The well-loss function, CQ2, and the effective wellbore radius constitute two very important ideas in Jacob’s classic study (1947). Both ideas were accorded extreme importance in the petroleum engineering field. Swift and Kiel published results of their award-winning study on non-Darcy flow in 1962, and the skin-effect concept (related to effective wellbore radius) was presented independently by both Hurst and van Everdingen in 1953.
Jacob’s well-loss function has been generalized to the form CQn in the current literature, although this form seems to work well only over the range of flow rates used in testing. The petroleum engineering approach suggests that the form should be C(ST + DQ)Q, where ST is the skin effect, a constant, and D is the non-Darcy flow coefficient, often a constant also. The new form contains CQn as a special case for a limited range of flow; however, n values would lie between 1 and 2. Field experience in water-well testing indicates n values from 2.5 to 2.7. Fetkovich (1973) presented information on oil and gas flow indicating that transmissivity depends upon pressure (thus also upon flow rate) for solution gas-drive oil production. There appears to be an analogy possible for high-rate production of gas-saturated water.