# 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 [1].

Oil Flowing Material Balance is applied to determine:

Oil Flowing Material Balance uses readily available Well flowing data: production rate, wellhead pressures and the fluid levels.

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

Finally, the Oil Flowing Material Balance equation:

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

Or

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

Where

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

## 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:

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

## Case Study

This Case Study demonstrates the application of the Oil Flowing Material Balance engineering technique using the E&P Portal.

The Study is based on the oil well from a field in West Siberia, Russia.

It is shown how to:

• Input the data to the E&P Portal;
• Apply the Oil FMB to estimate the well's STOIIP and JD;
• Save and export the analysis results.

All the input data is attached to the Case Study for the reference.

## Workflow

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

In case you need to calculate the flowing bottomhole pressure from the wellhead pressure:

In case you want to add the static reservoir pressures on the FMB Plot:

## Nomenclature

$B_{o}(P)$ = oil formation volume factor as a function of pressure, bbl/stb
$J_D$ = dimensionless productivity index, dimensionless
${J_D}_{norm}$ = dimensionless productivity index in terms of the oil pseudo pressure, dimensionless
$k_oh$ = oil permeability times thickness, md*ft
$N$ = stock tank oil initially in place, stb
${N_p}_{norm}$ = normalized cumulative oil production, stb
$P$ = pressure, psia
$\bar{P}$ = average reservoir pressure, psia
$P_{i}$ = initial pressure, psia
$P_{po}$ = oil pseudo pressure, psia
$P_{ref}$ = reference pressure, psia
$P_{wf}$ = well flowing pressure, psia
$q_o$ = oil rate, stb/d

### Greek symbols

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

## References

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