The Use of Multilinear Regression Models in Patterned Waterfloods: Physical Meaning of the Regression Coefficients

One of the reservoirs engineer's mission is to predict the behavior of hydrocarbon producing assets. Once this ability is developed he/she will try to manage tbe ''today" to maximize the future economic return of the asset. However, the techniques to predict future performance vary from an educated guess of an appropriate analogy to very complex numerical approximations. But what they all have in common is that they are analyzing performance in the past to say something about the future. Hence, most models rely on fitting or matching to historic data. Albertoni (2002) proposed yet another approach using well rate fluctuations in waterfloods to predict interwell connectivity. He expressed the total fluid production at a producer as a weighted linear combination of the injection rates at different injectors located in the same reservoir. The relationship between the weights and the formation geological characteristics were not clear. For example, injection wells with no hydraulic connection to a producer may still exhibit a significant or even a negative weight. This work explores the physical meaning of the weights and proposes a new way to interpret them. In addition, the original model has been expanded and is now able to incorporate flowing bottomhole pressure fluctuations. These insights are used to better understand the underlying assumptions of the model used by Albertoni (2002) and to construct a procedure for incorporating production data into geostatistical permeability distribution models. The new interpretation of the weights arises as an analogy between constrained regression and parallel flow from each injector to all the producers. The procedure shows that the weights can be interpreted as the ratio of inverse distance weighted average permeabilities of well pairs associated with each injector (transmissibilities). They can also be interpreted as individual injector-producer water allocation factors that would result if there were no other injectors. This has been confirmed with flow simulation. Finally, a new water allocation model is proposed that, in combination with a water-oil ratio power-law model, has been used to regress oil rates with encouraging results in synthetic and real datasets.