Capacitance-Resistance Model Used for Integrated Detection of Water Production
Authors: Carpenter Chris 
Published: December 2019

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper IPTC 19333, “Integrated Detection of Water Production in a Highly Heterogeneous and Tight Formation Using a CRM Model: A Case Study on Waterflooding Gaither Draw Unit, Wyoming, USA,” by Kailei Liu, China University of Geosciences; Xingru Wu, SPE, University of Oklahoma; and Kegang Ling, University of North Dakota, prepared for the 2019 International Petroleum Technology Conference, Beijing, 26–28 March. The paper has not been peer reviewed. Copyright 2019 International Petroleum Technology Conference. Reproduced by permission.
The Gaither Draw unit is a heterogeneous tight formation with an average permeability of less than 0.1 md. After substantial water injection, there was no clear benefit of injected water for any producer. However, knowing the distribution of the injected water is critical for future well planning and quantification of injection efficiency. The objective of this study is to show how the capacitance-resistance model (CRM) was used on this field and how it validated the use of other independent methods. This paper demonstrates that integration of different sources of data in reservoir management is critical.
Introduction
Unlike numerical reservoir simulation, the CRM requires only the injection rates of each injector and the production rates of each producer as input to evaluate reservoir performance. The connectivity and the time constant that are estimated by fitting production rates can provide useful information about geological features and reservoir heterogeneity. With a clear understanding of reservoir heterogeneity, flow barriers and high-permeability zones can be identified. Significant reservoir heterogeneity may lead to poor sweep efficiency. These characteristic features make the CRM (the development of which is outlined in the complete paper) a unique and practical tool to investigate water-flooding projects.
Basics of the CRM
The root of the CRM is the governing material-balance equation stating that the mass difference in an arbitrary control volume (CV) is equal to the mass difference between injected and produced fluid passing through this CV. Then, the governing material-balance equation is combined with a linear productivity model to obtain an ordinary differential equation. The semianalytical solution of the ordinary differential equation forms the CRM. In the field case, there are often many injectors and producers, which would be a large nonlinear optimization problem in the CRM. A CRM-producer (CRMP) model can be used to reduce the number of time constants and increase computational speed. The equations contributing to such a model are provided in the complete paper.
Case Study
The study area is located in the Parkman reservoir, which is a part of the Powder River Basin in southeast Montana and northeast Wyoming. The Parkman Sandstone Member of the Upper Creta-ceous Mesaverde formation is the oldest sandstone member in a widespread cycle of late Cretaceous regression. The Parkman reservoir consists of multiple stacked sands 5,000 to 9,500 ft deep. There are three dominant lithologies of the Parkman reservoir. The first is pro-delta shale and siltstone, which includes very fine and well-sorted sandstone. The second is medium-grained sandstone, which lies as coarsening-upward successions mixed with siltstone. The last is silt and mudstone, which gradually changes from exhibiting carbonaceous to lignitic characteristics.