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titleProductivity Index Analysis


The instantaneous Total Sandface Productivity Index for low-compressibility fluid and low-compressibility rocks  does not depend on formation pressure, bottomhole pressure and the flowrate and can be expressed as:

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J_t(t) = \frac{q_t}{p_i - p_{wf}(t)} =\frac{ 42 \pi \sigma }{ 2SS - 0.5 \, F \biggleft( - \frac{r_w^2}{4 \chi t} \biggright)  }



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titleIsobar Propagation


Isobar equation for a constant-rate production:

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p(t,r) = p_i + \frac{q_t}{4 \pi \sigma} \,  F \bigg( - \frac{r^2}{4 \chi t} \bigg) = {\rm const} \quad \rightarrow \quad \frac{r^2}{4 \chi t}= {\rm const}


Since the pressure disturbance at 

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bodyt=0
 moment was at well walls 
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bodyr=r_w
 then the formula for constant-pressure front propagation becomes:

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r(t) = r_w + 2 \sqrt{\chi t}

This leads to estimation of isobar velocity:

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u_p(t) = \sqrt{\frac{\chi}{t}}



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