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Determining concentration fields of tracer plumes for layered porous media in flow-tank experiments

Zhongbo Yu 7 Franklin W. Schwartz

Abstract In the laboratory, computer-assisted image analysis provides an accurate and efficient way to monitor tracer experiments. This paper describes the determination of detailed temporal concentration distributions of tracers in a flow-tank experiment by analyzing photographs of plumes of Rhodamine dye through the glass wall of the tank. The methodology developed for this purpose consists of four steps: (1) digitally scanning black and white negatives obtained from photographs of the flow­tank experiment; (2) calibrating and normalizing each digitized image to a standard optical-density scale by determining the relation between the optical density and pixel value for each image; (3) constructing standard curves relating the concentration in an optical density from five experimental runs with predetermined concentrations (2­97 mg/L); and (4) converting the optical density to concentration. The spatial distribution of concentration for two photographs was determined by applying these calibration and conversion procedures to all pixels of the digitized images. This approach provides an efficient way to study patterns of plume evolution and transport mechanisms. Résumé Au laboratoire, l'analyse d'images assistée par ordinateur est un moyen précis et efficace pour suivre certaines expériences de traçage. Ce papier présente comment sont déterminées dans le détail les

distributions temporelles de la concentration en traceur au cours d'une expérience d'écoulement en réservoir au moyen de l'analyse de photographies de panaches de rhodamine à travers la paroi de verre du réservoir. La méthodologie développée dans cette expérience suit quatre étapes: (1) digitalisation par balayage des négatifs noir et blanc des prises de vue de l'expérience d'écoulement en réservoir; (2) calibration et normalisation de chaque image digitalisée par rapport à une échelle étalon de densité optique en déterminant la relation entre la densité optique et la valeur des pixels de chaque image; (3) étalonnage de concentrations prédéterminées (2 à 97 mg/L); et (4) conversion de la densité optique en concentration. La distribution spatiale des concentrations pour deux photos a été déterminée en appliquant ces procédures de calibration et de conversion à tous les pixels des images digitalisées. Cette approche est une façon efficace pour étudier la manière dont évoluent les panaches ainsi que les mécanismes de transport. Resumen El análisis de imágenes por ordenador proporciona un método preciso y eficiente para estudiar los experimentos con trazadores en laboratorio. En este artículo se describe una metodología para la determinación detallada de las distribuciones temporales de concentración, en un ensayo de trazadores realizado en un tanque de flujo, a partir del análisis de fotografías de los penachos de Rodamina obtenidas a través de la pared transparente del tanque. La metodología comprende cuatro pasos: (1) Digitalización mediante escáner de los negativos en blanco y negro de las fotografías realizadas durante el experimento; (2) Calibración y normalización de cada una de las imágenes digitalizadas a una escala estándar de densidades ópticas, a través de la relación entre densidad óptica y el valor asignado a cada pixel en cada una de las imágenes; (3) Construcción de un estándar de concentraciones predeterminadas (2­97 mg/L); y (4) Conversión de las densidades ópticas a concentraciones de trazador. Mediante este procedimiento de calibración y conversión se determinó la distribución espacial de la concentración para dos fotografías. La metodología presentada proporciona un modo eficiente para estudiar la evolución de los penachos y los mecanismos de transporte.

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Received, March 1998 Revised, September 1998 Accepted, October 1998 Zhongbo Yu (Y) The Earth System Science Center, The Pennsylvanian State University, 248 Deike Building, University Park, PA 16802, USA Fax: c1-814-865-3191, e-mail: yu6essc.psu.edu Franklin W. Schwartz Department of Geological Sciences, The Ohio State University, Columbus, Ohio 43210, USA Supplementary material The color version of Figure 4 has been deposited in electronic form and can be obtained from http://link.springer.de/link/service/journals/10040 Hydrogeology Journal (1999) 7 : 236­240

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Key words laboratory experiments 7 tracer tests 7 hydrochemistry 7 variable-density flow 7 image processing

Introduction

In field tracer experiments, extremely detailed multilevel sampling is used to map temporal and spatial variations in concentration distributions in the study of mass transport, e.g., the USGS tracer experiment in Cape Cod (LeBlanc et al. 1991). In the laboratory, image-analysis techniques provide an accurate and efficient way to generate detailed concentration distributions (Schincariol et al. 1993) and to determine transient saturation fields in flow-tank experiments (Tidwell and Glass 1994). Schincariol et al. (1993) present a similar image procedure to determine concentration distributions only for a single layer from photographic data of flow-tank experiments where the tracer plumes can be observed through a glass wall. The experiments described below were designed to study how variable-density flow with accompanying instabilities is manifested in layered systems. The flow tank for these experiments was constructed of clear Plexiglass and was filled with various arrangements of glass beads; the setup is shown in Figure 1. Details on the tank, its features, and how it was set up for experiments are provided by Swartz (1993). The analysis presented here is based on the layered arrangement of glass beads where a high-permeability layer (mil 7 beads) is overlain by a lower permeability layer (mil 3 beads). A thin layer of mil 10 beads was added along the top of the tank. The tank was initially saturated with de-aired water containing 1107 mg/L NaCl, which has a specific density of 1.0036. The experiment began by adding less dense water (0.0 mg/L NaCl). All waters introduced to the tank were buffered by 2 mM potassium phosphate monobasic to maintain pH levels at 5.5­7.0. Rhodamine

Wt (Rwt; Krompton and Knowles, North Carolina) served as the tracer to visualize the flow and mixing processes. During the experiment, water samples were collected from the tank and black and white photography was taken to monitor the mixing processes. The results of the flow-tank experiments were examined using an image-processing methodology for multilayer porous-media systems based on the approach described by Schincariol et al. (1993). The methodology, including the computer procedures, was developed to process digitized photographs and to generate images of transient tracer plumes, which provide detailed spatial concentration distributions. The methodology was applied to images digitized from photographic data collected as part of a study on variabledensity groundwater flow (Swartz 1993).

Methods

The black and white photographic negatives of the spreading tracer photographed during the flow-tank experiments were scanned into digitized images using a Leafscan 35-SCSI digital scanning system with the resolution up to 2000 dots per inch (dpi). The image-processing system consisted of a Power Macintosh 8100/ 100AV, Adobe Photoshop 3.0, and NIH Image software (Manual of NIH Image 1994). The entire imageprocessing procedure includes the following steps: (1) scanning the negative films into the computer and saving digitized images in a preferred format; (2) constructing a curve that relates optical density and pixel value and performing image calibration; (3) constructing a standard curve that relates concentration and optical density; and (4) converting the optical density to concentration for each pixel, based on the standard curve and replotting the image with a normalized weight concentration. These steps are described in detail in the following sections. For the theories behind this procedure, see Schincariol et al. (1993).

Figure 1 Schematic diagram of laboratory setup for the flow-tank experiment

Overhead fluorescent lighting Flushing reservoir

Rhodamine wt. reservoir Peristaltic pump 182.9 cm Metal supporting brace

Hydrogeology Journal (1999) 7 : 236­240

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61 cm

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Digitizing Films The photographic negatives were converted to a digitized image in eight bits per pixel format using a Leafscan 35-SCSI digital scanning system at a resolution of 200 dpi. Before pre-scan can be applied, the scanner must be calibrated. After the pre-scan, many settings are readjusted from image to image, such as width, height, resolution, exposure time, and densitometer preferences. To maintain consistency among all the images that need to be processed, all settings except image width and height are kept constant. After conducting the final scan, the digitized image is output to Adobe Photoshop 3.0 and it is saved in a preferred format, such as JPEG, TIFF, and BMP. Image Calibration All the processes in this step were completed using the NIH Image software. The NIH Image software is a public domain program for image processing and analysis on Macintosh computers (web site: http:/ /rsb.info.nih.gov/nih-image/). It can acquire, display, edit, enhance, analyze, and animate images. Many formats of files, such as TIFF, BMP, JPEG, PICT, PICS, and MacPaint, can be read and written by this program, thereby providing compatibility with many other applications, including programs for scanning, processing, editing, and analyzing images. Spatial calibration is supported to provide real-world area and length measurements. Density calibration can be done against radiation or optical density standards using user-specified units. Image processing can be customized in three ways: (1) via a built-in Pascal-like macro language; (2) via externally compiled plug-in modules; and (3) on the Pascal source-code level. Results can be exported to files in a preferred format. When a photographic negative is scanned, the transmittance values at a set of equally spaced points on a rectangular raster are converted to digital form and recorded as the values of the pixels (picture elements) of the digital image. Small differences in lighting, exposure, or film development always occur and cause the optical density to vary from photograph to photograph. To correct for this variation, a gray scale of known transmittance values must be included in each negative or image. A curve relating optical density and pixel value can then be constructed using the pixel values recorded for points on the gray scale. In this way, the relation between pixel value and transmittance can be standardized across the collection of photographic negatives. A gray scale was used on each negative or image. The scale contains 20 steps, ranging from a nominal white of 0.0 optical density to a practical printing black of 2.0 optical density in a density increment of 0.10. In each digitized image, the average of the pixel value for each bar was computed and plotted against the known optical density value of the bar. A second-order polynomial function was applied to fit the measured data

Hydrogeology Journal (1999) 7 : 236­240

points and used to create a smoothed curve relating optical density and pixel value. Figure 2 shows the results for one image. This curve was then used to convert the pixel values from the scanned photograph into optical density values. The second-order polynomial curve-fitting function gave good results for all images. The best-fit curves (solid line) match well with the data points (circles). After the image has been calibrated, standard digital image-processing functions, such as flip, rotate, invert, and scale selection, can be applied. Median smoothing and background subtraction are not recommended, because the median smoothing shifts the concentration boundaries and causes artificial dispersion, even though it can reduce much of the noise of the image.

Constructing Concentration Standard Curves To convert the optical-density value to a concentration value for each pixel, a relationship between the tracer concentration and optical density must be available. Five experiment runs with various predetermined concentrations of the tracer (2­97 mg/L) were conducted to construct this relation, known as the concentration standard curve. Each run was photographed and the image was calibrated. Theoretically, the optical density of the tracer increases with the concentration. After each digitized image of five experiments was calibrated and processed, an average value of optical density for the region of a tracer with a predetermined concentration was obtained on each image of the experiment runs. Then the values of optical density for every run were plotted against the known concentrations; results are shown in Figure 3. A third-order polynomial function is the best fitting function that matches well with measured data points (circles) among those curve fittings, such as linear; second-, third-, fourth-, and fifth-order polynomial; and exponential. In the flowtank experiments, two horizontal layers, which have

Y = 0.079947 - 0.002232 X + 0.000033 X2 R2 = 0.9937

1.6 1.4 Optical density 1.2 1.0 0.8 0.6 0.4 0.2 0

60

100

140

180 220 Pixel value

260

300

Figure 2 Relation between optical density and pixel index (circles, data points) Q Springer-Verlag

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different hydraulic properties, were used and two curves relating concentration and optical density were produced. In Figure 3, standard concentrations range from 2­97 mg/L, whereas the optical density ranges from 0.74­1.05 on the upper layer and from 0.79­1.18 on the lower layer.

Converting Optical Density to Concentration Based on the standard curves (Figure 3), the optical density value of each pixel can be converted to a concentration value in each image. A Fortran program was written to convert the optical density to concentration for a multi-layer medium in the flow-tank experiment. The program basically consists of three parts: input, conversion calculation, and output. Two input files are required: one is a raw data file (an image file), which is output from the NIH Image software; and the other is a parameter file, which includes optical density values for background media of each layer and coefficients for standard curve fitting. The program is able to detect the size of the image file and input the file as a two-dimensional array (column and row). An estimated position (row number or column number) for the boundary between media is required by the program.

Y = -1023.38 + 4001.51 X - 5293.76 X2 + 2375.60 X3 R2 = 0.9837

Based on this number and the differences between two neighboring pixels, the program can determine the boundaries among multiple layers. Then the program applies the equations that fit the standard curve relating concentration and optical density for each layer to determine the concentration for the pixels where the tracers are present. The final two-dimensional array, which contains true concentration values for every pixel, is written out to a file, which can be re-input to most graphic softwares for graphic presentation and analysis. For graphic presentation and display of the concentration distribution, the SPYGLASS image-display software was used on a Unix system. The image can be displayed in gray and color scales (either continuous or banded). This image-processing procedure allows observing phenomena in the images in considerable detail and provides a tool for studying physical mechanisms in flow-tank experiments.

Application

The demonstration of this image-processing procedure was applied to one experiment, which was designed to study the instability of the tracer water, with a specific density of 1.0, flowing on dense water, with a specific density of 1.0036. The high-permeable layer was overlain by a lower-permeable layer in the flow tank. The Rhodamine tracer was injected at a constant rate of 0.57 mL/min laterally into the tank containing layered media saturated with NaCl water. Two negatives in the experiment were selected to illustrate the application. The procedures described above were applied to two negatives to produce a two-dimensional matrix containing the concentration value for each pixel. A resolution of 200 dpi was used in the scanning process, resulting in a two-dimensional matrix with a 500!160 grid. The new image pixel values were calibrated and converted to optical density using a secondorder polynomial function that was derived from the values measured for the gray scale on the image. Then the standard functions relating concentration and optical density (Figure 3) were applied to the image to convert the optical-density value to a concentration value for each pixel. Based on the known starting concentration, the true concentration was normalized to a weight concentration (from 0.0­1.0) for each pixel. The two-dimensional matrix of concentrations was used to generate an image showing normalized concentration. As shown in Figure 4, the tracer plume in the lower layer traveled faster than in the upper layer due to the difference in hydraulic conductivity. Both plumes moved upward because of the density difference in the two fluids. The plume in the lower layer traveled under the boundary between two layers for a distance of 65 cm before some of the plume from the lower layer entered the upper layer. One patch of the unstable

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120 Concentration (mg/L) 100 80 60 40 20 0

0.5 a

0.6

0.7 0.8 0.9 1.0 1.1 Optical density (upper layer)

1.2

1.3

120 Concentration (mg/L) 100 80 60 40 20 0

Y = -1624.14 + 5389.30 X - 6004.64 X2 + 2261.87 X3 R2 = 0.9811

0.5 b

0.6

0.7 0.8 0.9 1.0 1.1 Optical density (lower layer)

1.2

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Figure 3a,b Concentration standard curves showing relation between concentration and optical density. a Upper layer. b Lower layer (circles, data points) Hydrogeology Journal (1999) 7 : 236­240

240 Figure 4a,b Processed images of tracer plumes. a At a distance of 96.1 cm. b At a distance of 153.5 cm

NaCl = 1107 mg/L Q = 0.57 mL/min Distance traveled = 76.1 cm 0

100

0

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400

1.0 a

0.8 0.6 0.4 0.2 Normalized rhodamine wt. concentration

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NaCl = 1107 mg/L Q = 0.57 mL/min Distance traveled = 153.5 cm 0

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b

0.8 0.6 0.4 0.2 Normalized rhodamine wt. concentration

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plume created in the lower layer, which could not be observed in the laboratory, was observed on the processed image in Figure 4.

Dr. Eric J. Barron and the Earth System Science Center, The Pennsylvania State University; from Richard White, for reading the manuscript; and Philip J. Kolb, for his help with some of the graphics.

Summary

A high-resolution image-processing procedure for determining two-dimensional concentration fields in flow-tank experiments has been developed. This procedure provides an accurate and efficient way to obtain concentration fields with good temporal and spatial detail in multi-layer porous media and to study patterns of plume evolution and transport mechanisms. This study provides a framework for further development of image-processing techniques for heterogeneous media.

Acknowledgments Funding for this study was provided by the Office of Exploratory Research, U.S. Environmental Protection Agency (contract R 819976-01-0). The authors gratefully acknowledge the support in the preparation of this paper from Hydrogeology Journal (1999) 7 : 236­240

References

LeBlanc DR, Garabedian SP, Hess KM, Gelhar LW, Quadri RD, Stollenwerk KG, Wood WW (1991) Large-scale natural gradient tracer test in sand and gravel, Cape Cod, Massachusetts, 1, Experimental design and observed tracer movement. Water Resour Res 27 : 895­910 Manual of NIH Image (on-line, http://rsb.info.nih.gov/nih-image/), version 1.58, 1994 Schincariol RA, Herderick EE, Schwartz FW (1993) On the application of image analysis to determine concentration distributions in laboratory experiments. J Contam Hydro 12 : 197­215 Tidwell VC, Glass RJ (1994) X ray visible light transmission for laboratory measurement of two-dimensional saturation fields in thin-slab systems. Water Resour Res 30 : 2873­2882 Swartz CH (1993) An experimental investigation of variabledensity-driven flow in layered porous media. MS, The Ohio State University, USA Q Springer-Verlag

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