Computational mathematics find use in subsurface modeling

The need to understand how particles and molecules of various reactants behave on the molecular level has driven Guang Lin, a computational mathematics doctoral student at Brown University and research scientist at the Pacific Northwest National Laboratory, to develop models of these reactions. Geomechanical modeling is critical in petroleum engineering because so many of the aspects of extracting and transporting crude oil and gas involve controlling continuous reactions between the oil and the various trace biochemicals present in pipelines and storage tanks.

The primary way to model the molecular interactions is known as Dissipative Particle Dynamics (DPD). DPD simulations essentially average out the atoms in simple and complex fluids, treating molecules as an individual particle. The model can then “see” the process with significantly less computational power than if each individual atom were analyzed. This modeling technique also allows for longer time scales, enabling a more complete data set. Lin explained that this modeling technique is very useful in modeling the formation and growth of biofilms in various environments. “There is biofilm in everyday life, so we need to develop a model for biofilm growth.” Biofilms form on the inside of pipes, on boat hulls, and in other areas, and the DPD model allows the viewing of the reactions taking place and helps to better understand how the film forms and grows.

The DPD model allows for close examination of pore surface reactions, enabling a better view of how the reactants contribute to biofilm growth and corrosion on material surfaces. The large scale of pore reactions allows for a more generalized look at the reactions themselves, but also makes it more difficult to account for the uncertainties in the model itself. Lin explained that there is a need for accurate uncertainty estimation, because the computational power required for these models means that a lager-scale model with good uncertainty estimation would be preferable.

The dynamic numerical models used are notoriously difficult and expensive when it comes to uncertainty calculations, because of the immense computational power required. Lin has begun working on implementing what he calls eSTOMP, a scalable subsurface simulator. The simulator allows for dynamic uncertainty estimation, as well as optimization for more detail and shorter time scales, or less detail and longer time scales and a more complete data set. Lin showed how computational mathematics open up a world of possibilities in subsurface modeling, which has applications in many fields beyond just petroleum engineering.