Prediction of Bottom-hole Conditions For Wet Steam Injection Wells

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.

A novel analytical transient heat-conduction time function for heat transfer in steam injection wells considering the wellbore heat capacity

“…In this study, Beggs and Brill's two-phase flow correlation is adopted due to its simplicity and high accuracy, which has been fully confirmed in Refs. [21,22].…”

“…In Refs. [7,21], an injection time of 4.9 days or less was used for wellbore steadystate heat transfer calculation, the results of which also shown excellent performance. In fact, the pressure, temperature and steam quality of the injected fluid is a minorant function of the injection time.…”

A Semi-Unsteady State Wellbore Steam/Water Flow Model for Prediction of Sandface Condition in Steam Injection Wells

“…3, 4, and 8 show the prediction of our model, the prediction of Fontanilla and Aziz's model (9) , and the measured field data. For Field Test 1B, we also compare our results with those of Farouq Ali's model (8) as depicted in Fig.…”

“…In 1981, 1982, and 1985, respectively, Farouq Ali (8) , Fontanilla and Aziz (9) , and Yao (10) presented two simultaneous ordinary differential equations for estimating the steam pressure and quality, and solved these equations by using the fourthorder Runge-Kutta method. The major differences between these models were the type of correlations used to describe the multiphase flow inside the wellbore and the techniques to evaluate the formation temperature.…”

An Analytical Model for Simulating Heavy-Oil Recovery by Cyclic Steam Injection Using Horizontal Wells, SUPRI TR-118

“…Uniform steam distribution along the well is an important factor in the success of cyclic operations with a horizontal well (Mendonz~1998). The bottom-hole quality and pressure may be predicted iiom a wellbore model of the type discussed by Fontanilla and Aziz (1982). After injection for a'specified period of time, the well is shut-in and the steam is allowed to "soak" into the reservoir for another specified period.…”