Mathematical Problems in Engineering

Volume 2017, Article ID 5185360, 5 pages

https://doi.org/10.1155/2017/5185360

## Evaluation Method of Reservoir Producing Status Based on Cumulative Distribution Curve of Oil Displacement Efficiency

^{1}Research Institute of Enhance Oil Recovery, China University of Petroleum, Beijing 102249, China^{2}Research Institute of Petroleum Exploration & Development, PetroChina, Beijing 100083, China^{3}Chinese Academy of Engineering, Beijing 100088, China

Correspondence should be addressed to Cuo Guan; moc.361@oucnaug

Received 15 February 2017; Accepted 28 May 2017; Published 4 July 2017

Academic Editor: Anna Pandolfi

Copyright © 2017 Cuo Guan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper provides a method for evaluating the status of old oilfield development. This method mainly uses the abundant coring well data of the oilfield to obtain the cumulative distribution curve of the displacement efficiency after the displacement efficiency of the statistical wells in the study area in a similar period is ordered from small to large. Based on the cumulative distribution curve of displacement efficiency, combined with the reservoir ineffective circulation limit, the cumulative water absorption ratio of reservoirs and other data are used to study the reservoir producing degree, calculate the degree of oil recovery, evaluate the proportion of the remaining movable oil after water flooding, calculate the reservoir ineffective circulation thickness and ineffective circulation water volume, and so on.

#### 1. Introduction

At present, most of China’s oilfields have entered the stage of high water-cut development, in which the remaining oil in the reservoir is scattered, resulting in increasing difficulty of further potential tapping [1, 2]. Therefore, effective estimation of the reservoir producing status plays a vital role in the accurate evaluation of oilfield development effect. There are many methods for evaluating the reservoir producing status [3]. Based on the specialty, they are divided into geological and seismic methods: reservoir engineering [4], well test [5], numerical simulation methods, indoor experimental techniques, and so on. These methods have their own advantages and disadvantages. Practice shows that sealing coring well data can be used to give an intuitive, accurate, and quantitative description of the remaining oil distribution. Therefore, the rational use of existing coring well data and the statistical analysis of the oil displacement efficiency distribution can provide an effective means for thoroughly dissecting the reservoir producing status and the oil displacement status [6], which is of great significance for the quick and accurate evaluation of oilfield development status and the improvement of oil recovery.

#### 2. Evaluation Method Is Put Forward

Due to various development factors and geological factors, the distribution of remaining oil in the later stage of oilfield development presents a strong heterogeneity. According to the statistical results of the oil displacement efficiency of 1953 samples from 715 formations of 24 coring wells in an oilfield in a short period of time, the cumulative distribution curve of reservoir oil displacement efficiency is S-shaped. The logarithmic function, semilogarithmic function, and hyperbolic tangent function are used to fit the curve. It is found that degree of fitting between the cumulative probability distribution curve of the displacement efficiency and the hyperbolic tangent function is better [7]. Therefore, the hyperbolic tangent function is used to fit the cumulative probability distribution curve of displacement efficiency. As shown in Figure 1, curve A shows the cumulative distribution curve of the displacement efficiency at the time of taking out the core of the well, while curve B shows the cumulative probability distribution curve of the displacement efficiency under the residual oil saturation. The mathematical expressions of the curves A and B are, respectively, where is the mathematical formula of the hyperbolic tangent function for the cumulative distribution curve of the displacement efficiency at the time of taking out the core of the well, in which the value range is 0-1;* Ed* is the displacement efficiency at the time of taking out the core of the well, in which the value range is 0-1; , , , and are parameters obtained by fitting; is the mathematical formula of the hyperbolic tangent function for the cumulative probability distribution curve of the displacement efficiency under the residual oil saturation, in which the value range is 0-1; is the displacement efficiency under the residual oil saturation, in which the value range is 0-1; , , , and are parameters obtained by fitting.