Radial inflow equation

In the simplest case, for a pressure drawdown survey, the radial inflow equation indicates that the bottom hole flowing pressure is proportional to the logarithm of time. From the straight line plot ot pressure against the log (time), the reservoir permeability can be determined, and subsequently the total skin of the well. For a build-up survey, a similar plot (the so-called Horner plot) may be used to determine the same parameters, whose values act as an independent quality check on those derived from the drawdown survey. 

The flowrate of oil into the wellbore is also influenced by the reservoir properties of permeability (k) and reservoir thickness (h), by the oil properties viscosity (p) and formation volume factor (BJ and by any change in the resistance to flow near the wellbore which is represented by the dimensionless term called skin (S). For semisteady state f/owbehaviour (when the effect of the producing well is seen at all boundaries of the reservoir) the radial inflow for oil into a vertical wellbore is represented by the equation ... 

To design a radial-inflow turbine of the highest effleieney, the exit veloeity leaving the turbine must be axial. If the exit veloeity is axial, the Euler turbine equation reduees to... 

Equation 4 also provides additional insight on in-line wake coalescence in laminar flow. For a bubble to benefit from the upward motion of another s wake, it must follow in line below the leader. This occurs automatically for bubbles generated from the same point. Those not already in the wake must be drawn in radially. But any radial inflow that might bring in a bubble must decelerate to zero at the wake... 

The flow function F Q may be computed directly from the radial velocity profile of Eq. (170). Consider a cylindrical surface of radius r attached to the upper (heated) plate. From Fig. 16, it can be seen that all of the inflow across this surface ultimately appears as downflow at axial positions far from the end. The total downflow contained within a radius r is, by the defining equation Eq. (57), equal to the flow function. Thus,... 

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