When I was much younger I spent a lot of time driving the complex freeway network around San Francisco. Often there were several engineers in a car together, all motivated to understand how to get from where we were to where we were going more quickly. Eventually, the discussion turned to how similar the traffic was to the flow of water through pipes and conduits. We wondered if fluid flow science could be used to predict or even model traffic flow. After a few mornings of this the smartest guy in the car offered to buy lunch for the first guy that could verbalize the answer.

Confronted with a deafening silence he said that each car-particle in the “flowing” stream was different from fluid flow in at least one profound way (beyond its modularity). In the case of a car, where it was going to go, or what it was going to do, next depended on what happened in the car-module itself; while in a flowing stream, where any element of the flowing stream went was the result of a vector field of circumstances surrounding it. If course, our late friend Chuck was observing that the science we used in fluid mechanics was based on the Navier-Stokes analysis which was, in turn based on the Cauchy momentum equation, all of which predicted fluid motion based on fields of parameters (e.g., pressure, energy, temperature) over the field of flow. It also depends on conditions in the fluid itself as it encounters that Cauchy field.

Fluids have a lot of condition-dependent properties. They consist of solids, liquids, gasses, or combinations thereof. At any region, their flow-state condition impacts their density and viscosity, both of which have a lot to do with how they respond to the field of parameters around them. While most of elementary fluid mechanics is based on the idea of “homogeneous flow” it is very uncommon in the petroleum world to find one. Vapor pressure, for example, is the surrounding pressure required to maintain a liquid in a vapor-free state. If the surrounding pressure is below the vapor pressure some portion of the liquid will “flash” into vapor.

When the fluid temperature increases so does the vapor pressure. In any region of the pipeline, of course, the density of the fluid found there depends on how much of it is gas and how much is liquid. All parameters dependent on density are affected by these changes. Sometimes these changes impact the ability of process equipment to operate as intended. For example, a meter designed for gas flow measurement may mismeasure a gas-liquid stream of the same chemical composition.

A lot of process design goes into anticipating and mitigating such problems. The more precise understanding of the fluid field needs to be the more important these issues are. Of course accuracy and understanding of these issues can have a lot to do with process measurements and characterization of the impacts that may stem from them.

In leak detection there are a lot of fluid state issues, beginning with changes in density appearing as changes in velocity or changes in mass that adversely affect calculations based on unwarranted assumptions.

Observation of these conditions, or even the parameters that influence them, are exacerbated by the generally substantial distances pipelines traverse. Further, some parts of the pipeline may be buried, some parts may be exposed to sun and weather, and some may be buried in soil with weather-dependent thermal conductivity.

Observation may be difficult; and without it, precise parameter assessment and anticipation of the resulting fluid characteristics may not be possible. It all sounds impossibly complex but with some good design decisions and some anticipation of the likely effects, success is possible albeit with accuracy and sensitivity dependent on the quality of what can be known about the situation.

Can these issues be resolved by modeling? Generally yes, to a degree; but it remains impossible to manufacture data. One can draw a straight line between two points. One can draw a parabola or a hyperbola through a couple of points, and estimate a cubic with three. Beyond the simple things, either more data or more assumptions are required. Once upon a time I was assisting a researcher on a process enhancement issue.

During the discussion I observed that for a curve as complex as what he was expecting we needed more that the two points we could put a simple curve through. He then pronounced in jest that he could present a family of curves using but a single point. This guy was very smart and a pioneer in process control, and perhaps a lot of his ability came from knowing more about these process dynamics that the rest of us. In any case, he went on to do some really great things, but…