Motivation



Inputs & Outputs


InputsOutputs

field-average formation pressure at time moment

cumulative subsurface water influx from aquifer

initial formation pressure

subsurface water flowrate from aquifer

aquifer Productivity Index

aquifer relaxation time



Detailing Inputs


aquifer Productivity Index

central angle of net pay area ↔ aquifer contact

aquifer transmissibility

net pay area

aquifer area

aquifer relaxation time

aquifer total compressibility

aquifer pore compressibility 

aquifer water compressibility

aquifer volume 

aquifer effective thickness

aquifer porosity


Physical Model



Radial Composite Reservoir

Const Productivity Index Aquifer
J_{AQ} = \frac{q_{AQ}}{p_{AQ}(t)-p(t)} = \rm const
Pseudo Steady State Flow
p_{AQ}(t) = p_i - \frac{Q_{AQ}(t)}{V_{AQ} \cdot c_t}





Fig. 1. Fetkovich aquifer drive schematic



Mathematical Model

\tau \cdot \frac{d Q^{\downarrow}_{AQ}}{dt} +  Q^{\downarrow}_{AQ} = с_t \, V_\phi \cdot \left[  p_i - p(t) \right]
q^{\downarrow}_{AQ}(t)=\frac{d Q^{\downarrow}_{AQ}}{dt}

 which can be explicitly integrated:

Q^{\downarrow}_{AQ}(t) = J_{AQ} \, \exp \left( -\frac{t}{\tau} \right) \, \int_0^t   \big[ p_i - p(\xi) \big] \, \exp \left( \frac{\xi}{\tau} \right) \, d \xi



Assumption #1 = Const Productivity Index Aquifer:

q_{AQ} = \frac{d Q_{AQ}}{dt} = J_{AQ} \cdot ( p_{AQ}(t) - p(t))


Assumption #2 = Pseudo Steady State Flow:

p_{AQ}(t) = p_i - \frac{Q_{AQ}}{c_t \, V_\phi}


Eliminating one arrives to .


See Also

Petroleum Industry / Upstream / Subsurface E&P Disciplines / Field Study & Modelling / Aquifer Drive / Aquifer Drive Models

Reference

 1.   Fetkovich, M.J. 1971. A Simplified Approach to Water Influx Calculations—Finite Aquifer Systems. J Pet Technol 23 (7): 814–28. SPE-2603-PA. http://dx.doi.org/10.2118/2603-PA