Difference between revisions of "Gas Flowing Material Balance"

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(→‎Extra Plot to find the bpss)
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== Nomenclature  ==
 
== Nomenclature  ==
  
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:<math> A_p </math> = flow area, ft2
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:<math> GIIP </math> = gas initially in place, scf
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:<math> B </math> = correlation group, dimensionless
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:<math> G_p </math> = cumulative gas produced, scf
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:<math> B </math> = formation factor, bbl/stb
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:<math> P </math> = reservoir pressure (changing), psia
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:<math> C </math> = coefficient for liquid viscosity number, dimensionless
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:<math> P_{i} </math> = initial reservoir pressure (constant), psia
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:<math> D </math> = pipe diameter, ft
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:<math> P_{SC} </math> = pressure at standard conditions, psia
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:<math> h </math> = depth, ft
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:<math> T_i </math> = initial reservoir pressure (constant), °R
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:<math> H </math> = correlation group, dimensionless
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:<math> T_r </math> = reservoir pressure (constant), °R
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:<math> H_L </math> = liquid holdup factor, dimensionless
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:<math> T_{SC} </math> = temperature at standard conditions (constant), °R
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:<math> f </math> = friction factor, dimensionless
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:<math> V_g </math> = volume of gas in reservoir converted to standard conditions (changing), scf
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:<math> GLR </math> = gas-liquid ratio, scf/bbl
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:<math> V_r </math> = reservoir volume (constant), ft<sup>3</sup>
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:<math> M </math> = total mass of oil, water and gas associated with 1 bbl of liquid flowing into and out of the flow string, lb<sub>m</sub>/bbl
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:<math> z </math> = gas compressibility factor (changing), dimensionless
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:<math> N_D </math> = pipe diameter number, dimensionless
 
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:<math> N_GV </math> = gas velocity number, dimensionless
 
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:<math> N_L </math> = liquid viscosity number, dimensionless
 
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:<math> N_LV </math> = liquid velocity number, dimensionless
 
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:<math> p </math> = pressure, psia
 
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:<math> q_c </math> = conversion constant equal to 32.174049, lb<sub>m</sub>ft / lb<sub>f</sub>sec<sup>2</sup>
 
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:<math> q </math> = total liquid production rate, bbl/d
 
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:<math> Re </math> = Reynolds number, dimensionless
 
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:<math> R_s </math> = solution gas-oil ratio, scf/stb
 
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:<math> SG </math> = specific gravity, dimensionless
 
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:<math> T </math> = temperature, °R or °K, follow the subscript
 
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:<math> v </math> = velocity, ft/sec
 
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:<math> WOR </math> = water-oil ratio, bbl/bbl
 
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:<math> z </math> = gas compressibility factor, dimensionless
 
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===Greek symbols===
 
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:<math> \varepsilon </math> = absolute roughness, ft
 
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:<math> \mu </math> = viscosity, cp
 
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:<math> \rho </math> = density, lb<sub>m</sub>/ft<sup>3</sup>
 
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:<math> \bar \rho </math> = integrated average density at flowing conditions, lb<sub>m</sub>/ft<sup>3</sup>
 
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:<math> \sigma </math> = surface tension of liquid-air interface, dynes/cm (ref. values: 72 - water, 35 - oil)
 
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:<math> \psi </math> = secondary correlation factor, dimensionless
 
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===Subscripts===
 
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:g = gas<BR/>
 
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:K = °K<BR/>
 
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:L = liquid<BR/>
 
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:m = gas/liquid mixture<BR/>
 
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:o = oil<BR/>
 
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:R = °R<BR/>
 
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:SL = superficial liquid<BR/>
 
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:SG = superficial gas<BR/>
 
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:w = water<BR/>
 
  
 
== References ==
 
== References ==

Revision as of 12:06, 11 December 2017

Brief

Gas Flowing Material Balance is the advanced engineering technique to determine the Reservoirs GIIP and recovery as well as Well's EUR and JD.

Gas Flowing Material Balance is applied on the Well level given readily available well flowing data: production rate and tubing head pressure.

The interpretation technique is fitting the data points with the straight line to estimate GIIP and JD.

Math & Physics

Combining the gas pseudo state flow equation and the Gas Material Balance equation to get Gas Flowing Material Balance equation:

P_{\bar{P}}= P_{P_{wf}} + q_g b_{pss} [1]

where

b_{pss} = \frac{1422 \times 10^3\ T_R}{kh\ J_D}

Material balance pseudo-time:

t_{ca} = \frac{\mu_{gi} c_{gi}}{q_g}\int\limits_{0}^{t}\frac{q_g}{\bar{\mu_g} \bar{c_g}}dt

Discussion

well vs reservoir model start

Workflow

  1. Calculate the red \frac{P}{z} line:
    1. Given the GIIP
    2. Calculate the \frac{P}{z}=\frac{P_i}{z_i} \left (1- \frac{G_p}{GIIP}\right )
  2. Calculate the orange \frac{\bar{P}}{z} curve:
    1. Given the flowing wellhead pressures, calculate the flowing bottomhole pressures, P_{wf}
    2. Convert the flowing pressures to pseudopressures, P_{P_{wf}}
    3. Given the JD, calculate the b_{pss}
    4. Calculate the pseudopressure, P_{\bar{P}}
    5. Convert the pseudopressure to pressure, \bar{P}
    6. Calculate the \frac{\bar{P}}{z}
  3. Calculate the gray JD curve:
    1. Calculate the gas productivity index, J=\frac{q_g}{P_{\bar{P}}-P_{P_{wf}}}
    2. Calculate the JD, J_D=\frac{1422 \times 10^3\ T_R}{kh} J
  4. Change the red \frac{P}{z} line to match the orange \frac{\bar{P}}{z} curve
    1. Change the GIIP
    2. Change the intitial \frac{P}{z}
  5. Change the flat JD gray line to match the changing JD gray line
  6. Save the Gas Flowing Material Balance model
  7. Move to the next well

Extra Plot to find bpss

  1. Calculate the initial pseudopressure, P_{Pi}
  2. Calculate the material balance pseudo-time, t_{ca}
  3. Plot \frac{P_{P_i}-P_{P_{wf}}}{q_g} versus t_{ca}
  4. The intercept with the Y axis gives b_{pss} and J_D

Data required

Nomenclature

GIIP = gas initially in place, scf
G_p = cumulative gas produced, scf
P = reservoir pressure (changing), psia
P_{i} = initial reservoir pressure (constant), psia
P_{SC} = pressure at standard conditions, psia
T_i = initial reservoir pressure (constant), °R
T_r = reservoir pressure (constant), °R
T_{SC} = temperature at standard conditions (constant), °R
V_g = volume of gas in reservoir converted to standard conditions (changing), scf
V_r = reservoir volume (constant), ft3
z = gas compressibility factor (changing), dimensionless

References

  1. ↑ Mattar, L.; Anderson, D (2005). "Dynamic Material Balance (Oil or Gas-In-Place Without Shut-Ins)" (PDF). CIPC. 
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