Prediction of Bottom-hole Conditions For Wet Steam Injection Wells
Authors: Fontanilla Jerry P. , AZIZ Khalid 
Published: March 2010

Abstract
The design of steam injection projects requires a knowledge of the quality and pressure of steam at the sandface before it enters the formation. In order to make such predictions, the multiphase flow and energy balance equations must be solved simultaneously. There are very few multiphase correlations in the literature that could be applied to the down flow of steam.
A mathematical model was developed for multiphase, non-isothermal down flow of steam in pipes. Several correlations were tested against limited experimental data. A method was also developed to adjust one of the correlations to fit available experimental data.
The results of this investigation indicate the limitations of existing correlations and show the need for more experimental data.

Introduction
Wellbore heat loss and pressure drop for steam injection wells are often ignored and most thermal reservoir simulators as· same the sandface condition of the steam to be the same as that at the surface. This may be a good approximation for shallow wells, but for deep steam injection wells wellbore heat loss is often substantial.
One of the first workers to consider this problem was Ramey(l). He was primarily concerned with wellbore heat loss during the injection of hot water. Ramey developed a model with the following assumptions:The physical properties of the fluid and the formation are independent of depth and temperature.Heat transfer in the wellbore rapidly reaches steady state, while heat transfer to the formation occurs under transient conditions.The over-all heat transfer coefficient, U, is independent of depth.The frictional losses and kinetic energy effects are negligible.
Satter(2) improved Ramey's analytical model by making the over-all heat transfer coefficient, U, dependent on depth and the fluid properties a function of temperature. Holst and Flock(3) further improved the models proposed by Ramey and Satter to include friction losses and kinetic energy effects.
Pacheco and Farouq Ali(4), as well as Herrera et al(5), presented comprehensive models, but only considered single-phase fluid flow in the tubing.
In this paper, a mathematical model is presented that also accounts for two-phase flow in the tubing. Our objective is to see if available two-phase flow correlations, possibly with some minor modifications, are applicable to the down flow of wet steam.

Mathematical Model
Assuming constant rate of injection (flow rate in the tubing), the conservation of mass, the conservation of energy and the mechanical energy balance equations may be combined to yield the following two simultaneous ordinary differential equations(4.6).
(Equation in full paper)

Method of Solution
The method of solution chosen to simultaneously solve equations 1 and 2 is the Fourth Order Runge Kutta Method(l3).
The convergence of the method was tested to obtain the maximum ∆z that could be used without incurring appreciable truncation error. A ∆z of 100 ft was found to be adequate.
The computer model consists of a main program and six subroutines. A flow chart of the main program is shown in Table 1.