January 23, 2019

Simulating Mixed-Media Storage

Posted by Jason Lillywhite

I created a model for demonstrating how to simulate mixed-media storage that accounts for changing quantities of solids and water over time. This kind of model is useful in mine water management models (tailings facilities) and also for simulating sediment accumulation in reservoirs. GoldSim makes it easy to account for the changes in the media while also managing overflows and operations of inflows in a way that is easy to use and understand.  

The purpose of the mixed-media storage model is to account for changing quantities of solids and water in a storage facility over time. This model estimates the volumetric inflow of solids based on density and solid/water proportion of the material inflow. This inflow might be a slurry that has a high concentration of solids or just natural inflows with high sediment content. Either way, the basic concepts are the same. This model simulates the reduction in water capacity as the solids accumulate and account for entrained water in the solids so that it adequately accounts for the pooled water. Finally, this model accounts for storage and overflows using a geometric relationship of elevation-area-volume of the storage facility.

The following assumptions are made in this model:
  • The water portion is clean
  • The geometry of the void filled with water remains unchanged
  • Only water can overflow if overflow happens
  • Solids immediately settle in flat, even layers across the bottom of the pond.
  • Entrained water fills the voids in the settled solids at the same rate over time and within the vertical profile of the solids
  • Solids are not being compacted over time.

Input Parameters and Model Setup

The model runs for elapsed time (not calendar) for 20 days with 1-day basic time steps. This model uses metric units of m3 for volume, kg (or metric tons) for mass, and m3/d for flows. 

The upper bound of the reservoir is 400 m3. The inflow to the reservoir is based on a continuous dry solids throughput of 10 metric tons per day starting on day 3 and ending after day 15 of the simulation. The following slurry properties are used:
  • Dry solids density = 2.6 tonne/m3
  • Concentration of solids by volume = 20%
  • Void ratio in settled solids in the pond = 1.0
Elevation-Area relationship for the pond:
Elevation [m]    |    Area [m2]
       0.0          |          300
       0.5          |          500
       1.2          |          600

The spillway elevation is 1.0 m. This is the elevation at which point water will begin to overflow.

Note unscheduled events that occur at the bounds. Decide whether to allow unscheduled events or not. For this exercise, I will not allow them. You can do this as well by opening the Simulation Properties dialog, then click on "Advanced" Options.

Slurry Calculations

An important part of this model is correct accounting of solids and water volumes. This means we must have a good understanding of the properties of the solids within the water or slurry flowing into the storage facility. Using phase relationship equations and ratios we can solve for volumetric flows of water and solids separately:

With the volumetric inflows of solids and water known, we can build the rest of the model. 

Accumulation of solids and water

The model uses 2 Pool elements that keep track of the water separately from the solids on a volumetric basis. The total solid + water volume is also calculated so that the water level can be tracked through time using the elevation-area-volume relationship of the storage facility. The upper bound of the water pool starts at an initial value then we subtract from this amount the solids volume that is accumulating in the other pool.This upper bound controls the overflow from the water pool. Note that GoldSim must predict the next upper bound value if it is changing. Sometimes, overshooting of overflow can occur when the upper bound suddenly stops changing as is made evident in the model when looking at the pool volume compared to the upper bound after day 15.

Note that the initial upper bound of 400 m3 controls the total volume but not the water volume. The water volume is controlled by the reduced upper bound, which is closer to 350 m3 near the end of the simulation.

Entrained Water 

Entrained water can be an important component of the model if significant amounts of voids are keeping the water held up in the settled solids. This is because this water cannot be used and should be considered "lost" water. In this model, entrained water is lumped with the solids pool and is calculated as a function of an assumed void ratio (e) in the solids that settle out. Water must be removed from the water pool and added to the solids poll to include entrained water. 

As seen in the plot to the right, there are now 4 components that we are tracking: entrained water, solids, water, and the total volume. All of these are on a volume basis. Outflow from the water pool to the solids pool for entrained water is calculated as follows:

Estimating Water Surface Elevation

I use an elevation-area-volume table to estimate the water surface elevation as it changes through time. The important thing to remember when doing this is that you need to reference the total volume (solids + water) to calculate the water surface elevation since the solids are sitting below the water surface. 

Download the Model

If you are interested in playing with this model, you can download it from here. Please let me know know if you have any questions or comments. I hope you find this useful for your mine water modeling projects and/or water resources work.

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