Abstract
This article reports results of comparing the accuracy of the software package “INSOLAR.GSHP.12”, modeling non-steady thermal behavior of geothermal heat pump heating systems (GHCS) and of the similar model “conventional” using finite difference methods for solving spatial non-steady problems of heat conductivity. The software package is based on the method of formulating mathematical models of thermal behavior of ground low-grade heat collection systems developed by INSOLAR group of companies. Equations of mathematical model of spatial non-steady thermal behavior of ground mass of low-grade heat collection system obtained by the developed method have been solved analytically that significantly reduced computing time spent by the software complex “INSOLAR.GSHP.12” for calculations. The method allows to turn aside difficulties associated with information uncertainty of mathematical models of the ground thermal behavior and approximation of external factors affecting the ground. Use of experimentally obtained information about the ground natural thermal behavior in the software package allows to partially take into account the whole complex of factors (such as availability of groundwater, their velocity and thermal behavior, structure and arrangement of ground layers, the Earth’s thermal background, precipitation, phase transformations of moisture in the pore space, and more), significantly influencing the formation of thermal behavior of the ground mass of a low-grade geothermal heat collection system. Numerical experiments presented in the article confirmed the high convergence of the results obtained through the software package “INSOLAR.GSHP.12” with solutions obtained by conventional finite-difference methods.
Highlights
Today, geothermal heat pump heating systems (GHCS) are already widely used in temperate regions of the world (North America, Europe, and China [1])
The basis of the software package “INSOLAR.GSHP.12” is the mathematical modelling method based on two fundamental assumptions: 1. Ground mass of a low-grade geothermal heat collection system is treated as quasi-homogeneous body, to which the usual heat conduction equation applies; but with the only difference that heat and mass transfer characteristics are “effective” that allows to partially take into account mass transfer processes in the model
The reverse transition from the function of heat sinks effect on the natural behavior conditions of the ground mass to actual temperatures observed in the mass in the course of the heat collection system operation is carried out using substitution (10). This method of mathematical modelling of non-steady thermal behavior of ground low-grade heat collection systems has been implemented in the software package “INSOLAR.GSHP.12”, providing determination of optimal parameters of a heat collection system depending on the climatic conditions of the construction area, heatprotective characteristics of the building, performances of heat pumps, circulating pumps, heating devices, as well as their modes of operation
Summary
Geothermal heat pump heating systems (GHCS) are already widely used in temperate regions of the world (North America, Europe, and China [1]). In addition to implementation of heat and mass transfer processes, the ground mass thermal behavior models shall take into account the chemical and mineralogical nature of the ground skeleton, mechanical structure of solids material, degree of dispersion of the medium, shape and size of particles and pores, number of phases, quantitative relationships between phases and their mutual arrangement in the medium filling the pore space, as well as many other physical and chemical parameters Detailed account of these factors in the formulation of a mathematical model is a very serious problem, and its solution often is virtually impossible with the use of modern mathematical apparatus. The software package “INSOLAR.GSHP.12” developed by the Russian company INSOLAR-INVEST allows to simulate the thermal behavior of the ground mass of low-grade geothermal heat collection system in the long-term operation of GHCS [4], taking into account phase transformations of pore water in the ground [5, 6]
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