Sayantan Ganguly

Analytical solutions for transient temperature distribution in a geothermal reservoir due to cold water injection

An analytical solution to describe the transient temperature distribution in a geothermal reservoir in response to injection of cold water is presented. The reservoir is composed of a confined aquifer, sandwiched between rocks of different thermo-geological properties. The heat transport processes considered are advection, longitudinal conduction in the geothermal aquifer, and the conductive heat transfer to the underlying and overlying rocks of different geological properties. The one-dimensional heat transfer equation has been solved using the Laplace transform with the assumption of constant density and thermal properties of both rock and fluid. Two simple solutions are derived afterwards, first neglecting the longitudinal conductive heat transport and then heat transport to confining rocks. Results show that heat loss to the confining rock layers plays a vital role in slowing down the cooling of the reservoir. The influence of some parameters, e.g. the volumetric injection rate, the longitudinal thermal conductivity and the porosity of the porous media, on the transient heat transport phenomenon is judged by observing the variation of the transient temperature distribution with different values of the parameters. The effects of injection rate and thermal conductivity have been found to be profound on the results.RésuméUne solution analytique pour décrire la distribution transitoire de la température suite à une injection d’eau froide dans un réservoir géothermal est présentée. Le réservoir est composé d’un aquifère captif pris en sandwich entre des roches de propriétés thermo-géologiques différentes Les processus de transport de chaleur considérés sont l’advection, la conduction longitudinale dans l’aquifère géothermal et le transfert conductif de chaleur vers les roches sous et sus-jacentes aux propriétés géologiques différentes. L’équation de transfert de chaleur à une dimension est résolue en utilisant la transformée de Laplace sous l’hypothèse d’une densité constante et des propriétés thermiques à la fois de la roche et du fluide. Deux solutions simples sont ensuite dérivées, en négligeant d’abord la conductivité longitudinale de transport de chaleur et ensuite le transport de chaleur vers les épontes. Les résultats montrent que la perte de chaleur dans les épontes joue un rôle majeur en ralentissant le refroidissement du réservoir. L’influence de certains paramètres, tel que le débit d’injection, la conductivité thermique longitudinale et la porosité du milieu poreux, sur le phénomène transitoire du transport de chaleur est appréhendé en observant la variation de la distribution des températures dans le temps avec différentes valeurs des paramètres. Il apparait que débit d’injection et la conductivité thermique ont un impact important sur les résultats.ResumenSe presenta una solución analítica para describir la distribución transitoria de la temperatura en un reservorio geotérmico en respuesta a una inyección de agua fría. El reservorio está compuesto de un acuífero confinado, intercalado entre rocas de diferentes propiedades termo geológicas. Los procesos de transporte de calor considerados son advección, conducción longitudinal en el acuífero geotérmico, y la transferencia conductiva del calor a rocas subyacentes y suprayacente de diferentes propiedades geológicas. La ecuación de transferencia de calor unidimensional ha sido resuelta usando la transformada de Laplace con la suposición de densidad y propiedades térmicas constantes tanto de rocas como de fluidos. Se extrajeron dos soluciones simples, la primera despreciando la conductividad longitudinal del transporte de calor y por lo tanto del transporte de calor a las rocas confinantes. Los resultados muestran que la pérdida de calor hacia las capas de rocas confinantes juega un rol vital en retardar el enfriamiento del reservorio. La influencia de algunos parámetros, por ejemplo la tasa volumétrica de la inyección, la conductividad térmica longitudinal y la porosidad del medio poroso, sobre el fenómeno de transporte transitorio de calor son juzgados observando la variación de la distribución transitoria de la temperatura con diferentes valores de los parámetros. Se han encontrado los profundos efectos de la velocidad de inyección y de la conductividad térmica en los resultados.摘要研究展示了地热储由于冷水注入造成瞬时温度分布的解析解。热储由一个夹在不同地热特性岩层之间的承压含水层组成。考虑到的热传输过程有对流、地热含水层中的纵向传导、向上覆及下伏的具有不同地质特性的岩石的热传导。假定岩石和液体恒定密度和热特性并采用Laplace变换求解决一维热传导方程。随后推导出两个简单的 解决方法,首先忽略纵向传导的热传输,然后忽略传导到承压岩石的热传输。结果显示对承压岩石层的热损耗在减速热储的冷却上发挥至关重要的作用。有些参数如容积注入率、纵向人传导及多孔介质的孔隙度对瞬时热传输现象的影响根据观测瞬时温度分布的变化的不同参数值来判断。注入速率和热传导对结果有深远影响。ResumoÉ apresentada uma solução analítica para descrever a distribuição da temperatura em regime transitório num reservatório geotérmico em resposta à injeção de água fria. O reservatório é formado por um aquífero confinado, localizado entre rochas de diferentes propriedades térmicas e geológicas. Os processos de transporte de calor são a adveção, a condução longitudinal do aquífero geotérmico e a transferência de calor por condução para as rochas sub- e sobrejacentes de diferentes propriedades geológicas. A equação de transferência de calor unidimensional tem sido resolvida utilizando a transformada de Laplace, com a assunção das hipóteses de densidade e propriedades térmicas constantes das rochas e do fluido. São derivadas duas soluções simples, primeiro negligenciando a condutividade longitudinal do transporte de calor e, em seguida, o transporte de calor para as rochas confinantes. Os resultados mostram que a perda de calor para as camadas de rocha confinantes desempenha um papel vital no abrandamento do arrefecimento do reservatório. A influência de alguns parâmetros, como a taxa de injeção volumétrica, a condutividade térmica longitudinal e a porosidade do meio no fenómeno de transporte de calor em regime transitório, é avaliada observando a variação da distribuição de temperatura em transitório com diferentes valores dos parâmetros. Os efeitos da taxa de injeção e da condutividade térmica mostram ser muito grandes nos resultados obtidos.

Geothermal Reservoirs - A Brief Review

A brief discussion and review of the geothermal reservoir systems, geothermal energy and modeling and simulation of the geothermal reservoirs has been presented here. Different types of geothermal reservoirs and their governing equations have been discussed first. The conceptual and numerical modeling along with the representation of flow though fractured media, some issues related to non isothermal flow through fractured media, the efficiency of the geothermal reservoir, structure of the numerical models, boundary conditions and calibration procedures have been illustrated. A brief picture of the Indian scenario and some barriers related with geothermal power are discussed and presented thereafter. Finally some gaps of the existing knowledge and recent focuses of research are discussed.

Investigation of Thermal Performance of a Solar Pond With External Heat Addition

This study addresses the method of adding heat to a salt gradient solar pond (SGSP) from external sources and investigates the thermal performance of the pond. In this case, the external heat source is solar heat collected by evacuated tube solar collectors (ETSC), and collected heat is transferred to the lower-convective zone (LCZ) of the SGSP by circulating fluid from the LCZ. Results show that heat addition from the external source enhances the thermal performance of the SGSP in terms of heat recovery and thermal efficiency but with certain constraints. The heat addition efficiency reduces with increase in aperture area of the ETSC. Also with increasing heat addition, the heat removal from the SGSP has to be increased; otherwise, the SGSP efficiency reduces rapidly. Heat removal from SGSP has to be performed keeping in mind the heat demand and the quality of heat. The latter reduces with an increase of heat extraction beyond a certain limit. Hence, optimizing the range of parameters in case of adding heat from external sources is very important for the best performance of a SGSP.

Effectiveness of bottom insulation of a salinity gradient solar pond

This technical brief presents a study on the effectiveness of the bottom insulation of a salinity gradient solar pond (SGSP) in Melbourne, Australia. Insulation is applied at the bottom of a SGSP in order to minimize the heat loss from the SGSP to the ground underneath. But selection of optimum thickness of the insulation to extract the best thermal performance of an SGSP is a challenge as insulation involves significant investment. Hence, modeling heat loss from SGSP to the ground before and after applying the insulation is thus very essential. In this study, a layer of polystyrene is used as insulation at the bottom of SGSP. The temperature distribution in the SGSP and ground below it, the efficiency of the SGSP and the heat removal from SGSP are estimated for the SGSP without insulation and with insulation of different thicknesses. The results show that the insulation definitely reduces the heat loss from the SGSP to the ground, but to a certain extent. Insulation beyond a certain thickness is proved to be ineffective in increasing the efficiency or reducing the heat loss to ground and thus unable to enhance the thermal performance of the SGSP.