Velocity Estimation in Mixtures using Tomography

Abstract

In oil production a lot of water is usually pumped up together with the oil. For many reasons the reduction of the water production is a very important issue. The method presented in this paper is meant to provide a necessary tool for this. Most drilling wells consist of a network of bore holes. Some of them may produce water, others oil or a mixture. At the moment the net flow of all bore holes together is brought to the surface. It is desirable to be able to detect how much water a specific bore hole contributes. If this amount surpasses a critical value one could then consider to close that bore hole. This leads to the question how the composition of the flow in a pipe can be determined in situ. In this paper we analyze how tomography techniques, well-known from medical applications, can be applied in the case of a bore hole. These techniques allow to measure instantaneously the mass distribution over a cross section of the pipe. For velocity estimation, the idea is to detect the mass distributions at two neighbouring cross sections at successive times. Correlating the obtained time series, one might be able to estimate the local velocity profile. The basic idea was already mentioned in literature before, but it was believed that the number of correlations to be evaluated is so huge, that the approach would fail in practice. In this paper we describe the mathematical details of the method and conclude that the number of time consuming calculations is not necessarily a limiting factor. In addition, suggestions are made to facilitate the use of tomography for velocity estimation.