Difference between revisions of "Oil Flowing Material Balance"

Revision as of 07:03, 10 April 2018

Brief

Oil Flowing Material Balance (Oil FMB) is the advanced engineering technique published in 2005 by Louis Mattar and David Anderson ^[1].

Oil Flowing Material Balance is applied to determine:

Reservoirs STOIIP & EUR
Well's EUR and JD

Oil Flowing Material Balance uses readily available Well flowing data: production rate and bottomhole pressure.

The interpretation technique is fitting the data points with the straight lines to estimate STOIIP and JD.

Oil Flowing Material Balance in the E&P Portal

Math & Physics

The total pressure drop at the wellbore is:

\Delta P =P_i - P_{wf} = (P_i - \bar{P}) + (\bar{P}-P_{wf})

^[1]

Where

P_i - \bar{P}

, is pressure drop due to depletion defined by the Oil Material Balance

\bar{P}-P_{wf}

, is pressure drop due to Darcy's law

In terms of oil pseudo pressure the total pressure drop is:

\Delta P_{po}=P_{po}(P_i)-P_{po}(P_{wf}) = (P_{po}(P_i) - P_{po}(\bar{P})) + (P_{po}(\bar{P})-P_{po}(P_{wf}))

^[2]

Where

P_{po}(P) = B_o(P_i) \mu_o(P_i) \int\limits_{P_{ref}}^{P} \frac{1}{B_o(P) \mu_o(P)}dp

^[2]

P_{po}(\bar{P})-P_{po}(P_{wf}) = q_o \frac{141.2 B \mu}{kh\ J_D}

Finally, the Oil Flowing Material Balance equation:

Failed to parse (syntax error): {J_D}_{norm} = J_D - \frac{P_{po}(P_i) - {N_p}_{norm} \frac{J_D}{N}

Where

{J_D}_{norm} = \frac{141.2 B \mu}{kh} \frac{q_o}{\Delta P_{po}}

{N_p}_{norm} = \frac{P_{po}(P_i) - P_{po}(\bar{P})}{\Delta P_{po}}N

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

Upload the data required
Open the Gas Flowing Material Balance tool here
Calculate the red line:
1. Given the GIIP
2. Calculate the $\frac{P}{z}=\frac{P_i}{z_i} \left (1- \frac{G_p}{GIIP}\right )$
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. 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 $\frac{\bar{P}}{z}$
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, $J_D=\frac{1422 \times 10^3\ T_R}{kh} J$
Change the red line to match the orange curve
1. Change the GIIP
2. Change the intitial $\frac{P}{z}$
Change the flat JD gray line to match the changing JD gray line
Save the FMB model
Move to the next well

Extra Plot to find b_pss

Calculate the initial pseudopressure, $P_{Pi}$
Calculate the material balance pseudo-time, $t_{ca}$
Plot $\frac{P_{P_i}-P_{P_{wf}}}{q_g}$ versus $t_{ca}$
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

References

↑ ^1.0 ^1.1 Mattar, L.; Anderson, D (2005). "Dynamic Material Balance (Oil or Gas-In-Place Without Shut-Ins)" (PDF). CIPC.
↑ ^2.0 ^2.1 Stalgorova, Louis; Mattar, Ekaterina (2016). "Analytical Methods for Single-Phase Oil Flow: Accounting for Changing Liquid and Rock Properties". Society of Petroleum Engineers.

[Mattar2005-1] 1.0 ^1.1 Mattar, L.; Anderson, D (2005). "Dynamic Material Balance (Oil or Gas-In-Place Without Shut-Ins)" (PDF). CIPC.

[Stalgorova2016-2] 2.0 ^2.1 Stalgorova, Louis; Mattar, Ekaterina (2016). "Analytical Methods for Single-Phase Oil Flow: Accounting for Changing Liquid and Rock Properties". Society of Petroleum Engineers.

[1]

[2]

@@ Line 40: / Line 40: @@
 Finally, the [[Oil Flowing Material Balance]] equation:
-:<math> \frac{141.2 B \mu}{kh} \frac{q_o}{\Delta P_{po}} = J_D - \frac{P_{po}(P_i) - P_{po}(\bar{P})}{\Delta P_{po}}N\ \frac{J_D}{N}</math>
+:<math> {J_D}_{norm} = J_D - \frac{P_{po}(P_i) - {N_p}_{norm} \frac{J_D}{N}</math>
+Where
 :<math> {J_D}_{norm} = \frac{141.2 B \mu}{kh} \frac{q_o}{\Delta P_{po}} </math>

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Difference between revisions of "Oil Flowing Material Balance"

Revision as of 07:03, 10 April 2018

Contents

Brief

Math & Physics

Discussion