On the Relationship Between Levels of Seismicity and Pump Parameters in a Hydraulic Fracturing Job

The McGarr equation gives a means of estimating the amount of seismicity associated with a fluid injection/hydrofrac job. McGarr’s formula seems however to be little used: most examples in the literature contradict it. Here we analyse a number of hydrofrac datasets from gas shales to assess whether they satisfy the McGarr equation. In agreement with other authors we find that moment is proportional to injected volume but the equality is not satisfied. Combining McGarr’s formula with the Gutenberg-Richter Law allows estimates to be made of the number of events expected above a given magnitude. We show that the requirement of a finite moment budget implies that the Gutenberg-Richter b-value must be less than 1.5: b=1.5 corresponds to a fractal dimension for the underlying fault network of 3. Almost all of the datasets we analysed are characterized by b values greater than 1.5 implying that in these cases the Gutenberg-Richter Law is not consistent with the assumption of a finite moment budget. Based on the data analysed, we conclude that McGarr’s formula may well be valid for injection/fraccing but that most of the moment budget is lost in undetectably small events on length scales down to the grain-size.