Suppose we want to do leak detection on a segment of a pipeline transporting a petroleum fluid from one place to another. Perhaps this segment directly connects the ends, maybe a pump or compressor station at the high-pressure end to a storage facility or another pipeline at the low-pressure end. We may know the length, L, the diameter of flow, D, perhaps some pipe wall properties such as the wall roughness, the elevation of each end relative to a common datum, and some things about the fluid.

To define this as a hydraulic segment we draw a dotted line, a “box,” around it, generally with consideration of where the various instruments we use to observe its operation are located. Let’s assume we have observations (measurements) of pressure and flow at each end; four observations in all. Further, we know that the pressure inside the pipe is significantly higher that the pressure of the environment around it. In normal operation we would expect that:

• P1, upstream pressure, is greater than P2, the downstream pressure
• Q1, upstream flow, is more-or-less equal to Q2, downstream flow averaged over time

If a leak occurs on the segment, we would expect the following things to happen:

• Flow upstream of the leak would go up
• Flow downstream of the leak would decrease
• Upstream pressure would decrease
• Downstream pressure would decrease

A detection algorithm could be based on the idea that the coherent occurrence of all four of those conditions is “sufficient” to detect a leak. Each of those conditions is independently “necessary,” but all four are necessary for “sufficiency.” Considering that criteria for leak detection we need observability of those four measurements in a time scheme that ensures we can establish they are all the result of the same disturbance (the leak event).

Over time, the leakage rate usually stabilizes, and the leaking pipeline migrates its operation to a new steady state in which all four conditions are evident. If the leak is stable so will be this new operating condition. Those are the observations with which we can do our analysis.

The enormous assumption thus far in this discussion is that the fluid is everywhere the same – homogeneous throughout the segment and at its ends. What if the pressure drop at the leak location is sufficient to flash some of the normally liquid flow into gas? That might limit flow through the leak path and it might change the nature of flow inside the pipe near the leak location from liquid to multiphase.

We may also discover that a leak hole of a particular size might support a much smaller mass flow rate than might be expected if conditions in the leak were the same as in the pipeline. The fastest the fluid can leak is sonic velocity and the density of the fluid at low pressure will be much smaller than at pipeline conditions. There will be a blog about such issues in the future.

Note that the term “coherence” snuck in here. It’s there to foreshadow an upcoming blog about discerning whether of not a series of observed events are, in fact, related – spawned from the same event.

At present, though, the discussion is on necessary and sufficient conditions and the significance we might attach to them.

Suppose all of the conditions are met except the upstream flow decreases instead of increasing? Depending on the upstream process equipment (e.g., a pump) it might be possible the flow would remain constant as opposed to increasing but there is usually no way a leak would cause it to decrease. A bit more thought might reveal the detected condition is, while similar to what could be expected from a leak, exactly what would occur with a shutdown or a decrease to a lower flow rate. The presence of the other three conditions are a necessary outcome of a leak, but without the appropriate behavior of upstream flow they are not sufficient.

Often, there is some seldom-used feature or unusual operating condition that can mimic most of what is necessary for a set of events to be detected as a leak. Such things can result in false alarms. Possibly the most capable engineer I’ve ever worked with was once challenged with determining why a largely above-ground pipeline in Alaska would produce false alarms with no discernable reason whatsoever.

To service one of these “probably false” alarms he was driving across an uncharacteristically bright and sunny North Slope and found himself thinking, “Well, at least these things always happen on nice and sunny days!” With that thought he changed his thinking to sun-sensitive issues and discovered a subtle problem stemming from some unproductive assumptions about a key pipeline measurement. The irritating and recurring problem was over by the end of the day.

Understanding how the process system and automation equipment work is crucial: sometimes there is a problem to fix, sometimes some process condition is screaming for attention, sometimes there is an unproductive or incorrect assumption about how things actually work. All that is fixable. Sometimes there is just one more process condition or issue that you need to know. When that is the case you need to make a way to observe it.