Mathematical Models for Determining the Distribution of Fluid Flow Temperature along the Wellbore and Horizontal Pipeline

Abstract

This paper presents a proposed new indirect method determining instantly oil well debit using developed mathematical models. As a result integrated analysis using the models it has been revealed correlation between oil well debit and well throw out flow temperature. Therefore putting purpose was obtained. Mathematical models are developed for the distribution of fluid flow temperature along the length of the tubing from the well bottom to the wellhead and along the length of the oil pipeline from the collector of oil wells to the oil treatment unit. On the basis of experimental data, the authors propose formulas in the form of the relationship between oil emulsion (OE) viscosity, the flow temperature and concentration of water globule in OE and the coefficient of heat transfer from the fluid flow in the wellbore (WB) to the rock, and heat capacity and thermal conductivity of gas, water, rock and steel of the WB walls. This effect is demonstrated in the constructed diagrams. It is shown bottom temperature jump as a result of the Joule Thomson drosseling effect then connective transmitted up at flow rate v. In such case well-head or well outlet oil mixture (OM) flow temperature depend more of volume of stream flow than of bottom hole temperature. Thought in the paper, do not taking into consideration great casing annulus areas influence to the well outlet flow temperature. As shown from supporting paper the relative values og the thermal conductivity of the liquid column and gas column present in the casing annulus order less than well bore (WB) wall thermal conductivity. Consequently well outlet OM flow temperature will depends not only of the volume of stream flow, also of the bottom hole temperature and of the gas column and liquid column.A new method for determining the oil well flow rate by measuring the downstream temperature is developed. A mathematical model is proposed that allows calculating the thermal profile of the fluid along the wellbore for determining the oil well flow rate with account of the geothermal gradient in the rock surrounding the wellbore. It is shown, that unlike the existing methods the new proposed method allows determining the instantaneous discharge of a well very easily. One of the actual challenges in fluid (oil, water and gas) transportation from wells to oil treatment installation is determination of a law of temperature distribution along the length of a pipeline at low ambient temperature. That temperature leads to increase in viscosity and deposition of wax on inner surface of a pipe. To overcome that challenge it is needed to consider several defining characteristics of formation fluid (FF) flow. Complexity of a solution is caused by two factors. From the one hand, in most cases (especially on a late stage of field development) FF is an oil emulsion (OE) that contains gas bubbles. From the other hand, temperature gradient between fluid flow and the environment has significant value (especially in the winter period of the year). At the same time, the higher content of emulsified water droplets (EWD) in OE and lower flow temperature, the higher FF viscosity, and consequently productivity (efficiency) of oil pumping system is reduced. Performed research and analysis of field experimental data showed that a function of oil viscosity versus temperature has a hyperbolic law; a function of OE viscosity versus concentration of EWD has a parabolic one. A heat balance for a certain section of a pipeline in steady state of fluid motion using a method of separation of variables was established taking into account above mentioned factors, Fourier’s empirical laws on heat conductivity and Newton’s law on heat transfer. As a result, unlike existing works, an exponential law of distribution of temperature along the length of a pipeline is obtained. A law takes into account nonlinear nature of change in viscosity of OE from change in temperature of flow and concentration of water in an emulsion. As a result, in contrast to the existing works, the proposed exponential law of temperature distribution along the length of the pipeline is obtained, taking into account the nonlinear nature of variation of OE viscosity with the change in the flow temperature and the concentration of water in the emulsion. The results of the calculation are presented in the form of a table and graphs.