Accepted for Publication in Applied Geochemistry April 2015. Measuring
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ACCEPTED FOR PUBLICATION IN APPLIED GEOCHEMISTRY APRIL 2015. MEASURING FLOW RATES AND CHARACTERIZING FLOW REGIMES IN HOT SPRINGS B. R. Mathon1, M. A. Schoonen2,3, A. Riccardi4, M. J. Borda5 Department of Geosciences, Stony Brook University, Stony Brook NY11794-2100. ABSTRACT Detailed studies were conducted at Big Boiler hot spring in Lassen Volcanic National Park, CA, and Ojo Caliente hot spring in Yellowstone National Park, WY, to measure the flow rate and characterize the flow regime of hot spring drainages. These drainages represent some of the most dynamic interfaces between the hydrosphere and atmosphere with steep temperature gradients and chemical gradients. The rate of thermal disequilibrium and chemical disequilibrium dissipation depends on the flow rate and flow regime. The drainage of each hot spring was divided into ten or more segments and water samples were collected at segment boundaries. Fluid flow velocity throughout the drainage was measured using an in situ flow probe where possible and by determining the advancement of a red food dye tracer through the flow channel. A combination of field and laboratory studies was used to adapt a method based on the transport-controlled dissolution rate of gypsum to characterize the flow regime throughout the drainages. Laboratory experiments as a well as a deployment in an artificial drainage were 1 Current Address: Johnson State College, Department of Environmental & Health Sciences, Johnson, VT 05656 2 Corresponding author: [email protected] 3 Current Address: Environmental and Climate Sciences, Brookhaven National Laboratory, Upton NY. 4 Current Address: British Petroleum, Houston Texas. 5 Current Address: Golder Associates, 200 Century Parkway, Suite C, Mt. Laurel, New Jersey, USA 08054 1 conducted to validate the application of this method for hot spring environments. The deployment of the gypsum tablets was complemented by using digital videography to record the nature of the flow regime throughout the drainages. In situ flow probe measurements were not possible at all locations. The data obtained with the probe showed a range of values that was in reasonable agreement with the flow rates obtained using the dye tracer. The average flow rate based on advancement of dye tracer determined at Big Boiler was 0.22 m/s in both 2000 and 2001, while in Ojo Caliente flow rate varied from 0.39 m/s in 2001 to 0.45 m/s in 2002. The results of the gypsum dissolution measurement in the field yield boundary layer thicknesses between 8 and 38 micron, with most values between 15 and 25 micron, indicating well-developed turbulent flow throughout the drainages. The results, consistent with videography, indicate that gypsum dissolution rates based on the deployment of well-characterized and pure gypsum tablets can be used in hot-spring environments. An analysis of cooling rates within the drainages illustrates the importance of turbulent flow in cooling the waters. 2 1. INTRODUCTION Hot springs and their drainages represent some of the most dynamic interfaces between the hydrosphere and atmosphere with steep temperature gradients and chemical gradients. As hot spring waters discharge, the thermal disequilibrium and chemical disequilibrium with the atmosphere is the driving force for heat transfer (i.e., cooling of the water), mass transfer (e.g., degassing volatile species), and chemical reactions (e.g., mineral precipitation or oxidation) (Druschel et al., 2004). These processes are coupled as mass transfer and chemical reactions are typically temperature dependent and chemical reaction rates are often dependent on mass transfer of a reactant (e.g, ingassing of molecular oxygen) (Hill, 2009; Lemoine et al., 2003; Mills, 1999; Ocampo-Torres et al., 1994; Welty et al., 2001). The presence of microbial communities thriving on the disequilibrium conditions in the drainage adds another layer of complexity. The flow rate is an important factor as it dictates the overall mass transfer of solution through the system, while the flow regime dictates how rapidly thermal and chemical disequilibrium is dissipated in the system (Sherwood and Pigford, 1952). The flow regime, which can range from laminar to turbulent, depends on whether the flow is governed by viscous forces that tend to keep fluid parcels from moving chaotically versus inertial forces that induce chaotic movement among fluid parcels. In the laminar flow regime, the viscous forces dominate and the fluid flow can be represented by thin layers of fluid moving parallel to one another. The velocity of the fluid layer closest to the bottom is the lowest in an open channel governed by laminar flow. In turbulent flow, the layers are broken up 3 and fluid parcels move chaotically. The breakdown of laminar flow and development of turbulent flow is a gradual process and referred to as a transitional flow regime. Understanding the processes and obtaining rates for cooling, gas transfer and chemical reactions will ultimately allow for better geochemical and thermal modeling of hot springs. An understanding of the dissipation of the thermal disequilibrium and the dissipation of the chemical disequilibrium through abiotic processes will provide microbiologist and biogeochemists with the physicochemical constraints on microbes living in hot springs and their drainage systems. This may also allow one to evaluate to what extent microbes influence the dissipation of chemical and thermal disequilibrium. With a fundamental understanding of the physicochemistry of hot spring systems on Earth, it may be possible to constrain or characterize the physicochemical conditions of ancient hot spring systems found on Mars. It is already believed that images resembling terraced pools on Mars could have formed from discharging hydrothermal fluids (El Maarry et al., 2012; Farmer, 1996; Schulze-Makuch et al., 2007). The ability to understand how chemical disequilibrium is dissipated on Mars will provide insight as to whether life could have thrived near Martian hydrothermal systems. In this paper we present a detailed assessment of the physical characteristics, flow rate, and flow regime of drainages of two hot springs. Each drainage was divided into segments by establishing sampling stations where flow velocity was measured and flow regime was characterized along the drainage. While measuring flow velocities is relatively straightforward, it is a challenge to characterize flow regime in the drainages. One approach to characterize flow regime is to calculate Reynolds numbers for each segment of the drainages. Reynolds numbers, defined as the ratio of inertial forces 4 to viscous forces, provide an indication which of these forces dominates flow (Reynolds, 1883). If viscous forces dominate (low Reynolds numbers), the flow is laminar. Conversely, if inertial forces dominate (high Reynolds numbers) the flow is turbulent. However, calculating Reynolds numbers for hot spring drainages is fraught with uncertainty because empirical formulas have been developed for well-defined open channels and pipes, but are not available for the type of irregular drainages studied here (Mathon, 2002). As an alternative, we evaluated the applicability of a method to characterize the flow regime based on measuring the in situ dissolution rate of gypsum plates that yields boundary layer thicknesses. The smaller the value of the boundary layer, the more turbulent the flow. 2. BACKGROUND The in situ technique used here to characterize flow regime involves determining the dissolution rate of gypsum plates with a known surface area. The underlying assumption is that the rate-limiting step is transport from the mineral surface through a stationary layer into the bulk solution (Fig.1). It is assumed that fluid at the mineral Figure 1 Conceptual figure of the boundary layer developed on a surface of a binary mineral, CD, with C+ and D- as constituents. The arrows indicate the transition of constituent ions into the overlying fluid. The concentration profile in the solution film adjacent to the surface for either one of the constituent ions is schematically shown. Note that the boundary layer thickness will decrease with increasing flow rate parallel to surface and the onset of turbulence. 5 interface is in equilibrium with the mineral. The thickness of the stationary or boundary layer, δ, is dictated by the hydrodynamics of the system (Dreybrodt et al., 1992; Opdyke et al., 1987; Tengberg et al., 2005). A recent exhaustive literature review by Colombani (2012) has shown that the rate of gypsum dissolution is directly proportional to the disequilibrium between the bulk solution and the solution immediately adjacent to the mineral surface. Hence, the undersaturation of the bulk solution with respect to gypsum provides the driving force for the reaction. The difference between the calcium concentration in the bulk solution and at equilibrium with gypsum is commonly used to express the driving force (Opdyke et al., 1987; Tengberg et al., 2005). Hence, in equation 1, which describes the rate of gypsum dissolution, D is the diffusion coefficient 2+ 2 2+ 3 for Ca (aq) (cm /s), ceq is the equilibrium Ca (aq) concentration (mol/cm ), cb is the actual 2+ 3 Ca (aq) concentration in the bulk solution (mol/cm ) . The dissolution rate is determined on the basis of the mass loss of the tablet after 2.5 to 3 hours of exposure to the flowing water (equation 2). Rdiss = k(ceq-cb)=(D/δ )*(ceq-cb) (1) Rdiss = Δm/(A*Δt) (2) For Equation 2, Δm is mass loss (mol gypsum), A is the surface area (cm2), and Δt is the exposure time (s). The important assumptions underlying the use of this method in the field are (1) that the water is significantly undersaturated with respect to gypsum and (2) that the dissolution is governed by a transport-controlled mechanism as opposed to a surface- controlled mechanism. In a transport-controlled dissolution mechanism, the rate depends 2+ 2- on how quickly the constituent ions (here Ca and SO4 ) are removed from the mineral 6 surface to the bulk solution through the boundary layer. By contrast, in surface- controlled reactions, an elementary reaction step at the mineral surface is the rate-limiting step.