Many tight/shale gas wells exhibit linear flow, which can last for several years. Linear flow can be analyzed using square root-time plot, a plot of rate-normalized pressure versus square root of time. Linear flow appears as a straight line on this plot and the slope of this line can be used to calculate the product of fracture half-length and square root of permeability.

In this paper, linear flow from a fractured well in tight/shale gas reservoir under a constant flowing pressure constraint is studied. It is shown that the slope of square root-time plot results in an overestimation of fracture half-length, if permeability is known. The degree of this overestimation is influenced by initial pressure, flowing pressure and formation compressibility. An analytical method is presented to correct the slope of the square root-time plot to eliminate the overestimation of fracture half-length. The method is validated using a number of numerically-simulated cases. As expected, the square root-time plots for these simulated cases appear as a straight line during linear flow for constant flowing pressure. It is found that the newly-developed analytical method results in a more reliable estimate of fracture half-length, if permeability is known. Our approach, which is fully-analytical, results in an improvement in linear flow analysis over previously-presented methods.

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