FLUID TEMPERATURE MODELLING INJECTED AT SURFACE TEMPERATURE THROUGH VERTICAL AND DEVIATED WELLS. JESÚS
ALBERTO RODRIGUEZ MORA1.
This paper presents a brief bibliographic summary of the related well heat transfer models, most of them are designed for predicting heat loss along wells. All of those models lead to temperature profiles which show a lowering on fluid temperature during the injection from the wellhead to the wellbore, that make those models fit perfectly to the heat loss statement. The purpose of this article is to show a way to calculate the temperature increase of a fluid injected at surface temperature along a well by modifying an existing equation which was proposed by Boyun Guo (2004), this one satisfies the non-phase change of the injected fluid during its flow through the well, this implies that the selected model does not take into account latent heat change of the injected fluid, the previous fact is very important for this study because it is supposed that the injected fluid is not going to change its phase. Modifying Boyun Guo (2004) energy balance equation allowed to establish a profile temperature of a fluid injected at surface temperature into either a vertical or deviated well. It is also included a brief analysis of each of the parameters engaged on the process in order to determine the effect of those properties upon the injected fluid temperature.
Keywords: Fluid Temperature, Fluid at surface conditions, Modification, Temperature profile, Vertical and deviated wells.
1. Grupo de modelamiento de procesos hidrocarburos, GMPH, Escuela de Ingeniería de Petróleos, Universidad Industrial de Santander
En el presente documento se muestra una revisión bibliográfica de los modelos relacionados con la transferencia de energía térmica en un pozo, muchos de ellos están diseñados para predecir la perdida de calor a lo largo del pozo. Todos estos modelos conducen a perfiles de temperatura que muestran una reducción en la temperatura del fluido durante la inyección del fluido desde cabeza de pozo hasta la cara del pozo, lo cual permite que estos modelos encajen perfectamente con el tema de perdida de calor. El propósito de este documento es mostrar una forma de calcular la temperatura de un fluido a lo largo del pozo, el cual es inyectado a temperatura ambiente modificando una ecuación existente, la cual fue propuesta por Boyun Guo (2004). La modificación de dicha ecuación permitió establecer un perfil de temperatura de un fluido inyectado a condiciones de superficie, esto aplica tanto para pozos verticales, como para pozos desviados. Adicionalmente se incluye un breve análisis de cada uno de los parámetros que intervienen en el perfil de temperatura con el fin de determinar el efecto de tales propiedades sobre la temperatura del fluido inyectado.
Palabras Clave: Temperatura de fluido, fluido a condiciones de superficie, Modificación, Perfil de temperatura, Pozos verticales.
WELL HEAT TRANSFER MODELS
The following is a compilation of models available, all of them associated to the well heat transfer phenomena.
Alves L.N. (1992), this model presented a forecast for the flowing temperature, this one is applied to surface pipelines, production and injection wells, one and two phase fluids, it is also applied to vertical and deviated wells. When developed, the flow was considered on steady state.
Belrute R.M. (1991), on this document was found the developing of a temperature profile simulator that shows the profiles during circulating and closing periods, considering a complex wellbore and various fluids inside it. The simulator was designed for mud and cement flow. It takes into account the existence of heterogeneous formations, affecting on different ways the temperatures of the flowing fluids.
Dawkrajai et al (2006), they proposed an specific condition that identifies water inputs considering the temperature profile on a horizontal well. In order to show the change on the fluid temperature they used a predictive model on different production conditions. On the developing of this model the difference between rock and fluid temperature was not considered.
Boyun Guo (2004), proposed three heat transfer correlations in order to predict the heat loss and the temperature profiles on insulated wells. To make the model as simply as possible the author took into account the highest resistance on the thermal system will suppress the others, considering just the insulating layer as the highest resistance. Despite the fact that there is no insulating layer for this study, the second highest resistance engaged on the phenomena is the fluid occupying the annular space, which will be used for modeling the temperature. One of the solutions is focused in steady state, two of them are for transient flow. Those equations could be carried out upon different conditions, considering a non-change phase fluid during the process.
Hagoort et al (2004), they analyzed the Ramey (1962) classic method, which was proposed for calculating the temperature on injection and production wells. They showed that this method has an approximation to the experimental results on long injection and production periods, shorter periods produce overestimated results on the temperature prediction.
Rajiv Sagar (1991), showed two methods to predict a two phase temperature profile on the production stage along the well. The first model is taken from an steady state energy equation, this one takes into account heat transfer mechanisms on the wellbore. The second model is a simplified version, which is based on the Coulter Bardon (1979) equation, whose equation includes the heat transfer mechanisms proposed by Ramey (1962) & Willhite (1967). It was not considered radiation and convection coefficients.
Ramey (1962), presented an approach to the heat transmission problem when hot and cold fluids are injected into the wellbore, this allows to calculate the fluid temperature inside tubing and casing based on time and well length. This model considers the heat resistances inside the wellbore between the circulating fluid and rock. This model as showed by Hagoort (2004) indicates that Ramey’s model overestimate the temperature values on the earlier period of fluid injection.
Squier et al (1962), developed and solved a differential equation system which describes the temperature behavior when hot water is injected through a well. The model proposed describes the injection of hot water from surface to wellbore, the calculation is based on time and well length. This technique is applied to thermal recovery process, which means long injection periods. Compared to stimulation processes involving short periods of time, this model does not fit into the purpose of this study.
Tan X. et al (2011), developed mathematical models in order to simulate the temperature behavior along both vertical and horizontal wells, for controlling and evaluating acid stimulation on real time, this is done taking a temperature profile sequence on different periods of time, they consider an instantaneous temperature equilibrium between fluid and rock temperature.
Willhite (1967), selected specific methods to estimate the size of each component on the heat transfer process during hot water and vapor injection inside the well. The result was a methodology that allows the calculation of the global heat transfer coefficient (U). This value is considered as constant.
Yoshioka et al (2005), presented a model to predict the temperature profile on a horizontal well during steady state fluid production. The reservoir model is based on a correlation of mass and energy balance, considering a permeable and homogeneous enclosure. The model includes Joule Thomson effect, conductive and convective processes are also included. They also included the response when production rate, permeability and type of fluid are changed. They did not consider the formation fluid and the injected fluid velocity.
The analysis of the models above, led this study to take the one that fits properly into the objective of this research, that one is the model proposed by Boyun Guo (2004), this is the chosen one because it does not consider changes on the circulating fluid phase, it takes into account the well deviation angle, it is also easy to understand and manipulate. It considers just a resistance on the thermal energy transfer, this is the insulating layer covering the injection pipe.
WELL HEAT TRANSFER MODEL
On this section is shown the energy balance equation proposed by Boyun Guo (2004), the equations that represent the thermal energy loss on a fluid being injected, which are useful to calculate the temperature change on the hot fluid injected. Besides, it is also showed the modification to the original model, such change was applied on the overall energy equation modifying the equations that describe an increase on the temperature of the injected fluid.
MODEL FOR PREDICTING HEAT LOSS ON HOT INJECTED FLUIDS
The equation which represents the fluid heat loss will be explained using diagram 1 and the result is the equation 1.
Analyzing a section of the injected fluid (accumulation 2), it can be seen that this section losses thermal energy through the formation (heat flow “c”) and also to the lower layer (accumulation 1), furthermore, the upper fluid layer (accumulation 3) gives thermal energy to the section analyzed. The previous analysis could be summarized on the next equation, which represents the heat accumulation on a section of the injected fluid at higher temperature than the surface temperature.
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On the equation 2 it is shown the explicit solution for calculating the temperature of a hot fluid injected either a vertical or deviated well, that equation has been set to be on function of the constants α, β, γ, C, these constants are handled by equations 3, 4, 5 and 6, respectively.
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