Boiling and Condensation in Geothermal Reservoirs (1996)
Investigators: Shaun D. Fitzgerald and Cengiz Satik, Stanford University
Injection, Vaporization, Condensation
The primary aim of this research project is to gain a fundamental understanding of the controls upon the vaporization of water as it is introduced into a vapor-dominated reservoir and upon the condensation of steam as it moves in a liquid-dominated reservoir. The research is being conducted using both laboratory and theoretical approaches. The results of this analysis will help reservoir engineers to forecast field performance and to estimate likely thermal breakthrough times of injected water.
The study of phase change in geothermal reservoirs is pertinent to both vapor-dominated and liquid- dominated reservoirs. Most reservoirs are extensively fractured and as fluid is injected into the rock, some of the liquid boils. The liquid and newly formed vapor migrates into the porous rock bounding the fractures.
We are initially investigating fluid migration and phase change within (i) a porous medium and (ii) a fracture. The study involves the development and use of analytical, numerical and experimental techniques.
A numerical pore-network model has been developed in order to investigate phase change in porous media. The model includes effects of heat conduction from grains to the fluid and is being used to establish how the region of phase change develops with time. A numerical analysis of the development of two-phase convective heat pipes in fractured geothermal systems is also being conducted.
In addition we have developed similarity solutions that describe the growth of liquid-saturated zones around well bores as liquid is injected. These similarity solutions are particularly useful as they help expose the fundamental controls governing the fraction of injected liquid which can vaporize and be produced from nearby production wells.
A series of laboratory experiments have been conducted on the development of two-phase convective heat pipes and on injection of liquid into heated porous media and fractures. These experiments are currently being modified to enable the effects of capillarity and gravity to be studied in detail.
A number of important results have been obtained during the last year.
- The analytical similarity solutions developed for the case of injection into a liquid-filled reservoir have been tested by a series of analogous laboratory experiments. The results obtained from the experiments are in excellent agreement with those obtained from the theoretical prediction as illustrated in Figure 1.
Figure 1. Temperature vs distance (dimensionless) for injection of liquid from a radial source at 58.5oC into a liquid-filled porous medium originally at 20oC. The solid line represents the theoretical prediction and the symbols correspond to experimental data.
- The analytical similarity solutions developed for the case of injection into a vapor-filled reservoir have been tested by a series of analogous laboratory experiments. The results obtained from the experiments are in excellent agreement with those obtained from the theoretical prediction as illustrated below in Figure 2.
Figure 2. Temperature vs distance (dimensionless) for injection of liquid from a radial source at 75oC into a vapor-filled porous medium originally at 108oC. The solid line represents the theoretical prediction and the symbols correspond to experimental data.
- A number of experiments were conducted in which liquid was injected at a constant rate into a liquid- filled fracture. The temperature profiles which developed in the experiments were successfully compared with the predictions obtained from an approximate analytical solution as shown in Figure 3.
Figure 3. The variation of dimensionless temperature h as a function of the similarity variable x. The solid line represents the theoretical prediction and the symbols represent the results obtained from a series of experiments in rough-walled fractures.
- A number of experiments were conducted in which liquid was
injected at a constant rate into a vapor- filled fracture. The temperature profiles which developed in the experiments were successfully compared with the numerical predictions obtained from a version of the TOUGH2 simulator, modified to account for the properties of ether.
Figure 4. The variation of temperature as a function of distance. The solid line represents the numerical prediction and the symbols represent the results obtained from a series of experiments in rough-walled fractures.
- Experimental and numerical investigations of the development of a heat pipe have been conducted. We have confirmed that an oscillatory mode of instability in two-phase heat pipes can develop if the two-phase zone is sufficiently deep.
We will extend the research projects along the lines discussed in the previous sections. This research is being conducted by Acting Assistant Professor Shaun Fitzgerald, Research Associate Dr. Cengiz Satik, Research Assistant Noel Urmeneta and Undergraduate Research Assistant Catherine Tsui-Ling Wang. In addition we are collaborating with scientists from USC, LBL and the University of Bristol.
Fitzgerald, S.D., Wang, C. and Pruess, K. 1996 Laboratory and theoretical studies of injection into horizontal fractures. Proc. N.Z. Geoth. Workshop 18, 267-273.
Woods, A.W. and Fitzgerald, S.D. 1996 Laboratory and theoretical models of fluid recharge in superheated geothermal systems. J. Geophys. Res. 101(B9), 20391-20405.
Fitzgerald, S.D., Pruess, K. and van Rappard, D.M. 1996 Laboratory studies of injection into horizontal fractures. Proc. Stanford Geoth. Workshop 21, 113-118.
Satik, C. and Horne, R.N. 1996 An experimental study of boiling in porous media. Trans. Geothermal Resources Council 20, 839-843.
Satik, C. and Yortsos, Y.C. 1996 A pore-network study of bubble growth in porous media driven by heat transfer. J. Heat Trans. 118, 455-462.
Woods, A.W. and Fitzgerald, S.D. 1997 The vaporization of a liquid front moving through a hot porous rock. II. Slow injection. J. Fluid Mech. in press
Woods, A.W. and Fitzgerald, S.D. 1996 The effects of heat conduction on the vaporization of liquid invading superheated permeable rock. Proc. Stanford Geoth. Workshop 21, 421-425.