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 Drawdown survey (DD) survey the is calculated as field-average formation 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.
Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Dynamics / Pressure Diffusion / Pressure Diffusion @model
Petroleum Industry / Upstream / Subsurface E&P Disciplines / Well Testing / Pressure Testing
[ Pseudo-Time ]