Difference between revisions of "Gas Flowing Material Balance"

Revision as of 08:19, 11 December 2017

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}

^[1]

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

Workflow

Calculate the red line:
1. $\frac{P}{z}=\frac{P_i}{z_i} \left (1- \frac{G_p}{GIIP}\right )$
Calculate the orange 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. Calculate the $b_{pss}$
4. Calculate the pseudopressure, $P_{\bar{P}}$
5. Convert the pseudopressure to pressure, $\bar{P}$
6. Calculate the $\frac{\bar{P}}{z}$
Calculate the gray JD curve:
1. Calculate the gas productivity index: $J=\frac{P_{\bar{P}}-P_{P_{wf}}}{q_g}$

bsss

Calculate initial pseudopressure, $P_{Pi}$ Calculate material balance pseudo-time, $t_{ca}$ Plot $\frac{P_{P_i}-P_{P_{wf}}}{q}$ versus $t_{ca}$ . The intercept gives $b_{pss}$ and $J_D$ . Calculate the average reservoir pseudopressure from Gas Flowing Material Balance equation, $P_{\bar{P}}$

Data required

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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

References

↑ Mattar, L.; Anderson, D (2005). "Dynamic Material Balance (Oil or Gas-In-Place Without Shut-Ins)" (PDF). CIPC.

[Mattar2005-1] Mattar, L.; Anderson, D (2005). "Dynamic Material Balance (Oil or Gas-In-Place Without Shut-Ins)" (PDF). CIPC.

[1]

@@ Line 35: / Line 35: @@
 ## Calculate the <math> \frac{\bar{P}}{z}</math>
 #Calculate the gray [[JD]] curve:
-##Calculate the gas productivity index: <math>J=\frac{\bar{P}-P_{P_{wf}}}{q_g}</math>
+##Calculate the gas productivity index: <math>J=\frac{P_{\bar{P}}-P_{P_{wf}}}{q_g}</math>
 ##

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