Gas Flowing Material Balance

Brief

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

Gas Flowing Material Balance is applied to determine:

• Reservoirs GIIP & EUR
• 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 lines to estimate 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:

$P_{\bar{P}}= P_{P_{wf}} + q_g b_{pss}$

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:

• Well cumulative
• Reservoir cumulative

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

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 b_pss

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

• Create Field here
• Create or Upload Reservoirs here
• Input the Reservoirs GIIP and STOIIP here
• Create or Upload PVT (SG, Pi, Ti) here
• Upload Wells
• Create or Upload Wells Perforations here
• Create or Upload kh and JD here
• Upload Daily Measures

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

• Calculate the flowing bottomhole pressures using BHP Calculator
• Export flowing bottomhole pressures to Daily Measures here

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

• Create or Upload the static reservoir pressures, here
• Calculate Monthly Measures from the Daily Measures using Monthly Data Calculator

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*m

$P$ = 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