Lesson 8 - Modeling Advection via Suspended Particulates

In the previous Lesson, we discussed the transport of species mass via advection in a “flowing” Solid.  In this Lesson, we will discuss the transport of species via advection of particulate Solids suspended in a flowing Fluid (typically the Reference Fluid Water).

Before showing how you would actually simulate suspended particulates in GoldSim, let’s take a moment to discuss why they can be important with regard to advective transport.

The rate of advective mass transfer out of a Cell is equal to QC_W, where Q is the flow rate, and C_W is the effective concentration of the species in the water. Changing the effective concentration changes the advective mass transfer rate.

Assuming we have only one Solid (and Water), and M is the mass of species in the Cell, V is the volume of water, G is the mass of solid, F is the fraction of the solid suspended, K is the partition coefficient, and C_sol is the solubility limit, we can compute C_W under the various conditions we may encounter. To make the impact of these equations easier to understand, let’s assume the following values:

The effective concentration, C_W, can then be theoretically computed as follows for the various conditions outlined below:

K>0?	Solubility limit?	Fraction Suspended	CW Equation	CW  Value (g/m3)
No	No	NA		1
Yes	No	0		0.091
Yes	No	0.5		0.545
Yes	No	1		1
Yes	Yes	0		0.01
Yes	Yes	0.5		0.06
Yes	Yes	1		0.11

So what can we conclude from these equations (and example calculations)?

First,  if the species is not controlled by solubility, partitioning onto a Solid can obviously decrease the effective concentration (available for advection).  However, if some of that Solid is suspended, it can lessen this impact.  In fact, if all of the Solid is suspended, partitioning has no impact at all on the effective concentration.

Secondly, if the species is controlled by solubility, the solubility limit can also decrease the effective concentration (available for advection).  Again, however, if at least some of that Solid is suspended, it can lessen this impact.

These simple calculations demonstrate the potentially large impact of suspended Solids.  In particular, for species that sorb onto the suspended Solids, the effective concentration in water (and hence the advective mass transfer rate) can be significantly increased.

So now that we understand their impact, how do we tell GoldSim that Solids are suspended?  As discussed in Unit 5, Lesson 7 this is actually quite simple. In particular, when specifying a Solid medium, you select the box marked “S”:

When you do that, GoldSim assumes the Solid is suspended in the first Fluid that precedes it in the list of media for the Cell (i.e., the Fluid that is closest to it in the list). Hence, if you have multiple Fluids in the Cell, it is important where the Solid is added in the list of media.

What if only a portion of the Solid is suspended?  In this case, you would typically define two Solids (with or without the same properties), and specify that only one Solid is suspended:

When you specify a suspended Solid in a Cell, it changes the outputs from the Cell. The outputs from a Cell always include 1) the mass of each species in the pathway; and 2) the concentration of each species in each Medium in the pathway. In the example above, what you will see is that the Cell has five different outputs.  All five outputs are vectors of Species:

• Mass_in_Pathway: This is the total amount of mass (of each species) in the Cell.
• Concentration_in_Water: This is the total (effective) concentration (of each species) in Water.  Because there is a suspended solid present, this includes the mass associated with the suspended solid.  It has dimensions of mass/volume.
• Concentration_in_Sand: This is the total concentration (of each species) in the Solid named Sand. It has dimensions of mass/mass.
• Concentration_in_Suspended_Sand: This is the total concentration (of each species) in the Solid  named Suspended_Sand. It has dimensions of mass/mass.
• Dissolved_Conc_in_Water: This is the dissolved concentration (of each species) in Water.  It does not include the mass associated with the suspended solid, and includes only the mass dissolved in the Water itself. It has dimensions of mass/volume. Note that if the Solid were not suspended, this output would not appear.

We have two different Water concentrations here because we have specified that one of the Solids is suspended in the Water. Concentration_in_Water is the effective concentration we discussed above (used to compute the advective mass transfer rate). Dissolved_Conc_in_Water is the concentration you would observe if you could filter all of the suspended solids from the Water.  

When we create an advective Outflow from a Cell with suspended Solids, the following points are important to note:

• If the advective mass flux link is between two Cells, then the particulates are advected into the downstream Cell only if the Solid exists in that Cell.  (The Solid does not have to be specified as being suspended in the downstream Cell, but it must exist in that Cell.)  If it does not, GoldSim assumes that the Solid particulates are "filtered" out before entering the downstream Cell (and remain in the upstream Cell).
• If the advective mass flux link is between a Cell and any other type of pathway (we will discuss other pathway types in later Units), the particulates are always transported with the flowing fluid.
• If the Solid is not suspended in the downstream Cell (or the downstream pathway is not a Cell), conceptually, the particulates are assumed to immediately disintegrate upon entering the downstream pathway, with the species mass which was associated with them instantaneously partitioning among the available media in the pathway.
• In some cases, you may want to specify that the suspended particulates move at a different rate than the flowing water (and hence the dissolved solutes). To represent this, you can define an Advective Velocity Multiplier for the suspended Solid. This is a property of the Solid, and can be found by clicking on the Advanced Properties… button for the Solid:
  
  The default value is 1 (it moves at the same velocity as the Fluid).  But you can choose to have the suspended Solid move faster (values greater than 1) or slower (values less than 1) than the Fluid.

• As is the case for the advecting Fluid itself, GoldSim uses the advective Outflow to transport only species mass and does not keep track of the movement of the suspended Solid media through the pathway network.  That is, the advective Outflow has no effect on the quantity of the suspended Solid present in either the upstream or downstream Cell. As you do for the other media (e.g., Water), you should have a separate flow model to balance the particulate masses (if they are not constant).

In the next Lesson, we will work through an Exercise involving suspended Solids so that you can make sure you are comfortable with representing these in your models.