Using machine learning to estimate reservoir parameters in real options valuation of an unexplored oilfield

This paper is part of a research aims to develop a realistic valuation model of an unexplored oilfield using real options approach. We consider several sources of uncertainty, i.e. exploration outcome, reserve volume and production rate, oil prices, and interest rates. We make a realistic assumption for each uncertainty source. Exploration outcome follows a Bernoulli probability distribution, oil prices follows a two-factor mean-reverting process (the Schwartz-Smith model), and interest rates follows the Cox-Ingersoll-Ross model. Reserve volume and production rates are estimated using the compressible-liquid tank model with probabilistic reservoir and operational parameters. The complexity of the problem requires us to use Monte Carlo simulation to obtain the solution. An initial investigation using data from a particular reservoir found that 80% of the variance of the oilfield value was due to uncertain reservoir condition. We also found that if we could estimate those parameters accurately, the tank model has given close approximations on the reserve volume and production rates. The previous work on this issue suggested to generate parameter values from ‘similar’ reservoirs, where similarity was inferred based on lithology and depth. The probability dstribution of the parameters are assumed to be lognormal. We found this approach was rough and inaccurate. This motivated us to develop two different models to estimate those parameters. Our first model is an extension of the previous work using the Gaussian copula. In this model, instead of assuming lognormal probability distribution as in the previous work, we test the data against all possible distribution and choose the fittest one for each parameter. Association between parameters is modeled using the Gaussian copula. Our second model uses the exhaustive CHAID (Chi-square Automatic Interaction Detection) algorithm aims to estimate the net pay, porosity, initial oil saturation, initial oil formation volume factor, permeability, viscosity, initial pressure, and bottomhole pressure based on data assumed to be available prior to exploration, i.e. lithology, depth, deposition system and its confidence level, diagenetic overprint and its confidence level, structural compartmentalization and its confidence level, element of heterogeneity, and trap type. Other parameters like shape factor, skin factor, water compressibility, oil compressibility, and formation compressibility assumes some particular values. We use reservoir data from the Tertiary Oil Recovery Information System (TORIS) database to develop the models. We derive the CHAID model using data from 501 reservoirs which randomly divided into training set (70%) and test set (30%). We do not directly use the predicted values from the model. Instead, we use the algorithm to identify reservoirs that shared the same characteristic regarding a particular parameter, out of which the values of the parameters are generated during the simulation. We compared the results from both models and found that the CHAID-based model are more accurate. The novelty of this research comes from the use of machine learning to predict the values of parameters needed to estimate reserve volume and production rates in the valuation model of an unexplored oilfield. This contibutes in reducing uncertainty in the valuation of such risky assets.