, the synthetic seismograms of the wells PPT-6 are over-plotted on the appropriate seismic sections (Fig. 2) to find out the suitable seismic wavelet for the study. On the seismic sections there is a small fault between PPT-5 and PPT-6. However, the reservoirs between both can be believed to communicate each other, hence it is interpreted that blocks have a same gas/water level. Therefore, we neglect the fault on the following maps for this study. We draw the top horizon of 1275 m Sandstone following the interpretation considered for the tuning effect. Also we define the gas/water contact on the seismic sections. Then both horizons are carefully converted into the depth domain where the gas/water contact level is set to -1260 m (Fig. 3). The broad and higher domal structure appeares in the southern part SPE 59408 Estimation of Reservoir Properties by Monte Carlo Simulation Kazuo Nakayama/JGI, Inc. 2 NAKAYAMA SPE 59408 over which we had recorded a prominent AVO phenomenon in the previous study (Pertamina, 1996). Monte Carlo Simulation Methodology. To assign property values to the seismic interpretation in general, it is necessary to combine seismic attributes with reservoir properties and to find relationship between them. After establishing the relationship, we can apply it to the whole seismic volume to obtain reservoir properties. The problem, however, is that there are only few well data which can be used as sample data to find the relationship. In our Monte Carlo Simulation tool, many pseudo wells are generated by using Monte Carlo simulation to make the sample data set bigger (de Groot et al., 1996). By giving geologic constraints to the simulator, we can control the simulation and generate only plausible pseudo wells, eliminating unrealistic ones. For each of the simulated pseudo wells, log and synthetic seismogram are generated and they are used as sample data in addition to the factual well data. Then the artificial neural network (ANN) is used for finding the relationship between seismic attributes and well log properties at both factual and pseudo well positions. Neural network is data-driven computing technique to find out nonlinear relationships. We let neural network learn a non-linear model using sample data (training network), and the trained network is applied to the seismic data to obtain the lateral predictive results. Simulating pseudo wells. In the PPT field, total seven (7) wells were drilled to date, but there are only two well data available for the 1275m reservoirs. We need more data to establish the relationship between seismic attributes and reservoir properties. To check how reservoir properties influence seismic attributes, we firstly generated several sets of pseudo wells based on simple models (Model 1 to 3) where only one variable is changed. Then Monte Carlo Simulation (Model 4) takes place where three variables are changed simultaneously. These pseudo wells are used for finding the relationship. Model 1: Changing gas column height (Fig. 4). Total 40 pseudo wells were generated in which gas column height changes from 20 m to 0 m. Other reservoir properties of these pseudo wells are taken from the average values of the factual wells, i.e. a 20 m-thick sand with 25 % porosity and 40 % water saturation. Synthetic seismograms for the pseudo wells were also generated. Fig. 4 reveals seismic polarity shift at the top of the target sand. The top of gas sand corresponds to black peaks where gas column is thick enough, whereas that of very thin gas sand or water sand becomes to white troughs. The interpretation of top of gas sand on the seismic section thus does not always follow the same peak, and must be carefully traced. This is called ‘Tuning Effects’ caused by moderately thin gas sands. The structural interpretation in the previous section has accounted for this effect. Model 2: Changing gas sand porosity (Fig. 5). In this model, porosity of the 20 m-thick gas sand is changed from 25 % to 10 %. Water saturation is fixed to 40 %. It should be noted that the black peak at the top of the gas sand appears only when the sand has porosity of 23 % or more. The bright spot phenomena (black peaks at the top of the gas sand) throughout the culmination on the seismic section suggest that porosity of the sand is more than 23 % in the whole area. Model 3: Monte Carlo simulation (Fig. 6). Monte Carlo simulation is used to generate 500 pseudo wells based on a more complex model. Sand thickness, gas column height and porosity are changed simultaneously, based on the factual well data and other geological knowledge. Other values are fixed to the average of the factual well data. The reason why we changed only three properties is that changing too many properties results in difficulty in finding the relationship. Water saturation, for example, which is one of the most important reservoir properties, is also fixed to 40 % because it causes the same effect to seismic attributes as porosity does, and it is difficult to distinguish each other. Training neural network. Artificial neural network (ANN) is used for finding the relationship between seismic attributes and reservoir properties, which is extracted from the pseudo wells generated by Monte Carlo Simulation (Fig. 6). The advantage of neural network for finding the relationship is that it can manipulate multi-variable problems without knowing the theory or principles behind them. Basic algorithm of neural network is to determine the best fitting weights in the following equation by training sample data set. y(x) = Ówi fi (x) where x is the input (seismic attribute), y(x) is the output (reservoir property), fi (x) is the basic function, wi is the weights and i is the number of node. In this study, we selected nine (9) seismic attributes for the inputs and two (2) reservoir properties for the outputs (gas column height and average porosity of the sand) after the plot of possible data sets (Fig. 7), and use Multi-Layer-Perceptrons network of five (5) sigmoidal type nodes. See other references for the details of neural network technique (Shultz et al., 1994a, 1994b; Ronen et al., 1994). Fig. 8 is the neural network and its performance trained by the pseudo wells which is generated by the Monte Carlo Simulation (Model 3). Nodes are colored relative to their contribution to the outputs, where dark nodes indicate to be most important whereas light ones are less important. The curves showing network performance (right-down portion of Fig. 8) indicate strong relationship between gas column height and seismic attributes, suggesting prediction result is reliable. On the other hand, the relationship between sand porosity and seismic attributes is rather weak, suggesting prediction result is less reliable. Now we determine every weighting factor in the equation, establishing neural network. SPE 59408 ESTIMATION OF RESERVOIR PROPERTIES BY MONTE CARLO SIMULATION 3 Applying neural network. The established neural network (equation with known weights) was applied to the attributes readable from the real seismic data to obtain gas column height and sand porosity along the seismic lines. These predictive results were calibrated so that the consistency remains at the factual well locations. Then the contouring routine was applied with the Kriging Analysis on these results of more than 300 points over the area (Figs. 9 & 10). Based on variograms for eighteen directions with ten degree step, both properties show anisotropy with N70W and N20E. The variogram of N20E shows the best spatial correlation in the eighteen directions and that of N70W shows the worst spatial correlation. Fig. 9 depicts thicker (up to 27 m) gas sand to the south of PPT-1. The fact that this area is corresponding with the structural high strongly suggests the existence of a gas sand. Porosity of the gas sand ranges from 23 % to 27 % (Fig. 10). It tends to become higher to the north and to the south of PPT-6. Note that the derived porosity is the equivalent, assuming the water saturation to be 40 %. The thickness of gas sand is considered to be net vales and the estimated porosity to be averaged within the net pay zone because they might be intercalated with thin waste layers which are negligible. Reserve Estimation Using our final map showing the distributions of gas thickness (Fig. 9) and porosity (Fig. 10), we can easily calculate the reserves by summing up the gas volume at each grid point (in this study the grid interval is set to be 100 m). The estimated reserves is over 110 BCF. The previous estimation was 1781 MMm (= 63 BCF). There are some basic differences on the constant parameters; The water saturation (Sw) and porosity (φ) set to be 37 % and 20 %, respectively, for the previous study, whereas they are set to be 40 % and 25 % (average, variable to grid to grid), respectively, for this study. Considering the effect from this difference, we re-calculate the previous estimate to be 2120 MMm (= 75 BCF) using Sw = 40 % and φ = 25 %. The correction factor of 0.84 (= 1781/2120) indicates the error caused by the difference of estimation of Sw and φ. Therefore, we apply this correction factor to the reserves estimated here, and obtain the amount 92 BCF (= 110 BCF * 0.84). This number is considered to be a reserve caused by a volumetric increase resulted from this study with previous parameter values for Sw and φ. In conclusion for the reserve estimation, this study shows some increase of available volume which could be occupied by gas. The estimated reserves for the field may increase to be 92 BCF or 110 BCF at maximum. The result from this study implicates at least that a large domal structure with some local culminations may exist in the southern part of the PPT gas field. Conclusions In this study, we try to re-evaluate the reservoir extension of the shallow gas zone in Pantai Pakam Timur (PPT) gas field using a new method of reservoir characterization by Monte Carlo Simulation before some development stage starts. The new well was drilled later at the location suggested from this study. The result is quite agreeable with the estimation (21-24 m of prediction versus about 21 m of observation)(see the location of PPT-7 in Fig. 9). The points cleared by this study are follows; Monte Carlo Simulation was successfully applied to the real gas field to determine the distribution of basic reservoir characteristics (net thickness of gas sand and averaged porosity). In this study, we estimate the various seismic expressions from the theoretical modeling of pseudo-wells by randomly changing two parameters, gas column thickness and porosity. Using artificial neural network, then, the relationship of seismic expression and the parameters are established, and the distribution can be inferred through the observed seismic records. In applying Monte Carlo Simulation method, the volume estimation is also obtained considering the heterogeneity of the reservoir property over the field. According to the final maps, the total estimated reserves by summing up the volume of gas at each grid point is 92 to 110 BCF, which is 50% more than the previous estimations. Acknowledgments We thank Indonesia Nippon Oil Cooperation Co, Ltd. (INOCO) for giving us an opportunity to apply the model to the real field, and for permission for publication. Our thanks are also toward Pertamina for permission of this article.