Infinite Acting Radial Flow (IARF)

Time interval of pressure transition when pressure variation $\begin{array}{l}\Delta p\end{array}$ is evolving logarithmically in time:

(1)	$\begin{array}{l}\displaystyle \Delta p = p_{wf}(0) - p_{wf}(t) \sim p_{wf}(0) - p_i - \frac{q_t}{4 \pi \sigma} \, \bigg[ - 2S + \gamma - \ln \bigg( \frac{4 \chi t}{r_w^2} \bigg) \bigg]\end{array}$

and hence the pressure log-derivative stays constant:

(2)	$\begin{array}{l}\displaystyle \Delta p ' = \frac{d \, \Delta p}{d \, \ln t} = \frac{q_t}{4 \pi \sigma} = \rm const\end{array}$

Since IARF is normally used to define a flow regime during a certain finite period of time, the term "infinite acting" is a misnomer.

The other popular occurrence of IARF is before PSS (Fig.2) and SS (Fig. 3).


Fig. 2. PTA Diagnostic Plot with IARF regime developing after 100 hrs until PSS at 1,000 hrs	Fig. 3. PTA Diagnostic Plot with IARF regime developing after 100 hrs until SS at 1,000 hrs

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