Saturday, March 6, 2010

Transient Effects Revisited

Today I had a chance to check out the book "Fundamentals of basin and petroleum systems modeling" by Thomas Hantschel and Armin Kauerauf (Springer-Verlag, 2009). It seems that the transient effects may be still fundamentally misunderstood (and underestimated). Their fig. 3.4a on page 109 (shown below) shows a 1D model going through the deposition, hiatus, and erosion stages. With the assumption that the heat flow at the base of the sediment stays constant at 60 mW/m2, the model predicts small  (±5 mW/m2) changes in heat flow in the sediment column. The authors conclude that the transient effect is smaller than that caused by radioactivity within the sediments. You may click on the image to see a version with better resolution.
When evaluating transient effects, it may not be appropriate to assume constant heat flow at base sediments.  You can see from the figure that the forced base boundary is limiting the extent of the transient effects. With a deeper boundary, the heat flow change should be more significant. More importantly, by setting the boundary at base of sediments,  it considers only the process of heating the sediments, but misses the problem that the deposition of the new layer also puts the entire lithosphere out of equilibrium by moving the surface boundary.

The figure below shows this concept. After adding the new sediments, to establish steady state thermal equilibrium again (green curve), temperature, therefore heat flow must change through out the entire lithosphere, not just within the new sediments. Secondly, since the entire lithosphere needs to be heated (not just the sediments) to reach the new equilibrium, it may take much, much longer (lithosphere is typically 10-20 times thicker than the sediments) than heating the sediments alone (see my previous post on this below).

Below is a model with same conditions as the Hantschel and Kauerauf's model, except that it does not assume a constant heat flow at the base of sediments. Rather the temperature at base of the lithosphere at 120 km is fixed at 1330 °C. The transient effects are much stronger compared to the figure at the top.

The following figure shows the predicted heat flow at the base of the sediment column  through time. You see that it is far from constant. From an initial 60 mW/m2, basal heat flow decreases to 48 mW/m2 at the end of the deposition period, and increases gradually during the hiatus. Then it increases to 72 mW/m2 at the end of the erosion period.
This indicates a ±12 mW/m2 change over 10 million years with deposition and erosion rates of 250 meters/my, a bit higher than the average deposition rate. However, the deep water of the Gulf of Mexico has deposition rates several times as high, and the heat flow at the base of sediment today is around 35 mW/m2, while a steady state heat flow would have been about 50 mW/m2.

In recently uplifted parts of North Africa, we see higher heat flows today. Follwing this analysis, it may be concluded that the heat flow prior to the uplift could be 10 mW/m2 lower depending on erosion rates. See this post for details.

The basin modeling literature is littered with papers making assumptions of heat flow at the base of sediments independent of deposition/erosion rates. Where sedimentation rates are high, or vary significantly over time, the application of such thermal models can cause significant errors in estimating the maturity and timing of petroleum generation. To be fair to the authors, this was how I used to do it in the 90s. But I have learned my lessons from those who learned before me.