Capillary pressure curves from centrifuge data: A semi-iterative approach

S. Subbey, J. E. Nordtvedt

    Research output: Contribution to journalArticle

    5 Citations (Scopus)

    Abstract

    The problem of determining capillary pressure functions from centrifuge data leads to an integral equation of the form ?xa K (x.t) f(t)dt = g(x). x ? [a.b]. where the kernel K is known exactly and given by the underlying mathematical model. g is only known with a limited degree of accuracy in a finite and discrete set of points x1.....XM. However, the sought function f(t) is continuous. By the nature of the right-hand side, g(x), equation (1) is a discrete inverse problem which is ill-posed in the sense of Hadamard [9]. By a parameterization of the sought function, equation (1) reduces to a system of linear equations of the form Ac = b + e. where b is the observation vector and A arises from discretization of the forward problem. e is the error vector associated with b, and c contains the model parameters. The matrix A is usually ill-conditioned. The ill-conditioning is closely connected to the parameterization of the problem [23]. In this paper a semi-iterative regularization method for solving the Volterra integral equation in the e2-norm, namely, Brakhage's v-method [2], is investigated. The iterative method is tested on synthetically generated, and on experimental data.

    Original languageEnglish
    Pages (from-to)207-224
    Number of pages18
    JournalComputational Geosciences
    Volume6
    Issue number2
    DOIs
    Publication statusPublished - Jun 2002

    Keywords

    • Capillary pressure
    • Ill-posed
    • Inverse
    • Regularization
    • Semi-iterative

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