THE VAPORIZATION OF A LIQUID FRONT MOVING THROUGH A HOT POROUS ROCK .2. SLOW INJECTION

We present a series of similarity solutions to describe the temperatur e field as liquid spreads from a line source into a porous rock satura ted with liquid of higher temperature. We identify slow and fast flow regimes. In the slow flow regime, the liquid is heated to the far-fiel d temperature by conduction of heat from the far held. In the fast flo w regime, there is negligible conduction of heat from the far field. I nstead, the liquid is heated to the far-field temperature by cooling a region of the host rock near the source, and an internal boundary lay er develops within the newly injected liquid. We successfully test our quantitative theoretical predictions with a series of laboratory expe riments in which water was injected into a consolidated bed of sand fi lled with liquid of different temperature. We extend our model to desc ribe the vaporization of liquid as it spreads slowly from a central so urce into a superheated porous rock. A further family of similarity so lutions shows that the rate of vaporization depends upon the injection rate as well as upon the initial superheat of the reservoir. For high injection rates: the liquid is typically heated to the interface temp erature long before reaching the interface. The rate of vaporization t hen becomes independent of the initial liquid temperature, and depends mainly on the reservoir superheat. For lower injection rates, heat is conducted from ahead of the boiling front into the liquid. As a resul t, for progressively smaller injection rates, an increasing fraction o f the liquid vaporizes, until virtually all the liquid boils, and only a very small liquid zone develops in the rock. Again, we successfully test our theoretical predictions with a laboratory experiment in whic h liquid water was injected into a superheated layer of permeable sand stone.