# Gas Flowing Material Balance

## Brief

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]

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

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

## Workflow

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:

## Nomenclature

$b_{pss}$ = 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

### Subscripts

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

## References

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.