Pipeline Geotechnics: Heat Transfer & Thermal Conductivity

Thermal Properties of Soil

In the offshore space, we normally consider heat transfer through saturated soil to be dominated by conduction, rather than convection or radiation. If one takes a conceptual view of soil in which the material is considered as a continuum, then it would be logical that if a discrete part of this continuum were to be tested, then the properties should be representative of the whole. This assumption forms the basis on which many of the test methods for soil have been developed. Given that we assume the dominant heat transfer mechanism is convection and that we consider the material as a continuum the best practice solution for measuring heat transfer has become the thermal conductivity probe.

Needle Probe Thermal Conductivity Measurement

The test method for thermal conductivity measurement is defined in ASTM D5334-8, you can read some of the commentary on the test method here. The test apparatus and typical test results are presented in Figure 1 below.

Figure 1: Schematic of test equipment for thermal conductivity needle probe apparatus
Schematic of thermal conductivity measurement with a needle probe

It’s interesting that this test method has become accepted best practice as the accuracy of test method is very sensitive to a number of parameters. Firstly, according to Manohar, Yarbrough & Booth, the method provides very repeatable results on dry soil, however, it is further stated that a reference material should be selected that has a “thermal conductivity” similar to the specimen being tested.

For most naturally occurring soils one can expect to find a quantity of moisture within the void space, and so it is very common that soils are partially saturated. In the offshore environment, if one assumes there are no free gasses in the void space, the soil can be considered to be totally saturated.

The second condition for achieving accurate results is to select an appropriate reference material. Different laboratories tend to use different reference materials to calibrate the needle probe, these can vary from agar jelly to glycol, but most certainly not quartz or other minerals. I’m a little uncertain how glycol can be used, given it is a high viscosity liquid in which convection may also occur. Perhaps somebody can educate me?

Limitations of the Needle Probe

In the author’s experience, once samples of high permeability / free draining soils such as sand arrive in the laboratory they can not be expected to be fully saturated. If the soil specimen being tested is not re-saturated then the needle probe test could be performed on soil that is in a partially saturated state – even though the in-situ soils are fully saturated.

The sensitivity of the method to the degree of saturation, is something not widely appreciated and having reviewed the results of tests performed on over 500 sand samples, this can introduce a degree variability that is difficult to normalise for, or attribute to the correct cause. In some cases the observed variability is mistakenly assumed to be a feature of the in-situ soil rather than a side-effect of sample preparation and test procedure: i.e. poorly defined boundary conditions. I would say there is a real and pressing need to establish a more controlled test method based on reliable boundary conditions: luckily Dr. Stuart Haigh at Cambridge University is focusing some research effort on this point.

Consequences for Design

If we look at the a subset of the data available for thermal conductivity testing on sand soil in the North Sea, (Figure 2) we can see the suggestion of a trend (I removed some of the data for clarity). We can perhaps argue that for increasing moisture content we would expect a reduction in thermal conductivity. We may also pick another trend, and that is for lower moisture content, say less than 22%, there is much more pronounced scatter in the results. Interesting.

Figure 2: Thermal conductivity measurements versus moisture content for North sea sand
Thermal conductivity measurements for sand soil and varying moisture content for North sea sediments

If we choose to pivot the data differently, we can look at dry density versus thermal conductivity. In doing so, we are really considering the effect of degree of grain packing, void ratio or relative density. Remembering that the samples tested were from offshore sites and should be fully saturated, the chart below (Figure 3) should show us a clear trend for increasing density:

Figure 3: Thermal Conductivity of sand soil in the North sea vs Dry density

Thermal conductivity measurements for all types of sand soil and varying dry density

It doesn’t. Perhaps this is because we have a range of soils with different grading, different mineralogy etc? Lets take a look at slightly silty fine sand from southern north sea (Denmark, Netherlands and UK) with a moisture content of 25% (Figure 4):

Figure 4: Thermal Conductivity for slightly silty fine sand with moisture content of 25% vs Dry density

Graph of thermal conductivity measurements for slightly silty fine sand vs dry density for a moisture content of 25%

Again, what this chart is telling us is a little confused: fixed moisture content, fixed grading (as far as we can) and similar mineralogy but still a distinct lack of a trend. It’s rather unfortunate that even if we narrow the data set, there’s still a factor of two between the upper and lower bound values for soil at the same dry density. My hypothesis is that the large range in TC for the same dry density on soils with the same grading and mineralogy is a function of the degree of saturation and possible inconsistent calibration. Most laboratories do not provide enough data to normalise for the degree of saturation, so it’s hard to validate that hypothesis.

The Effect of Permeability

I started off by defining heat transfer in soil as being dominated by conductivity. It is feasible that heat transfer through a saturated soil with sufficiently high permeability might also be partially controlled by convection. Some work performed to investigate this effect is presented below in Figure 5:

Figure 5: The effect of permeability on total heat transfer coefficient, U

Graph showing the change in total heat transfer coefficient for increasing soil permeability

In this case, we consider the total heat transfer out of a pipeline covered by soil with a measured thermal conductivity between 1.6 and 2.0 W/mK. We vary the permeability of the soil over the pipeline and see how this affects the total heat transfer coefficient. For a permeability of greater than 1.0 x 10-4 m/s we start to see that the total heat transfer increases rapidly implying that conduction is no longer the dominant heat transfer mechanism. Considering this effect we can say several things:

1) We need to think a little about how we define heat transfer through soil: a measuring technique that is based on an assumed transfer mechanism is always going to be of limited use and potentially misleading in certain cases;

2) If permeability has such an effect on total heat transfer above the identified threshold, it could be the case that some of the scatter in Figure 2 could be due to convection along the side of the thermal probe.

Closing Remarks

Having discussed the need to define heat transfer through a soil for in-place design of pipelines it should be apparent that the current industry best practice for defining and measuring heat transfer is less than ideal. The needle probe is a tool that is capable of providing reasonable estimates of thermal conductivity if the boundary conditions are well defined. In practice, it seems as though boundary conditions are not well defined and so we don’t truly understand what conditions the reported results represent.

I personally think we need to move away from “thermal conductivity” and start to work in terms of total heat transfer irrespective of mechanism. This will require a more robust testing method with better defined boundary conditions that is capable of testing a larger volume of soil.

NB