Phase Volume Correlations

With Piper, you can calculate in-situ phases as a function of temperature and pressure by way of either the Wilson equilibrium ratio method or the Peng Robinson equation of state.

Equilibrium Ratios

Piper includes the Wilson equilibrium ratio calculation. This is the most basic equilibrium ratio method and is also used as a first iteration approximation of equilibrium ratios for the Peng-Robinson equation of state.

The Wilson equilibrium ratio correlation is as follows:

Where is calculated for each component and where are all stored parameters for each component.

Peng-Robinson Equation of State

Piper uses the Peng Robinson equation of state to solve for phase volumes in the pipeline. Piper requires a 12 component compositional definition to use Peng Robinson.

Piper currently does not perform volume translation on its Peng-Robinson solution.

Water is also currently considered outside of the equation of state model.

The following iterative process is used to calculate equilibrium ratios and from that the molar volumes of the gas and oil phases. Note that Wilson equilibrium ratios are calculated as the first guesses of the equilibrium ratios.

Procedure for calculating gas and oil phases from Equilibrium ratios

Once equilibrium ratios have been solved for, the volumes of each component

Oil Phase:

Gas Phase:

Calculation of C7+ Properties

The 12 component composition that Piper uses has one pseudo-component, the C7+fraction.The C7+fraction is intended to represent the combined influence of all components greater than C7in the flash calculation process. Therefore a set of equivalent pseudo-properties need to be calculated for the component. These are described below:

The parameter , which is used in the Standing Equilibrium ratio correlation can be calculated as follows (from PVT and Phase Behavior of Petroleum Fluids - Danesh):

Where is calculated as follows (from PVT and Phase Behavior of Petroleum Fluids - Danesh):

Boiling Point

The boiling point can be calculated from the Soreide correlation (from Phase Behavior – Whitson):

Critical Properties

Once the boiling point is calculated the critical properties can be calculated for each pseudo-component. The calculation of critical temperature and pressure follows the process described by Twu. The process involves a number of calculations but they aren’t difficult (all of the steps below are from Phase Behavior – Whitson) :

1. Calculate for each pseudo-component:

2. Calculate for each pseudo-component:

3. Calculate paraffin specific gravity for each pseudo-component:

4. Calculate paraffin critical volume for each pseudo-component:

5. Calculate paraffin critical pressure for each pseudo-component:

6. Calculate for each pseudo-component:

7. Calculate for each pseudo-component:

8. Calculate for each pseudo-component:

9. Calculate for each pseudo-component:

10. Calculate for each pseudo-component:

11. Calculate for each pseudo-component:

12. Calculate for each pseudo-component:

13. Calculate for each pseudo-component:

14. Calculate for each pseudo-component:

Acentric Factor

The acentric factor can be calculated from the Lee-Kesler correlations:

1. Calculate the reduced normal boiling point  for the fraction:

2. If < 0.8, then calculate the acentric factor for each pseudo-component using the following:

3. If 0.8, then calculate the acentric factor for each pseudo-component using the following:

Post-phase calculation properties

Once the phase calculations (either Peng-Robinson or Wilson) has been completed, fluid properties for both the gas and oil phases need to be calculated. This section describes the methods used to calculate each property.

Calculation of Oil Density for Compositional Model

The Standing-Katz method with the Vogel-Yarborough treatment of Nitrogen is used to calculate the density of the oil. Corrections made include nitrogen, ethane density, and methane density.

1. Add the weight fraction of the nitrogen to the weight fraction of the ethane to form a new ethane content for the purpose of this calculation

2. Calculate the molecular weight of the to  with the following summations:

3. Calculate the molar volume of the to  with the following summation, where ( is the liquid density of each component:

4. Calculate the density of the liquid

5. Calculate the density of the

6. Calculate the molecular weight of the to  components with the following summations:

7. Calculate the molar volume of the to components with the following summation, where (is the liquid density of each component except for ethane which has its density replaced with the density calculated in the calculation above

8. Calculate the density of the liquid

9. Calculate the density of the

10. Calculate the molecular weight of the to components with the following summations:

11. Calculate the molar volume of the to components with the following summation, where (is the liquid density of each component except for ethane which has its density replaced with the density calculated in the calculation above

12. Calculate the density of the liquid

The Vogel corrections are applied to Standing-Katz when the in-situ oil density is required.

Calculation of Oil Viscosity for Compositional Model

The Lorenz, Bray and Clark correlation is used to calculate compositional oil viscosity.

1. Calculate the coefficients of the Lorenz, Bray and Clark equation




2. Calculate the mixture viscosity parameter

3. Calculate the term required to calculate reduced oil density

4. Calculate the reduced oil density ():

5. Calculate , which will be used in the calculation of

6. Calculate for each component of Table 2

If :

If :

7. Calculate the viscosity of the live oil at atmospheric pressure (

8. Use the Lorenz, Bray and Clark equation used to calculate viscosity

Gas Compressibility

When Peng-Robinson is selected, the gas compressibility comes directly from the equation of state solution.

When Wilson is selected, gas compressibility is calculated using BWR after converting the full composition into an equivalent gas gravity.

Gas Viscosity

Gas viscosity for both Peng-Robinson and Wilson are calculated using the Carr et al. gas viscosity correlation.

Exclusion of Water from the Compositional Model

Water is not currently considered in the equation of state routine. The exclusion of water was done in the interests of minimizing solution time of the equation of state model, and while keeping in mind that the intent of Piper is to perform pipeline hydraulics calculations, which tend to have only a secondary and tertiary link to the impact of water of condensation and gas dissolved in water.

Instead of including water in the equation of state model black oil like adjustments are made to the gas molar volume and water volume.

Adjustments to dissolved gas in the water are made using the Meehan correlation prior to the equation of state calculation, which therefore effectively removes the gas volume that is dissolved in the water phase.

Adjustments to evaporated water in the gas are made using the Bukacek correlation post-phase volume calculations.

Black Oil in Piper allows for calculation of the change in fluid volumes between in-situ and standard conditions.

When using the Black Oil phase volume calculations, each node in the system will have gas, oil, and water reported in standard conditions and in-situ volumes. While the total standard conditions volumes for each fluid will be consistent throughout the system, the in-situ volumes account for the changing pressure and temperature and the effect on free gas and water relative to those in solution or vapour phase. The image below illustrates the comparison of standard conditions and in-situ volumes.

The change in free gas and water for in-situ volumes between two nodes are determined from the Rso, Rsw, and WoC for the pressure and temperature of each node. When the change in pressure and temperature between two nodes result in an increasing Rso or Rsw, there will be less free gas at the in-situ conditions of the second node.

The equations used are listed below. A single equation for each Rsw and WoC are provided. The equation used for Rso is dependent on the correlation selected for Oil PVT in the Correlations dialog.

Solution Gas Oil Ratio

Vasquez & Beggs

Developed from data obtained from fields all over the world and generally applicable for all oil types. Covers a wide range of pressures, temperatures and oil properties.

Coefficient

API < 30

API > 30

C1

0.0362

0.0178

C2

1.0937

1.1870

C3

25.7245

23.931

De Ghetto et al

The above equations are suitable for oils with gravity of 10° < API < 22.3°. A modified version of the De Ghetto equations exists for oils below 10°, however this is outside the range of Piper intended use.

Glaso

This correlation is based on North Sea crude-oil data. It is suitable for oil gravity of 22° < API < 48° and believed to be less accurate for Rso > 1400 scf/STBO. This equation cannot be used for p > 19285 psia as a result of the pb* equation.

Hanafy et al

This correlation has been developed independent of oil gravity and temperature. Comparisons have demonstrated that it is more applicable to light oils.

Rso = 0 when p 157.28 psia.

Standing

Applicable for oil gravity of 16° < API < 64°

Petrosky and Farshad

Applicable for oil gravity of 16° < API < 45°. For Gulf of Mexico oils, it has been found to provide improved results over Standing, Vasquez and Beggs, and Glaso.

Velarde at al

Applicable for oil gravity of 12° < API < 55°

Solution Gas Water Ratio

The above equation describes gas solubility in pure water. The following equation corrects the Rsw for salinity.

Water of Condensation

Nomenclature

 

Description

Units

γg

Gas gravity

 

γAPI

API oil gravity

°API

p

System pressure

psia

psep

Separator pressure

psia

Rso

Solubility of gas in oil

scf/STBO

Rsw

Solubility of gas in water

scf/STBW

S

Salinity of water

Weight % of NaCl

T

Temperature

°F

Tsep

Separator temperature

°F

WoC

Water of condensation

STBW/MMscf