TABLE OF CONTENTS The steady-state analytical solutions are the simplest form of horizontal well solutions. These equations assume steady state, i.e., pressure at any point in the reservoir does not change with time.
In practice, very few reservoirs operate under steady-state conditions. In fact, most reservoirs exhibit change in reservoir pressure over time. In spite of this, steady-state solutions are widely used because (1) they are easy to derive analytically; (2) it is fairly easy to convert steady-state results to either transient and pseudo-steady state results by using concepts of expanding drainage boundary over time and effective wellbore radius and shape factors, respectively; and (3) steady-state mathematical results can be verified experimentally by constructing physical models in a laboratory. This is explained below.
From the standpoint of physics, Fourier's law of heat conduction, Ohm's law for flow of electricity, and Darcy's law for flow through porous media are similar.
where
q = heat transfer rate, BTU/hr
k = thermal conductivity, BTU/(hr-ft- F)
A = cross-sectional area, ft 2
?T = temperautre difference, F
?x = distance, ft
where
I = current, amperes
V = voltage, volts
R = resistance, ohms
where
q = flow rate,cm 3/sec
k = permeability, darcy
A = cross-sectional area, of flow cm 2
? = viscosity, cp
?p = pressure drop, atmospheres
?x = distance, cm
A comparison of Ohm's law and Darcy's law yields
Since the early days...
