Let's continue talking about Reservoir Geostatistical Modeling. The pivotal role of Geostatistical Modeling in the general framework of Static and Dynamic Reservoir Characterization is well known. It is also well known that constructing a Geostatistical Model is time-consuming, complex, and challenging. As discussed in my first post, it requires the integration of multiple complex datasets of variate scales, data preparation, feature engineering, etc.
Once the Base Case of the Geostatistical Model has been completed, a reliable (usually very large) number N of realizations is required to successfully represent the subsurface complexities, its intrinsic heterogeneity-variability, and above all, access and quantify the key uncertainties that propagate from inputs through the whole model-building process itself. So, a WHOLE SET of N stochastic realizations, NOT a single one, is required to build a solid and predictive Model of the Reservoir (see Geostatistical Reservoir MOdeling by Clayton Deutsch).
It must be emphasized: the N geostatistical realizations, not a single one, are as a whole THE MODEL of the RESERVOIR.
To estimate this number N of reañizations, it's required to carry out a Monte Carlo process where probability distributions are assigned to the reservoir variables that contribute the most to model uncertainty. Typically the metric selected to perform this process is the Original Oil In Place or STOIIP.
Then, a histogram of the STOIIP is built, and realizations are added systematically, as shown in the animation above until a bell-shaped histogram is obtained (Central Limit Theorem); at this point, the corresponding number N of realizations (or greater) is considered good enough, and reliable to represent and quantify the Geostatistical Model uncertainty.
As mentioned before, this FULL SET of N realizations ALWAYS will be required to MAKE PREDICTIONS regarding the static and dynamic performance of the reservoir. Indeed, the N realizations must be used to evaluate key Statistical Summaries, namely, reservoir volumes ( STOIIP), Probability and Joint-Probability Distribution volumes, etc. In the dynamic instance (fluid-flow simulation), it is a regular practice to consider p10, p50, and p90 percentiles realizations, which are obtained after the already described ranking process of the N geostatistical realizations (see animation above).
Carrying out the previous process is of paramount importance in any reservoir modeling task, particularly regarding the modeling of mature fields. In this scenario, a proper quantification and analysis of uncertainties are imperative to successfully address the issues of delineation of By-passed Oil/Gas areas, and perform a valid volumetric evaluation of the remaining hydrocarbons.
Before making predictions, it is also a good practice to check and recheck the model using Minimum Acceptance Criteria and any relevant-independent data/information at hand. As an example, results of a Geochemical study (MICROscopic scale), and results of interpretation of Seismic Inversion Volumes (MACROscopic scale), were available and used to validate and cross-check the model.
The top of the figure below depicts well (a) and well (b). In both wells, a comparison of synthetic-STOIIP-log (on the right track) evaluated using the Model of the Reservoir and the presence of Kerogen/Organic Matter reported by the microscopic geochemical analysis (second track, from right to left), is made. A remarkable correspondence shows up.
Next, at the bottom of the figure, in well (c) the synthetic-STOIIP-log (on the right track) is compared now with Inversion-Seismic-derived and original well logs (Seismic Attributes and AVO were also considered). Again, a solid correspondence is obtained, particularly at the top of the interval. The prediction power of the model has been tested successfully at both extremes of the scale.
Techniques and methods like those presented here could be directly adapted, as I have already done in previous posts, to be applied in other domains of knowledge: MINING INDUSTRY, PUBLIC SECURITY, RETAIL, etc.
Please leave your comments below, and kindly share and contact me if you require additional information. I'll be glad to answer all your questions.
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