Faculty Interaction

Juan Santos

Department of Mathematics
Purdue University

Brief Project Description:

Professor Juan Santos is a faculty member in the Mathematics Department at Purdue University. Some aspects of Prof. Santos' research involve the numerical modeling of wave propagation in fluid saturated porous materials, with application in seismic methods in partially frozen sandstones, gas hydrates in ocean bottom sediments, bone poroelasticity and evaluation of freezing conditions of foods by ultrasonic techniques. The technical staff of ITaP has previously consulted with Professor Santos regarding running some of his memory and CPU-intensive jobs on our IBM SP system. More recently, ITaP staff have identified that Prof. Santos' calculations might run more efficiently on our Linux clusters, and we spent some effort assisting him with porting his MPI application from the IBM SP to our recycled cluster.

Prof. Santos has now been able to complete the running of several memory intensive jobs on our recycled cluster (using as many as 32 nodes) that he was previously unable to complete.

More specifically, the work of Prof. Santos involves the numerical simulation of an ultrasonic wave traveling through s sedimentary reservoir of porous rock, and saturated with a two-phase fluid. (Gas and water are used in the numerical experiments). Both homogeneous fluid distributions and fractal patches of fluid distribution in the porous spaces are used to investigate the waves behavior inside the rock. The mode conversion at the interfaces is also observed and studied. Prof. Santos also takes into account fractal permeability in observing the wave scattering.

A snapshot of the "vertical velocity of the solid phase" at a specific time step has been included (Figure 1).

Another aspect analyzed by Prof. Santos is the dissipation mechanism due to wave-induced fluid flow caused by mesoscopic scale heterogeneities, which are those larger than pore size but smaller than wavelengths in the seismic range (1- 100 Hz). These heterogeneities can be due to local variations in lithological properties or to patches of immiscible fluids. For example, a fast compressional wave traveling across a porous rock saturated with water and patches of gas induces a greater fluid pressure in the gas patches than in the water saturated parts of the material. This in turn generates fluid flow and slow Biot waves which diffuse away from the gas-water interfaces generating significant losses in the seismic range. The numerical experiments of wave propagation in alternating porous layers saturated with either gas or water designed by Prof. Santos have shown that the mesoscopic loss mechanism can be significant in the seismic band, confirming some earlier theoretical results. Figures 2, 3, 4 show traces of the vertical velocity of the solid phase for a periodic gas-water saturated porous medium and the corresponding to the same medium but saturated with either gas or water. These figures illustrate this important upscaling effect.


Figure 2. Traces of the vertical component or the velocity of the solid phase. Periodic gas-water saturated case


Figure 3. Traces of the vertical component or the velocity of the solid phase. Water saturated case


Figure 4. Traces of the vertical component or the velocity of the solid phase. Gas saturated case

ITaP has received acknowledgement for technical assistance in some of Prof. Santos' research, which can be viewed at http://www.math.purdue.edu/~santos/