Multiscale Analytical Derivative Formulations for Improved Reservoir Management

The exploitation of subsurface resources is, inevitably, surrounded by uncertainty. Limited knowledge on the economical, operational, and geological setting are just a few instances of sources of uncertainty. From the geological point of view, the currently available technology is not able to provide the description of the fluids and rock properties at the necessary level of detail required by the mathematical models utilized in the exploitation decision-making process. However, even if a full, accurate description of the subsurface was available, the outcome of such hypothetical mathematical model would likely be computationally too expensive to be evaluated considering the currently available computational power, hindering the decision making process.

Under this reality, geoscientists are consistently making effort to improve the mathematical models, while being inherently constrained by uncertainty, and to find more efficient ways to computationally solve these models.

Closed-loop Reservoir Management (CLRM) is a workflow that allows the continuous update of the subsurface models based on production data from different sources. It relies on computationally demanding optimization algorithms (for the assimilation of production data and control optimization) which require multiple simulations of the subsurface model. One important aspect for the successful application of the CLRM workflow is the definition of a model that can both be run multiple times in a reasonable timespan and still reasonably represent the underlying physics.

Multiscale (MS) methods, a reservoir simulation technique that solves a coarser simulation model, thus increasing the computational speed up, while still utilizing the fine-scale representation of the reservoir, figures as an accurate and efficient simulation strategy.

This thesis focuses on the development of efficient algorithms for subsurface models optimization by taking advantage of multiscale simulation strategies. It presents (1) multiscale analytical derivative computation strategies to efficiently and accurately address the optimization algorithms employed in the CLRM workflow and (2) novel strategies to handle the mathematical modeling of subsurface management studies from a multiscale perspective. On the latter, we specifically address a more fundamental multiscale aspect of data assimilation studies: the assimilation of observations from a distinct spatial representation compared to the simulation model scale.

As a result, this thesis discusses in detail the development of mathematical models and algorithms for the derivative computation of subsurface model responses and their application into gradient-based optimization algorithms employed in the data assimilation and life-cycle optimization steps of CLRM. The advantages are improved computational efficiency with accuracy maintenance and the ability to address the subsurface management from a multiscale view point not only from the forward simulation perspective, but also from the inverse modeling side.