Gas Flowing Material Balance

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Gas Flowing Material Balance (Gas FMB) is the advanced engineering technique published in 1998 by Louis Mattar [1].

Gas Flowing Material Balance is applied to determine:

Gas Flowing Material Balance uses readily available Well flowing data: production rate and tubing head pressure.

The interpretation technique is fitting the data points with the straight lines to calculate GIIP and JD.


Gas Flowing Material Balance in the E&P Portal

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} [2]


 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


Gas Flowing Material Balance can be applied to:

  • single well
  • multiple wells producing from the same Reservoir.

The X axis on the Gas Flowing Material Balance Plot can be selected as:

Example 1. Multiple wells producing from the same Reservoir. X axis - Wells cumulative FMBex1.png Example 2. Multiple wells producing from the same Reservoir. X axis - Reservoir cumulative FMBex2.png Example 3. Shifted Model Start (to account for gas injection) FMBex3.png


  1. Upload the data required
  2. Open the Gas Flowing Material Balance tool here
  3. 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 )
  4. 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}
  5. 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
  6. 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}
  7. Change the flat JD gray line to match the changing JD gray line
  8. Save the FMB model
  9. 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

In case you need to calculate the flowing bottomhole pressure from the wellhead pressure:

In case you want to add the static reservoir pressures on the FMB Plot:


 b_{pss} = reservoir constant, inverse to productivity index, psia2/cP/MMscfd
 c = compressibility, psia-1
 GIIP = gas initially in place, MMscf
 G_p = cumulative gas produced, MMscf
 J = gas productivity index, MMscfd/(psia2/cP)
 J_D = dimensionless productivity index, dimensionless
 kh = permeability times thickness, md*ft
 P = pressure, psia
 \bar{P} = average reservoir pressure, psia
 P_P = pseudopressure, psia2/cP
 q_g = gas rate, MMscfd
 t = time, day
 t_{ca} = material balance pseudotime for gas, day
 T = temperature, °R
 z = gas compressibility factor, dimensionless

Greek symbols

 \mu = viscosity, cp


g = gas
i = initial
R = °R
wf = well flowing


  1. Mattar, L.; McNeil, R. (1998). "The "Flowing" Gas Material Balance" (PDF). Journal of Canadian Petroleum Technology. Petroleum Society of Canada. 
  2. Mattar, L.; Anderson, D (2005). "Dynamic Material Balance (Oil or Gas-In-Place Without Shut-Ins)" (PDF). CIPC.