Water management

Capacitance-Resistance Model Used for Integrated Detection of Water Production

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.


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.


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 waterflooding 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 Cretaceous 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 prodelta 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.

Core analysis and well logging showed that the net pay of the Parkman reservoir is 60 ft, with 10% average effective porosity. In addition, the reservoir is very heterogeneous, its porosity ranges from 2 to 12%, and its permeability ranges from 0.0001 to 1 md. The average pore-pressure gradient of the Parkman formation is 0.37 psi/ft. The bubblepoint of the reservoir is less than 1,000 psi and the reservoir is highly undersaturated. To date, approximately 170 horizontal wells have been completed in the Parkman reservoir since 2009 with multistage hydraulic fracturing.

The field study area consists of two units, 21 Mile Butte and the Gaither Draw unit. There are seven injection wells in this field. Six were originally production wells before being converted to injection wells. The first injection well began operating in September of 2010. For all injection wells, injection rates were initially high, and then decreased dramatically. More oil was recovered from 21 Mile Butte, while water was mainly produced from the southern part of the Gaither Draw unit, particularly in south Gaither. Also, horizontal wells produced more fluid than did vertical wells in the same area.

CRM analysis usually yields a more-reliable model with more injection and production data. There are 50 production wells in the field. The monthly production and injection-rate data used in tuning the CRM to obtain weights and the time constant without considering later well-activity transfer of special wells are taken from June 2007 to ­January 2017. With the CRMP approach, the number of unknown parameters is reduced to 408. Because of the low permeability and high heterogeneity of this reservoir, each injection well is assumed to be connected only with surrounding producers. The whole field can be divided into seven zones to conduct the CRM analysis (Fig. 1). In this study, the authors selected Regions 2 and 7 as examples in which the method can be illustrated.

Fig. 1—The seven zones into which the study field is divided for CRM analysis.


The authors first studied performance in Region 2, where injection well Davis 14-10HPWI supports four production wells (GDU23-10, GDU44-9, GDU24-10, and GDU44-10). By applying an optimization algorithm, the connectivity coefficients and time constants were obtained for all production wells. Well GDU44-9 has the highest connectivity coefficient, which means that this well has the highest waterflooding support. However, the same well has the highest time constant, which means that it is least affected by injection.

Petrophysical study shows that Region 7 has low permeability. In this region, injection well Heiland 11-33 HPWI is assumed to support surrounding production wells GDU 41-33, Heiland 23‑33, GDU14-33, GDU 43-33, and GDU 33‑33. The higher weight of a production well indicates that the well receives more water support. A larger time constant indicates that the storage effect of the reservoir medium is so strong that most injected water is saturated around the injector.

To validate these results with CRM, the authors performed a full-field model. At the end of the simulation, it was evident that most of the injected water is stored near the injection wells because of low permeability. The simulation results are consistent with CRM optimization results.

Liquid levels in each well were measured regularly using a gas gun to determine reservoir pressure surrounding the tested wells. The interpreted results also supported the hypothesis that most of the injected water is in the region near the injection wellbore if the permeability is low in the region; high pressure (a high liquid level) was observed.


Waterflooding is a challenging process because of declining water injectivity and concerns about detrimental effects, especially for tight formations where production wells need pressure maintenance but the injectivity is limited. Once water injection starts, engineers will have concerns about the destination of the injected water. Many practices have been developed in the literature, usually suggesting integrated water-­injection management through examination of different sources of information. In this study, the authors focused on CRM modeling on the basis of production- and injection-history data in the Gaither Draw unit. The following conclusions were drawn from the study:

  • When CRM is used in a heterogeneous tight-oil reservoir, the assumption that injectors are only connected with surrounding producers is useful for CRM model application. This will significantly reduce the number of unknown parameters. However, when the permeability is low, the solution from CRM may not be very useful because the wells with large time constants have large weight to satisfy the optimization constraints.
  • Because of the assumptions and constraints of CRM, the obtained connectivity weight is not meaningful if the production wells have not ben influenced by support from injection wells. In this situation, the calculated results of time constraints and connectivity weight could be a local minimum in the optimization procedure.
  • Some producers that benefit from the injection are identified. If the connectivity between an injector or producer pair is high and the time constant is small, one can conclude that the producer benefits from that particular injection well. For the case studied in this paper, the authors validated the observation using full-field reservoir numerical simulation and pressure from liquid-level interpretation.
  • Even with substantial water injection in the Gaither Draw unit, most injected water remains around the injectors and pressurized regional areas surrounding the injectors. For many injector/producer pairs, the presence of large time constants with high connectivity indicates that most injected water is stored in the interwell regions; the pressure of the interwell regions will increase consequently.

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.