Oil Flowing Material Balance

Brief

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

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:

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

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:

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

Where

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

$P_{po}(\bar{P})-P_{po}(P_{wf}) = q_o \frac{141.2 B_o(P) \mu_o(P)}{kh\ J_D}$

Finally, the Oil Flowing Material Balance equation:

$\frac{141.2 B_o(P) \mu_o(P)}{kh} \frac{q_o}{\Delta P_{po}}= J_D -\frac{P_{po}(P_i) - P_{po}(\bar{P})}{\Delta P_{po}}N\ \frac{J_D}{N}$

Or

${J_D}_{norm} = J_D -{N_p}_{norm} \frac{J_D}{N}$

Where

${J_D}_{norm} = \frac{141.2 B_o(P) \mu_o(P)}{kh} \frac{q_o}{\Delta P_{po}}$

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

Discussion

Oil Flowing Material Balance can be applied to:

• single well
• multiple wells producing from the same Reservoir.

The X axis on the Oil Flowing Material Balance Plot can be selected as:

• Well cumulative
• Reservoir cumulative

Note what Oil Flowing Material Balance accounts for the changing PVT properties of the oil.

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 Oil Flowing Material Balance tool here
3. Estimate the N (red line X-axis intercept)
4. Calculate the average reservoir pressure $\bar{P}$ based on N, known production data and using Oil Material Balance equation
5. Calculate the ${J_D}_{norm}$
6. Calculate the ${N_p}_{norm}$
7. Plot the orange ${J_D}_{norm}$ vs ${N_p}_{norm}$ line:
8. Change the N to match the orange line with the red one
9. Change the gray JD line Y-axis intercept to match the changing JD
10. Save the Oil Flowing Material Balance model
11. Move to the next well

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

$B_{o}(P)$ = oil formation volume factor as a function of pressure, bbl/stb

$J$ = 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

$P_i$ = initial reservoir pressure, psia

$P_{po}$ = oil pseudo pressure, psia

$P_{ref}$ = reference pressure, 14.7 psia

$P_{wf}$ = well flowing pressure, psia

$q_g$ = gas rate, MMscfd

$t$ = time, day

$t_{ca}$ = material balance pseudotime for gas, day

$T$ = temperature, °R

$z$ = gas compressibility factor, dimensionless

$N$ = stock tank oil initially in place, stb

Greek symbols

$\mu_o(P)$ = oil viscosity as a function of pressure, cp

Subscripts

g = gas

i = initial

R = °R

wf = well flowing