This study addresses a few issues regarding the experimental design and analysis (EDA) methods, and its applications in multiple deterministic modelling to quantify hydrocarbon in-place (HCIIP) probability distribution curves. They include (1) the suitability of using Latin Hypercube design (more than 3 levels in the input variables) compared with the 3-level fractional factorial designs (FFD) (e.g. 2k-p FFD with centre & axial runs); (2) multidimensional kriging versus response surface method as the analysis technique to fit surrogate equation models; (3) the selection of test runs to evaluate the fitted surrogate equation models; (4) sensitivity of the assigned input probability values on the output response distribution curve; (5) the confidence interval of the cumulative probability distribution curve at median (P50) or other percentiles (e.g. P10 & P90); and (6) how to select representative 3D geological models at P10, P50 and P90.

In this study, an Excel spreadsheet, which mimics the 3D geological modelling workflow to estimate the oil in-place volume, is used to compare the above mentioned designs and analysis techniques. Some guidelines to select representative test runs/models to evaluate the fitted surrogate equation models are discussed. In multiple deterministic modelling, all the input uncertainties will normally be quantified with an uncertainty range from low, base to high values, and with their assigned probability values. Then, a decision tree can be built to visualise the full range of all the possible 3D geological models, and their respective probability of occurrence can be calculated from the probability of the input uncertainties. Combining the probability and the predicted responses from the evaluated surrogate equation model, the output response (e.g. oil in-place) probability distribution curve can then be built. Sensitivity of the input probability values on the output response distribution curve is briefly discussed. There will be some errors associated with the predictions from the surrogate equation models, and therefore confidence interval must be generated to account for them. With the P10, P50 and P90 output response values, the confidence intervals and the probability of occurrence, some representative 3D geological models at P10, P50 and P90 can be selected.

A 3D multiple deterministic modelling case study is then used to demonstrate the methodology in estimating the oil in-place distribution curve of a synthetic reservoir that is adopted from an actual fluvial reservoir.

In conclusions, the EDA methods can be used to minimise the number of 3D geological models that must be generated to build good HCIIP probability distribution curves. By using bootstrapping and normal confidence interval, fitting errors can be quantified and representative 3D geological models for P10, P50 and P90 values can be selected accordingly.

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