Difference between revisions of "Mobility Ratio"

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[[Mobility Ratio]] determines the relative rate of one fluid to another (etc. water to oil).
 
[[Mobility Ratio]] determines the relative rate of one fluid to another (etc. water to oil).
The waterflood is driven by pore volumes of injected fluid. Everything that is of practical interest occurs between zero to three pore volumes injected <ref name=DW/>.
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:<math> M \le 1</math> oil is dominant flowing phase, stable flow.
 +
:<math> M > 1</math> water preferentially flows in the reservoir, unstable flow, fingering.
  
===Equation===
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==Equation==
:<math> M = \frac{k_w/ \mu_w}{k_o/ \mu_o}=\frac{k_{rw}}/ \mu_w}{k_{ro}}/ \mu_o}=\frac{q_w B_w{q_o B_o}</math>
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:<math> M = \frac{k_w/ \mu_w}{k_o/ \mu_o}=\frac{k_{rw}/ \mu_w}{k_{ro}/ \mu_o}=\frac{q_w B_w}{q_o B_o}</math>
  
 
where
 
where
  
:<math> A </math> = Area, m2
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:<math> B_o </math> = oil formation volume factor, m3/m3
:<math> B_{wi} </math> = Injected water formation oil factor, m3/m3
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:<math> B_w </math> = water formation volume factor, m3/m3
:<math> h </math> = Net pay, oil saturated thickness, m
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:<math> k_{rw} </math> = relative water phase permeability, function of the phase saturation, fraction
:<math> HCPV </math> = Hydrocarbon pore volume, m3
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:<math> k_o </math> = oil phase permeability, function of the phase saturation, fraction
:<math> HCPV_{inj} </math> = Injected hydrocarbon pore volumes, fraction
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:<math> k_o </math> = relative oil phase permeability, function of the phase saturation, mD
:<math> W_i </math> = Cumulative water injection volume, m3
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:<math> k_w </math> = water phase permeability, function of the phase saturation, mD
:<math> \phi </math> = Porosity, fraction
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:<math> M </math>= mobility ratio, fraction
:<math> S_o </math> = Oil saturation, fraction
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:<math> \mu_o </math> = oil viscosity, cP
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:<math> \mu_w </math> = water viscosity, cP
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:<math> q_o </math> = oil rate, cc/sec
 +
:<math> q_w </math> = water rate, cc/sec
  
===Related definitions===
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Rule of thumb:
Dimensionless injected pore volume:
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:<math> M = 0.333 \mu_o</math>
:<math> W_{iD} = \frac{W_i * B_{wi}}{PV} = \frac{W_i * B_{wi}}{A * h * \phi}</math>
 
  
Injected movable pore volume:
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==Example==
:<math> MOPV_{inj} = \frac{W_i * B_{wi}}{MOPV} = \frac{W_i * B_{wi}}{A * h * \phi *(1-S_{wc}-S_{orw})}</math>
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Determine the [[Mobility Ratio]] using the following data<ref name=DW/>:<BR>
 +
Core is at 70% water and 30% oil saturation. Water phase permeability is 248 mD, oil phase permeability is 50 mD. Water viscosity is 1 cP, oil viscosity is 3 cP.
  
where
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:<math> M = \frac{248/1}{50/3} =15 </math>
  
:<math> S_{wc} </math> = Connate water saturation, fraction
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In this case the mobility of water is 15 times higher than the mobility of water.
:<math> S_{orw} </math> = Residual oil saturation to water, fraction
 
  
 
==See Also==
 
==See Also==

Latest revision as of 09:02, 4 April 2022

Brief

Mobility Ratio determines the relative rate of one fluid to another (etc. water to oil).

 M \le 1 oil is dominant flowing phase, stable flow.
 M > 1 water preferentially flows in the reservoir, unstable flow, fingering.

Equation

 M = \frac{k_w/ \mu_w}{k_o/ \mu_o}=\frac{k_{rw}/ \mu_w}{k_{ro}/ \mu_o}=\frac{q_w B_w}{q_o B_o}

where

 B_o = oil formation volume factor, m3/m3
 B_w = water formation volume factor, m3/m3
 k_{rw} = relative water phase permeability, function of the phase saturation, fraction
 k_o = oil phase permeability, function of the phase saturation, fraction
 k_o = relative oil phase permeability, function of the phase saturation, mD
 k_w = water phase permeability, function of the phase saturation, mD
 M = mobility ratio, fraction
 \mu_o = oil viscosity, cP
 \mu_w = water viscosity, cP
 q_o = oil rate, cc/sec
 q_w = water rate, cc/sec

Rule of thumb:

 M = 0.333 \mu_o

Example

Determine the Mobility Ratio using the following data[1]:
Core is at 70% water and 30% oil saturation. Water phase permeability is 248 mD, oil phase permeability is 50 mD. Water viscosity is 1 cP, oil viscosity is 3 cP.

 M = \frac{248/1}{50/3} =15

In this case the mobility of water is 15 times higher than the mobility of water.

See Also

References

  1. Wolcott, Don (2009). Applied Waterflood Field DevelopmentPaid subscription required. Houston: Energy Tribune Publishing Inc.