Transient flow is defined as a flow regime where/when the radius of pressure wave propagation from wellbore has not reached any boundaries of the reservoir. During transient flow, the developing pressure funnel is small relative to the reservoir size. Therefore, the reservoir acts like an infinitively large reservoir from transient pressure analysis point of view.
Assuming single-phase oil flow in the reservoir, several analytical solutions have been developed for describing the transient flow behavior. They are available from classic textbooks such as that of Dake (1978). A constant-rate solution expressed by Eq. (1) is frequently used in production engineering:

pwf = flowing bottom-hole pressure, psia
pi= initial reservoir pressure, psia
q= oil production rate, stb/day
uo= viscosity of oil, cp
k= effective horizontal permeability to oil, md
h= reservoir thickness, ft
t= flow time, hour
f= porosity, fraction
ct= total compressibility, psi
rw= wellbore radius to the sand face, ft
S= skin factor
Log= 10-based logarithm log10

Because oil production wells are normally operated at constant bottom-hole pressure because of constant wellhead pressure imposed by constant choke size, a constant bottom-hole pressure solution is more desirable for wellinflow performance analysis. With an appropriate inner boundary condition arrangement, Earlougher (1977) developed a constant bottom-hole pressure solution, which is similar to Eq. (1):

Which is used for transient well performance analysis in production engineering.

Equation (2) indicates that oil rate decreases with flow time. This is because the radius of the pressure funnel, over which the pressure drawdown (pi – pwf) acts, increases with time, that is, the overall pressure gradient in the reservoir drops with time.

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