Particle Size Distribution Correction Method Using a Simulated Annealing Technique

The procedure for obtaining the particle size distribution by visual inspection of a sample involves stereological errors, given the cut of the sample. A cut particle, supposedly spherical, with radius R, will be counted as a circular particle with radius r, r <= R. The difference between r and R depends on how far from the center of the sphere the cut was performed. This introduces errors when the extrapolation of the properties from two to three dimensions during the analysis of a sample. The usual method is to correct the distribution by probabilistic functions, which have large errors. This paper presents a method to reduce the error inherent to this problem. The method is to compute a simulation of the preparation process in a sample whose structure can be described by non-penetrating spheres of various diameters which meet a known probability distribution function, for example, a log-logistic function, or even a constant function. For each distribution radius, a number of spheres is generated and virtually cut, generating a bi-dimensional (2D) distribution. The 2D curves of the spheres distribution obtained in this simulation are compared with that obtained by the experimental procedure and then the parameters of the three-dimensional distribution function are adjusted until the 2D curves are similar to the experimental one using the optimization method Simulated Annealing for the curve-fitting. In future this method will be applied to the analysis of the oil reservoir rocks.