Statistical and fuzzy infill drilling recovery models for carbonate reservoirs

This paper presents statistical and fuzzy-logic infill drilling recovery forecast models for West Texas San Andres and Clearfork carbonate reservoirs. Also presented are statistical and fuzzy-logic primary and initial waterflood recovery forecast models. These oil recovery forecast models are useful for a quick oil recovery evaluation of the carbonate reservoirs. A similar approach should be applicable to other carbonate plays. The statistical infill drilling recovery forecast models were developed and improved over the last eight years. Initially, the statistical approach encountered a lot of uncertain and unconsistent choice of variables and sets of data points from the database. After numerous trials and reviews, the use of both simple and lumped variables has improved the statistical oil recovery forecast models. We have applied various techniques for identifying fuzzy models for waterflood infill drilling oil recovery of the West Texas Carbonate reservoirs. Developing a fuzzy model requires identifying the premise structure, premise parameters, and consequence parameters. The premise structure identification involves the selection of input variables. We have developed an iterative procedure to select variables based on model performance. The selection of variables is flexible enough to include domain knowledge. In addition, we use a fuzzy clustering technique to identify the number and parameters of the membership functions based on the data. In a Takagi-Sugeno type fuzzy rule, the consequence is a linear equation of the input variables. The parameters in rules are identified using a least-squares method. The fuzzy-logic based model is shown to be superior to the statistical models.