Uncertainty in Thermal Basin Modeling: An Interval Finite Element Approach

Uncertainty assessment in basin modeling and reservoir characterization is traditionally treated by geostatistical methods which are normally based on stochastic probabilistic approaches. In this paper, we present an alternative approach which is based on interval arithmetic. Here, we discuss a fnite element formulation which uses interval numbers rather than real numbers to solve the transient heat conduction in sedimentary basins. For this purpose, a novel formulation was developed to deal with both the special interval arithmetic properties and the transient term in the differential Equation governing heat transfer. In this formulation, the “stiffness” matrix resulting from the discretization of the heat conduction equation is assembled with an element-by-element technique in which the elements are globally independent and the continuity is enforced by Lagrange multipliers. This formulation is an alternative to traditional Monte Carlo method, where it is necessary to run a simulation several times to estimate the uncertainty in the results.We have applied the newly developed techniques to a one-dimensional thermal basin simulation to assess their potential and limitations.We also compared the quality of our formulation with other solution methods for interval linear systems of equations.