An investigation of heat and mass transfer mechanisms within the earth

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Elder, J.W. 1961 An investigation of heat and mass transfer mechanisms within the earth. [s.l.]: [s.n.]. Report / Geophysics Division 35 13p

Abstract: The surface heat flux except in regions of hot springs or volcanism is uniform over the earth's surface. However, within the Taupo depression area of N.Z., 30 km x 200 km, there are several areas where the geothermal gradient is of the order of 100 times normal and hot spring and steaming ground areas discharge the order of 100 times normal and hot spring and steaming ground areas discharge the order of 100 kg/sec km2 of fluid, the heat flux over the whole averaging 20 times normal. The high geothermal gradient persists to only a few 100 m below the surface. The depression which is similar to a large caldera 5 km deep is filled with lava flows and volcanic debris and the pores of this fill are saturated with water. It is the movement of this water which is solely responsible for the transport of heat in the depression. Water movement in the greywacke basement is of minor importance. The excess heat is supplied by the volcanic activity beneath the area. When a fluid permeates a porous rock the actual path of an individual fluid particle cannot be followed analytically but the flow can be represented by a macroscopic law discovered by Darcy. This law involves the permeability (conductivity to flow) of the rock and is definable provided the masses of fluid considered have a length scale large compared with the scale of the porous structure, the joints of fissures of the rock. In fact it is possible to consider the permeability of a system containing pores, joints and fissures as having a permeability which is a function of the volume of the flow considered. The permeability is by far the most important physical parameter of a hydrothermal system. The permeability concept still applies even when the flow in the rock voids is turbulent. The fundamental assumption of this part of the work is that provided the temperature distribution and the mass flux on the boundary of the flow system, and the permeability and thermal conductivity of the porous material within the boundary are specified the behaviour of the flow system is determinate. The system can be formulated mathematically by four partial differential equations the continuity, momentum, energy and diffusion equations. For non-isothermal conditions these equations are difficult to solve analytically but one can be conveniently solved with scale models (analogue computers) in the laboratory. The principle hydrothermal system of importance in the Taupo depression is a free convective system. For such a system the principle parameter is the Rayleigh number which measures the ratio of heat transport by the flow to that transported by conduction. It has been shown that in the Taupo depression the Rayleigh number is very large (106 the recirculation is large and the recharge small. Rather like a pot boiling on the stove....large convection velocities and very small mass discharge (auth)