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(1) 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

p_{ref}

reference pressure

\tau(t)

pseudo-time  at time moment t

\mu(p)

dynamic fluid viscosity

c_t(p)

total compressibility

p(t)

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 (PTARTA ) of strongly compressible fluids.

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

The usual practise is to select p_{ref} = p(t=0) as the bottom-hole pressure at initial time moment.

Selection of p(t) depends on objectives.

In Pressure Build Up (PBU) survey the p(t) is calculated as sandface bottom-hole pressurep(t) = p_{wf}(t).

In Drawdown survey (DD) survey the p(t) is calculated as field-average formation pressurep(t) = p_r(t).

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


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 ]


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