Dominant Communication Trends Determined by Nonparametric Statistics
Authors: De S. Pizarro J.O. , Lake L.W. , Firoozabadi A. 
Published: March 2010

Abstract
This paper addresses the use of the Spearman rank coefficient, a nonparametric statistical method, to estimate lateral autocorrelation and permeability trends. This approach provides an alternative to interference tests considering only production and injection rates. The objectives of this work are to validate this technique, point out its advantages/limitations and show results from its application to a field.
We performed a set of numerical experiments using a flow simulator and different synthetic permeability fields. The results highlight the dependence of the proposed method on reservoir parameters. The method can indicate the presence of transmissibility barriers, permeability anisotropy and, in some situations, range anisotropy.
Next, we present a field case to demonstrate the application of the method. The Canto do Amaro field, located in the Potiguar basin, Brazil, is chosen because of a small well spacing and a previous comprehensive reservoir characterization study using geostatistics. The results obtained provide a better understanding of how rank analysis can be used as an effective reservoir characterization tool.

Introduction
A major source of information in a developed field comes from the widely available measurements of production and injection rates at existing wells. If this information could be used as a reservoir characterization tool to indicate anisotropy and communication trends, progress could be achieved in reservoir management without the cost of additional data. This paper aims to provide more insight into such an approach.
The results were obtained from two different investigations. First, we performed a s t of numerical experiments using a flow simulator and different synthetic permeability fields. Then, we chose a field case to illustrate a practical application.

Background
The advantages of using data from interference tests are well described in the literature(1). This type of test can provide information on reservoir properties that cannot be obtained from ordinary pressure buildup or drawdown tests.
The well-test analysis approach needs production and pressure data to estimate the reservoir properties and requires a well intervention. An alternative way to perform interference tests would onsider only the analysis of injection and production fluid rates. If successful, this approach would be attractive since the fluid rate information is widely available.
Parametric statistics compare the statistic from a sample with an assumed population parameter; usually the statistics are the mean and variance of a distribution. Nonparametric statistics, however, do not involve any assumption about the distribution of the population. Therefore, the approach is parameter free and its required assumptions are fewer and less restrictive than those associated with parametric tests(2). This feature makes its use appropriate to data that do not fit a specific distribution or where the distribution type is unknown. One additional advantage is that nonparametric techniques can be used with scores that are not exact in any numerical sense, but which, in effect, are simple ranks. ranks. Journel(3) presented one of the first applications of nonparametric statistics in the petroleum industry. He introduced a nonparametric Kriging approach in which the data were described through their rank order.