Generalizations Of The Heat Balance For Thermal Recovery Projects
Authors: Cox Dave O. 
Published: December 2007

Abstract
A general three-dimensional heat balance is presented that includes the effects of heat presented that includes the effects of heat injection or production, heat generation in situ, conduction and convection with loss terms, and variations in formation properties both with time and location. Simplifications of the heat balance are presented for hot waterfloods, steam-soak and -drive processes, and combustion methods.
The applicability and use of superposition are examined in detail. A general criterion for the applicability of superposition is shown. Some effects of changes in injection rate or operating procedure are evaluated for a simple solution of the procedure are evaluated for a simple solution of the heat balance. Geometries for which superposition is valid with this solution are determined also.
A model for forecasting production rates from thermal-drive projects is developed. This model extends the Myhill and Stegemeier development for predicting the ultimate recovery from steam drive to predicting the ultimate recovery from steam drive to hot water drive and combustion drive, and furthermore, allows prediction of the time behavior of such processes. Field results from the literature are processes. Field results from the literature are compared with predictions from the model. Results correlate well and suggest that the method is a useful screening tool for estimating performance from average reservoir parameters.

Introduction
During the past 15 years, thermal recovery methods have become an increasingly more important means of recovering ail. Hot waterflooding, steam-soak and -drive processes, and combustion methods all have been demonstrated to be viable methods for the recovery of some heavy oil reserves, although no single thermal recovery process is applicable universally.
A heat balance is necessary for complete evaluation of thermal recovery projects. Generally, the heat balance in the literature is presented with inherent assumptions about the nature of injected fluids and the temperature distribution and geometry of the reservoir. The assumptions and the simplifications used to solve the heat balance normally limit the applicability of a resulting solution to a very specific problem, and the complexity of many of the solutions preclude rapid use.
It often is difficult to determine what relationship a given solution to the heat balance has to the amount of oil recoverable with a thermal recovery process. The rate of recovery and the effects of changes in operations generally are not ascertainable unless with considerable effort. The critical factors governing producing rate and oil recovery may be hard to single out.
The approach followed in this paper has been to retain generality as much as possible without sacrificing simplicity. The heat balance is presented in entirely general form, and solved in a presented in entirely general form, and solved in a manner so as to be applicable to all thermal recovery processes with minor limitations, as was previously processes with minor limitations, as was previously done by Prats. The heat balance is coupled then with a simple displacement model to obtain an easy-to-use production model sufficiently accurate for preliminary screening and can predict the ultimate recovery and rate-time behavior of thermal projects and determine the effects of changes in projects and determine the effects of changes in injection rate or operating procedures.

THE HEAT BALANCE
The general heat balance for thermal recovery projects may be expressed verbally in the following projects may be expressed verbally in the following manner: the amount of heat (enthalpy) contained within any given volume at any time is equal to the amount of heat injected into the volume, less the amount of heat produced from the volume, plus the amount of heat generated within the volume, less losses of heat from the volume to its surroundings.