MODELLING OF CALCIUM CARBONATE PRECIPITATION IN NATURAL KARST ENVIRONMENTS UNDER HYDRODYNAMIC AND CHEMICAL KINETIC CONTROL A Thesis Presented to The Graduate Faculty of The University of Akron In Partial Ful¯llment of the Requirements for the Degree Master of Science Brad L Justice May, 2006 MODELLING OF CALCIUM CARBONATE PRECIPITATION IN NATURAL KARST ENVIRONMENTS UNDER HYDRODYNAMIC AND CHEMICAL KINETIC CONTROL Brad L Justice Thesis Approved: Accepted: Advisor Dean of the College Dr. Curtis Clemons Dr. Ronald F. Levant Co-Advisor Dean of the Graduate School Dr. Eric Wright Dr. George R. Newkome Faculty Reader Date Dr. Gerald Young Department Chair Dr. Kevin Kreider ii ABSTRACT Rimstone dams are barriers composed mainly of calcium carbonate deposited from solution in ground and surface waters. These structures form a subclass of travertine formations which include owstone and stalactites, and often appear in close proxim- ity to these features. The initial formation of rimstone dams requires some degree of cave slope, a semi-continuous ow of water, and the preexistence of irregularities in the cave oor. These dams develop at heights from a few millimeters to several me- ters within free-surface streams, and create a self-propagating dam and pool structure which grows upward. The genesis and evolution of rimstone dams is theorized to be the result of hydrodynamic and chemical-kinetic control. The purpose of this paper is to develop a model, the scope of which encompasses both hydrodynamics and the reactive transport, which is qualitatively consistent with observed and experimentally derived results, and method for analyzing the mechanism governing the formation of these unique rimstone features. iii TABLE OF CONTENTS Page LIST OF TABLES . vi LIST OF FIGURES . vii CHAPTER I. INTRODUCTION . 1 II. CALCIUM CARBONATE PRECIPITATION MODEL . 7 2.1 Hydrodynamic Model . 7 2.2 Reactive Transport Model . 14 III. SOLUTION PROCEDURE . 22 3.1 Hydrodynamics Solution Procedure . 22 3.2 Reactive Transport Solution Procedure . 27 3.3 Free Boundaries Solution Procedure . 41 IV. RESULTS AND CONCLUSIONS . 44 4.1 Analysis of Reactants Driving Precipitation and Dissolution . 44 4.2 Interpretation of Hydro-Chemical Dynamics . 45 4.3 Conclusions . 49 BIBLIOGRAPHY . 51 iv APPENDICES . 53 APPENDIX A. HYDRODYNAMIC CALCULATIONS . 54 APPENDIX B. REACTIVE TRANSPORT CALCULATIONS . 56 v LIST OF TABLES Table Page 3.1 Non dimensional variables . 23 3.2 Summary of Geochemical Parameters of Groundwater in Tributaries of the Mystic River, Scott Hollow Cave [1]. 31 3.3 Chemical kinetics constants and their values. M = mmol ¢ cm¡1. 33 3.4 Values of Parameters used in the Hydrodynamics and Reactive Transport Models . 38 3.5 Mathematically derived values for the backward reaction rate coef- ¯cients at the water- mineral surface: M = mmol ¢ cm¡3 . 41 vi LIST OF FIGURES Figure Page 1.1 Photograph montage of rimstone dams from Yellowstone National Park and two caves. Courtesy NPS. 6 2.1 Schematic of Dam Initiation and Formation . 8 4.1 The concentration ¯eld for a ¯lm thickness of 0.002cm. 46 4.2 Wave number k v. Growth rate for depth d = 0:002cm. 47 4.3 Wave number k v. Growth rate for depth d = 0:00225cm. 47 4.4 Wave number k v. Growth rate for depth d = 0:0025cm. 48 4.5 Wave number k v. Growth rate for cave oor slope of 20± . 48 vii CHAPTER I INTRODUCTION Rimstone dams are barriers composed mainly of calcium carbonate deposited from solution in ground and surface waters. These structures form a subclass of travertine formations which include owstone and stalactites, and often appear in close proxim- ity to these features. Figure 1.1 shows the variety of environments, structures, and topological features which are inherent in rimstone dams. The initial formation of rimstone dams requires some degree of cave slope, a semi-continuous ow of water, and possibly the preexistence of irregularities in the cave oor. These dams develop at heights from a few millimeters to several meters within free-surface streams, and create a self-propagating dam and pool structure which grows upward. The genesis and evolution of rimstone dams is theorized to be the result of hydrodynamic and chemical-kinetic control. The chemically controlled processes of calcium carbonate precipitation and dissolution have been rigorously studied. These chemical processes have been care- fully determined via extensive experimentalization. All such e®orts are characterized by dissolved carbon dioxide from the atmosphere, transport of reactants from the solution to the mineral surface of the cave oor, and the e®ects of pH determining dissolution or precipitation. 1 Plummer et al. [2] pioneered investigations of this area by performing rigorous experiments on calcium carbonate dissolution and precipitation processes. The model employed was based on the surface reactions described by the experimentally derived rate law dubbed the PWP equation. This equation, assuming similar hydrodynamic conditions in the natural environment, relates chemical species, reaction mechanisms, and surface controlled kinetics to the dissolution and precipitation rates of calcium carbonate in travertine formations. Dreybrodt et al. [3] [4] [5] utilized Plummer's studies as a catalyst for further investigation of these chemical processes. Experiments were carried out on both dissolution and precipitation of calcium carbonate. Dreybrodt constructed a model which encompassed surface controlled deposition/precipitation, di®usion of reactants in the bulk solution, and the slow conversion of CO2 to H2CO3. The PWP equation was utilized to describe the surface reactions. Thin ¯lm water ow over rock surfaces was approximated by plug ow with constant velocity on a at plane of calcium carbonate for both laminar and turbulent ow characteristics. The reactants in the bulk solution were assumed to be fast in order to use mass balance laws to describe ¡ + ¡ the mutual dependence of CO2, OH , H , and HCO3 . These studies revealed the importance of ¯lm thickness in explaining the di®erent morphologies in the deposition of calcium carbonate. It was discovered that the model predicted a hydraulic jump from laminar to turbulent ow for su±cient water ¯lm thickness. It was theorized that this transition in ow characteristics contributed to the rate of dissolution and precipitation of calcium carbonate. 2 Chou et al. [6] was able to demonstrate that the dissolution and precipi- tation of many other carbonate minerals could be described by the PWP equation of Plummer et al. Later, Arakaki [7] extended the work of Plummer, Chou, and Dreybrodt to include other surface speciation at the calcium carbonate surface. This study predicted the dominant role of pH on the dissolution and precipitation. The investigation of hydrodynamic processes has been limited to observations at various sites of dam growth, and carefully derived experimental results. These e®orts demonstrate observed relationships between ow characteristics, cave oor slope, and water ¯lm thickness, and their inuences on rimstone dam initiation, structure, and evolution. The initiation and evolution of rimstone dams has been observed to exhibit complex dynamics since the processes of dam growth change the ow characteristics. Veni [8] observed abrupt hydrodynamic changes due to the geometry of the rimstone dam structures. The ow characteristics changed from laminar to turbulent ows once the water passed over the lips of the dam and pool structures. He also developed a model assuming uniform water chemistry, uniform water depth, and dynamics following initial calcium carbonate precipitation. This model theorized the hydraulic jump from laminar to turbulent ow and demonstrated a relationship between cave oor slope and the height and frequency of rimstone dam growth. A mathematical relationship between slope and the velocity, gravitational acceleration, and the ¯lm thickness of the water ow was utilized to assess this relationship. 3 It was found that rimstone dam height and frequency increased as the slope of the cave oor increased. Xing et al. [9] investigated hydrodynamic conditions on various rimstone dam structures. This e®ort is based on thin ¯lm water ows following the initial formation of rimstone dams and the e®ects of non-constant and semi- continuous ows characteristic of seasonal changes and the e®ects of rimstone dam growth on the hydrodynamics. It was observed that di®erent ow characteristics at di®erent locations in caves a®ected the geometry of rimstone dams which is indicative of the di®erent type of structures observed in caves. It was theorized that initial formation of rimstone dams required thin ¯lm water ows and non-uniformities in the cave oor. The cave evolution and its e®ects on the dynamics of the water ow and subsequent changes of the structure of rimstone dams was also discussed. It was found that after initial formation of the rimstone dams, the subsequent evolution in the shape of deposits was inuenced by the surface waves of the water ow which was theorized to be similar to the mechanism driving the deposition of beach sand by ocean waves. It was also found that as the cave evolved, the supply of water to the rimstone dams became constant due to the formation of the dam pool structure inherent in these deposits. Baker et al. [10] conducted a comparative study of the work of Plummer and Dreybrodt and the e®ects of thin ¯lm water ow. This e®ort theorized that the inconsistencies between theoretical growth rates and experimental growth rates of calcium carbonate deposits