# Viscosity tuning for PVT Analysis in VMGSim

*Herbert Loria - VMG Calgary*

### Introduction

Oil viscosity, like any other physical property, is affected by both temperature and pressure. An increase in temperature causes a decrease in viscosity. A decrease in pressure causes a decrease in viscosity, provided that the only effect of pressure is to compress the liquid. In addition, in the case of reservoir fluids, a decrease in the amount of gas in solution in the liquid causes an increase in viscosity, and, the amount of gas in solution is a direct function of pressure.

The following figure shows the relationship of the viscosity of a reservoir oil to pressure at constant temperature. At pressures above the bubble point, the viscosity of the oil in a reservoir increases almost linearly as pressure increase. However; as reservoir pressure decreases below the bubble point, the liquid changes composition. The gas that evolves takes the smaller molecules from the liquid, leaving the remaining reservoir liquid with relatively more molecules with large complex shapes. This changing liquid composition causes large increments in viscosity of the oil in the reservoir as pressure decreases below the bubble point [1].

Oil Viscosity is measured in a rolling-ball or a capillary viscometer designed to simulate **differential liberation** experiments. Measurements are made at several values of
pressure in a stepwise process [1]. The liquid used in each measurement is the liquid remaining after gas has been removed at that pressure.

The behaviour of the oil viscosity in a reservoir is difficult to model with the common viscosity correlations and models (Andrade, Twu, American Petroleum Institute, Letsou-Stiel, Beggs and Robinson, etc.) since most of them are only temperature dependent or are only valid for certain temperature or density ranges. The Expanded Fluid viscosity model, recently implemented in VMGSim [2], is an excellent candidate to model the viscosity of reservoir fluids since it is direct function of pressure and density.

The objective of this document is to show that the viscosity of oils from reservoir fluids measured in PVT analyses can be simulated by the Expanded Fluid model and how to tune the model’s interaction parameters to match any available experimental data.

### PVT Analysis Unit Operation – Viscosity Calculation

Oil viscosity calculations in the new **PVT Analysis** unit operation of **VMGSim** are based on differential liberation experiments, where the liquid and gas
composition change in every pressure step below the saturation pressure. If the **Expanded Fluid** correlation is the active viscosity model in the **Property
Package** used for PVT calculations then, the following viscosity trends can be obtained through different pressures stages.

If experimental data is available the **Expanded Fluid** model can be adapted to match those values. The following example, based on the Reservoir Characterization and PVT
Analysis of a previously presented newsletter article [3], will be used to illustrate this process.

#### PVT Analysis Example

As mentioned before this example is the continuation of the one presented in a previous newsletter article [3], the example starts with a stream containing an already characterized reservoir
fluid, the fluid was characterized using the **PIONA Characterization** scheme and its physical properties were regressed using an **Oil Source** unit operation. The
reservoir fluid is black oil with a molecular weight of 98.3, and standard liquid density of 72.68 API and a saturation pressure of 2634.7 psia at 220 F.

The viscosity data for this reservoir fluid is provided in the next figure [1].

To calculate these viscosities, the **Reservoir Fluid** stream is connected to a **PVT Analysis** unit operation, there the **Viscosity (Vis)** box is
checked in the **Summary** tab and the different pressure stages from the previous table are added.

It is interesting to observe that the active viscosity model, the **Expanded Fluid** method, although it does not match the liquid viscosities *a priori*, it is predicting
the right tendency of viscosity vs. pressure, i.e. the viscosity increases with pressure after the Saturation point. If the viscosity model is switched to Default (Advanced Peng Robinson
Empirical [4]) it will be noted that the liquid viscosity becomes constant for pressures above the saturation point, as seen it the next plot, making the default model unsuitable for PVT
analyses.

The **Expanded Fluid** model can be further tuned to match the liquid viscosity and this can be done by using the recently improved **OilProp** unit operation [4], a
unit operation to regress the interaction parameters of viscosity and density models to match provided experimental data. To tune the liquid viscosity, an **OilProp** unit
operation is added to the case, the following settings are entered and the Material Stream with the reservoir fluid is added as the *Reference Stream* in *Mix_0*:

Then, in the *Property Curves* frame the *Viscosity Curve* is selected and the 17 experimental Oil viscosity points are added, note that since the oil viscosity will be tuned
the **OilProp** is set to calculate *Liquid* phase viscosity.

The unit operation is ready to tune the interaction parameters of the Expanded Fluid viscosity model to match the experimental data; the **Plot** tab shows a figure where the
difference between the calculated and experimental values can be seen.

Now, the regression is performed by clicking on the **Regress Parameter** button and once it is finished, the **Plot** tab will show the updated results.

Now return to the **PVT Analysis** unit operation and observe that the oil viscosity values now match the experimental data, the average absolute error between experimental and
calculated values is 3.3 %.

The new **PVT Analysis** unit operation along with the **Expanded Fluid** model and the **OilProp** unit operation are very useful tools for the design
and simulation of PVT analyses experiments in VMGSim.

### References

[1] **MacCain Jr., W. D.** *The Properties of Petroleum Fluids* 2^{nd} Ed*.* Tulsa, OK: PenWell Publishing Company, 1989

[2] **Loria, H., Motahhari, H., Satyro, M.A. and Yarranton H.W.** *Process Simulation Using the Expanded Fluid model for Viscosity Calculations* Chemical Engineering
Research and Design, 2014, **92**, 2083-2095

[3] **Loria, H.** *Reservoir Fluid Characterization nd PVT Analysis in VMGSim* Inside VMG, May 2015

[4] **VMG Inc.** *VMGSim 9.0 User Manual*, 2014