Boiling and Condensation in Geothermal Reservoirs (1995)
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 (condensation) of water (steam) as it is introduced into a vapor- (liquid-) dominated geothermal reservoir. The research is being conducted using a number of innovative techniques including laboratory and theoretical methods. 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 depleted regions of liquid-dominated reservoirs. Most reservoirs are extensively fractured and as fluid is injected into a vapor-dominated rock, some of the liquid boils. Furthermore, some of the liquid and newly formed vapor migrates into the porous rock bounding the fractures.
At present there is insufficient knowledge of the fundamental behavior of fluid flow within porous media and fractures to develop a model of the coupled problem. Hence, in this research project, we are initially focusing on the end-member problems of fluid migration and phase change within (i) a porous media and (ii) a fracture.
(i) In the study of phase change within porous media, a number of novel theoretical approaches are being pursued. Pore-network modeling technique is being used to analyze the complex flows resulting from steam migration into a liquid-filled lattice. Using this technique we are able to study how the morphology of the vapor-liquid transition zone depends upon the degree of heterogeneity in the porous media, the latent heat and the rate of supply of fluid. In addition to this theoretical method, one-dimensional similarity solutions are being developed in order to determine how the rate of boiling(condensation) depends upon injection rate, reservoir superheat and geometry.
Laboratory methods are also planned. In particular, experiments in both glass micromodels and real geothermal rock samples will be conducted in order to improve our understanding and to verify the results obtained from the theoretical studies.
(ii) The study of liquid injection into a fracture is being undertaken theoretically as well as experimentally. We are initially investigating the fluid flow within a single fracture and have constructed a transparent Hele-Shaw cell in order to visualize the flow. The series of experiments scheduled include liquid injection into (i) a cold, dry fracture, (ii) a cold, liquid-filled fracture, (iii) a hot, liquid-filled fracture and (iv) a hot, vapor-filled fracture. These results will reveal the fundamental flows in rough- walled fractures within liquid- and vapor-dominated geothermal reservoirs.
A number of theoretical studies have been conducted for the case without phase change and our experimental results will initially be used to verify these findings. The situation in which boiling occurs is much more complex and numerical simulations are required.
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.
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. However, these solutions are highly idealized and only apply to certain injection scenarios such as constant rate for injection in a radial geometry. In order that other rates and geometries of injection may be examined, we are also developing a numerical model.
Experimental work has commenced on the injection of water into a fracture. The laboratory apparatus has been constructed and initial experiments have been performed. We are currently focusing our attention on the case in which no boiling occurs in order that the effects of fluid dispersion resulting from the fracture roughness may be isolated. This will enable the effects of phase change on the morphology of a propagating liquid-vapor interface in subsequent experiments to be analyzed.
A number of important results have been obtained during the last year.
1. The propagation of the transition zone was found to be highly unstable if steam migrates into a liquid-dominated zone. However, the growth rate of the steam fingers depends upon the latent heat of condensation. Hence, the interface is more stable when the transition zone is at lower pressures and temperatures.
2. The fraction of liquid that vaporizes varies non-monotonically with injection rate. At low rates of injection, thermal diffusion can become important and reduce the vaporizing fraction; that is, more of the heat from the hot rock is used to heat the water surrounding the injection well. At high rates of injection the pressure, and hence temperature, at the liquid-vapor interface can increase significantly so that vaporizing fraction decreases. It therefore appears that an optimal injection rate exists for injection from a radial source.
3. The morphology of a liquid-vapor transition zone within a fracture is very different from that within a porous medium. Fingers of liquid tend to spread rapidly away form the injection site. The rapid movement of liquid along preferential pathways within a uniform fracture indicate that the danger of premature thermal breakthrough from an injection well is greater than had previously been envisaged.
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 and Research Associate Dr. Cengiz Satik. We have recently engaged the services of three undergraduate students to assist in experimental work. In addition we are collaborating with scientists from USC, LBL and the University of Cambridge.
Fitzgerald, S.D. & Woods, A.W. 1995 Experimental and theoretical studies of liquid injection into vapor-dominated reservoirs. Proc. N.Z. Geoth. Workshop 17, 169-173.
Fitzgerald, S.D. & Woods, A.W. 1995 Instabilities during liquid migration into superheated hydrothermal systems. Proc. Stanford Geoth. Workshop 20, 183-189.
Fitzgerald, S.D. & Woods, A.W. 1995 On vapour flow in a hot porous layer J. Fluid Mech. 293, 1-23.
Fitzgerald, S.D. & Woods, A.W. 1995 Natural recharge following exploitation of a vapour- dominated geothermal system. World Geothermal Congress 3, 1605--1607.
Satik, C. & Yortsos, Y.C. 1994 A Study of vapor-liquid flow in porous media. Proc. Stanford Geoth. Workshop 19, page 107.
Satik, C. & Yortsos, Y.C. 1995 Pore network studies of steam injection in porous media. S.P.E. Annual Meeting, SPE 30751.
Satik, C., Li, X. & Yortsos, Y.C. 1995 Scaling of bubble growth in a porous medium, Phys. Rev. E, Vol. 51(4), 3286-3295
Satik, C. & Yortsos, Y.C. 1995 A pore network study of bubble growth in porous media driven by heat transfer, Paper submitted to J. Heat Trans.
Woods, A.W. & Fitzgerald, S.D. 1995 Injection into vapour-saturated geothermal reservoirs. World Geothermal Congress 3, 1609--1611.
Woods, A.W. & Fitzgerald, S.D. 1995 Laboratory and theoretical models of fluid recharge in superheated geothermal systems. (submitted to J. Geophys. Res.)
Roland N. Horne, Shaun Fitzgerald, Sandy Costa
Stanford Geothermal Program
Dept. of Petroleum Engineering
Stanford, CA 94305-2220