An environmental consulting firm is conducting a site investigation on the abandoned industrial site which is 200 m by 150 m in size shown in figure. A number of piezometers were installed on site to get information about the subsurface aquifer. Geologic samples were obtained from the drill cuttings and sent for analysis. Hydraulic conductivity of the aquifer solids was found to be 0.32 m/d and the porosity was found to be 0.36.

The groundwater hydraulic gradient was found to be 0.0012, sloped downward to the southwest corner of the site, and oriented at 35 degrees to the south western corner of the site. Groundwater head was measured to be 92 m above mean sea level in a piezometer which was located at the southwest corner of the site. The general relationship between head and location in a 2-dimensional aquifer is as follows:

 H(x,y)= H(x₀ ,y₀ )+ (x- x₀ )*cosΘ*(dh/dl) +(y-y₀)* sinΘ*(dh/dl)
Where H(x₀,y₀) is the head measured at the location (x₀,y₀), θ is the angle that the hydraulic gradient makes with the line y=y₀ (i.e., the horizontal line that intersects x0, y0), dh/dl is the magnitude of the hydraulic gradient. The following plan view represents information about the hydraulic gradient at the site:

1.a. Sketch a flowsheet of the steps which you will take to simulate the groundwater aquifer at this site by computing the groundwater head with the spatial resolution of 1 meter in the x-direction and 1-meter in the y-direction. Make sure to note how you plan to organize data with scalar, vector and matrix elements.

b. prepare a well-documented MATLAB program to simulate the groundwater aquifer at this site by computing the groundwater head with a spatial resolution of 1 meter in the x-direction and 1 meter in the y-direction. You must describe the rationale for any supporting calculations or assumptions made.

c. Create a contour plot of head values in the x-y plane. This plot is a ‘bird’s-eye’ view of the topographical contours of constant head on the water table.

d. Create transect (also called cross-section) plot showing vertical head as a function of distance:

i. In x-direction, at the distance of 30 m north of the southwest corner of the site.

ii. In y-direction, at the distance of 56 m east of the southwest corner of the site.

2. Characteristic properties of the aquifer could be used to compute groundwater velocities, vgroundwater(L/T), according to:

V_grounwater=K_H/η (dh/dl)

where K_H (L/T) is hydraulic conductivity of the porous media in the aquifer, η is the porosity of the porous media, (dh/dl) is the hydraulic gradient. Note that the velocity of groundwater only has meaning in the direction of the hydraulic gradient that is always perpendicular to contour lines of constant head.

a. Compute velocity of groundwater at this site.

b. Supposing that hydraulic gradient is constant in the region around the industrial site, use the groundwater velocity to compute the travel time between a spill located at 75 m east and 75 m north of the southwest corner of the site and a private groundwater well located 36 m south and 4 m east of the southwest corner of the site. Note that these locations are located on a line parallel to the hydraulic gradient and perpendicular to your contour lines.