Johan Claesson

SIMULATION MODEL FOR THERMALLY INTERACTING HEAT EXTRACTION BOREHOLES

The proper design of heat pump systems that use deep boreholes to extract heat from the ground requires a precise model of the thermal processes in the ground. One problem is the interaction between the connective heat flow in the channels in the borehole and the conductive process in the ground. Another important problem is the thermal interaction between boreholes. A computer model for these thermal processes is presented. The three-dimensional problem with its complex geometry is, by a rather intricate superposition, reduced to cylindrically symmetric ones, one for each borehole or symmetry group of boreholes. Recipes for the choice of meshes are given. The accuracy of the model is shown to be very good.

Conductive heat extraction to a deep borehole: Thermal analyses and dimensioning rules

The ground is a virtually unlimited, ubiquitously accessible heat source and sink for heat pumps. Deep boreholes may be used as heat exchangers in the ground. We present an extensive analysis of such a heat extraction (or injection) borehole. The effects of stratification of the ground, climatic variations, geothermal gradient, and groundwater filtration are dealt with. A basic tool for the analysis is the solution for a heat-extraction step. The thermal disturbance at and near the ground surface is shown to be negligible. Thermal recharge in order to improve the heat-extraction capacity a few months later is shown to be futile. The thermal processes in the borehole are, in good approximation, represented by a single borehole resistance. Formulae that relate the heat-extraction rate to the required extraction temperatures are given. They are based on superpositions of steady-state, periodic, and extraction-step solutions. A response-test method is proposed for the determination of three important parameters: average thermal conductivity in the ground, borehole thermal resistance, and average undisturbed ground temperature.

Multipole method to calculate borehole thermal resistances in a borehole heat exchanger

Ground-source heat pump systems use borehole heat exchangers to transfer heat to and from the ground. An important feature is the local thermal resistances between the heat carrier flow channels in the borehole and the surrounding ground. The counter-flow heat exchange between the pipes is also important, particularly for the axial temperature variation. These resistances can be represented by a thermal network between the pipes and the ground. The borehole thermal resistance is readily obtained from the network. A fairly intricate mathematical algorithm, the multipole method, to compute the temperature fields and, in particular, the thermal resistances is presented. This article focuses on the application of the model, leaving the detailed mathematics to a background report. The formulas and methodology required for any particular case are presented in detail. The multipole method gives a solution with very high, and easily verified, accuracy for the steady-state heat conduction in a region perpendicular to the borehole axis. It is fairly straightforward to implement the algorithm in any design software. The computational time requirements are negligible.

Heat loss to the ground from a building—I. General theory

Abstract The heat flow to the ground from a building depends on the complicated thermal process in the ground. An extensive analysis of the processes involved is presented in this series of papers. A main goal is to obtain sufficiently accurate, and as simple as possible, formulae for the heat flow to be used for design purposes. This first papers presents the general theory that is used. The main difficulties in obtaining manageable formulae concern the three-dimensionality of the thermal problem, the strong temporal variability of the outdoor temperature, and the large number of parameters involved in describing foundation geometry, thermal insulation and so on. Superposition and dimensional analysis are used to meet these difficulties. Basic components of the thermal process are the steady-state solution, the solutions for a periodic outdoor temperature and a unit step of the outdoor temperature. The dimensional analysis leads to a steady-state heat loss factor, corresponding factors for the periodic solution and the temperature step. The penetration range of the two transient processes is studied in detail. It is shown that these normally involve only a region around the periphery. So-called edge solutions, which are two-dimensional and depend on the parameters near the periphery only, may be used.

Steering Parameters for Rock Grouting

In Swedish tunnel grouting practice normally a fan of boreholes is drilled ahead of the tunnel front where cement grout is injected in order to create a low permeability zone around the tunnel. Demands on tunnel tightness have increased substantially in Sweden and this has led to a drastic increase of grouting costs. Based on the flow equations for a Bingham fluid the penetration of grout as a function of grouting time is calculated. This shows that the time-scale of grouting in a borehole is only determined by grouting over-pressure and the rheological properties of the grout, thus parameters that the grouter can choose. Pressure, grout properties and the fracture aperture determine the maximum penetration of the grout. The smallest fracture aperture that requires to be sealed thus also governs the effective borehole distance. Based on the identified parameters that define the grouting time-scale and grout penetration an effective design of grouting operations can be set up.

Isothermal moisture flow in building materials:: modelling, measurements and calculations based on Kirchhoff’s potential

Abstract The modelling of non-linear, isothermal moisture flow in porous media without hysteresis is considered. Different formulations based on different potentials for the Fickian moisture flow are compared. Kirchhoff’s flow potential, i.e. the integral of any state-dependent moisture flow coefficient, is introduced. The problem with a highly variable flow coefficient vanishes. The theoretical, numerical and computational basis for isothermal moisture transport in building materials using Kirchhoff potentials is described. It is shown that the use of Kirchhoff’s potential has clear advantages compared to models using a moisture flow coefficient. There is a conceptual simplicity. Only the relation between moisture content and Kirchhoff’s potential is used in the internal process, while the relation between Kirchhoff’s potential and any intensive variable is needed at boundaries. Precisely these relations are obtained in measurements, while the flow coefficients require a troublesome derivation. The use of Kirchhoff’s potential simplifies considerably the numerical calculation, since flow coefficients and ensuing interpolation problems are avoided. Complete sets of data for moisture flow and equilibrium are given for five common building materials. In two examples, numerical calculations are compared to experimentally determined moisture distributions.

Heat loss to the ground from a building—II. Slab on the ground

Abstract The heat flow to the ground from a rectangular slab with an even thermal insulation is analysed. The steady-state heat loss factor is given in complete diagrams for any ratio between length and width of the slab and for any constant insulation of slab and ground surface. A two-dimensional edge approximation for time-dependent heat loss at the perimeter of the slab is introduced. New analytical solutions for the edge heat loss due to periodically variable outdoor temperature or a step change in the outdoor temperature are presented. The effect on the heat loss due to different variations of the outdoor temperature is easily analyzed with these solutions. For example, daily periodic variations can certainly be neglected. Based on this, simple design rules for the heat loss during a heating season and the peak effect are given.

Unexpected experimental results for capillary suction in wood: Analysis on the fibre level

Abstract A series of simple experiments on capillary water uptake in rectangular sticks of Scots Pine (Pinus sylvestris L.) gave some unexpected results. Sticks of sapwood and heartwood with lengths of 100, 200 and 300 mm, with the four long sides sealed, were used in the experiments. The samples were allowed to suck water, one group for 1000 h and one group for 1900 h. After exposure, as anticipated, the heartwood samples had a moisture content (MC) distribution with high values at the bottom and steeply decreasing values towards the top. The sapwood samples, in contrast, had moisture distributions with high MC at the bottom and the top, and low MC in the middle. Additional experiments to study flow paths and timescales of the process were performed using dyed water. A Fickian approach is discussed in some detail. It is clear that the process represented by the experimental results cannot be explained within a Fickian framework. The analysis has to be done on the fibre level, where an explanation is proposed. The influence from bordered pits is of significant importance and their resistance dominates the timescales. A key factor in the proposed explanation is the high lateral capillary conductivity within the saw-damaged top surface. However, some questions remain unanswered.

A transient pressurization method for measurements of airtightness

By measuring the pressure decline in a pressurized air volume from which air is leaking it is possible to determine the air leakage rate as a function of the pressure difference. The leakage rate is proportional to the time derivative of the pressure. The formula, which is quite simple, accounts for temperature change of the air and volume change of the chamber. The derivation of the equation relating air leakage to pressure drop is described. Initial tests of the method have been performed and the derived equation shows good agreement with air leakage rates obtained by theoretical as well as standard steady-state methods.

On the use of the diffusion equation in test case 6 of DECOVALEX

Test case 6 of DECOVALEX addresses the hydromechanical behavior of fractured crystalline rocks submitted to high pressure testing between of inflatable packers. The objective of the present study is to analyze the possibilities of the diffusion equation to account that the flow rate increases with time when a constant pressure is maintained between the borehole packers.