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.

Math & Physics

Combine 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:

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

Workflow

1. Convert initial pressure to pseudopressure, $P_{Pi}$
2. Convert flowing tubing pressure to flowing bottomhole pressure, $P_{wf}$
3. Convert all flowing pressures to pseudopressures, $P_{P_{wf}}$
4. Calculate material balance pseudo-time, $t_{ca}$

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