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The deep borehole heat exchanger systems (DBHE) are offering potential low carbon heating for buildings. However, the study of DBHE is hindered by both modeling and system complexity. Although some analytical models of DBHE are presented in literature, the involved expression of complex integral calculation on the contrary slows down the computation speed and many calculations are redundant in algorithm. In this study, a Response Factor Matrix method (RFM) is proposed based on simple analytical expression and well-designed data structure for DBHE. The RFM can be prefabricated and then used in each time step updates of temperature field. A superposition algorithm is designed for fast computation of DBHE array. The proposed model and algorithms are verified by measurements from two independent engineering projects. Based on the new tool, both thermal radius and heating capacity of DBHE array are investigated in details. The step-ascending pattern of thermal radius is recognized. The correlation of borehole spacing and system heating capacity is identified. In the end, the computational efficiency of the new tool is justified and some outlooks are proposed for a further development and applications. • A fast computational model is proposed for single and multiple deep borehole system. • The proposed new model is verified through comparison with experimental data. • The thermal impact radius of deep borehole system is investigated. • The spacing of deep borehole array is critical for system heat capacity. [ABSTRACT FROM AUTHOR]

The radius evolution for the synchronous collapse motion of a circular vapor bubble cluster in an ideal and infinite fluid is studied. With the assumption that all bubbles are evenly distributed around the circumference and have the same initial conditions, we establish the associated governing equation for this case from a modified Rayleigh–Plesset equation. The inverted analytical solution in the form of t = t (r) and analytical approximations in the form of r = r (t) for the radius evolution to the initial value problem of the dimensionless governing equation are derived. These novel analytical approximations extend the previous ones for a single bubble by adding the effects of surface tension and multiple bubbles. In addition, we point out that the analytical results and dynamic behaviors for multiple bubbles will degenerate into the corresponding ones for single bubbles when the radius of the bubble cluster approaches to infinity. • The governing equation for the synchronous collapse motion of a circular vapor bubble cluster is established. • The inverted analytical solution and analytical approximations are derived. • The effects of surface tension and multiple bubbles are included in the obtained solutions. • The limiting behaviors of the circular vapor bubble cluster are discussed. [ABSTRACT FROM AUTHOR]

• Combined impact of conduction, dispersion and buoyancy-driven flow on thermal losses of ATES is assessed. • Conduction always occurs and dominates dispersion effects, buoyancy-driven flow effects depend on conditions. • Storage geometry (A/V and L/R th) influences the recovery efficiency for all storage temperatures. • For conduction dominated conditions, the geometry is improved by decreasing A/V (smallest at L/R th =2). • For conditions with high potential for buoyancy-driven flow, increasingly smaller L/R th (<1) decreases thermal losses. The technical and economic success of an Aquifer Thermal Energy Storage (ATES) system depends strongly on its thermal recovery efficiency, i.e. the ratio of the amount of energy that is recovered to the energy that was injected. Typically, conduction most strongly determines the thermal recovery efficiency of ATES systems at low storage temperatures (<25 °C), while the impact of buoyancy-driven flow can lead to high additional heat losses at high storage temperatures (>50 °C). To date, however, it is unclear how the relative contribution of these processes and mechanical dispersion to heat losses across a broad temperature range is affected by their interaction for the wide range of storage conditions that can be encountered in practice. Since such process-based insights are important to predict ATES performance and support the design phase, numerical thermo-hydraulic ATES simulations were conducted for a wide range of realistic operational storage conditions ([15–90 °C], [50,000–1,000,000 m3/year]) and hydrogeological conditions (aquifer thickness, horizontal hydraulic conductivity, anisotropy). The simulated heat loss fractions of all scenarios were evaluated with respect to analytical solutions to assess the contribution of the individual heat loss processes. Results show that the wide range of heat losses (10–80 % in the 5th year) is the result of varying contributions of conduction, dispersion and buoyancy-driven flow, which are largely determined by the geometry of the storage volume (ratio of screen length / thermal radius, L/R th) and the potential for buoyancy-driven flow (q 0) as affected by the storage temperature and hydraulic conductivity of the aquifer. For ATES systems where conduction dominates the heat losses, a L/R th ratio of 2 minimizes the thermal area over volume ratio (A/V) and resulting heat losses for a given storage volume. In contrast however, the impact of dispersion decreases with L/R th and particularly for ATES systems with a high potential for buoyancy-driven flow (q 0 > 0.05 m/d), increasingly smaller L/R th ratios (<1) strongly reduce the heat losses due to tilting. Overall, the results of this study support the assessment of thermal recovery efficiencies for particular aquifer and storage conditions, thereby aiding the optimization of initial ATES designs. [Display omitted] [ABSTRACT FROM AUTHOR]