VELOCITIES OF CONVECTIVE ASCENDING FLOW IN GEOTHERMAL SYSTEMS BASED ON STATIC TEMPERATURE LOGGING DATA ANALYSIS AND SIMULATION STUDY Masaji Kato 1 , Mineyuki Hanano 2 and Katsuhiko Kaneko 1 1 Hokkaido University, Sapporo, Hokkaido 060-8628 Japan 2 Japan Metals & Co., Ltd., 1-3-6 Saien, Morioka-city, Iwate 020-0024 Japan Key Words: ascending flow velocity, hydrothermal convection, static temperature log, one-dimensional flow analysis, two-dimensional numerical simulation ABSTRACT Macroscopic velocities of convective ascending flow in hydrothermal convection systems show typical characteristics. Our objective is to clarify its characteristics of the systems. In this study, we conducted static temperature logging data analyses and numerical simulation studies. From simple one- dimensional analyses based on static temperature logging data, it was found that the velocities of convective ascending flow in active convection systems had the same order of values. Simulation studies for liquid-dominated hydrothermal systems were also conducted in order to clarify the effects of heat source temperature or permeability structure on the velocities of ascending flow. As a result, in spite of large difference of heat source temperature or permeability structure in a practical range, ascending flow velocity changes only in less than one order of magnitude. 1. INTRODUCTION Convective ascending flow is an important phenomenon for understanding hydrothermal convection system and therefore for geothermal development. Hydrothermal convection systems have one or more domains of convective ascending flow. In this study, based on static temperature logging data from several geothermal areas, simple one-dimensional analysis for estimating macroscopic velocities of ascending flow in active convection systems was employed. The results may be closely related to the structure of permeability and consequently to the stress condition. Hydrothermal convection can be representative as fluid and heat flows in a porous medium heated from below. Numerical simulation studies for liquid-dominated hydrothermal systems, therefore, were also conducted in order to clarify the effects of the permeability structure or the heat source temperature on the velocities of ascending flow in this study. 2. GOVERNING EQUATIONS Simple governing equations for fluid flow and energy transport are used in this study. Since liquid-dominated hydrothermal systems in natural state before exploitation are treated here, it is assumed that the flow region is represented by a porous layer, the fluid is single-phase (only water), and mass and heat flow is under the steady state. Accordingly, mass, momentum and energy balance equations of mass and heat flow in a porous medium are as follows (e.g. Donaldson, 1962): 0 ) ( = ⋅ ∇ v f ρ (1) 0 = + - ∇ v k g μ ρ f p (Darcy's equation) (2) T T c m f pf 2 ∇ = ∇ ⋅ λ ρ v (3) where boldface type indicates a vector or a second-order tensor quantity. In the above equations, f ρ , c pf and μ are the density, the specific heat and the dynamic viscosity of fluid, respectively. v is the Darcian velocity vector of fluid. k is the permeability tensor of the porous medium and m λ is the isotropic thermal conductivity of the saturated porous medium. g is the gravity vector. T is the equilibrium temperature of saturated porous medium and P is the pressure of saturating fluid. 3. ONE-DIMENSIONAL ANALYSIS FOR VERTICAL FLOW IN RESERVOIR In liquid-dominated hydrothermal convection, preferred orientation of hot-water flow possibly appears. Dominant vertical ascending flow may exist in the layer just above heat source, such as magma intrusion. While, dominant descending water flow may also occur in the layer. In those cases, one- dimensional analysis of vertical flow can be useful to estimate the vertical flow velocity and the vertical permeability of the layer. Reducing equation (3), we obtain the differential equation for one-dimensional steady-state flow of heat and fluid through saturated homogeneous porous media (Bredehoeft and Papadopulos, 1965): 0 d d d d 2 2 = - z T z T α (4) where m z f pf v c λ ρ α / = . v z is the component of velocity in the z (vertical) direction (positive downward). Solving equation (4) with the condition that T = T 1 at z = z 1 and T = T 2 at z = z 2 (z 1 and z 2 are arbitrary if their points are in the layer and z 1 < z 2 ), we can obtain the following equation: ( ) { } ( ) { } 1 exp 1 exp 1 2 1 1 2 1 - - - - = - - z z z z T T T T α α (5) In this equation, if T 1 = T 0 at z 1 = 0 and T 2 = T L at z 2 = L (the length of vertical section over which temperature measurements extend) then the solution obtained by Bredehoeft and Papadopulos (1965) appears. Assuming steady ascending flow in a homogeneous half- infinite porous medium and the boundary conditions that T = T 0 at z = 0, and 0 d / d → z T and r T T → as ∞ → z when 2647 Proceedings World Geothermal Congress 2000 Kyushu - Tohoku, Japan, May 28 - June 10, 2000