Capillary pressure curves from centrifuge data: A semi-iterative approach
The problem of determining capillary pressure functions from centrifuge data leads to an integral equation of the form integral(a)(x)K(x,t)f(t) dt=g(x), xis an element of[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+ epsilon, (2) where b is the observation vector and A arises from discretization of the forward problem. epsilon 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 l(2)-norm, namely, Brakhage's nu-method [2], is investigated. The iterative method is tested on synthetically generated, and on experimental data.
capillary pressure semi-iterative inverse ill-posed regularization