Nonisothermal Single- and Two-Phase Flow Through Consolidated Sandstones
Authors: Arihara N. , Ramey H.J. , Brigham W.E. 
Published: December 2007

Abstract
This study concerns nonisothermal single- and two-phase flow of a single-component fluid (water) in consolidated porous media. Linear flow experiments through cylindrical consolidated cores were performed. Both natural (Berea) and synthetic cement-consolidated performed. Both natural (Berea) and synthetic cement-consolidated sand cores were used. Fabrication of the synthetic sandstones was important to permit reproducible fabrication of high-porosity, low-permeability sandstones with thermowells, pressure ports, and glass-tube capacitance probe guides cast in place. Both hot-fluid and cold-water injection experiments were carried out in natural and synthetic sandstones. The thermal efficiency of hot-water and cold-water injection was found to depend on heat injection rate: the higher the heat injection rate, the higher the thermal efficiency. One important result of this study is that much of the previous work with nonisothermal single-phase flow in unconsolidated sands may be extended to consolidated sandstones despite the differences in the isothermal flow characteristics of these systems. In two-phase boiling flow experiments, hot, compressed liquid water entered the upstream end of the core, moved downstream, started vaporizing, and flowed through the remainder of the core as a mixture of steam and liquid water. Significant decreases in both temperature and pressure occurred within the two-phase region. Even for large temperature changes, it was found that two-phase flow can be nearly isenthalpic and steady state if heat transfer between the core and the surroundings is at a low level.

Introduction
Geothermal energy is being given much attention as a new source of energy. Prime questions in geothermal energy extraction are (1) how much energy can be recovered, and (2) how fast can it be extracted? To find useful answers to these questions, the basic nature of the boiling flow of water in porous media must be understood. Literature on oil recovery by hot-fluid injection and underground combustion presents some of the important features of nonisothermal, two-phase flow that appear pertinent to geothermal reservoirs. The injection of hot water to effect oil recovery was commonly considered before 1930. In 1930, Barb and Shelley mentioned a rumor that hot-water flooding had been tried in New York State and abandoned because of excessive cost. The heating and economic results of hot-water injection were evaluated in this pioneering study. pioneering study. The next study of heat transport in a formation caused by hot-fluid injection was presented by Stovall in 1934. Both laboratory and field experiments were described. Field determination of both wellbore heat losses and vertical losses from a heated formation were described in this remarkable study. Apparently, the next study of vertical heat loss on hot-fluid injection was published by Lauwerier in 1955. It was assumed that injection rate, Vw, and temperature, Ti, would remain constant; thermal conductivity in the direction of flow was zero; and the thermal conductivity in the flooded layer perpendicular to the direction of flow was infinite so that the temperature in the flooded layer, T1, was always constant at a given location in the flooded zone. Prats has called the latter condition the "Lauwerier assumption." The conductivity in the overburden and underburden, 2, was assumed to be finite and constant. The loss of heat from the injected fluid to the adjacent strata resulted in a decrease in temperature in the direction of flow. Lauwerier derived the temperature both in the injection interval and the adjacent strata as a function of time and distance. In 1959, Marx and Langenheim presented a solution for a heat-loss problem related to the one considered by Lauwerier, but where the heated region remained at a constant temperature equal to the injection temperature. Vertical heat loss reduced the size of the heated region.
SPEJ
P. 137