Pollution Detection

Pollution Detection: Modeling An Underground Spill

Through Hydro-Chemical Analysis

Given the location and elevation of eight groundwater monitoring wells (two more wells exist at unknown locations), a complete chemical analysis taken periodically at each well between 1990 and 1997, and the general direction of groundwater flow, it is possible to accurately estimate the location, source, time of origin, and total volume of pollutants seeping underground. In the case of a suspected leak in a chemical storage facility built over homogenous soil, cost and safety prohibited collection of analytical data directly below the suspected sight of the spill. Data from monitoring wells surrounding the periphery of but not necessarily directly in the suspected polluted region are used in a mathematical model to determine whether a leak has occurred, the time and location when the leak occurred, and the amount of liquid that has leaked during the data collection period. To more clearly convey the situation being modeled in this problem and others of its type, a diagram clarifying the position of monitoring wells and the region as a whole is included in Appendix 1.

ASSUMPTIONS AND JUSTIFICATIONS

All monitoring wells are located below ground and are contained within an aquafer. This aquafer has an unobstructed constant flow rate which is inversely proportional to the porosity of the soil medium. The monitoring wells are permanent, allow free flow through their measuring devices, have no effect on the chemical or geological composition of the region, and provide an accurate reflection of the surrounding area. This ensures that the wells themselves do not contaminate or pollute the region to be assessed (Soliman et. al. 32).

The total volume of fluid is constant in each well and all wells have the same total volume. Assuming a consistent volume between wells allows direct ratios to be assessed comparing concentrations of solutes in each well.

Different chemicals may travel through the aquafer at different rates. Chemical substances have a constant and specific ability to move in aqueous solutions depending on polarity of the molecules, hydrophobicity, and the initial concentration of each compound.

Some chemicals found present in the data set occur naturally in the groundwater and are not products of pollution. Any chemical that exhibits no significant change in concentration at any monitoring well over the course of the data collection period can be removed from consideration in the data. In addition, certain naturally appearing chemical components of groundwater can be expected to fluctuate between standard levels as listed in appendix 3 (British Columbia Ministry of Environment, Lands, and Parks).

Concentration of pollutants are highest near their source, and concentrations decrease as time and distance from their source increases. This assumption is supported by the given data.

The given data set is incomplete. Some trends may be misrepresented or missed entirely due to lack of available data. Also, the values that are given must be appropriately evaluated so as not to treat the N/A values as zero.

Discrepancies in the type of data available can be attributed to variations in the equipment used or in sampling and analyzing techniques over the course of the study and should not always be interpreted as changes in the environment, especially those occurring on the same data in every sample tested.

Pollution is defined as a contaminant that is harmful to an organism, while contamination refers to the concentration of a substance that is greater than would occur naturally, but not necessarily causing harm (Blatt 76). In this problem, we will assume both terms refer to the artificial contamination of an underground region, regardless of the effect the contaminants have on organisms.

DEALING WITH DATA

In order to effectively use or interpret such a large and varied data set, specific criterion must be employed to organize and sort the known information. We converted this data from its original spreadsheet form into a database so that we could set up queries and selectively access any portion of the information. There were several components of the data which were not chemical concentrations, but other factors necessary for a thorough chemical analysis such as specific conductivity and total dissolved solids. These were separated and stored in another spreadsheet. Although methods of modeling pollution exist which use these measurements, these models do not because a significant pattern could not be detected in these values to indicate the presence of absence of pollution. Using line graphs mapping the concentration of a given chemical at all dates and at each well, we were able to identify those chemicals that exhibited a negligible change in concentration. These were also removed and stored in a separate spreadsheet. This left twenty three chemicals from an original set of 106 measurement categories.

DETERMINING THE PRESENCE OF POLLUTION

From the rapid increases shown in the line graphs of chemical concentrations over time, it was apparent that new pollution had occurred in this region over the testing period. Those chemicals detected as new pollutants include: Acetone, Bicarbonate, Ammonia, Arsenic, Barium, Calcium, Chloride, Iron, Lead, Magnesium, Manganese, Nickel, Nitrate/Nitrite, Potassium, Sodium, TDS, Sulfate, Vanadium, and Zinc.

When observing the change in concentration of all chemicals together, we observed that the concentration of the majority of the chemicals in the active data set rose and fell together, indicating that each was a constituent of a single liquid involved in the spill. Although the concentrations of all active chemicals in the data set followed obvious trends, the changes in concentration were much more amplified for some than for others. These amplified chemicals were chosen as indicator chemicals to clearly track the movement of the spill. To further simplify spill detection, the concentrations of these indicator chemicals (Chloride, Sulfate, and Nitrate/Nitrite) were added together to form a composite indicator chemical, the concentration of which indicates the presence of pollution at each test sight on a given date. These chemicals were also chosen because they are common components of pollutants and are often used to monitor pollution (B. C. Ministry of Environment, Land, and Parks).

Because the data set was not complete and the measurements were not taken consistently for all chemicals at all points or on all dates, it was important to ensure that the concentration of this composite indicator did not misrepresent trends in the movement of the spill due to a lack or abundance of data for a given well or on a given date. When choosing chemicals to serve as indicators for the spill it was essential to find chemicals which were measured consistently on the same dates and at all wells throughout the data collection period. Three chemicals which fit this criterion in this data set were Chloride, Sulfide, and Nitrate/Nitrate, those used to generate the composite indicator. We also went through the data set and eliminated those dates which were recorded twice, taking an average of the concentrations listed at each well, and corrected other abnormalities in the data until each of these three chemicals had exactly one value at each test location on all dates needed. Exceptions to this include those wells for which values are not available at the beginning of the testing period. These are added as data from these wells became available.

THE TIME OF THE SPILL

A series of line graphs showing the concentration of the composite indicator at a given well over time can be used to estimate the time of the spill. When plotted together so each line represents a monitoring well, these graphs of concentration over time will show when concentrations first start to increase and at which well(s) this increase is first recorded. This record of which wells show the first rise in concentration provides a rough estimation of the location of the source as well. Using the line graph shown in appendix 4 helps determine that two spills probably occurred, the first between July, 1991, and March, 1993. During these times, the concentrations in wells believed to be closest to the spill increased dramatically, than receded back toward normal levels. The second probably began in January, 1995 and continued at least until January, 1997. At this time, concentrations were starting to descend, but this could result from a decrease in the rate at which the spill is leaking and may not indicate that the leak has stopped.

LOCATING THE SOURCE

The line graphs generated by queries from the database are extremely useful in determining the presence of a spill, the time at which it occurred, and the chemicals involved. However, finding the source of the spill is more effectively accomplished with a visual interpolation showing the concentration of the composite indicator at each well over time. This way we can determine where the concentrations rose first and the general direction the spill moved in. Knowing the general direction of the spill, we can develop bounds within which the source of the spill must lie. This can be done in three dimensions by creating a Voronoi polygon. This method of interpolation organizes data points into a triangles with their natural neighbors and partitions areas around each known point into polygons such that an arbitrary point placed in the polygon is closer to that data point than any other. The triangulation of a map is unique, and effectively weights the value of any point in the region as a function of its distance from three natural neighbors.

While the line graphs show approximate dates when a spill might have occurred and at which wells the changes in concentration were detected, this method interpolates between the known data points to show more precisely the location of the spill source. Generating a series of diagrams of the concentration of the composite indicator chemical at each well over a selection of dates, the progress of the spill is very apparent, and the location of the source can be found by following the flow patterns in the underground system backward from the point where the spill first occurred. The map in appendix 7 shows the location of the pollution source found using Voronoi polygons.

PROBLEM 2:

A PROCEEDURE FOR EVALUATING UNDERGROUND CONTAMINATION

The problem of detecting the presence of underground liquids is an old one, and due to its applications in locating water sources, petroleum reserves, and mineral deposits, an abundance of information about techniques and methods is available. Drilling sampling or monitoring wells is clearly necessary at some point to determine the exact properties of an underground region. However, such sampling and the analysis that follows is time consuming, dangerous, expensive, and has the potential to contaminate or destroy the flow of groundwater in the region. There are numerous surface or superficial measurements which help determine the most effective placement of such wells. In addition, data gained from existing wells can help determine the need for and placement of additional monitoring wells when properly applied.

Several useful measurements can be gained from a surface geophysical survey before drilling a well, including gravitational, electrical, and magnetic conductance readings. These involve the passage of electrical current or magnetic fields through surface soil and measuring the drop in voltage or potential magnetism, as well as the density at a given location. By comparing the conductance of surface soils at various locations in the region, the presence of sand or gravel beds can often be detected below the surface (Walton, 61). This is useful because sand and gravel beds have a high porosity, or ability to contain free flowing fluids in the form of groundwater tables known as aquifers. These aquifers are the mechanism by which underground pollutants are contained and spread, so an understanding of the flow and direction of the aquifer is crucial to accurately predicting the location or the source of contaminants (Soliman, et. al., 32).

Drilling and Monitoring A Well

Once the location of an initial well has been decided upon (surface measurements should indicate the presence of an aquifer — a geological unit capable of storing and transmitting substantial volumes of water), several types of wells are available. Because drilling the initial bore hole for the well is the most dangerous and expensive part of the process, permanent monitoring wells such as those used in collecting the data set for this problem are the most economical in the long term. Such a well should be capable of detecting the direction and rate of flow of fluids in the aquifer, the level of the water table, and should be able to provide core samples to be chemically analyzed in a laboratory. These wells must be permeable to water in the region and cannot disrupt flow in the aquifer or introduce new contaminants due to the drilling process or corrosion of the well itself over time.

How Many Wells Are Needed?

The number of wells needed to determine the source, time, and volume of an underground chemical spill may vary widely based on the circumstances of the spill. For the models described here, a minimum of three wells are necessary. From the initial well, the direction and flow of the water system can be determined, along with the concentration values of chemicals dissolved in the groundwater. Additional wells should be drilled along the path of the water table, considering the general location of a chemical storage facility or other suspected source of contamination, if known. If contaminants are detected by the initial well, others should be drilled ‘downstream’ to the spill, and if no contaminants are detected, wells should be drilled ‘up stream’, or possibly along a different aquifer, depending on the geological constitution of the region.

When at least three wells are available to detect the flow and concentration of contaminants, the following models can be used to estimate the location of the source of any contaminants found to be present, as well as the time of a spill, and the total volume of liquid spilled. In each case, the more wells used for data collection, the more accurate predictions can be made about the spill.

Model #1: A Graphical Approach

This model requires the assessment of chemical concentrations at at least three different locations on at least three dates per location. The more wells or locations of data collection, the more accurate the model. The first step is to enter the concentration values into a database so that they can be accessed by date, collection location, chemical, or concentration. Typically, a complete chemical analysis is performed in a laboratory, generating lots of data, most of which is not necessary in solving this type of problem (as seen in the data accompanying this problem). Using the database, line graphs showing concentrations of all chemicals by date can be generated for each well or collection location. From these graphs, the presence of pollution can be determined, as well as the date of significant changes in concentration of measured chemicals. Dramatic increases in concentration indicate the introduction of a pollutant in this model.

In many cases, as in this problem, many of the chemicals detected in a chemical analysis will rise and fall simultaneously. This indicates that they are components of a common pollutant. It is possible that the chemicals would fall into two apparent groups, indicating that two liquids are leaking. In this case, one, or preferably a group of detected chemicals are consolidated to form an indicator chemical. This simplifies future graphs by allowing only one concentration value to be monitored. However, when creating a consolidated indicator, it is imperative that the data be consistent. The same type of data must be available at all sites and on all dates, or adjustments such as those described above under ‘DETERMINING THE PRESENCE OF POLLUTION’ must be incorporated to prevent anomalies in the data set from drastically misrepresenting the concentration of chemicals detected in the groundwater.

Having developed a consolidated indicator by adding the concentration values of representative chemicals at each site on a given date, new graphs can be generated to determine the time and source of a spill. Overlaying graphs showing concentrations over time at each well can effectively be used to determine the time of a spill. It is useful to collect enough data to develop a baseline concentration for the chemicals being measured. Tables published by the EPA, the British Columbia Department of the Environment, Land, and Parks, and other regulatory agencies list normal ranges of concentrations of various chemicals in groundwater and are also useful in distinguishing those chemicals present naturally in a system from those caused by pollution (see appendix 2).

Interpreting these graphs is relatively simple. On a chart showing the location of each well or test location, identify those wells (if any) which never show a definite increase in concentration of the indicator. Then the well or wells reached first by high concentration values and the wells showing the highest concentration of chemical overall must be identified. Using this information, as well as the direction and rate of flow in the system (measured at each well or given in the problem statement), the contaminants can be traced back to an estimated source location. The results of this process for each of the two spills indicated are included in appendix 5. Both spills reached wells nine and twelve fastest, showing an increase at wells three and eleven, and seven later. This indicates that both spills began somewhere in the region surrounding the point (8000, 4500). The delay of the spill reaching well seven may be due to a pattern in the flow direction of the aquifer. It may at first seem strange that well three shows less concentration than well seven, which is clearly farther from the spill. This is probably due to the lower elevation of this well. The measurements taken at the top, bottom, and middle of the monitoring wells indicate that the spill is seeping in a downward direction, and that it never reaches the bottom of the wells. This also explains why well thirteen, directly in the path of the spill, never shows an increase in chemical concentration—its only samples were taken from the bottom of the well.

Strengths and Weaknesses

The greatest strength of this method is its efficiency in interpreting a large and complex data set. Most computers are able to build and utilize such a database from a spreadsheet, and once the data is organized, the time needed to compute and interpret the results is minimal. Because it bases the placement of new wells on information gathered by existing ones and provides rough approximations with as few as three wells, it is very efficient in terms of drilling and well maintenance. However, it provides only a very general approximation of the time and location of the source, and has the potential to be greatly affected by irregularities in the positioning of the wells or uneven flow patterns in the groundwater system. In situations where samples are unavailable directly below a suspected pollution source, leaks cannot be detected until they have already penetrated into the groundwater supply, precluding attempts to stop the leak before it poses a problem to the surrounding community. This method provides no way to accurately determine the volume of polluting liquid spilled.

Model #2: Interpolation with Triangulation in Three Dimensions

Using the same methods described above, this model requires the creation of a database and line graphs to determine the presence of a pollutant and the chemicals involved. It also uses changes in the concentration of a composite indicator of chemicals to monitor the flow of the pollutant.

Computational geometry describes a method known as natural neighbor interpolation by which sets of highly irregular data can be organized and represented visually. Using Delaunay triangulation, a unique set of triangles can be arranged in an arbitrary set of points. The value of an arbitrary point is defined entirely locally based on the values of the three nearest known points, the vertices of the triangle in which the point lies. Delaunay triangulation and Voronoi polygons are extremely useful for interpolation in this type of system for two primary reasons: 1) They provide a linear system by which the value of any arbitrary point can be determined, and the original data points are exactly recovered if solved for using this system. 2) The interpolation of every point is influenced only by its natural neighbors such that irregularities in the data set are reflected in the model but do not distort the accuracy of the model at other points (Sambridge, Braun, and McQueen, 3). Please see appendix 6 for more information about Voronoi polygons, Delaunay triangulations, and convex hulls.

A computer program, Geomview takes concentrations stored in the database and the location coordinates of the monitoring wells, and generates a convex hull which represents of the spill as a whole. The convex hull is the outermost surface of a Voronoi polygon, comprised of smaller tetrahedrons called datum, representing the space between three ‘natural neighbors.’ Each datum has a specific and constant concentration based on the known concentrations at the three points which define it (Watson, 108). The data entered into this program are divided such that only concentrations above an established baseline appear in the visual model representing the spill. The program weights each datum by volume at a specific concentration, and by adding each of these weighted concentrations, calculates the total volume of liquid in the spill. The outermost walls of a Voronoi polygon, known as a convex hull, can be used in this model to visually represent the location and volume of the entire contaminated area of the spill. Appendix 7 shows the spill defined by this data set at six dates during the data collection period and the volume of the contaminated area at that time.

This model is also useful in determining the source of the chemical spill. It produces a new diagram on every date requested based on the concentrations entered from the data set for that date. At the start of the data collection period, no pollution is visible. As time progresses, the diagram clearly indicates which wells experienced higher than normal concentrations of the indicator chemical. The approximate source of contamination, as well as the direction of flow in the groundwater table are apparent when several successive convex hulls are viewed together. The estimated source of contamination is identified on the Voronoi polygons shown in appendix 8.

Error Analysis

In order to test the error of this model and the linear model, a data set can be computed for which the source location of contaminant, the date on which the leak occurred, and the total volume of liquid spilled are known. The difference between predicted values and the actual location, time, and volume, divided by the actual values determines the percent-error of the interpolation. The amount of error will depend on numerous factors specific to the individual test including how far the source is from the nearest monitoring well, the flow rates in the underground system, the size of the spill, the number of monitoring wells, and many more factors.

Strengths and Weaknesses

This model is inherently stronger than the graphical method because it allows a three dimensional visualization of the data and because it uses a unique and algorithmic interpolation to evaluate the presence of contaminants between known points. Delaunay triangulations and the Voronoi polygons and convex hulls which can be derived from them are extremely accurate when used to interpolate in highly irregular data sets because of the natural neighbor principle. The presence of irregular data points or wide variations in distribution of points will be reflected in the resulting projection, but will not result in a misrepresentation of the data or inaccurately skew the values of known points (Sambridge, Braun, and McQueen). The more data points available, the more accurate this interpolation will be because, like any interpolation, the model is most accurate nearest the known points.

Because the data set given with this problem is highly irregular and contains very few sampling locations, the predictions of this method may not be entirely accurate, but they are highly superior to most interpolation methods. As with the previous model, this method cannot detect a spill until it has already entered the water table. Also, the only obvious method of error analysis is to test more points. The values given are still approximations, and the process of sorting such a large data set is still rather tedious. If such a method were employed from the start of a project and data were collected in a specific and consistent manner, analysis using this model would be relatively simple using the database and the processes described here.

This model can determine whether or not a leak has occurred, approximate the time of the spill, and give an estimated location of the source of the spill. Its greatest advantage is its ability to determine the volume of contaminated area and to model its location underground. When the initial concentrations of chemicals in the leaking liquid are known, this model can also determine the volume of liquid that has leaked. This model is extremely cost effective in that it generates approximate boundaries of a spill based on known information. Successive wells should be drilled at these boundaries to ensure that the spill is in fact accurately predicted by the current information. If new wells detect additional areas of the spill, new boundaries will be generated and the process can be repeated. In either case, unnecessary wells are never drilled once a contaminated area is identified.

RESULTS and RECOMENDATIONS

From the data given for this problem, we discovered that new pollution had occurred in this region during the testing period between 1990 and 1997. Two separate spills of the same liquid occurred, the first beginning in July 1991and ending approximately in March, 1993, and the second beginning in January 1995 and tapering off about February 1997, although possibly continuing for the remainder of the collection period. These spills originated from the region marked on the map in appendix 5. The liquid spilled was composed of the following chemicals which were released into the ground as pollutants: Acetone, Bicarbonate, Ammonia, Arsenic, Barium, Calcium, Chloride, Iron, Lead, Magnesium, Manganese, Nickel, Nitrate/Nitrite, Potassium, Sodium, TDS, Sulfate, Vanadium, and Zinc. The total volume of the polluted area by 1997 was approximately 32 million cubic feet. When the initial concentration of the composite indicator in the liquid that spilled is available, it is possible to determine the total volume of liquid leaked by weighting each datum of a Voronoi polygon and finding the sum of the concentrations, multiplied by the total volume of contaminated area.

Recommendations for future testing include:

Identify surface properties to most effectively place the initial monitoring well.

Test the same chemicals on the same dates at all wells to ensure complete and accurate data.

Use the information generated by previous wells to predict the borders of the spill and place additional wells along this boundary to minimize the number of test locations needed to accurately determine the size of the spill.

Determine the rate and direction of flow of the aquifer in which monitoring wells are located to accurately predict the time and location of the pollution source.