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High Pressure Region Gas Flow Rate

 

High Pressure Region Gas Flow Rate Formula

  • The gas flow rate from a high-pressure region in a reservoir is often modeled using equations that describe how gas moves through porous rock.  A common starting point is the inflow performance relationship (IPR) for a gas well. For a simple case, the flow rate might look like this:
\( Q_g \;=\;  C \cdot (  p_r^2  -  p_w^2  )  \) 
Symbol English Metric
 \( Q_g \) = Gas Flow Rate \(MSCF \;/\; d\)  -
\( C \) = A Constant Based on Reservoir Properties (Permeability, Reservoir Thickness, and other Factors) \(diensionless\)   -
\( p_r \) = Reservoir Pressure (High Pressure in the Region) (psi) \(lbf\;/\;in^2\)  -
\( p_f \) = Flowing Bottomhole Pressure (Low Pressure at the Well) (psi) \(lbf-sec\;/\;ft^2\) -
\( B_f \) = Average Gas Formation Volume Factor  \(bbl \;/\; SCF\) -
High pressure region gas flow rate in a petroleum reservoir, gas often exists in high-pressure regions, think deep underground formations where pressures can reach thousands of psi due to the weight of overlying rock and fluids.  This could be a gas cap above an oil layer, a standalone gas reservoir, or even a high-pressure pocket within a mixed hydrocarbon system.  The gas flow rate is how much gas moves out of that high-pressure region over time, usually driven by the pressure difference between the reservoir and the wellbore during production.
 
High Pressure Region  -  Deep reservoirs might have pressures from, say, 2,000 to 10,000 psi or more, depending on depth and geology.  This high pressure is the energy source pushing the gas toward the well.
Gas Flow Rate  -  This is typically measured in units like standard cubic feet per day (SCF/day) or million standard cubic feet per day (MMSCFD).  The rate depends on the pressure drop, the reservoir’s rock properties (like permeability), and the gas’s own characteristics (like viscosity).
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High Pressure Region Gas Flow Rate Formula

  • The previous equation simplifies things a bit.  In reality, high-pressure gas doesn’t behave perfectly, its compressibility changes, and at very high pressures near the wellbore, turbulence (non-Darcy flow) can slow things down.  Engineers adjust for this with a real gas compressibility factor (Z) and sometimes a turbulence term, making the formula more like:
\( Q_g \;=\; \dfrac{  k \cdot h \cdot ( p_r^2 - p_f^2 )  }{  1424 \cdot  \eta \cdot Z \cdot T \cdot                \left(  ln \left( \dfrac{ r_d }{ r_w } \right)  + S  \right)  }\) 
Symbol English Metric
 \( Q_g \) = Gas Flow Rate \(MSCF \;/\; d\)  -
\( k \) = Permeability \(mD\) -
 \( h \) = Thickness of Reservoir \(ft\)  -
\( p_r \) = Reservoir Pressure (High Pressure in the Region (psi) \(lbf\;/\;in^2\) -
\( p_f \) = Flowing Bottomhole Pressure (Low Pressure at the Well) (psi) \(lbf\;/\;in^2\) -
\( \eta \)  (Greek symbol eta) = Gas Viscosity \(cP\) -
\( T \) = Compressibility Factor  \(diensionless\)  -
\( T \) = Temperature  \(R\) -
\( r_d \) = Drainage Radius (How Far the Reservoir Extends) \(ft\) -
\( r_w \) = Wellbore Radius \(ft\) -
\( S \) = Skin Factor \(diensionless\) -

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

High Pressure Region Gas Flow Rate Formula
\( Q_g \;=\; \dfrac{  7.08 \cdot 10^{-6} \cdot k \cdot h \cdot ( p_r - p_f )  }{  \eta \cdot B_f \cdot \left(  ln \left( \dfrac{ r_d }{ r_w } \right)  - 0.75 + S  \right)  }\) 
Symbol English Metric
 \( Q_g \) = Gas Flow Rate \(MSCF \;/\; d\)  -
\( k \) = Permeability \(mD\) -
 \( h \) = Thickness of Reservoir \(ft\)  -
\( p_r \) = Reservoir Pressure (High Pressure in the Region)(psi) \(lbf\;/\;in^2\) -
\( p_f \) = Flowing Bottomhole Pressure (Low Pressure at the Well) (psi) \(lbf\;/\;in^2\) -
\( \eta \)  (Greek symbol eta) = Gas Viscosity \(cP\) -
\( B_f \) = Gas Formation Volume Factor  \(bbl \;/\; SCF\) -
\( r_d \) = Drainage Radius (How Far the Reservoir Extends) \(ft\) -
\( r_w \) = Wellbore Radius \(ft\) -
\( S \) = Skin Factor \(diensionless\) -