Mapping Fractures and High-Permeability Channels in Waterfloods by Use of Injection and Production Rates
Authors: Denney Dennis 
Published: February 2015

This article, written by Senior Technology Editor Dennis Denney, contains highlights of paper SPE 121353, ’A Novel Method for Mapping Fractures and High-Permeability Channels in Waterfloods Using Injection and Production Rates,’by Kun-Han Lee, SPE, Antonio Ortega, Amir Mohammad Nejad, SPE, Nelia Jafroodi, SPE, and Iraj Ershaghi, SPE, University of Southern California, prepared for the 2009 SPE Western Regional Meeting, San Jose, California, 24-26 March. The paper has not been peer reviewed.
This paper extends previous work for managing waterfloods by estimating flow characteristics from only injection and production rates. The method estimates the finite-impulse-response (FIR) curve corresponding to the fluid flow between all injector/producer pairs. Reservoir parameters, such as connectivity between wells, can be estimated from this curve, which can be used to characterize variations of relative flow as a function of storage capacity, thus making it possible to quantify the het-erogeneity of flow paths between wells.
Introduction
In waterflooding, injection rates often can be correlated with gross rates of the surrounding producers by monitoring pressure data. To estimate this correlation, the whole region of injectors/producers is viewed as a system, with the injectors as the system input and the producers as the system output. Methods to estimate the directional transmissivity of flow on the basis of injection- and production-rate data are desirable because injection- and production-rate data are routinely available with high temporal resolution for many reservoirs.
The problem of estimating reservoir properties from injection/production rates is considered a system-identification problem, where injection rates are input and production rates are output. This method could be considered a standard multiple-input/-output (MIMO) system. It is reasonable to assume that the effect on production of each injector can be modeled as a linear FIR filter applied to the injection rates. This FIR curve can be analogous to the response obtained from pulse testing. Modeling the reservoir as a linear FIR-MIMO system is proposed, for which system identification can be solved by use of the least-squares method with truncated order. The main contribution is providing a dynamic approach to estimate the flow characteristics between wells by use of only injection and production data.
Injector/Producer Relationships
In a waterflood, production rates are influenced by reservoir transmissibility, bottomhole flowing pressures, and the pressure changes caused by fluid injections. To capture the injector/producer relationships, various models describe the production rates resulting from injection rates and other factors.
Injector/Producer Model. A general linear-FIR model was used in which production rates were determined partly by a linear combination of the surrounding FIR-filtered version of injection rates. This FIR-MIMO model is very general and can be used to approximate many different models developed by previous researchers, such as a streamline model that describes the relationship between injectors and producers by many imaginary streamlines and capacitance models that use only two parameters to describe the relationship between each injector/producer well pair.