Inferring Interwell Connectivity Only From Well-Rate Fluctuations in Waterfloods
- Alejandro Albertoni (U. of Texas at Austin) | Larry W. Lake (U. of Texas at Austin)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- February 2003
- Document Type
- Journal Paper
- 6 - 16
- 2003. Society of Petroleum Engineers
- 4.1.5 Processing Equipment, 1.2.2 Geomechanics, 5.4.1 Waterflooding, 5.1.1 Exploration, Development, Structural Geology, 5.1.2 Faults and Fracture Characterisation, 5.1 Reservoir Characterisation, 6.1.5 Human Resources, Competence and Training, 5.5 Reservoir Simulation, 5.6.5 Tracers, 5.6.4 Drillstem/Well Testing, 4.1.2 Separation and Treating, 5.2.1 Phase Behavior and PVT Measurements, 1.6 Drilling Operations
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This paper presents a practical technique to quantify communication between wells in a reservoir using only production and injection rate data. The technique combines a constrained multivariate linear regression analysis with diffusivity filters to provide information about permeability trends and the presence of transmissibility barriers. The method was developed and tested using a numerical simulator and then applied to a waterflooded field in Argentina. The simulation results indicate that the connectivity between wells is described by coefficients that only depend on geology and relative position between wells; they are independent of injection/production rates. The results of this work can be used to improve the performance of an existing waterflood by suggesting how well patterns might be changed or managed. They could also be used to model flow in the reservoir.
Production and injection rates usually based on monthly well tests are the most abundant data available in any waterflooding project. Valuable and useful information can be obtained from the analysis of these data. Typically, reservoir description and characterization together with observation of injection and production rates is used to determine the influence of each injector on producers. Ultimately, the final objective is the optimization of operations and economics and the maximization of oil recovery of existing waterfloods. This may include changes in injection patterns, assignment of priorities in operations, recompletion of wells, and infill drilling.
There have been previous statistical approaches that compared the rate performance of a production well with that of the surrounding injectors. Heffer et al.1 used Spearman rank correlations to relate injector/producer pairs and associated these relations with geomechanics. Refunjol2 also used Spearman analysis to determine preferential flow trends in a reservoir. She related injection wells with their adjacent producers and used time lags to find an extreme coefficient value. Sant'Anna Pizarro3 validated the Spearman rank technique with numerical simulation and pointed out its advantages and limitations. Panda and Chopra4 used artificial neural networks to determine the interaction between injector/ producer pairs within a pattern. Soeriawinata and Kelkar,5 who also used Spearman rank analysis, suggested a statistical approach to relate injection wells and their adjacent producing wells. They applied the superposition principle to introduce concepts of constructive and destructive interference. Additional reference can be found in Araque-Martinez's work.6
The main objectives of this work are to quantitatively determine the communication between wells in a waterflood and to perform the analysis fieldwide, analyzing multiple well influences in a single step. This work shows that distant injectors (from different patterns) can significantly affect production.
We view the reservoir as a system that processes a stimulus (injection) and returns a response (production). In a waterflood, there are typically several injectors and producers acting at the same time; moreover, the effect of the reservoir on the input/output signals will depend on the location and the orientation of each stimulus-response pair. Taking this into account, the technique presented here uses different statistical approaches based on constrained multiple linear regression to infer connectivity. In addition, we use diffusivity filters to account for the time lag and attenuation that occurs between stimulus and response.
The technique is first applied to two synthetic fields of different sizes and then to a waterflooded field in Argentina.
The technique uses the liquid (oil and water) production rates and the injection rates of every well in a waterflood as input data. Both rates are in reservoir volumes. The gas rate is not included in the analysis; periods with no significant free gas production must be selected for the analysis. The reason for this will be discussed later. The location of the wells must also be provided. All the cases and studies presented in this paper were performed using standard spreadsheets, and the implementation of this technique into software does not demand a significant amount of effort. The simplicity of the method and the always-available production and injection data make this technique a very practical tool.
Two different approaches aimed at solving this problem are presented in this paper: multivariate linear regression (MLR) and balanced multivariate linear regression (BMLR). The use of one or the other approach will depend on the type of waterflood and the data that are being analyzed. First, both MLR and BMLR approaches are explained without the use of diffusivity filters; then, later in this section, the concept of diffusivity filters is presented.
Multivariate Linear Regression (MLR).
We say that a waterflood is unbalanced when the fieldwide injection rate is significantly different from fieldwide liquid production rate. If this is the case, the MLR approach must be used.
In this model, the estimated production rate of a producer j is given by:
where N=the total number of producers and I=the number of injectors. This equation states that at any time the total production rate at well j is a linear combination of the rates of every injector plus a constant term, ß0j. The factors ßij are the weighting factors, and the constant term ß0j accounts for the unbalance. If the injection rates are known, the coefficients ßij and the term ß0j need to be determined.
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