Abstract:A new method is presented to evaluate thermal interactions between vertical geothermal boreholes. The finite line source (FLS) solution is extended to consider thermal interactions between groups of boreholes. Groups of boreholes that share similar temperatures and heat extraction rates are identified using hierarchical agglomerative clustering, and each group is represented in the model as a single equivalent borehole. Each equivalent borehole is split into segments, and temporal and spatial superposition of … Show more
“…This solution is extended to consider time-dependent fluid temperatures inside the U-tube by means of a coefficient updating scheme. The radial and axial heat conduction in the soil around GHEs, and the interactions between GHEs, are modeled with the FLS solution by considering thermal interactions between equivalent boreholes as proposed by Prieto and Cimmino [19]. The transient multipole method is coupled to the FLS solution to consider both of the short-and long-term effects around GHEs, and to a discretized finite difference model of the advection heat transfer process inside the U-tubes.…”
Section: Mathematical Modelmentioning
confidence: 99%
“…The finite line source (FLS) solution can then be superimposed to evaluate a penalty on the temperatures predicted by the transient multipole method. Additionally, the equivalent borehole method of Prieto and Cimmino [19] is used to simplify the thermal interaction problem and obtain a computationally-efficient simulation model of the bore field by only requiring the simulation of a limited number G of equivalent boreholes instead of the entire field of N b boreholes.…”
Section: Thermal Interactions Between Ground Heat Exchangersmentioning
confidence: 99%
“…Recently, Prieto and Cimmino [19] proposed a methodology to account for thermal interactions among boreholes as interactions between equivalent boreholes sharing similar borehole wall temperatures and heat extraction rates. The field is divided into G equivalent boreholes using a hierarchical aglomerative algorithm.…”
Section: Spatial and Temporal Superposition Of The Finite Line Source...mentioning
confidence: 99%
“…In the case of the imposed inlet fluid temperature, a system of equations must be built and solved to evaluate heat extraction rate profiles and borehole wall temperature profiles along all GHEs in the field. Prieto and Cimmino [19] proposed a method to limit the sizes of the systems of equations by forming groups of similarly behaving boreholes and modeling each of these groups using a single equivalent borehole. This results in an efficient and robust method that allows the study of geothermal fields composed of thousands of GHEs.…”
Section: Introductionmentioning
confidence: 99%
“…This paper introduces a new methodology to study the transient heat transfer for both the interiors and exteriors of GHEs, considering fluid flow inside the pipes, fluidto-soil heat conduction via grout, thermal interactions among GHEs and axial effects. The equivalent borehole method of Prieto and Cimmino [19] is used to model the exteriors of the GHEs, including thermal interactions between GHEs. The transient multipole method of Prieto and Cimmino [36] is used to model the interiors of the GHEs, including temperature penalization to account for thermal interactions.…”
The study of heat transfer in ground heat exchangers (GHEs) considering the fluid advection inside the pipes; the heat transfer between the fluid and the ground through the grout material; and the thermal interaction between GHEs is a challenging task. The present paper presents a new semi-analytical method that takes into account the aforementioned effects to consider both the short- to long-term effects of GHEs. The heat transfer between the fluid and grout was studied by a transient multipole expansion considering time-dependent fluid temperatures and an advection model for the pipes obtained from an energy balance on the heat carrier fluid. Thermal interactions were analyzed using an equivalent borehole method while penalizing the transient multipole expansion to include thermal interaction effects. Validation of the short-term predictions was performed by comparing the proposed model to experimental data found in the literature and to an FEA model. The proposed model was then compared with a FEA model in long-term simulations of a geothermal field comprised of 24 GHEs for multi-annual simulation. The method resulted in substantial reduction in computational time while preserving good accuracy when compared with the FEA model.
“…This solution is extended to consider time-dependent fluid temperatures inside the U-tube by means of a coefficient updating scheme. The radial and axial heat conduction in the soil around GHEs, and the interactions between GHEs, are modeled with the FLS solution by considering thermal interactions between equivalent boreholes as proposed by Prieto and Cimmino [19]. The transient multipole method is coupled to the FLS solution to consider both of the short-and long-term effects around GHEs, and to a discretized finite difference model of the advection heat transfer process inside the U-tubes.…”
Section: Mathematical Modelmentioning
confidence: 99%
“…The finite line source (FLS) solution can then be superimposed to evaluate a penalty on the temperatures predicted by the transient multipole method. Additionally, the equivalent borehole method of Prieto and Cimmino [19] is used to simplify the thermal interaction problem and obtain a computationally-efficient simulation model of the bore field by only requiring the simulation of a limited number G of equivalent boreholes instead of the entire field of N b boreholes.…”
Section: Thermal Interactions Between Ground Heat Exchangersmentioning
confidence: 99%
“…Recently, Prieto and Cimmino [19] proposed a methodology to account for thermal interactions among boreholes as interactions between equivalent boreholes sharing similar borehole wall temperatures and heat extraction rates. The field is divided into G equivalent boreholes using a hierarchical aglomerative algorithm.…”
Section: Spatial and Temporal Superposition Of The Finite Line Source...mentioning
confidence: 99%
“…In the case of the imposed inlet fluid temperature, a system of equations must be built and solved to evaluate heat extraction rate profiles and borehole wall temperature profiles along all GHEs in the field. Prieto and Cimmino [19] proposed a method to limit the sizes of the systems of equations by forming groups of similarly behaving boreholes and modeling each of these groups using a single equivalent borehole. This results in an efficient and robust method that allows the study of geothermal fields composed of thousands of GHEs.…”
Section: Introductionmentioning
confidence: 99%
“…This paper introduces a new methodology to study the transient heat transfer for both the interiors and exteriors of GHEs, considering fluid flow inside the pipes, fluidto-soil heat conduction via grout, thermal interactions among GHEs and axial effects. The equivalent borehole method of Prieto and Cimmino [19] is used to model the exteriors of the GHEs, including thermal interactions between GHEs. The transient multipole method of Prieto and Cimmino [36] is used to model the interiors of the GHEs, including temperature penalization to account for thermal interactions.…”
The study of heat transfer in ground heat exchangers (GHEs) considering the fluid advection inside the pipes; the heat transfer between the fluid and the ground through the grout material; and the thermal interaction between GHEs is a challenging task. The present paper presents a new semi-analytical method that takes into account the aforementioned effects to consider both the short- to long-term effects of GHEs. The heat transfer between the fluid and grout was studied by a transient multipole expansion considering time-dependent fluid temperatures and an advection model for the pipes obtained from an energy balance on the heat carrier fluid. Thermal interactions were analyzed using an equivalent borehole method while penalizing the transient multipole expansion to include thermal interaction effects. Validation of the short-term predictions was performed by comparing the proposed model to experimental data found in the literature and to an FEA model. The proposed model was then compared with a FEA model in long-term simulations of a geothermal field comprised of 24 GHEs for multi-annual simulation. The method resulted in substantial reduction in computational time while preserving good accuracy when compared with the FEA model.
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