Motivation


Inputs & Outputs

InputsOutputs

field-average formation pressure at time moment

Cumulative Gas Cap expansion at surface conditions

Initial formation pressure

Instantaneous Gas Cap expansion flowrate at surface conditions

Initial Gas Cap reserves at surface conditions



Gas Cap compressibility factor at pressure





Physical Model

Isothermal expansionUniform pressure depletion in Gas Cap



Mathematical Model


Q_{GC}(t) =  V_{GC} \cdot \left( 1- \frac{B_{gi}}{B_g(p)} \right) = V_{GC} \cdot \left( 1 - \frac{Z_i}{p_i} \, \frac{p}{Z(p)}  \right)
q_{GC}(t) = \frac{dQ_{GC}}{dt}

where

Gas formation volume factor at pressure

Gas formation volume factor at Initial formation pressure

Gas Cap compressibility factor at Initial formation pressure

Proxy Models


Ideal Gas ()

Q_{GC}(t) = V_{GC} \, \left( 1 - \frac{p}{p_i}\right)
q_{GC}(t) =  -   \frac{V_{GC}\cdot p_i}{p^2(t)}\cdot
 \frac{d p}{dt}

In this case the only parameter of the gas cap model is its initial volume


See Also

Petroleum Industry / Upstream / Subsurface E&P Disciplines / Field Study & Modelling / Gas Cap Drive

[ Depletion ] [ Saturated oil reservoir ] 


Low pressure depletion 

Q^{\downarrow}_{GC}(t) = V_{gi} \cdot  \frac{\delta p(t)}{p_i} 
q^{\downarrow}_{GC}(t) =    \frac{V_{gi}}{p_i}\cdot
 \frac{d p}{dt}

When pressure depletion is not strong  then compressibility factor maybe considered as relatively constant :

\delta Z = \dot Z \, \delta p \sim 0

which leads to:

Q^{\downarrow}_{GC}(t) = V_{gi} \cdot \left( \frac{Z}{p} \cdot \frac{p_i}{Z_i} - 1 \right) = V_{gi} \cdot \left( \frac{p_i}{p} - 1 \right) = V_{gi} \cdot \left( \frac{p_i}{p_i - \delta p} - 1 \right) = V_{gi} \cdot \left( \frac{1}{1 - \frac{\delta p}{p_i}} - 1 \right) \approx V_{gi} \cdot \left( 1 + \frac{\delta p}{p_i} - 1 \right) = V_{gi} \cdot  \frac{\delta p(t)}{p_i}