One of the most challenging aspects of determining the performance of a crude oil piping system is determining the fluid properties necessary for hydraulic analysis. Properties critical to accurate results such as viscosity, density and vapor pressure can vary significantly because the molecular makeup varies widely, and blends complicate the landscape even further. In many cases, an oil piping system must accommodate a number of different crudes, which presents a significant challenge to the engineer responsible for designing, evaluating or improving flow and efficiency in a crude oil piping system.
Clearly, the preferred method is to the obtain the properties from the specific crude or crudes for which the piping system is destined, since the accuracy of the analysis is only as good as the input data. But what about when the full spectrum of probable crudes is unknown? The relationships between various properties of petroleum fluids has been studied by numerous individuals and it is very difficult to find generalized equations for how these properties vary by temperature. However, by patching some of the studies together and applying regression techniques to data mined from empirical sources some coarse correlations can be derived to approximate how the properties change.
To assist our customers in the design, evaluation and troubleshooting of crude oil piping systems, Engineered Software, Inc. has developed some representative crude oil fluid parameters. Since crudes are generally described as being light, medium or heavy, using an industry recognized term to define the different representative fluids along this vector makes the most sense. The American Petroleum Institute (API) has defined API gravity as the indicator of crude “heaviness” and it is a function of the fluid’s density relative to water. The higher the API gravity (measured in degrees), the less dense the fluid. Most pumpable crudes fall in the range of 15 to 45 API degrees, so providing parameters for representative fluids in 5 API degree steps across this range was deemed to be of sufficient granularity.
The first parameter to be determined was fluid density because of its impact on power required to pump the fluid. Density data versus temperature is readily available in graphical form in Crane’s Technical Paper Number 410 (TP-410), Flow of Fluids Through Valves, Fittings and Pipe, in the graph “Specific Gravity – Temperature Relationship for Petroleum Oils.” The data from the technical paper was digitized and a 2nd order polynomial regression was performed after converting specific gravity to density. Interpolation was used to arrive at temperature and density data pairs for the select API degrees, then another round of regression was applied to that data to determine the appropriate coefficients for the selected APIs. See data plotted below with Crane data points shown as crosses and the interpolated points as dots.
Viscosity, which has an impact on flow, head, efficiency, power and pump NPSHr, required a little more empirical work. Viscosity and API gravity data was extracted from a public pipeline report and analyzed. While there was a coarse correlation – lower API numbers corresponded with higher viscosity – there was still a significant range of viscosities associated with the heavier crudes (see following chart).
As opposed to continuing with a power function regression on the entire data set, data was aggregated around five API values (approximately 20, 30, 35, 40 and 55 API) to arrive at “typical” viscosity values for these data clusters over a range of temperatures. These typical values were then used to generate the appropriate coefficients to determine the viscosity as a function of temperature for the representative API fluids; the purple diamond points on the graph below show the resultant viscosities for the 30°C condition.
Vapor pressure is used in piping system analysis and troubleshooting to determine where flow may be choked or cavitation may occur due to a phase change occurring in the pipes, pumps or devices. Crude oils, being a mixture of compounds which have different vapor pressures, tend to have a range of pressures over which the constituents vaporize at a specific temperature. Furthermore, looking at empirical data (graph below), we see the relationship between API gravity and vapor pressure is very weak, with a wide range of vapor pressures for a narrow range of API gravity. In our range of interest, the logarithmic regression shown passes through roughly the midpoint of the weighted values, so this was used to develop the representative values. The user should recognize that the actual vapor pressure may be >50% higher than what the regression would predict, and evaluate their system with this in mind. Another option is to create a custom fluid with a higher vapor pressure if the pressure anywhere in the system approaches the representative vapor pressure. It bears repeating, especially given the variation that exists, that actual test data from the fluid being pumped through the system in question is far superior to any approximation.
Using a formula included in the EPA’s Emissions Factors Documentation AP-42 Section 7.1, we can derive the coefficients for true vapor pressure versus temperature for crude oils with the API gravities of interest, as shown in the following graph.
Armed with density, viscosity and vapor pressure behavior approximations for a range of temperatures and API gravities, an engineer can analyze crude oil piping systems for their performance. Fluids with these representative properties are available for PIPE-FLO® Professional users to download and use in their models when the measured crude oil properties are not available.