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Uncertainty in Thermal Basin Modeling: An Interval Finite Element Approach

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Reliable Computing

Abstract

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.

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Authors and Affiliations

  1. PETROBRAS R&D Center, Rua Jequitibá 950, Cidade Universitária, Ilha do Fundão, Rio de Janeiro, RJ, 21941-598, Brazil

    Sebastião C. Pereira

  2. IBM Thomas J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY, 10598, USA

    Ulisses T. Mello

  3. Federal University of Rio de Janeiro, P.O. Box 68506, Rio de Janeiro, RJ, 21945-970, Brazil

    Nelson F. F. Ebecken

  4. Center for Reliable Engineering Computing (REC), School of Civil & Environmental Engineering, Georgia Institute of Technology, 210 Technology Circle, Savannah, GA, 31407-3038, USA

    Rafi L. Muhanna

Authors
  1. Sebastião C. Pereira
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  2. Ulisses T. Mello
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  3. Nelson F. F. Ebecken
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  4. Rafi L. Muhanna
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Correspondence to Sebastião C. Pereira.

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Pereira, S.C., Mello, U.T., Ebecken, N.F.F. et al. Uncertainty in Thermal Basin Modeling: An Interval Finite Element Approach. Reliable Comput 12, 451–470 (2006). https://doi.org/10.1007/s11155-006-9014-5

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  • DOI: https://doi.org/10.1007/s11155-006-9014-5

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