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Long-term ground-temperature changes in geo-exchange systems.

Article Excerpt
INTRODUCTION

When the amount of heat injected into the ground is significantly lower than the amount of heat collected from the ground there is a so-called "thermal imbalance" in the ground. A similar (reverse) phenomenon also occurs when the amount of heat extracted is greater that the amount of heat rejected into the ground. If ground thermal imbalance persists year after year, it leads to thermal interaction among boreholes in multiple boreholes configurations. Consider, for instance, the center borehole of a 3 x 3 square bore field shown in Figure 1. Over time, heat diffusion from the eight neighboring boreholes interacts with heat diffused from the center borehole. The heat released from the center borehole is "trapped" and stored in the ground surrounding the borehole. Consequently, the ground temperature near the center borehole increases. The same phenomenon occurs for the other eight boreholes. However, the problem is less severe at the periphery, where heat can diffuse unobstructed toward the far-field since there are no neighboring boreholes in that direction. This phenomenon can result in significant ground-temperature changes in the borefield region after a few years, resulting in a decrease of heat pump performance.

[FIGURE 1 OMITTED]

Long-term temperature changes are usually quantified using the concept of temperature penalty, [T.sub.p], which represents an effective increase (or decrease) of the undisturbed ground temperature. This paper concentrates on the evaluation of [T.sub.p]. First, a methodology to evaluate [T.sub.p] is proposed. The methodology is applied to several cases, including the ones reported in the ASHRAE Handbook-HVAC Applications (ASHRAE 2003). The second part of the paper offers design engineers an approximate method to evaluate [T.sub.p].

IMPACT OF LONG-TERM GROUND-TEMPERATURE CHANGES

One of the main factors influencing geo-exchange systems economics is the length of the ground heat exchanger (GHX). It is therefore important to predict ground heat transfer as precisely as possible to size GHX systems properly. Furthermore, ground heat transfer predictions are important in annual simulations to accurately predict the heat pump inlet temperature.

GHX Sizing

There are several ways of calculating the required length of a GHX. In this work, the equation recommended by ASHRAE (2003) is used. This equation was modified by Bernier (2000) to take the following form:

L = [[[q.sub.h][R.sub.b] + [q.sub.y][R.sub.y] + [q.sub.m][R.sub.m] + [q.sub.h][R.sub.h]]/[[T.sub.mean] - ([T.sub.g] + [T.sub.p])]] (1)

where L is the total borehole length required. The variables [q.sub.h], [q.sub.m], and [q.sub.y] represent ground loads where the indices h, m, and y refer to hourly, monthly, and yearly values, respectively. The sign convention used in this paper is the following: positive values of q are associated with heat rejection in the ground. The values of [R.sub.y], [R.sub.m], and [R.sub.h] represent effective thermal resistances for three thermal pulses. The periods of these pulses are problem dependent. These values are generally of the order of ten years, one month, and six hours, respectively. Borehole thermal resistance is represented by [R.sub.b]. The values of [T.sub.g] and [T.sub.mean] are the undisturbed ground temperature and the average fluid temperature in the borehole for design conditions, respectively. Borehole thermal interaction from adjacent bores is accounted for by introducing a temperature penalty, [T.sub.p]. This temperature represents an effective increase (or decrease) of the undisturbed ground temperature to account for ground thermal imbalance. Equation 1 is evaluated for both heating and cooling conditions. The longer of the two calculated values gives the required borehole length.

As shown in the example presented in Table 1, ground thermal imbalance can have a significant impact on L. This table presents calculated values of [T.sub.p] for a 10 x 10 borefield for two cases. The first case represents a typical situation experienced in a cold climate (where [T.sub.g] = 10[degrees]C and [T.sub.mean] = 0[degrees]C) where the number of heating hours, represented here using the concept of equivalent full load hours, is greater than the number of cooling hours. The second case is representative of a hot climate (where [T.sub.g] = 15[degrees]C and [T.sub.mean] = 35[degrees]C) without heating. Values of [T.sub.p] are obtained using a method described later in this paper.

Table 1. Impact of Neglecting [T.sub.p] in the Calculation of L Annual Thermal Imbalance Equivalent [T.sub.g], [T.sub.mean], Full Load [degrees]C [degrees]C kWh kW Hours, hours Heating = 1500 10 -1.76 x [10.sup.5] -20.1 Cooling = 500 Heating = 15 35 8.80 x [10.sup.5] +10.5 Cooling = 2000 Equivalent Full Load [T.sub.p, L with thermal interaction/ Hours, hours [degrees]C L without thermal interaction Heating = 1500 -2.1 1.26 Cooling = 500 Heating = +10.5 1.51 Cooling = 2000 Based on the following conditions:...

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