Test borehole

This panel describes the instrumented borehole of the test, as it was designed and built: its dimensions, its pipes and its grout. The geometry is taken from the drill record, the pipe product sheet and the completion report, and the two interpretation models read it directly.

The panel uses that geometry to compute a theoretical effective borehole resistance R_b^*, together with its breakdown into R_f, R_p and R_g, exactly as the design module would for the same borehole. This theoretical value exists to be compared against the experimental R_b^* that an interpretation method deduces from the measured record, when that method delivers one: the first-order approximation always does, and the short-term g-function does as well, implicitly, through its calibrated parameters. Holding the two together, the geometry-based expectation on one side and the test-based measurement on the other, is what this panel and the console pages that follow are for.

Not every value entered here was measured on this test. The grout conductivity λ_g is the clearest example: it is the value the product was specified at, not something a thermal response test can see directly, and every resistance computed from it, R_g and R_b as much as R_b^*, inherits that status.

Borehole configuration - All five configurations are available: single U-tube, the two double U-tube arrangements, coaxial and standing column. A thermal response test is run on whatever borehole was drilled, and the resistance breakdown below is computed for the configuration you select, exactly as it is in the design module.

Active length — H (m) - The length of borehole that actually exchanges heat with the ground. Above-ground piping, and any piping not embedded in grout, is excluded from H. This field sits on this panel in the TRT module because the module has no borehole-field layout panel of its own. H matters twice: it converts the measured heating power into the unit power q = Q/H that both regressions fit, and it is an input of the short-term g-function. It is the most consequential figure on this panel, for the reason given at the end of this page.

Borehole diameter — d_b (m) - At least the diameter of the drill bit. In soft or incompetent rock it can be increased to account for lateral abrasion. It sets the grout resistance R_g and, through r_b = d_b/2, the critical time t_cr = 5 r_b²/α_s before which the line-source approximation does not apply.

Pipe inner and outer diameters — d_i, d_o (m) - The inner diameter fixes the flow velocity, and with it the Reynolds number, the exchange surface and the residence time of the fluid in the loop. The two together give the pipe wall thickness and hence the pipe resistance R_p. Both are entered as diameters on this panel; the models work in radii and halve them internally.

Shank spacing — s (m) - The distance between the two legs of the U-tube, used for the resistance breakdown shown below. The short-term g-function does not read this field: it calibrates its own spacing s against the measured temperatures, over a range it derives from d_b and d_o (see Analysis with the short-term g-function).

Pipe thermal conductivity — λ_p (W/m·K) - Used to compute the pipe resistance R_p, and an input of the short-term g-function. Since the range of values of the pipe volumetric heat capacity is narrow, a fixed C_p = 1.9 × 10⁶ J/m³/K is assumed.

Grout thermal conductivity — λ_g (W/m·K) - Used for the resistance breakdown shown below. Like the shank spacing, it is not an input the interpretation depends on: the short-term g-function calibrates its own λ_g and C_g against the data, precisely because the conductivity achieved in the field is rarely the one printed on the bag.

As these values are entered, a scaled cross-section of the borehole (the grout annulus, the two pipes of the U-tube and their spacing) is drawn alongside the inputs. A unit slip or a transposed diameter shows up in the drawing before it propagates into the analysis.

One quantity the breakdown needs is not entered anywhere on this panel: the ground thermal conductivity λ_s. It is taken from the first-order model as soon as it has a result, falling back to the design module's default of 2.5 W/m·K when the test has not yet been fitted. Refine the regression window in the first-order model and every resistance below follows; the λ_s in play at any moment is the one reported on the FOA page of the console.

Which model reads which configuration - The first-order approximation fits a line source without reference to the pipe arrangement, so it applies to any of the five configurations above (see Analysis with first-order approximations). The short-term g-function does not: its network was trained on single U-loop boreholes only, so its own panel carries a configuration selector frozen on Single U-Loop, and everything it reports, including its own R_b^*, is computed for a single U-tube regardless of what this panel shows (see Analysis with the short-term g-function). Read its results with that in mind whenever the test borehole is not one.

Which input feeds which model - The fields do not all carry the same weight, which is worth knowing when deciding how carefully each must be established:

• H — read by both models, and the most consequential geometric input of the two interpretations.
• d_b — read by both: it sets t_cr for the first-order approximation and the borehole diameter for the short-term g-function model.
• d_i, d_o, λ_p — read by the short-term g-function, and by the Reynolds number of the phase statistics; the first-order approximation does not use them.
• s, λ_g — used for the breakdown on this panel only. The short-term g-function calibrates its own spacing and grout properties against the data.

Summary & charts: the resistance breakdown of the test borehole

The resistance breakdown, at the operating point of the test - The design module evaluates the borehole resistance at its design temperature limits and its design flow rate per borehole. A thermal response test has neither: the breakdown reported here is recomputed instead at the measured operating point, the mean flow rate and the mean fluid temperature of the heating phase reported on the console's phase-statistics page. It follows the phase boundaries, so moving them moves this table too. This is also why the panel shows a single column, headed Heating, instead of the cooling and heating columns of the design module: a TRT is a heat injection, and there is no cooling phase to report.

Three resistances in series between the fluid and the borehole wall combine into the local borehole resistance R_b, a cross-sectional quantity that treats each leg of the U-tube as if it exchanged heat with the ground on its own, independently of the other:

• Convective resistance R_f — between the fluid and the pipe inner wall, set by the flow regime (Reynolds number) and therefore by the fluid, the flow rate and the pipe inner diameter.
• Pipe resistance R_p — the conduction across the pipe wall, set by the pipe diameters and the pipe conductivity λ_p.
• Grout resistance R_g — from the pipe outer wall to the borehole wall, set by the grout conductivity λ_g and the position of the pipes.

The three come from the explicit multipole formulas: the single U-tube form of Claesson and Javed (2018), and the double U-tube form of Claesson and Javed (2019) for the configurations that carry four pipes. These closed-form expressions, rather than an iterative solve, are what let the breakdown update at every change of an input; Javed and Claesson (2017) present the same second-order theory in a form compact enough to check by hand.

R_b leaves out one real effect: the warm fluid on its way down heats the cooler fluid on its way back up, through the grout, over the full depth of the borehole, a thermal short-circuit between the two legs that a cross-sectional resistance cannot see. The panel accounts for it and reports the effective resistance R_b^*, which is always at least as large as R_b and grows further above it with a longer borehole, a higher flow rate, or pipes placed closer together, exactly as it does in the design module. Alongside it, the panel also reports two more figures that state that same gap in different terms: the vertical advective resistance R_η = R_b^* − R_b, the resistance the short-circuit itself is worth, and the borehole efficiency χ, the same gap expressed as a single dimensionless figure rather than as two resistances to compare. Neither R_b nor R_b^* accounts for the thermal capacity of the pipes, grout and fluid, which is why the first-order approximation requires the borehole to have reached a thermal steady state before its heating-phase intercept can be read as R_b^*.

The effective-resistance-versus-flow-rate chart - Beside the table, a chart titled Borehole thermal resistance plots R_b^* against flow rate for the borehole configuration and ground conductivity currently on this panel, with a vertical marker at the same mean flow rate of the heating phase used for the table. It draws four stacked, cumulative bands rather than four independent curves, in the order the legend lists them bottom to top: the advective short-circuit term alone, then that term plus R_g, then plus R_p, and the topmost boundary closes the stack at the total R_b^*.

Because the bands are cumulative, an individual resistance reads as the thickness of its band, not the height of any single curve above the axis: R_p, for instance, is the vertical gap between the third boundary and the one below it, not the height of either curve on its own. Hovering a boundary reports the flow rate and the cumulative resistance up to that boundary, labelled accordingly, which gives an individual band's thickness without judging it by eye; the Toggle tooltips on or off button of the main toolbar suppresses these the same way it does on every other chart.

TRT in practice: the conditions that decide whether R_b^* is trustworthy

The active length first of all. A 10 % error on H induces a 10 % error on the ground thermal conductivity λ_s, and it carries into R_b^* as well. The relation is one to one, because H sets the unit power q = Q/H that enters the regression slope in direct proportion, so nothing downstream can compensate for it: a careful regression on a wrong H simply returns a wrong number, confidently. Establish H from the completion record rather than from the drilled depth, and exclude every metre of pipe that is not embedded in grout.

Flow regime next. A flow rate high enough to keep the loop turbulent is the precondition for a meaningful R_b^*. The high convective resistance of laminar or transitional flow inflates the measured R_b^* and depresses λ_s, and no interpretation can undo it after the fact. The regime follows from the pipe inner diameter and the measured flow rate, so confirm the Reynolds number of the heating phase in the console phase statistics before trusting the resistance.

Pipe placement and spacers. The resistance depends strongly on where the pipes sit in the borehole. The models assume pipes held apart at their spacing; in reality they tend to cluster together during grouting unless spacers are installed along the full depth. A set of pipes resting against one another can easily double the effective resistance, so a value that comes out higher than the completion would suggest may be telling you about the installation rather than about the ground.

Grout quality. The grout conductivity depends on the water-to-solids ratio and on thorough mixing. A poorly mixed or over-diluted grout delivers a conductivity below its specification, permanently raising R_b^*. When the short-term g-function calibrates λ_g to a value well below the product figure, poor grout placement is a likely explanation.

Using the measured R_b^*. The first-order approximation obtains its R_b^* from the intercept of the heating-phase line, once the slope has fixed λ_s; the recovery phase yields only λ_s, since the borehole resistance is carried in the heating-phase intercept alone. The short-term g-function obtains its own R_b^* implicitly, as the resistance produced by the calibrated grout, spacing and geometry across the full transient, a third figure alongside the one on this panel and the one from the first-order approximation, all three computed by the same multipole method but from different inputs: entered here, fitted by the first-order approximation, calibrated by the short-term g-function. Agreement between them is a good sign; a marked discrepancy usually points to a non-turbulent flow, an unstable heating power, or a completion unlike the one assumed. What a test returns is the effective resistance, not the internal resistance between the two legs Lamarche et al. (2017). Marcotte and Pasquier (2008) show how much the figure moves with the way the mean fluid temperature is formed. The R_b^* returned by a test is valid for the conditions of that test, its flow rate, its fluid and the geometry of the test borehole, and should not be transferred unchanged to a design that differs in any of them. Its proper use is as the field-validated anchor a designer reproduces before exploring alternatives (a higher design flow rate, a more conductive grout) in the design module. Once the system runs, the same quantity can be re-estimated from operating records rather than from a dedicated test, which is a useful way to see whether the installed field behaves as the tested borehole did (Mikhaylova et al., 2017).

A standing column well is not a closed loop. The configuration selector accepts one, and the breakdown above is computed for it, but neither interpretation model on this page accounts for what actually sets a standing column well apart: it exchanges water directly with the aquifer, and that exchange continues even without a bleed. Where the formation is tight enough that conduction dominates, the well behaves close enough to a closed loop that the first-order approximation still returns a plausible conductivity. Where a sufficiently permeable layer is present, the continuous recirculation between the supply and the return sets up a radial flow within that layer, and the resulting advective heat transport inflates the apparent conductivity well beyond anything conduction alone would produce, even with no short-circuiting to the surface during the test. Robert et al. (2022) document exactly this on a standing column well tested through a layered aquifer, where the first-order approximation returned a thermal conductivity too high to be physical once the permeable layer was reached.