Wolfgang Dreybrodt

The kinetics of calcite dissolution and precipitation in geologically relevant situations of karst areas: 2. Closed system

A general theory of dissolution and precipitation rates at CaCO3 surfaces from calcareous solutions in contact with an atmosphere containing CO2 is presented. The three rate-determining processes, kinetics at the CaCO3 surface, diffusion into the bulk and conversion of CO2 into HCO−3 are treated simultaneously. In all cases the dissolution or precipitation rates are given by R = α([Ca2+]eq − [Ca2+]), where α is a function of CO2 pressure, thickness of the water film covering the CaCO3 surface, and temperature. α depends also on the hydrodynamic conditions of flow. Under turbulent flow the rates increase by one order of magnitude, since in comparison to laminar flow diffusion is significantly enhanced by eddies. We have carried out experiments to measure the time dependence of [Ca2+] in stagnant and turbulently-stirred water films covering CaCO3 surfaces for various temperatures, CO2 pressures and film thicknesses. From the exponential behaviour of [Ca2+](t) the value of α can be determined. Good agreement with the theoretical predictions is obtained. Furthermore, precipitation rates from supersaturated solutions were measured and found to be in good agreement with the theory. Our results are summarized in a table and figures, which provide the geologist data from which in all situations, being geologically relevant in karst areas as far as open system is concerned, dissolution and precipitation rates can be derived easily.

Testing Theoretically Predicted Stalagmite Growth Rate with Recent Annually Laminated Samples: Implications for Past Stalagmite Deposition

Annually laminated stalagmites deposited over the last 30–160 years are analysed to determine their growth rate. Three natural and artificial cave sites in England, France, and Belgium were chosen for their wide range of variability in growth rate determining variables, and multiple samples were taken from each site. The annual nature of laminae deposition within the stalagmite calcite was confirmed by comparison to the date of cave/void opening, 14C analyses, or by using dated event horizons. Measured stalagmite growth rate was determined from annual laminae thickness measurements and compared to that theoretically predicted from the chemical kinetics of the calcite precipitation reaction. A good agreement is observed between empirical observations and theoretical predictions, although two complicating factors, variations in calcite porosity, and seasonal cessation of the water supply to the samples, both affect the growth rate. Implications for the extraction of palaeoclimate information from stalagmite growth rate are discussed.

Dissolution kinetics of natural calcite minerals in CO2-water systems approaching calcite equilibrium

We have measured dissolution rates of various natural calcite samples, e.g marbles, limestones and marine pelagic sediments, in CO2H2O solutions of fixed PCO2 and temperature during their approach to equilibrium with respect to calcite. The runs have been carried out as batch experiments using the free-drift technique (PCO2: 5·10−3atm; T: 20°C), where size fractioned particles of 100 μm were kept in suspension by turbulently stirring the solution. In each experiment three natural specimens and for reference one of synthetic NBS Calcite (SRM 915) have been investigated. The dissolution rates observed for all natural samples can be represented by an empirical rate law given as R=α1(1 − CCs)n1 at Ca2+ concentrations C<xCs (n1 ≈ 1.5−2.3, α1 ≈ 1.6·10−7−2.2·10−7 mmol cm−2 s−1, x ≈ 0.6−0.8). Above this concentration the empirical reaction order switches to a higher value of n2 ≈ 3–4. In contrast, NBS Calcite exhibits a linear rate law of R=α(1-CCs) with α ≈ 1.6·10−7 mmol cm−2s−1, which closely follows the dissolution rates predicted by the mechanistic dissolution model (PWP model) of Plummer et al. (1978). Experiments on NBS Calcite in a solution containing 10 μM KH2PO4 exhibited results very similar to natural specimens, displaying inhibited dissolution with respect to synthetic calcite, when approaching equilibrium. Only minor influence of phosphate was observed on the dissolution rates of natural samples. From this observation we suggest a model in which Ca2+ ions are adsorbed to lattice sites (kinks) active to dissolution, blocking further dissolution there. By an attractive interaction between these ions and impurities (heavy metals or phosphate) on the surface of natural materials their adsorption enthalpy increases with increasing coverage Θ of physisorbed Ca2+ ions on the surface. From this we derive a rate law: REMP(C)=(1−θ)RPWP; C=[θ(1−θ)]ƒexp [−(Uo+Uo′θ)KBT] where RPWP is the rate predicted by the PWP model; and (1 − Θ) gives the amount of surface sites still active to dissolution, which is represented by the Fowler-Frumkin isotherm. Our results show that the binding enthalpy Uo is a property of the pure calcite surface, whereas Uo′ is dependent on the origin of the materials. Using this rate equation we have examined a variety of calcite dissolution data published in the literature and, in all cases, have found them to obey closely the suggested rate law. Especially the earlier published data on inhibition of calcite dissolution by heavy-metal ions, e.g. Cu2+ and Sc3+, fit well into our model. It reconciles with many apparently conflicting results and explains the dissolution rates from the chemical reactions proposed by L.N. Plummer and coworkers and adsorption processes of the solute, both acting simultaneously.

Principles of Early Development of Karst Conduits Under Natural and Man-Made Conditions Revealed by Mathematical Analysis of Numerical Models

Numerical models of the enlargement of primary fissures in limestone by calcite aggressive water show a complex behavior. If the lengths of the fractures are large and hydraulic heads are low, as is the case in nature, dissolution rates at the exit of the channel determine its development by causing a slow increase of water flow, which after a long gestation time by positive feedback accelerates dramatically within a short time span. Mathematical analysis of simplified approximations yields an analytical expression for the breakthrough time, when this happens, in excellent agreement with the results of a numerical model. This expression quantifies the geometrical, hydraulic, and chemical parameters determining such karst processes. If the lengths of the enlarging channels are small, but hydraulic heads are high, as is the case for artificial hydraulic structures such as dams, it is the widening at the entrance of the flow path which determines the enlargement of the conduit. Within the lifetime of the dam this can cause serious water losses. This can also be explained by mathematical analysis of simplified approximations which yield an analytical threshold condition from which the safety of a dam can be judged. Thus in both cases the dynamic processes of karstification are revealed to gain a deeper understanding of the early development of karst systems. As a further important result, one finds that minimum conditions, below which karstification cannot develop, do not exist.

The kinetics of the reaction CO2 + H2O → H+ + HCO3− as one of the rate limiting steps for the dissolution of calcite in the system H2OCO2CaCO3

Abstract Dissolution of CaCO3 in the system H2OCO2CaCO3 is controlled by three rate-determining processes: The kinetics of dissolution at the mineral surface, mass transport by diffusion, and the slow kinetics of the reaction H2O + CO2 = H+ + HCO3−. A theoretical model of Buhmann and Dreybrodt (1985a, b) predicts that the dissolution rates depend critically on the ratio V A of the volume V of the solution and the surface area A of the reacting mineral. Experimental data verifying these predictions for stagnant solutions have been already obtained in the range 0.01 cm V A cm . We have performed measurements of dissolution rates in a porous medium of sized CaCO3 particles for V A in the range of 2·10−4 cm and 0.01 cm in a system closed with respect to CO2 using solutions pre-equilibrated with an initial partial pressure of CO2 of 1·10−2 and 5·10−2 atm. The results are in satisfactory agreement with the theoretical predictions and show that especially for V A −3 cm dissolution is controlled entirely by conversion of CO2 into H+ and HCO3−, whereas in the range from 10−3 cm up to 10−1 cm both CO2-conversion and molecular diffusion are the rate controlling processes. This is corroborated by performing dissolution experiments using 0.6 μmolar solutions of carbonic anhydrase, an enzyme enhancing the CO2-conversion rates by several orders of magnitude. In these experiments CO2 conversion is no longer rate limiting and consequently the dissolution rates of CaCO3 increase significantly. We have also performed batch experiments at various initial pressures of CO2 by stirring sized calcite particles in a solution with V A = 0.6 cm and V A = 0.038 cm . These data also clearly show the influence of CO2-conversion on the dissolution rates. In all experiments inhibition of dissolution occurs close to equilibrium. Therefore, the theoretical predictions are valid for concentrations c ≤ 0.9 ceq. Summarising we find good agreement between experimental and theoretically predicted dissolution rates. Therefore, the theoretical model can be used with confidence to find reliable dissolution rates from the chemical composition of a solution for a wide field of geological applications.

Surface controlled dissolution rates of gypsum in aqueous solutions exhibit nonlinear dissolution kinetics

Abstract The effective dissolution rates of gypsum are determined by mixed kinetics, where the rate constants of dissolution at the surface and the transport constant of molecular diffusion of dissolved material are similar. To obtain the surface reaction rate law it is necessary to know the transport constant. We have determined the surface rate law for monocrystalline selenite by using a rotating disc set-up, where the transport coefficients are well known. As a result, up to a calcium concentration of 0.6 · c eq , we find a nearly linear rate law R s = k s l (1− c s / c eq ) n 1 , where c s is the total calcium concentration at the surface and c eq the equilibrium concentration with respect to gypsum, n 1 = 1.2 ± 0.2, and k s l = 1.1 · 10 −4 mmol cm −2 s −1 ± 15%. We also employed batch-experiments for selenite, alabaster and gypsum rock samples. The result of these experiments were interpreted by using a transport constant determined by NaCl dissolution experiments under similar physical conditions. The batch experiments reveal a dissolution rate law R s = k s l (1− c s / c eq ) n 1 , k s l = 1.3 · 10 −4 mmol · cm −2 s −1 , n 1 = 1.2 ± 0.2 for c ≤ 0.94 · c eq . Close to equilibrium a nonlinear rate law, R s = k s 2 (1− c s / c eq ) n 2 , is observed, where k s 2 is in the order of 10 mmol · cm −2 s −1 and n 2 ≈ 4.5. The experimentally observed gypsum dissolution rates from the batch experiments could be accurately fitted, with only minor variations of the surface reaction constant obtained from the rotating disk experiment and the transport coefficient from the NaCl dissolution batch experiment. Batch experiments on pure synthetic gypsum, reveal a linear rate law up to equilibrium. This indicates inhibition of dissolution in natural samples close to equilibrium, as is known also for calcite minerals.

A mass transfer model for dissolution and precipitation of calcite from solutions in turbulent motion

Abstract A film theory model for dissolution and precipitation of calcite from a plane surface in a H2OCO2CaCO3 solution under turbulent flow conditions is presented. It takes into account: (1) molecular diffusion across a diffusion boundary layer of thickness ϵ adjacent to the liquid-solid interface; (2) slow conversion of CO2 into HCO−3 and H+; and (3) heterogeneous chemical reactions at the surface of solid CaCO3. The rates depend heavily on the thickness of the boundary layer. The parameter ϵ is determined by the hydrodynamic conditions of the problem. Its value can be found either experimentally by dissolution experiments entirely determined by diffusional mass transport, such as dissolution of CaSO4, or by hydrodynamic correlations. We have calculated dissolution and precipitation rates of calcite for various values of Ca2+ and CO2 concentrations in the solution, and various values of ϵ. The results are compared to data of calcite dissolution by rotational disc experiments and show satisfactory agreement. Finally, we discuss the consequences of our results with respect to dissolution of limestone in karst terranes.

Early development of Karst aquifers on percolation networks of fractures in limestone

We have modeled flow and dissolution processes within percolation networks representing stochastic primary fracture systems in limestone. At the beginning of karstification, flow is evenly distributed on all fractures available. As the system develops by dissolutional widening of the fractures, preferred flow pathways evolve, which attract more and more flow, until at breakthrough the total flow rate increases dramatically. These breakthrough times have been investigated with regard to their dependence on the initial fracture aperture width, the dimension of the evolving karst aquifer, hydraulic gradients, connectivity of the percolation network, and the chemical parameters, such as higher-order rate constants and exponents, and equilibrium concentration. They exhibit a behavior similar to that of breakthrough times for one-dimensional conduits [Dreybrodt, 1996]. Our results show that the structure of the evolving karst aquifer is determined by the initial geological setting. However, the final conduits are selected from competing pathways with potential breakthrough times close to each other, whereby the details of the distribution of undersaturation with respect to calcite play an important role.

Hydrodynamic control of inorganic calcite precipitation in Huanglong Ravine, China: Field measurements and theoretical prediction of deposition rates

Abstract Hydrochemical and hydrodynamical investigations are presented to explain tufa deposition rates along the flow path of the Huanglong Ravine, located in northwestern Sichuan province, China, on an altitude of about 3400 m asl. Due to outgassing of CO 2 the mainly spring-fed stream exhibits, along a valley of 3.5 km, calcite precipitation rates up to a few mm/year. We have carried out in situ experiments to measure calcite deposition rates at rimstone dams, inside of pools and in the stream-bed. Simultaneously, the downstream evolution of water chemistry was investigated at nine locations with respect to Ca 2+ , Mg 2+ , Na + , Cl − , SO 4 2− , and alkalinity. Temperature, pH, and conductivity were measured in situ, while total hardness, Ca T , and alkalinity have been determined immediately after sampling, performing standard titration methods. The water turned out to be of an almost pure CaMgHCO 3 type. The degassing of CO 2 causes high supersaturation with respect to calcite and due to calcite precipitation the Ca 2+ concentration decreases from 6·10 −3 mole/1 upstream down to 2.5·10 −3 mole/1 at the lower course. Small rectangular shaped tablets of pure marble were mounted under different flow regimes, i.e., at the dam sites with fast water flow as well as inside pools with still water. After the substrate samples had stayed in the water for a period of a few days, the deposition rates were measured by weight increase, up to several tens of milligrams. Although there were no differences in hydrochemistry, deposition rates in fast flowing water were higher by as much as a factor of four compared to still water, indicating a strong influence of hydrodynamics. While upstream rates amounted up to 5 mm/year, lower rates of about 1 mm/year were observed downstream. Inspection of the marble substrate surfaces by EDAX and SEM (scanning electron microscope) revealed authigeneously grown calcite crystals of about 10 μm. Their shape and habit are indicative of a chemically controlled inorganic origin. By applying a mass transfer model for calcite precipitation taking into account the reaction rates at the surface given by Plummer et al. (1978), slow conversion of CO 2 into H + and HCO 3 − , and diffusional mass transport across a diffusion boundary layer, we have calculated the deposition rates from the hydrochemistry of the corresponding locations. The calculated rates agree within a factor of two with the experimental results. Our findings confirm former conclusions with respect to fast flow conditions: reasonable rates of calcite precipitation can be estimated in reducing the PWP-rate calculated from the chemical composition of the water by a factor of about ten, thus correcting for the influence of the diffusion boundary layer.

The inhibiting action of intrinsic impurities in natural calcium carbonate minerals to their dissolution kinetics in aqueous H2O–CO2 solutions

We have measured the surface controlled dissolution rates of natural calcium carbonate minerals (limestone and marble) in H2O–CO2 solutions by using free drift batch experiments under closed system conditions with respect to CO2, at 10°C with an initial partial pressure of carbon dioxide of 5 · 10−2 atm. All experiments revealed reaction rates F, which can be described by the empirical relation: Fn1 = kn1 · (1 − c/ceq)n1 for c < cs, which switches to a higher order n2 for calcium concentrations c ≥ cs described by Fn2 = kn2 · (1 − c/ceq)n2. kn1 and kn2 are rate constants in mmole/(cm2 · s), ceq is the equilibrium concentration with respect to calcite. The values of the constants n1, n2, kn1, kn2 and cs depend on the V/A ratio employed, where V is the volume of the solution and A is the surface area of the reacting mineral. Different calcium carbonate minerals exhibit different values of the kinetic constants. But generally with increasing V/A, there is a steep variation in the values of all kinetic constants, such that the rates are reduced with increasing V/A ratio. Finally with sufficiently large V/A these values become constant. These results are explained by assuming intrinsic inhibitors in the bulk of the mineral. During dissolution these are released from the calcite matrix and are adsorbed irreversibly at the reacting surface, where they act as inhibitors. The thickness d of the mineral layer removed by dissolution is proportional to the V/A ratio. The amount of inhibitors released per surface area is given by d · cint, where cint is their concentration in the bulk of the mineral. At low thicknesses up to ≈3 · 10−4 cm in the investigated materials, the surface concentration of inhibitors increases until saturation is attained for thicknesses above this value. To analyze the surface concentration and the type of the inhibitors we have used Auger spectroscopy, which revealed the presence of aluminosilicate complexes at the surface of limestone, when a thickness of d ≈ 10−3 cm had been removed by dissolution. In unreacted samples similar signals, weaker by one order of magnitude, were observed. Depth profiles of the reacted sample obtained by Ar-ion sputtering showed the concentration of these complexes to decrease to the concentration observed in the unreacted sample within a depth of about 10 nm. No change of the concentration with depth was observed in unreacted samples. These data suggest that complexes of aluminosilicates act as inhibitors, although other impurities cannot be excluded.