Modelling of unstructured problems in well drilling

Abstract

The use of information analysis procedures in solving complex problems is one of the main stages in the design of the information system for a studied phenomenon. It means that for the systematic evaluation of the parameters of different nature, the system’s objectives are structured. One of the decision-making methods in the study of multi-criteria problems is the hierarchy analysis proposed by the American scientist T. Saaty. According to Saaty, the method "is a closed logical construction that, by using simple rules, ensures analysis of complex problems in all their diversity and leads to the best solution." The method consists in decomposing the problem into simpler parts with further expert evaluations of the components and mathematical processing of the expert judgments. This article illustrates the capability of the hierarchy analysis in considering the problem of the cuttings transport along the borehole of a controlled directional well with a large deflection of the vertical. The problem is modeled as a hierarchy that is considered complete when each element of a specified level works as a criterion for the elements of a lower level. The relative importance of the criteria is defined using a paired comparison matrix that allows us to estimate the true weight of each element and determine the degree of its importance. The modelling has defined the matrix eigenvector that indicates the importance order of the compared objects in quantitative terms. The maximum eigenvalue of the matrix approximately equals to the matrix order, which (based on the requirements) allows us to classify the matrix as homogeneous. The given algorithm of the hierarchy analysis application allows us to estimate the weights of the influencing factors and the generalized characteristics of the variants for the problems of cuttings removal when drilling directional wells.