Capillary Pressure Curves from Centrifuge Data: A Semi-Iterative Approach |
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Authors: | S Subbey J-E Nordtvedt |
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Institution: | (1) Department of Pet. Engineering, Heriot-Watt University, Edinburgh, EH14 4AS, UK;(2) Department of Physics, University of Bergen, Allegt. 55, N-5007 Bergen, Norway |
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Abstract: | The problem of determining capillary pressure functions from centrifuge data leads to an integral equation of the form
a
x
K(x,t)f(t) dt=g(x),x a,b],(1)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 x
1,...,x
M
. 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+ ,where b is the observation vector and A arises from discretization of the forward problem. 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 2-norm, namely, Brakhage's -method 2], is investigated. The iterative method is tested on synthetically generated, and on experimental data. |
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Keywords: | capillary pressure ill-posed inverse regularization semi-iterative |
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