A ${250}^{\text{'}}$ deep test borehole was originally drilled in $1996.$ In $2013,$ we performed a TRT$.$ Here's

the information we have:

Prior to running the TRT$,$ the temperatures at depths were measured on ${10}^{\text{'}}$ to

$20$'intervals. This data is found in the file: Undisturbed$\_$temperatures $.$ xlsx

The measurements have been reduced to $1$ minute intervals $($from $10-$second intervals$).$

Two pairs of carefully calibrated thermocouples were used, from which two values of

mean fluid temperature were produced. You'll see there are slight differences, which

reflect the limitations we have in calibrating temperature sensors$.$ The measured total

power in Watts is based on the electricity used by the fixed capacity heating element,

the variable$-$capacity heating element, and the pump. The data are summarized in

TRT$\_$data$\_$reduced.xlsx$.$

The borehole was drilled with a ${4\mathrm{.}5}^{\text{'}\text{'}}$ bit and grouted with enhanced thermal grout with

thermal conductivity of $0\mathrm{.}85Bt\frac{u}{h*ftF}.$ The grout was $"63\mathrm{.}5\%TG{85}^{,}$ the "world's

first thermally enhanced grout" from GeoPro. However, the formation contains layers

of sandstone, shale, and clay, and the borehole diameter may be nonuniform. They

expected to have to add $20$ bags of grout to fill the hole. On the day that it was done,

they used $21$ without filling the hole, and it settled to be ${55}^{\text{'}}(17$ m $)$ below the ground

surface. They later filled this in with another $5$ bags, by pouring dry grout into a wet

borehole. Probably not an ideal procedure! $[$But$,$ as I think I mentioned in class...there

may be no such thing as a perfect test.$]$

The U$-$tube is $1^{\text{'}\text{'}}$ SDR$-11$ HDPE. The shank spacing was not controlled, as far as I know.

Determine the average undisturbed ground temperature for the borehole. Please consider

how the individual measurements should be weighted.

Estimate the effective thermal conductivity based on the period from $12$ hours to the end of

the measurement period.

Estimate the effective borehole thermal resistance based on the period from $12$ hours to

the end of the measurement period.

Estimate the effective thermal conductivity sequentially, starting with the period $12$ hours

to the end of the measurement period, then $12$ hours $+1$ minute, $12$ hours $+2$ minutes, etc.

$($If you want to use a larger time interval, say $12$ hours $+10$ minutes, $12$ hours $+20$ minutes,

etc., that's fine.$)$