Modeling Mining Impacts on Groundwater

Transcription

1 Modeling Mining Impacts on Groundwater Brad Walton, Erik R. Sundberg, Anh Vo, Center for Applied Mathematics, University of St. Thomas, Freshwater Society, St. Paul, MN 1. Abstract Mining has often been a contested issue due to its potential to negatively impact the environment. Proposed gravel mining in Rosemount, Minnesota by Dakota Aggregates is no different. Our current research and past research done by Jeff Markle and Carrie Jennings found that it is unlikely that the proposed project at the Rosemount mining will have any negative impacts on the environment, most specifically, the trout population of the Vermillion River. This research, however, is still important because it could provide future guidelines for mining companies to follow in order to preserve Minnesota s beautiful natural resources. The results of this study suggest that a 200 meters setback is reasonable and safe for the environment. This result was determined by simulating the groundwater flow near the mining site through numerical modeling with finite difference methods implemented in Mathematica. We found that temperature fluctuation were more severe in the first 100 meters and stabilized after 200 meters. 2. Introduction. Minnesota is known as the land of 10,000 lakes. Along with those lakes, there are many rivers in the state that contain many valuable natural resources. One of the most important living resources is Minnesota s trout stock. Trout require specific, stable conditions in order to survive; most notably a temperature range between six and eight degrees Celsius is necessary for successful incubation. If temperatures exceed 11.7 degrees Celsius, the trout mortality rate rises to 50%. This reinforces the importance of environmentally conscious mining. Dakota Aggregates is beginning a 40-year mining plan on the UMore Park site two miles southeast of Rosemount, Minnesota in Dakota County. Dakota Aggregates Mining Operation has 1800 acres of land containing 200 million tons of aggregate reserves. They feature 2 miles of overland conveyor systems and the facility operates mostly on electricity rather than fossil fuels. Upon completion, they will create a 400 acre pit lake with an average depth of 75 feet. Figure 2.1 shows an image depicting mining plans for Dakota County from an article by Carrie Jennings.

2 Figure 2.1 Mining at the UMore site has the potential to reduce surface water delivery to the Vermillion River and its tributaries. Mining after a certain depth can cause groundwater to rise to the surface, making a pit lake that is exposed to radiation and other environmental factors that can heat up the groundwater. Heat from these pit lakes can diffuse and/or advect through the ground and aquifer body over time, which is a phenomenon known as groundwater thermal plumes. Figure 2.2 The migration of the thermal plumes is the main concern that this paper will analyze. Thermal plumes have the potential to heat the Vermillion River and cause the temperature to rise to a level that is unhealthy for the trout population and other biota living in the river. That is why the Freshwater Society determined that it was important to use the UMore Park mining site for this research. Our goal was to find the distance from the source at which the temperature of thermal plumes ceases to increase by creating a model of the situation. Finding such a distance would mean that Dakota Aggregates would be able to map out their future mining sites without worrying about dangerously heating the Vermillion River. The reason for choosing the UMore site is simple - the University of Minnesota has a large collection of measurements and data that make the site an ideal location to model. In

3 addition, this mining site is important to the state of Minnesota because it provides cheap, high quality gravel to the Twin Cities infrastructure without requiring much transportation. 3. Previous work. Carrie Jennings has been instrumental in our research. She came up with the idea for our project, provided many of our materials, and introduced the problem to us. Jennings is the Research and Policy Director of Freshwater Society, which has stressed the importance of preserving Minnesota s valuable freshwater resources through education and restoration for over fifty years. In her recent work for the Vermillion River watershed joint powers board, Jennings suggests adopting a setback similar to the 250 meters established in a study by Jeff Markle on thermal plume migration. Overall, she concluded that the current mining at the UMore site is unlikely to impact the Vermillion River and the trout population, however, modeling is still quite useful because it can be applied in the future for mines closer to the river. In her own words, although it has been determined that the pit lake being created on the UMore Property will not affect groundwater flow to the Vermillion, the dense dataset could be used to predict thermal plume migration in similar settings that are more likely to impact the Vermillion. The UMore Property has detailed measurements of flow rate, grain size and mineralogy and lends itself to modeling (Jennings). Much of the research done by Jennings is based on past work done by Jeff Markle of Western Ontario University. The mine he researched, surrounding Tricks Creek in Canada, has many similar properties to the UMore site. Minnesota also has a fairly similar climate to that region of Canada, so we believe it is reasonable to draw some connections. In his 2007 article, Thermal Plume Transport from Sand and Gravel Pits, Markle introduces the potential threat of thermal plumes on wildlife and discusses the methodology of his study. He monitored aggregate extraction and temperatures of various wells across the mining site. Markle also used the Kozeny-Carman equation in his work to determine the groundwater velocity. This equation is derived from Darcy s Law, which has proven to be instrumental in our research. Another useful resource from this article was Markle s discussion and values of hydraulic conductivity, permeability, and porosity of various types of gravel. We were able to use many of those values in our work - which will be described in the the next section. The values from Jeff Markle s paper are shown in Figures 3.1 and 3.2.

4 Figure 3.1 Figure 3.2 In another article by Markle, he found that the average groundwater velocity at his site was approximately 2.8 meters per day and that the average thermal plume velocity was about 1.2 meters per day. Those results are highly significant to us because they provide an estimate of what we should use for our site. Markle also found an interesting property of groundwater, as the meters below ground surface (BGS) increase, the water temperature becomes more stable. In some cases the temperature of the groundwater is higher in January than it is in September. Markle s results can be seen below in Figure 3.3.

5 Figure Derivations of the Advection-Conduction Equation and Kozeny-Carman Equation. There are three main types of heat transfer: radiation, convection, and conduction. We are not as concerned about radiation compared to convection and conduction in our project because we are looking at groundwater thermal plumes rather than water at the surface. However, radiation from sunlight can cause heating if there is a lake or stream above ground that is connected to groundwater through the water table. The water table, for reference, is the level that water sits at in equilibrium. As opposed to radiation, convection and conduction are highly significant for our models. Convection is the process by which heat is transferred within a system by the tendency of the fluid to circulate in the presence of a heat differential. Essentially, fluid with a higher temperature contains particles with higher energy and a higher collective pressure within the thermal system. These high energy particles have a tendency to disperse into areas of lower pressure - which would be areas of cooler fluid. This creates a flowing motion within the fluid that can heat a body of water over time with a constant influx of heat - such as a groundwater thermal plume. One thing to note is that convection and advection refer to the same phenomenon, the difference being that convection typically refers to vertical circulation of heat whereas advection refers to horizontal circulation. As

6 it is more applicable to our situation, this paper will mostly refer to the phenomenon as advection. where ρ is the density of groundwater, c is the specific heat of groundwater, u is the temperature of groundwater, v is the ground-flow velocity, and n is the outward normal to a reference volume. Conduction (diffusion) is similar to advection in the regard that it involves the transfer of heat through a medium. The primary difference between the two is the structure of the heat flux. Fluids exhibiting conduction do not transfer heat through circulation, but rather through direct contact with cooler fluids. On a molecular level, when a particle with higher energy collides with a particle with lower energy, it transfers some of its energy to the other particle. This means that when a thermal plume enters a cooler groundwater stream, it brings with it millions of high energy particles that each have the potential to transfer their energy to existing water in the stream, consequently heating the entire system. When referring to fluids, conduction is also often called diffusion. where K is the the thermal conductivity and k is the thermal diffusivity. Now that we have defined the processes by which groundwater can be heated to a potentially environmentally dangerous level, we need to examine the equations that can determine how much heat will theoretically be transferred. One of the most significant equations is the aforementioned Darcy s Law, that gives theoretical values for fluid transport velocities in horizontal (v) and vertical (w) directions, respectively. where π is permeability, p B - p A is the pressure difference, g is acceleration of gravity, L is the length of the thermal system, μ and ν are the dynamic and kinematic viscosities (respectively), and φ is porosity.

7 For reference, viscosity is essentially a measure of the thickness of a fluid. For example, a fruit smoothie would be more viscous than tap water. The smoothie is thick, with small solid chunks in it that cause it to flow more slowly - which is why viscosity is significant in calculating velocity of groundwater. Permeability, also known as hydraulic conductivity in this case, is measured in meters squared and determines how much fluid is able to pass through a thermal system. In contrast, porosity is the percentage of open space for fluid to flow into in the system. Both of these can determine the course of the groundwater flow. A mineral deposit could be highly porous but not highly permeable, meaning that it would have high volumes of water flowing into it and staying there with a low amount passing through. Similarly, a mineral deposit could be highly permeable but not highly porous, so that high amount of the water would pass through with little of it filling open spaces within the deposit. Fortunately for us, Dr. Markle had provided values for each of these in his research. Another important equation in the scope of our research is the advection-conduction equation. It is derived from the heat balance applied to an arbitrary volume of the groundwater system that assumes that the rate at which heat is added to the volume is due to the total heat flux into the volume across its boundary and to the internal heat sinks (sources). This equation is at the center of our model of the temperature evolution u ( x, y, t ) as a function of space and time: where the terms on the right describe the temperature changes due to heat diffusion, heat advection (convection), and internal sources (sinks), respectively. 5. Methodology We used the finite differences method to solve the advection diffusion partial differential equation numerically given boundary and initial conditions. Finite differences method allows us to replace a partial differential equation with a linear system of algebraic equations. The finite differences method can be performed in many different dimensions, with different boundary conditions, and even different schemes entirely, making it highly applicable for our case.

8 Figure 5.1 This method works by using a difference quotient to approximate a derivative. This can be performed by using a forward or backward finite difference scheme. Forward scheme solves for the temperature at the next time-step, j+1, assuming that all other values in the equation are evaluated at the time-step, j, before. Backward scheme solves for the temperature at the current time-step, j, assuming that all other temperature values in the equation are also evaluated at time step j. The first step in the procedure for finite differences method is to generate a grid of our domain. We used a mesh-centered finite differences grid to split up our domain into boxes, with corners known as nodes. These nodes are where we can store our values of approximate temperature solutions to the differential equation. We will be mostly focused on a two-dimensional domain for our advection-conduction equation. Such a domain is illustrated in Figure 5.2.

9 Figure 5.2 Having two-dimensions to implement our codes is valuable because we can modify permeability and porosity values for different depths and horizontal distances, and can also introduce the Kozeny-Carman value into vertical advection. In our Mathematica codes, we set Lx as the length in the x-direction of our domain, nz as the number of nodes in the horizontal direction, Ly, as the depth length in the y-direction, ny, as the number of nodes for the vertical depth, T as the total time that we want to look at, and m as the number of time steps we want to split up our time.

10 Figure 5.3 Figure 5.3 is a diagram of how we setup our background domain using a two-dimensional visual. The blue box indicates the potential pit lake with a horizontal distance of 25 meters and 5 meters in depth, the green line indicates the distance from the surface to where groundwater is found. The horizontal length is 100 meters and vertical depth is 10 meters. Although the values for the time step can be changed, we need to be careful with the units that we use so that it can fulfill the stability condition. The next step is to establish an algebraic system of equations for the points in the grid where the solution is unknown. The advection-conduction equation for 2-dimension is u t + vu x + wu x = k(u xx + u yy ) + f (1) where u(x,y,t) is the temperature function of space and time, v is the horizontal velocity in meters per second, w is the vertical velocity (from the Kozeny-Carman equation) in meters per second, k is the thermal diffusivity, and f is the source or sink of heat. After discretization and substituting the difference quotient for each partial derivatives, we get a new equation that will allow us to formulate a linear system of equation. For a forward scheme, the 2-dimensional advection-conduction will be simplified to

11 u j+1 i,k = ( 1 s j s s )u s )u 1,i,k sj 2 2,i,k 1 2 j 2 + ( j + s j i,k 1,i,k 1 j + s u s )u u t)f 1 + ( j + s j i+1,k 2,i,k 2 + s j i+1,k ( j i,k+1 i,k i 1,k (2) and the backward finite difference scheme will be u j = ( 1 + s s )u s )u i,k sj+1 + 1,i,k sj ,i,k j+1 ( j s i,k 1,i,k 1 j+1 s u s )u u t)f 1 ( j+1 + s j+1 i+1,k 2,i,k 2 s j+1 i+1,k 1 2 ( j i,k+1 i,k j+1 i 1,k (3) where The variables in equation (4) serve as the stability parameters for each advection and conduction part in the equation. For conduction, we want our stability parameters, s 1 and to be less than ½. For advection, we want our stability parameters, and to s 2 be less than 1. When inputting large values for distances, the forward scheme will be a lot more unstable compared to the backward scheme. We note that we did not carry out full stability analysis for the advection diffusion equation, which is quite subtle. The final step is to solve the linear system to get an approximate value at each node. The linear system of equations comprise of the finite difference stencils depending on which discretization method and boundary condition is used. Since we have three different parameters, we need to vectorize equations (2) and (3) to get a matrix. We will get a square A matrix of (nz+1)(ny+1) by (nx+1)(ny+1) size, multiplied by our solution x vector comprised of the known temperature values at a given time step and the right hand side vector, b, is given by the temperature vector that is unknown. s j 1,i,k s j 2,i,k (4) (5)

12 For cases with Dirichlet boundary conditions, the value at A[1,1] index in the matrix and at A[nx+1,ny+1] is equal to 1 because of the prescribed temperature conditions at both ends. For Neumann boundary conditions, we need data on the heat flux that are not available, or an estimate calculated from the data on simultaneous temperatures and distances between wells. Such boundary conditions are more difficult to impose in our project as the available temperature data points are not always coordinated in time and are not uniform enough in space to calculate the boundary flux accurately, thus making Dirichlet a more favorable boundary condition for our project. For Dirichlet approach he temperature data are available from 2009 Monitoring project of groundwater temperature at different BGS (below ground surface) levels at the UMore Park site. 6. Results We developed a code in Wolfram Mathematica package notebook environment that has certain flexibility in modeling thermal plume in a groundwater system. It allows to program thermal conductive (diffusive) and thermal advective (convective) properties of the gravel/sand and groundwater via imported measured data (including permeability and porosity), or such properties can be prescribed as functions of space and time. It also provides for modeling systems with internal sinks and sources of heat. We have both forward in time and backward in time finite differences options. The backward option has advantage of unconditional stability thus providing a better choice for the time step that could only be dictated by accuracy. However, to include advection (advection) we would still be limited by transport stability. One of the possible ways to bypass this issue is to determine the velocity field from a forward difference simulation or from (imported) measured data and, subsequently, use it as a sink (source) term for backward in time finite differences simulation where the time step can be chosen reasonably large for a longer period prediction of thermal plume. Our first simulation, Figure 6.1, was fairly simple. We created a model without a finished lake or daily temperature oscillations as a control to observe how the temperatures will change when we include a lake and daily oscillations. This model has a length of 100 meters. We decided to display our results as a 2-dimensional graph because it allows us to display scenarios using different depth values to better understand the temporal changes in temperature at those values. For this case, we observed temperatures as a function of time with depths of 0, 2, 2.5, and 3 meters in the y direction and we held the x-value (horizontal distance) constant at 80 meters.

13 Figure 6.1 At a depth of 0 meters (surface level), the temperature is the highest because it is the depth where the most heat is added to the system via radiation from the sun and other environmental factors. In contrast, at a depth of 3 meters our thermal system is heated less by above-water sources and therefore exhibits a lower and less varied range of temperature. These results, as simplistic as they are, make sense intuitively. The deeper the groundwater, the cooler and more constant the temperature will be. For our next case, shown below in Figure 6.2, we added daily temperature oscillations to the model while keeping our parameters the same. We used the data for the daily temperatures provided via Google as an example, however, the temperatures can be implemented more accurately with data from an excel sheet imported into the Mathematica code. With the Google data as an example, we can see fluctuations in temperatures for daily oscillations at the surface level, which is similar to Markle s graph mentioned in section 3.

14 Figure 6.2 Adding daily temperature oscillations confirmed our hypothesis that temperatures close to the surface, most notably at a depth of 0 meters and shown in red, are less stable. The amplitude of the temperature waves decreases as the number of meters below ground surface increases. The next major step in our research was to add a lake and advection and daily temperature oscillations to our model. This is shown in Figure 6.3. The addition of the lake eliminated the high amplitudes of the surface level temperature waves. This is because a lake allows more internal heat transfer to occur within the thermal system, forcing the extreme high and low temperatures to essentially average each other out each day. We will examine temperature as a function of time for x equal to 20, 40, 60, and 80 meters. We hold y-direction constant at 2.5 meters because that is the depth where groundwater is found.

15 Figure 6.3 Finally, we added advection and horizontal decay to our model to make it more representative of what will actually be happening on the UMore site. First we observed the results at 100 meters in Figure 6.4.

16 Figure 6.4 These results present an issue. The temperature is steadily increasing the distance is at 100 meters. This means that if we were to adopt a setback of 100 meters, the groundwater would likely heat the river. The next logical step was to increase the setback to 200 meters, and the results are shown in Figure 6.5.

17 Figure 6.5 The results for the 200 meter model provide more information. When x is equal to 200 meters, the temperature has reached an equilibrium and the groundwater will not cause the river to heat up significantly at this distance from the source. Therefore, we believe that there should be a minimum mining setback of 200 meters from any bodies of water. 7. Conclusions and Recommendations The results of this paper suggest that sand and gravel mining companies should adopt a 200 meter setback from lakes and rivers. Those results are comparable to the previous work done by Jeff Markle, who recommended a setback of 250 meters. However, before any regulations are implemented, further research should be done that involves implementing daily oscillations rather than yearly, stabilizing forward models, more models featuring lake inclusion/exclusion, implementation of sinks/sources, and finally, working in modeling software such as Hydrus or MODFLOW. Current mining by Dakota Aggregates is unlikely to impact the Vermillion River and its trout stock as it is about 3.88 miles away from the closest point on the river, but future plans could potentially jeopardize Minnesota s natural resources. The goal of this project was to determine a safe setback distance, rather than the arbitrary one mile that is currently the state law. We believe that a 200 meter setback not only provides more

18 financial and employment opportunities for mining companies, but that it will also be environmentally conscious and safe for wildlife. 8. Acknowledgements We would like to acknowledge the University of St. Thomas, the Center for Applied Mathematics, and the Freshwater Society for making this project possible. We would also like to acknowledge Dr. Jeff Markle and his study for being the basis for this project, Dr. Carrie Jennings from the Freshwater Society for formulation the objectives for our research and providing us with the necessary data for our research, Dakota Aggregates Mining for giving us a hands-on tour of their project and the mining site, Dr. Chuck Regan from the Department of Natural Resources for taking his time to visit us and feedback for our first progress report, Dr. Jeni McDermott for teaching us about groundwater flow and serving as a resource for any geological questions, Dr. Mikhail Shvartsman for being our advisor on this project, and Dr. Magda Stolarska for overseeing the entire project. 9. Bibliography Devito, K.J., Mendoza, C.A., & Smerdon, B.D. The Impact of Gravel Extraction on Groundwater Dependent Wetlands and Lakes in the Boreal Plains, Canada. Springer- Verlag Jennings, Carrie E., The Impact of Aggregate Mining in the Vermillion River Watershed, Minnesota. Freshwater Society Markle, Jeff M. Thermal Plume Transport From Sand and Gravel Pits Potential Thermal Impacts on Cool-Water Streams. Electronic Thesis and Dissertation Repository Markle, Jeff M. & Schincariol, Robert A. Thermal Plume Transport From Sand and Gravel Pits- Potential Thermal Impacts on Cool Water Streams. Elsevier, Journal of Hydrology, 338, p , 2007.