How to Solve and Calculate for a Dimensionless Pressure Drop, Oil Rate, Oil FVF, Oil Viscosity in Well Testing | The Calculator Encyclopedia

To calculate the dimensionless pressure drop, five essential parameters are needed, and these parameters are Permeability-Thickness Product (kh), Pressure Drop (ΔP), Oil Rate (Q_o), Oil Viscosity (μ_o), and Oil FVF (B_o).

The formula for calculating dimensionless pressure drop:

P_D = ^khΔP / _141.2QoBoμo

Where;

P_D = Dimensionless Pressure Drop
kH = Permeability-Thickness Product
ΔP = Pressure Drop
Q_o = Oil Rate
μ_o = Oil Viscosity
B_o = Oil FVF

Let’s solve an example;
Find the dimensionless pressure drop with a permeability-thickness product of 70, a pressure drop of 30, an oil rate of 49, an oil viscosity of 19 and oil FVF of 31.

This implies that;

kh = Permeability-Thickness Product = 20
ΔP = Pressure Drop = 30
Q_o = Oil Rate = 49
μ_o = Oil Viscosity = 19
B_o = Oil FVF = 31

P_D = ^khΔP / _141.2QoBoμo
P_D = ^{20 x 30}/_{141.2 x 49 x 31 x 19}
So, P_D = ^{20 x 30}/_4075173.19
P_D = ⁶⁰⁰/_4075173.19
P_D = 0.000147

Therefore, the dimensionless pressure drop is 0.000147 psi.

Calculating the Permeability-Thickness Product when Dimensionless Pressure Drop, Pressure Drop, Oil Rate, Oil Viscosity and Oil FVF

kh = ^{P_D x 141.2Q_oB_oμ_o} / _ΔP

Where;

kh = Permeability-Thickness Product
P_D = Dimensionless Pressure Drop
ΔP = Pressure Drop
Q_o = Oil Rate
μ_o = Oil Viscosity
B_o = Oil FVF

Let’s solve an example;
Find the permeability-thickness product with a dimensionless pressure drop of 28, a pressure drop of 16, an oil rate of 21, an oil viscosity of 18 and oil FVF of 24.

This implies that;

P_D = Dimensionless Pressure Drop = 28
ΔP = Pressure Drop =16
Q_o = Oil Rate = 21
μ_o = Oil Viscosity = 18
B_o = Oil FVF = 24

kh = ^{P_D x 141.2Q_oB_oμ_o} / _ΔP
Then, kh = ^{28 x 141.2 x 21 x 24 x 18} / ₁₆
kh = ^35867059.8 / ₁₆
kh = 2241691.2

Therefore, the permeability-thickness product is 2241691.2.

Read more: How to Calculate and Solve for Well, External and Dimensionless Radius | Nickzom Calculator

Calculating the Pressure Drop when Dimensionless Pressure Drop, Permeability-Thickness Product, Oil Rate, Oil Viscosity and Oil FVF

ΔP = ^{P_D x 141.2Q_oB_oμ_o} / _kh

Where;

ΔP = Pressure Drop
P_D = Dimensionless Pressure Drop
kh = Permeability-Thickness Product
Q_o = Oil Rate
μ_o = Oil Viscosity
B_o = Oil FVF

Let’s solve an example;
Find the pressure drop with a dimensionless pressure drop of 38, a permeability-thickness product of 24, an oil rate of 11, an oil viscosity of 8 and oil FVF of 12.

This implies that;

P_D = Dimensionless Pressure Drop = 38
kh = Permeability-Thickness Product = 24
Q_o = Oil Rate = 11
μ_o = Oil Viscosity = 8
B_o = Oil FVF = 12

ΔP = ^{P_D x 141.2Q_oB_oμ_o} / _kh
ΔP = ^{38 x 141.2 x 11 x 12 x 8} / ₂₄
Then, ΔP = ^5666073.6 / ₂₄
ΔP = 236086.4

Therefore, the pressure drop is 236086.4.

Calculating the Oil Rate when Dimensionless Pressure Drop, Permeability-Thickness Product, Pressure Drop, Oil Viscosity and Oil FVF

Q_o = ^khΔP / _{PD x 141.2Boμo}

Where;

Q_o = Oil Rate
P_D = Dimensionless Pressure Drop
kh = Permeability-Thickness Product
ΔP = Pressure Drop
μ_o = Oil Viscosity
B_o = Oil FVF

Let’s solve an example;
Find the oil rate with a dimensionless pressure drop of 60, a permeability-thickness product of 30, a pressure drop of 34, an oil viscosity of 11 and oil FVF of 25.

This implies that;

P_D = Dimensionless Pressure Drop = 60
kh = Permeability-Thickness Product = 30
ΔP = Pressure Drop =34
μ_o = Oil Viscosity = 11
B_o = Oil FVF = 25

Q_o = ^khΔP / _{PD x 141.2Boμo}
That is, Q_o = ^{30 x 34} / _{60 x 141.2 x 25 x 11}
Q_o = ¹⁰²⁰ / _2329800
Q_o = 4.37e-4

Therefore, the oil rate is 4.37e-4

Calculating the Oil FVF when Dimensionless Pressure Drop, Permeability-Thickness Product, Pressure Drop, Oil Rate and Oil Viscosity

B_o = ^khΔP / _{PD x 141.2Qoμo}

Where;

B_o = Oil FVF
P_D = Dimensionless Pressure Drop
kh = Permeability-Thickness Product
ΔP = Pressure Drop
Q_o = Oil Rate
μ_o = Oil Viscosity

Let’s solve an example;
Find the oil FVF with a dimensionless pressure drop of 40, a permeability-thickness product of 10, a pressure drop of 7, an oil rate of 3 and oil viscosity of 5.

This implies that;

P_D = Dimensionless Pressure Drop = 40
kh = Permeability-Thickness Product = 10
ΔP = Pressure Drop = 7
Q_o = Oil Rate = 3
μ_o = Oil Viscosity = 5

B_o = ^khΔP / _{PD x 141.2Qoμo}
Hence, B_o = ^{10 x 7} / _{40 x 141.2 x 3 x 5}
B_o = ⁷⁰ / ₈₄₇₂₀
B_o = 8.26e-4

Therefore, the oil FvF is 8.26e-4.

Calculating the Oil Viscosity when Dimensionless Pressure Drop, Permeability-Thickness Product, Pressure Drop, Oil Rate and Oil FVF

μ_o = ^khΔP / _{PD x 141.2QoBo}

Where;

μ_o = Oil Viscosity
P_D = Dimensionless Pressure Drop
kh = Permeability-Thickness Product
ΔP = Pressure Drop
Q_o = Oil Rate
B_o = Oil FVF

Let’s solve an example;
Find the oil viscosity with a dimensionless pressure drop of 20, a permeability-thickness product of 9.5, a pressure drop of 4.6, an oil rate of 3.5 and oil FVF of 4.

This implies that;

P_D = Dimensionless Pressure Drop = 20
kh = Permeability-Thickness Product = 9.5
ΔP = Pressure Drop = 4.6
Q_o = Oil Rate = 3.5
B_o = Oil FVF = 4

μ_o = ^khΔP / _{PD x 141.2QoBo}
μ_o = ^{9.5 x 4.6} / _{20 x 141.2 x 3.5 x 4}
So, μ_o = ^43.7 / ₃₉₅₃₆
μ_o = 0.001105

Therefore, the oil viscosity is 0.001105.

How to Calculate for a Dimensionless Pressure Drop Using The Calculator Encyclopedia

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the dimensionless pressure drop.

To get the answer and workings of the dimensionless pressure drop using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.

You can get this app via any of these means:

Web – https://www.nickzom.org/calculator-plus

To get access to the professional version via web, you need to register and subscribe for NGN 1,500 per annum to have utter access to all functionalities.
You can also try the demo version via https://www.nickzom.org/calculator

Android (Paid) – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator
Android (Free) – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator
Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8
Once, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Petroleum under Engineering

Now, Click on Well Testing under Petroleum

Now, Click on Dimensionless Pressure Drop under Well Testing

The screenshot below displays the page or activity to enter your values to get the answer for the dimensionless pressure drop according to the respective parameters, which are the Permeability-Thickness Product (kh), Pressure Drop (ΔP), Oil Rate (Q_o), Oil Viscosity (μ_o) and Oil FVF (B_o).

Now, enter the values appropriately and accordingly for the parameters as required by the Permeability-Thickness Product (kh) is 20, Pressure Drop (ΔP) is 30, Oil Rate (Q_o) is 49, Oil Viscosity (μ_o) is 19 and Oil FVF (B_o) is 31.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the dimensionless pressure drop and presents the formula, workings and steps too.