Shaun D. Fitzgerald

A note on induced stress changes in hydrocarbon and geothermal reservoirs

Abstract Earthquakes have been induced by oil and gas production, where pore pressures have decreased, in some cases by several tens of MPa. It has previously been suggested that such earthquakes are caused by poroelastic stressing of crust surrounding the reservoir. Induced earthquakes are also common in geothermal fields, such as The Geysers, where strong correlations between both steam production and condensate injection, and earthquake activity have been observed over the last several decades. Stress measurements within hydrocarbon reservoirs show that the least horizontal stress decreases with declining reservoir pressure, as predicted by poroelasticity. For circular disk-shaped reservoirs, isothermal reduction in pore pressure induces a relative horizontal tension within the reservoir. Production-induced stressing may promote frictional sliding on pre-existing faults. Within the reservoir itself, normal faulting is promoted if the regional stress is extensional and the Biot coefficient is sufficiently large, α>0.85 for reasonable coefficients of friction. On the other hand, dilatant fracturing and normal faulting are always promoted, in extensional environments, near the edge of the reservoir or in regions of high pore-pressure gradient. It is suggested that such fracturing could enhance fracture permeability in tight rocks adjacent to portions of the reservoir that experience large reductions in pore pressure due to production. In regional compressional environments, production modestly favors reverse faulting above and below the reservoir. The ratio of thermal to poroelastic stress can be quite large in geothermal reservoirs such as The Geysers. Reservoir-wide energy balance considerations suggest that the average temperature has declined at The Geysers by 6°C during the past 20 years. Reservoir average stress changes are thus on the order of ∼2 MPa, and are certainly much larger near injection wells and steam-producing fractures.

The vaporization of a liquid front moving through a hot porous rock

We develop an analytical model to describe the generation of vapour as water moves through a hot porous rock, as occurs in hot, geothermal reservoirs. Typically the isotherms in the liquid lag behind the water-vapour interface and so water is supplied to the interface at the interface temperature. This temperature is lower than that in the rock far ahead of the interface. Therefore, as the hot porous rock is invaded with water, it cools and the heat released is used to vaporize some of the water. At low injection rates, vapour formed from the injected liquid may readily move ahead of the advancing liquid-vapour interface and so the interfacial pressure remains close to that in the far field ahead of the interface. The mass fraction that vaporizes is then limited by the superheat of the rock. For larger injection rates, the interfacial vapour pressure becomes considerably greater than that in the far field in order to drive the vapour ahead of the moving interface. As a result, the interfacial temperature increases. The associated reduction in the thermal energy available for vaporization results in a decrease in the mass fraction of vapour produced. Since the vapour is compressible, the motion of the vapour ahead of the interface is governed by a nonlinear diffusion equation. Therefore, the geometry of injection has an important effect upon the mass fraction of water that vaporizes. We show that with a constant supply of water from (i) a point source, the mass fraction of water which vaporizes increases towards the maximum permitted by the superheat of the rock; (ii) a line source, a similarity solution exists in which the mass fraction vaporizing is constant; and (iii) a planar source, the liquid-vapour interface steadily translates through the rock with a very small fraction of the injected water vaporizing.

Transient ventilation dynamics following a change in strength of a point source of heat

We investigate the transient ventilation flow within a confined ventilated space, with high- and low-level openings, when the strength of a low-level point source of heat is changed instantaneously. The steady-flow regime in the space involves a turbulent buoyant plume, which rises from the point source to a well-mixed warm upper layer. The steady-state height of the interface between this layer and the lower layer of exterior fluid is independent of the heat flux, but the upper layer becomes progressively warmer with heat flux. New analogue laboratory experiments of the transient adjustment between steady states identify that if the heat flux is increased, the continuing plume propagates to the top of the room forming a new, warmer layer. This layer gradually deepens, and as the turbulent plume entrains fluid from the original warm layer, the original layer is gradually depleted and disappears, and a new steady state is established. In contrast, if the source buoyancy flux is decreased, the continuing plume is cooler than the original plume, so that on reaching the interface it is of intermediate density between the original warm layer and the external fluid. The plume supplies a new intermediate layer, which gradually deepens with the continuing flow. In turn, the original upper layer becomes depleted, both as a result of being vented through the upper opening of the space, but also due to some penetrative entrainment of this layer by the plume, as the plume overshoots the interface before falling back to supply the new intermediate layer. We develop quantitative models which are in good accord with our experimental data, by combining classical plume theory with models of the penetrative entrainment for the case of a decrease in heating. Typically, we find that the effect of penetrative entrainment on the density of the intruding layer is relatively weak, provided the change in source strength is sufficiently large. However, penetrative entrainment measurably increases the rate at which the depth of the draining layer decreases. We conclude with a discussion of the importance of these results for the control of naturally ventilated spaces.

Transient natural ventilation of a room with a distributed heat source

We report on an experimental and theoretical study of the transient flows which develop as a naturally ventilated room adjusts from one temperature to another. We focus on a room heated from below by a uniform heat source, with both high- and low-level ventilation openings. Depending on the initial temperature of the room relative to (i) the final equilibrium temperature and (ii) the exterior temperature, three different modes of ventilation may develop. First, if the room temperature lies between the exterior and the equilibrium temperature, the interior remains well-mixed and gradually heats up to the equilibrium temperature. Secondly, if the room is initially warmer than the equilibrium temperature, then a thermal stratification develops in which the upper layer of originally hot air is displaced upwards by a lower layer of relatively cool inflowing air. At the interface, some mixing occurs owing to the effects of penetrative convection. Thirdly, if the room is initially cooler than the exterior, then on opening the vents, the original air is displaced downwards and a layer of ambient air deepens from above. As this lower layer drains, it is eventually heated to the ambient temperature, and is then able to mix into the overlying layer of external air, and the room becomes well-mixed. For each case, we present new laboratory experiments and compare these with some new quantitative models of the transient flows. We conclude by considering the implications of our work for natural ventilation of large auditoria.

Instabilities during liquid migration into superheated geothermal reservoirs

We examine the stability of a vaporizing liquid front migrating through a permeable rock. We show that such liquid-vapor fronts may become unstable if a sufficient fraction of the liquid vaporizes. This instability is a result of the different speed of the fluid on each side of the front. We also identify that short-wavelength perturbations are stabilized by thermal conduction, while long-wavelength perturbations are stabilized as a result of the compressibility of the vapor. Furthermore, under conditions typical of geothermal reservoirs, where the pressure is ∼10 atm and the temperature is ∼200°–300°C, we find that if the permeability of the system is smaller than ∼10−15 m 2, then these two stabilizing mechanisms overlap and the system becomes stable to perturbations of any wavelength. We also examine the role of gravity in suppressing the instability of an ascending front and promoting the instability of a descending front. We apply our results to the vapor-dominated geothermal reservoirs at Larderello, Italy, and the Geysers, California, to predict conditions under which liquid fronts, advancing into superheated vapor, are stable.

The vaporization of a liquid front moving through a hot porous rock. Part 2. Slow injection

We present a series of similarity solutions to describe the temperature field as liquid spreads from a line source into a porous rock saturated with liquid of higher temperature. We identify slow and fast flow regimes. In the slow flow regime, the liquid is heated to the far-field temperature by conduction of heat from the far field. In the fast flow regime, there is negligible conduction of heat from the far field. Instead, the liquid is heated to the far-field temperature by cooling a region of the host rock near the source, and an internal boundary layer develops within the newly injected liquid. We successfully test our quantitative theoretical predictions with a series of laboratory experiments in which water was injected into a consolidated bed of sand filled with liquid of different temperature. We extend our model to describe the vaporization of liquid as it spreads slowly from a central source into a superheated porous rock. A further family of similarity solutions 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 temperature long before reaching the interface. The rate of vaporization then 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 result, for progressively smaller injection rates, an increasing fraction of 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 which liquid water was injected into a superheated layer of permeable sandstone.

On vapour flow in a hot porous layer

The motion of isothermal vapour in a permeable rock is governed by a nonlinear diffusion equation for the vapour pressure. We analyse vapour flow described by this equation in both bounded and unbounded domains. We then apply these solutions to describe the controls on the rate of vaporization of liquid invading a hot permeable rock. In an unbounded domain, we determine asymptotic similarity solutions describing the motion of vapour when it is either supplied to or removed from the reservoir. Owing to the compressibility, these solutions have the property that vapour surfaces migrate towards the isobar on which the vapour has the maximum speed. In contrast, if vapour is supplied to or removed from a closed bounded system sufficiently slowly then the vapour density and pressure rapidly become approximately uniform. As more vapour is added, the mean pressure gradually increases and vapour surfaces become compressed. If liquid slowly invades a hot bounded porous layer and vaporizes, the vapour pressure becomes nearly uniform. As more liquid is added, the reservoir gradually becomes vapour saturated and the vaporization ceases. In an open bounded system, with a constant rate of vapour injection, the flux of vapour across the reservoir becomes uniform. If liquid is injected slowly and vaporizes then again the vapour flux becomes spatially uniform. However, the vapour flux now increases slowly as the liquid invades further into the rock, as a result of the decreased resistance to vapour flow from the interface to the far boundary.

Laboratory and theoretical models of fluid recharge in superheated geothermal systems

The phase changes that occur as water invades a superheated geothermal reservoir were studied experimentally. Cold liquid ether was injected into a hot, isothermal bed of sand, and the rate of vaporization and thermal evolution of the sand bed were measured. When the ether was injected from below, the ascending vaporization front remained nearly planar. In accord with theoretical models, an isothermal layer of saturated liquid developed behind the front, and the mass fraction vaporizing was proportional to the reservoir superheat. In a second experiment, liquid was injected from below into a thermally stratified reservoir in which an initially superheated layer was overlain by a supercooled layer. As vapor produced at the ascending front rose into the supercooled region, it condensed and produced a two-phase saturated layer above the superheated zone, even though injection was from below. In a third experiment, liquid was injected from above into an isothermal superheated bed of sand. As the vaporizing liquid front migrated downward, hot vapor rose through the descending liquid. This vapor maintained the upper part of the reservoir close to the saturation temperature even though cold liquid was continuously supplied from above. In addition, fingers of liquid descended ahead of the main front into the superheated zone. Liquid transported in these fingers accumulated at the base of the reservoir in a layer of saturated liquid. Much of the subsequent vaporization occurred at the ascending front as the thickness of this liquid layer increased. Only the intermediate part of the reservoir remained superheated. Our experiments demonstrate that the geometry of recharge and the initial thermal structure of the reservoir have an important control on the phase changes in active geothermal systems. In many cases, recharge of liquid in a superheated region of a reservoir can lead to vapor production and transport and this may cause initially supercooled regions to become saturated. Also, if the liquid front becomes unstable, a two-phase zone may develop from an initially superheated region.

Briefing: Natural ventilation—the key to cutting energy demand

Buildings use up nearly half the UKs total energy output. Shaun Fitzgerald and Andrew Woods of the BP Institute report on their pioneering work into natural ventilation systems that offer engineers a genuine opportunity to build a more sustainable, low-energy future.