Multi-rate drawdown test

Given:

• a discrete flowrate history 

  LaTeX Math Inline
  body \{ \, (\Delta t_1, q_1) , \, (\Delta t_2, q_2) , \, (\Delta t_3, q_3) , \, (\Delta t_{N-1}, q_{N-1}) , \, (\Delta t_N, q_N) , \, \}

   (see Fig. 1)
  
  
• vertical well and homogeneous reservoir with no boundaries
  
  
• duration of the last drawdown interval 

  LaTeX Math Inline
  body \Delta t_N

   reaching radial flow regime

the superposition time 

\ln t_s = \ln (t-t_{N-1}) - \sum_{i=1}^{N-1} \frac{q_i - q_{i-1}}{q_{N-1}}  \ln (t-t_{i-1}) = \ln \Delta t - \sum_{i=1}^{N-1} \frac{q_i - q_{i-1}}{q_{N-1}}  \ln \left( \Delta t + \sum_{i=1}^{N-i} \Delta t_i \right)

The pressure response at time moment 

p_{wf}(t_s) = p_i + \frac{q_N B}{4 \pi \sigma} \ \ln t_s

which has the same format as for a single rate drawdown test with flowrate 

Multi-rate build-up test

...

Given:

• a discrete flowrate history 

  LaTeX Math Inline
  body \{ \, (\Delta t_1, q_1) , \, (\Delta t_2, q_2) , \, (\Delta t_3, q_3) , \, (\Delta t_{N-1}, q_{N-1}) \, \}

   followed by a shut-in period 

  LaTeX Math Inline
  body (\Delta t_N, q_N = 0)

    (see Fig. 2)
  
  
• vertical well and homogeneous reservoir with no boundaries
  
  
• duration of the last shut-in 

  LaTeX Math Inline
  body \Delta t_N

   reaching radial flow regime

the superposition time 

\ln t_s = \ln (t-t_{N-1}) - \sum_{i=1}^{N-1} \frac{q_i - q_{i-1}}{q_{N-1}}  \ln (t-t_{i-1}) = \ln \Delta t - \sum_{i=1}^{N-1} \frac{q_i - q_{i-1}}{q_{N-1}}  \ln \left( \Delta t + \sum_{i=1}^{N-i} \Delta t_i \right)

The pressure response at time moment 

p_{wf}(t_s) = p_i + \frac{q_{N-1} B}{4 \pi \sigma} \ \ln t_s

which has the same format as for a single rate drawdown test with flowrate 

See Also

...

Petroleum Industry / Upstream / Subsurface E&P Disciplines / Well Testing / Pressure Testing / Pressure Transient Analysis (PTA) /  PTA Diagnostic Plot

[ Well & Reservoir Surveillance ] [ Pressure Diffusion ] [ Pressure log-log plot ]