Gas Flowing Material Balance

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:

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

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 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
• Upload Wells here
• Upload Daily Measures here

Nomenclature

$A_p$ = flow area, ft2

$B$ = correlation group, dimensionless

$B$ = formation factor, bbl/stb

$C$ = coefficient for liquid viscosity number, dimensionless

$D$ = pipe diameter, ft

$h$ = depth, ft

$H$ = correlation group, dimensionless

$H_L$ = liquid holdup factor, dimensionless

$f$ = friction factor, dimensionless

$GLR$ = gas-liquid ratio, scf/bbl

$M$ = total mass of oil, water and gas associated with 1 bbl of liquid flowing into and out of the flow string, lb_m/bbl

$N_D$ = pipe diameter number, dimensionless

$N_GV$ = gas velocity number, dimensionless

$N_L$ = liquid viscosity number, dimensionless

$N_LV$ = liquid velocity number, dimensionless

$p$ = pressure, psia

$q_c$ = conversion constant equal to 32.174049, lb_mft / lb_fsec²

$q$ = total liquid production rate, bbl/d

$Re$ = Reynolds number, dimensionless

$R_s$ = solution gas-oil ratio, scf/stb

$SG$ = specific gravity, dimensionless

$T$ = temperature, °R or °K, follow the subscript

$v$ = velocity, ft/sec

$WOR$ = water-oil ratio, bbl/bbl

$z$ = gas compressibility factor, dimensionless

Greek symbols

$\varepsilon$ = absolute roughness, ft

$\mu$ = viscosity, cp

$\rho$ = density, lb_m/ft³

$\bar \rho$ = integrated average density at flowing conditions, lb_m/ft³

$\sigma$ = surface tension of liquid-air interface, dynes/cm (ref. values: 72 - water, 35 - oil)

$\psi$ = secondary correlation factor, dimensionless

Subscripts

g = gas

K = °K

L = liquid

m = gas/liquid mixture

o = oil

R = °R

SL = superficial liquid

SG = superficial gas

w = water