Value of information analysis for time-lapse seismic data in reservoir development
Keywords: Energy Resources Engineering.

A framework to evaluate the value of information (VOI) for spatial problems in the earth sciences is presented, and a computationally efficient methodology is proposed to evaluate the VOI using the framework. The VOI is a decision-analytic metric that quantifies the additional value that could be created by collecting information before making a decision, and it is the highest amount that the decision-maker should be willing to pay to collect the information. Time-lapse seismic data is often acquired to aid in making reservoir development decisions like well placement decisions or well control decisions, but does the data generate enough additional revenue to justify its cost? This question can be answered by evaluating the VOI of time-lapse seismic data in the context of making reservoir development decisions. VOI problems in the earth sciences require special formulation because the uncertain variables of interest, the data and the decision alternatives are usually high-dimensional spatial variables. In the case of VOI analysis of time-lapse seismic data, the uncertain variables of interest are the reservoir properties like porosity, permeability, saturation, etc. that affect the production and thereby the prospect values. The decision might be a well placement decision or a well control decision. The VOI can be assessed as the interplay between three main components: the prior uncertainty, the reliability of the information and the decision situation comprising alternatives and prospect values. The VOI framework presented in this thesis represents the prior spatial uncertainty in the reservoir properties using an ensemble of realizations. The information reliability is implicitly modeled using conditional expectations of the prospect values on the data outcomes. Since the VOI analysis has to be done a priori, i.e. before actually collecting the information, the conditional expectation of the prospect values for every possible dataset has to be taken into account. This makes the rigorous Monte Carlo workflow computationally intractable for evaluating the VOI in complex, high dimensional cases. Therefore, we propose a computationally efficient workflow called simulation-regression to compute the VOI in such cases. Rather than estimating the conditional expectation of the values given the data by building a posterior distribution of reservoir properties for each dataset, simulation-regression seeks to directly estimate the conditional expectation by regressing the values on the data. In a reference case presented in this work, simulation-regression is found to be two orders of magnitude less computationally expensive than the rigorous Monte Carlo workflow, while giving similar results as the rigorous workflow. We demonstrate the simulation-regression methodology using three realistic cases. The VOI of time-lapse seismic data in the context of a reservoir development decision involving the choice of a drilling design alternative is computed using Partial Least Squares Regression (PLSR), Principal Components Regression (PCR) and random forests. Another case demonstrates the use of simulation-regression when the number of decision alternatives is infinite. This case, involving sequential well placement and well control decisions, incorporates the role of optimization in choosing the decision alternatives, which is likely in real field cases. To make the large number of optimizations computationally feasible, a flow diagnostic proxy, namely Lorenz coefficient, is used in the optimization. The third and final case illustrates VOI computation using simulation-regression for a reservoir development decision inspired from the Gullfaks field in Norway. The prior uncertainty is modeled using real field data, but the decision alternatives are not the actual alternatives that were considered in the field. So, this case only serves as a demonstration of the simulation-regression workflow.