# Thermal Response Test

**Thermal Response Test (Termisk Responstest in Swedish)**

A Thermal Response Test (TRT) is conducted in order to establish some critical parameters needed to calculate the dimensioning (number, geometric configuration, depth and spacing of the bore holes) of the Bore Hole Thermal Energy Storage (BTES) as accurate as possible given certain heating and cooling loads.

If not conducted these parameters has to be estimated on basis of whatever clues that exists. For e.g. granite and other igneous rocks the values can vary substantially and the effect is that the size of BTES (amount of bore holes and/or meters drilled) can vary with as much as 30 percent. So without a TRT the BTES can be either over seized, unnecessarily expensive or under sized, not being able to deliver the necessary amount of heating and cooling.

What is measured is the temperature , the conductivity, and the Thermal bore hole resistance.

Temperature is the undisturbed average temperature in the bedrock along the bore hole, in degrees Celsius.

Conductivity, commonly named lambda, is the bedrocks ability to conduct heat as an average along the length of bore hole. It is measured in W/mC (Watt per degree Celsius or Kelvin and per meter).

Bore hole resistance is measured in Cm/W and is of course also an average value. Bore hole resistance is the barrier for heat transfer that exists between the fluid in the heat exchanger and the wall of the surrounding rock. Effectively it shows the temperature difference between the fluid and the rock wall that will almost immidiately be established, depending on the power of the heat that is added, or extracted, from the bore hole.

These parameters describes the thermal properties of the bedrock surrounding the bore hole well enough to be used in a simulation model, e.g. Earth Energy Designer, for dimensioning the BTES (EED is described in another document).

In order to conduct a TRT one bore hole need to be drilled. That bore hole can later on be used in the BTES so it is not a additional cost.

The drilling of a bore hole, apart from enabling a TRT, also gives valuable information about the properties of the bedrock like the subterranean water level, fissure zones, type of rock (soft, hard etc), pressure etc which greatly helps when the cost for drilling the entire BTES is calculated.

**Requirements**

Electricity must be available within 100 meters from the bore hole with frequency 50-60 Hertz, voltage of 380-400 V and 16 Ampere of power..

**Below is a description of the measurement procedure and calculations**

The equipment used is in principle, a circulation pump, a heater and a temperature logger with a number of sensors. The equipment is connected to the collector in the bore hole filled with a fluid, usually a mixture between water and alcohol. The fluid is then made to circulate with the pump and the temperature is logged every 5 minutes. The temperature is logged in the fluid going into the collector and coming out of it, and also the temperature of the surrounding.

At first the fluid is circulated, usually 10-24 hour, without the heater, to establish the natural temperature in the ground. Then the heater is turned on at a certain power and that will continuously heat the fluid. This part usually lasts 48-100 hours. The speed of the pump and the power of the heater is set to be as similar as possible as it will be in the sharp GSHP installation that eventually will be undertaken.

Sketch showing the set up, in principle:

First the fluid is circulated for some 10-24 hours to get the undisturbed natural temperature in the ground.

After that the heater is turned on and the fluids temperature at first increases fast followed by a period of steady temperature increase that will be slower and slower. The temperature difference of in and out of the fluid is the heat absorbed by the surrounding bedrock, and the inclination of this temperature curves is a result of the thermal properties in the bore hole and the bedrock surrounding it. This phase typically lasts 48-100 hours.

Following graph shows an example logged temperatures (click to enlarge):

**Theory**

In a thesis written by Signhild Gehlin at Luleå Tekniska högskola (LTU-LIC-1998:37) practice and theory of Thermal Response Test is described, and it is the method described in the thesis that is used here.

In the thesis a mathematical function, a formula, is defined that describes how the mean temperature (mean of in and out temperatures) of the fluid, Tf, develops over time with constant addition of heat with the power Q.

The formula is an approximation of an analytical function and a certain time must pass (0.5 to 1 hour with the parameters we normally use in these tests) in order for it to be a good approximation:

Tf= Q/(4*pi*L*H)*ln(t)+(Q/H*(1/(4*pi*L)*(ln(4*a/(rborr*rborr))-Ec)+Rb)+Tsur) (1)

Q is power of the heat added , H: active depth of bore hole, L: the average conductivity, a is diffusivity (quote between conductivity and the heat capacity of the rock), t is time in seconds from start of heater, rborr is the radius of the bore hole, Ec is Eulers constant (0,5772), Rb is the heat resistance of the bore hole (Bore hole resistance), and Tsur is the undisturbed, natural, temperature of the ground.

The equation can also be stated as Tf= k*ln(t) + m, (2) which is the formula for a straight line.

Thus, if you plot the relation between the fluid mean temperature, Tf, and ln(t), the natural logarithm of time in seconds since the heater was started, you should have a straight line, except for the first hour (after an hour ln(t) is about 8.2).

Below is an example (click to enlarge):

Y-axis shows temperature in degrees Celsius and the X-.axis shows the natural logarithm of time.

If the measurements are accurate it should be a good approximation of a straight line, after the first hour (where ln(t) is 8,2). The inclination of the line can be calculated using regression analysis. Then we will have a value of k in equation (2). As we know Q (power) and H (the depth of the bore hole) we can now calculate L, the conductivity of the rock, surrounding the bore hole, from the first part of equation (1). (I.e. Tf= Q/(4*pi*L*H)*ln(t).)

When L is known Rb can be calculated from equation (1) as all the other parameters are known (except for the heat capacity that has to be approximated based on what type of rock it is), and by choosing a Tf and a ln(t) for some point on the curve in the graph.

Now that we know L, the conductivity, Rb and Tsur (the undisturbed mean temperature of the rock) we can calculate a theoretical mean temperature curve and, if all measurements and calculations are valid that curve should conform with the measured curve.

Below is an example (click to enlarge):