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 talk, an alternative interval-based approach will be present. A solution for the transient heat conduction in sedimentary basins will be introduced using an interval finite element approach. For this purpose, a novel formulation is 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 using an element-by-element technique in which the finite elements are globally independent and lagrange multipliers are used to enforce continuity. This formulation is suggested as an alternative to traditional Monte Carlo method, where repetitive simulations are required to handle uncertainty and worst case system response is underestimated. The newly developed technique is applied to a one-dimensional thermal basin simulation to assess its potential and limitations. Numerical results will be introduced and their quality assessed. 1 Introduction Determinist numerical simulations are normally used to predict the behavior of geological systems. The predicted behavior or performance is normally used for risk assessment. A well known limitation of determinist simulations is that they provide a single set of results that do not convey information about the uncertainty associated with input parameters or coefficients. To overcome this limitation, uncertainty assessment is typically coupled with stochastic probabilistic approaches in which the input simulation parameter set is stochastically defined and multiple simulations are executed to estimate the uncertainty associated with a probabilistic distribution of the input parameter set space. While effective, this approach is rather expensive computationally. In addition, in deterministic numerical simulations, such as the traditional finite element approach, all the parameters are assumed to be precisely known. However, frequently in basin modeling this is not the case, since imprecise or fuzzy information may be present in the geometry, age, and material properties of the basin. Stochastic or probabilistic approaches have been developed to account for this kind of uncertainties. However, in these approaches material properties are normally treated as