Heat Transfer During Hot Fluid Injection Into an Oil Reservoir

Abstract

The engineering evaluation of thermal recovery processes depends on the ability to predict their behaviour in the field. Such a prediction, whetherbased on physical or mathematical models, requires an accurate accounting of the thermal energy utilized by the process. This paper presents a criticalreview of the important contributions to the literature concerning heattransfer during hot fluid injection into an oil reservoir. The heat transfer mechanisms, the resulting energy balance equation and the restrictive assumptions necessary to obtain analytical solutions of the energy balanceequation are discussed. These solutions yield information relative to the thermal efficiency of the process and the temperature distributions within the reservoir and the surrounding impermeable media. However, to date, the published techniques have been limited to injection into a linear or radial homogeneous sand with constant physical properties and have not considered multidimensional heat transfer completely. We have applied a recently published numerical technique to the solution of the energy balance equation in order to remove these limitations. The accuracy of the numerical method for the case of one-dimensional fluid flow is demonstrated in the paper by comparing the calculated thermal efficiency for hot water injection into a water sand to the corresponding analytical solution. A comparison with published experimenta lresults demonstrates the utility of the method and confirms our understanding and analysis of the heat transfer mechanisms. Introduction Predictions of the field behaviour of thermal recovery processes require anaccurate accounting of the energy that is injected into (or generated within)the reservoir. Numerous heat transfer models of the basic thermal processeshave been formulated and solved analytically (c.f. ref. 6, 7, 8, 14, 16, 19).Although limited in scope because of necessary restrictive assumptions, these solutions have proved useful in the development of interpretative mathematical models of the processes (12, 20, 21). For heat transfer during the forward underground combustion process, numerical (3, 4) as well as analytical solutions have been obtained. The following sections discuss the heat transfer mechanisms that take placeduring the injection of hot fluid into an oil reservoir, the energy balance equation and the assumptions necessary to obtain analytical solutions of the energy balance equation. All of the analytical solutions that have appeared inthe literature are limited to a consideration of one-dimensional incompressible fluid flow in a homogeneous sand with constant physical properties. This paper presents a numerical solution of the energy balance that is not hampered bysuch assumptions, and compares it with published experimental results.

Application of iterated Laplace transformation to tracer transients in heterogeneous porous media

“…Note that transverse Peclet number Pt embedded in l is defined by Eq. (19). While both Stehfest and Dubner and Abate methods yield quite accurate results for low longitudinal Peclet number (i.e.…”

“…In other words, sensible energy injection into horizontal oil reservoirs confined by impermeable layers [19], or into aquifers [20,21]is possible to model as a boundary dominated system. As the existence of a horizontal fracture in porous media specially in oil reservoirs is unlikely, the tracer transport in a horizontal fracture will not be considered in this work.…”

An Analytical Model of Temperature and Stress Fields During Cold-Water Injection Into an Oil Reservoir

“…Then, the volumetric flux varies only with radial distance from the injection well, which allows the development of an analytical temperature solution. For the purpose of determining the temperature field (Spillette 1965) or immiscible-displacement performance prediction (Dykstra and Parsons 1950), the incompressible-fluidflow assumption is quite reasonable for cases of slightly compressible liquids such as in ordinary waterflooding, hot-water injection, and so on.…”

Transient flowing-fluid temperature modeling in reservoirs with large drawdowns

“…One of the earliest models for estimating temperature distribution during steam injection was presented by Lauwerier (1955). Subsequently, several models were presented by Spillette (1965) and Satman et al (1979) using different approaches. More recently, Tan et al (2012) compared some of these solutions and offered a solution of their own.…”