A Capacitance Model To Infer Interwell Connectivity From Production and Injection Rate Fluctuations
Authors: Yousef Ali A. , Gentil Pablo H. , Jensen Jerry L. , Lake Larry W. 
Published: December 2006

Summary
This paper presents a new procedure to quantify communication between vertical wells in a reservoir on the basis of fluctuations in production and injection rates. The proposed procedure uses a nonlinear signal-processing model to provide information about preferential-transmissibility trends and the presence of flow barriers.
Previous work used a steady-state (purely resistive) model of interwell communication. Data in that work often had to be filtered to account for compressibility effects and time lags. Even though it was often successful, the filtering required subjective judgment as to the goodness of the interpretation. This work uses a more complicated model that includes capacitance (compressibility) as well as resistive (transmissibility) effects.
The procedure was tested on rates obtained from a numerical flow simulator. It was then applied to a short-time-scale data set from an Argentinean field and a large-scale data set from a North Sea field. The simulation results and field applications show that the connectivity between wells is described by model coefficients (weights) that are consistent with known geology, the distance between wells, and their relative positions. The developed procedure provides parameters that explicitly indicate the attenuation and time lag between injector and producer pairs in a field without filtering. The new procedure provides a better insight into the well-to-well connectivities for both fields than the purely resistive model.
The new procedure has several additional advantages. Itcan be applied to fields in which wells are shut in frequently or for long periods of time.allows for application to fields in which the rates have a remnant of primary production.has the capability to incorporate bottomhole-pressure (BHP) data (if available) to enhance the investigation about well connectivity.

Introduction
Production and injection rates are the most abundant data available in any injection project. Valuable and useful information about interwell connectivity can be obtained from the analysis of these data. The information may be used to optimize subsequent oil recovery by changing injection patterns, assignment of priorities in operations, recompletion of wells, and infill drilling.
A variety of methods have been used to compare the rate performance of a producing well with that of the surrounding injectors. Heffer et al. (1997) used Spearman rank correlations to relate injector/producer pairs and associated these relations with geomechanics. Refunjol (1996), who also used Spearman analysis to determine preferential-flow trends in a reservoir, related injection wells to their adjacent producers and used time lags to find an extreme coefficient value. De Sant'Anna Pizarro (1998) validated the Spearman rank technique with numerical simulation and pointed out its advantages and limitations. Panda and Chopra (1998) used artificial neural networks to determine the interaction between injector/producer pairs. Soeriawinata and Kelkar (1999), who also used Spearman rank analysis, suggested a statistical approach to relate injection wells and their adjacent producing wells. They applied superposition to introduce concepts of constructive and destructive interference. See also the works of Araque-Martinez (1993) and Barros-Griffiths (1998).
Albertoni and Lake (2003) estimated interwell connectivity on the basis of a linear model with coefficients estimated by multiple linear regression (MLR). The linear-model coefficients, or weights, quantitatively indicate the communication between a producer and the injectors in a waterflood. Filters were adopted to account for the time lag between producer and injector.
In this work, as in Albertoni and Lake (2003), the reservoir is viewed as a system that converts an input signal (injection) into an output signal (production). However, we use a more complete model that includes capacitance (compressibility) as well as resistive (transmissibility) effects. For each injector/producer pair, two coefficients are determined; one parameter (the weight) quantifies the connectivity, and another (the time constant) quantifies the degree of fluid storage between the wells. This work shows that the new model better captures the true attenuation and time lag between injector and producer pairs.
The new procedure resolves several limitations of the previous methods and extends the applications to a wide range of real cases. It can be applied to fields in which wells are shut in frequently or for long periods of time, it allows for application to fields in which the rates have a remnant of primary production, and it has the capability to use BHP data (if available) to enhance the investigation of the well's connectivity.