t^*(t) = \mu_(p_{ref}) \cdot c_t(p_{ref}) \cdot \tau(t) = \mu_(p_{ref}) \cdot c_t(p_{ref}) \cdot \int_0^t \frac{dt}{\mu(p) \, c_t(p)}

where

	reference pressure
	pseudo-time at time moment
	dynamic fluid viscosity
	total compressibility
	bottom-hole pressure or field average formation pressure as function of time (see below)

It is widely used in Pressure Diffusion @model and transient data analysis (PTA / RTA ) of strongly compressible fluids.

The choice of reference pressure is made by engineer depending on common sense and objectives of the study.

The usual practise is to select as the bottom-hole pressure at initial time moment.

Selection of depends on objectives.

In Pressure Build Up (PBU) survey the is calculated as sandface bottom-hole pressure: .

In case the Normalized Pseudo-Time is used to linearize the Pressure Diffusion equation the choice of reference pressure is not going to affect the solution.

Normalized Pseudo-Time does represent a time in terms of physical property and has the same dimension unlike Pseudo-Time.

See also