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 THEORETICAL TECHNIQUE FOR PREDICTING THE 
 
 CUMULATIVE IMPACT OF IRON AND MANGANESE 
 OXIDATION IN STREAMS RECEIVING 
 
 DISCHARGE FROM COAL MINES 
 
 JUL 1 6 1986 
 
 kiWliittfSlTY OF ILLINOIS 
 
 ^ URBANA-CHAMPAIGN 
 
 U.S. GEOLOGICAL SURVEY 
 
 Water Resources Investigations Report 86-4039 
 

THEORETICAL TECHNIQUE FOR PREDICTING THE CUMULATIVE IMPACT OF IRON AND 
 MANGANESE OXIDATION IN STREAMS RECEIVING DISCHARGE FROM COAL MINES 
 
 by Keith E. Bobay 
 
 U.S. GEOLOGICAL SURVEY 
 
 Water-Resources Investigations Report 86-4039 
 
 The person charging this material is re¬ 
 sponsible for its return to the library from 
 which it was withdrawn on or before the 
 Latest Date stamped below. 
 
 Indianapolis, Indiana 
 1986 
 
UNITED STATES DEPARTMENT OF THE INTERIOR 
 
 DONALD PAUL HODEL, Secretary 
 GEOLOGICAL SURVEY 
 Dallas L. Peck, Director 
 
 For additional information write to: Copies of this report 
 
 can be purchased from: 
 
 U.S. Geological Survey 
 
 6023 Guion Road, Suite 201 
 
 Indianapolis, Indiana 46254 Western Distribution Branch 
 
 U.S. Geological Survey 
 Box 25425, Federal Center 
 Denver, Colorado 80225 
 (Telephone: [303] 234-5888) 
 
CONTENTS 
 
 Page 
 
 Abstract... 1 
 
 Introduction. 2 
 
 Background. 2 
 
 Purpose and scope. 2 
 
 Approach. 3 
 
 Description of technique. 4 
 
 Computer programs used. 4 
 
 One-dimensional, steady-state stream, water quality program. 4 
 
 pH, redox, and equilibrium equations (PHREEQE) program. 6 
 
 Assumptions and modifications of the programs. 6 
 
 Coupling of the programs. 9 
 
 Physical and chemical options of the programs. 12 
 
 Simulations of cumulative impacts of iron and manganese oxidation using 
 
 representative data from a small watershed, southwestern Indiana. 13 
 
 Characteristics of the data. 13 
 
 Simulations with discharges from zero to five coal mines. 16 
 
 Sensitivity analyses. 20 
 
 Summary and conclusions. 25 
 
 Selected references. 27 
 
 ILLUSTRATIONS 
 
 Figure 1. Diagram showing hypothetical inflows and subreaches of a 
 
 receiving stream. 5 
 
 2. Diagram showing interactions of the primary programs. 10 
 
 3. Flowchart of the two primary programs. 11 
 
 4. Graphs of simulated dissolved-iron (II) and dissolved- 
 
 manganese (II) concentrations. 17 
 
 5. Graphs of simulated dissolved-oxygen concentrations and pH.... 18 
 
 6. Graphs showing the sensitivity of the technique to changes 
 
 in chemical parameters. 22 
 
 7. Graphs showing the sensitivity of the technique to changes 
 
 in physical parameters. 23 
 
 8. Graphs showing the sensitivity of the technique to changes 
 
 in kinetic parameters.. 24 
 
 I 
 
 -iii- 
 
TABLES 
 
 Page 
 
 Table 1. Morphometric characteristics of the simulated streams and 
 
 mine discharges. 14 
 
 2. Initial quality and chemical characteristics of the 
 
 simulated streams and mine discharges. 14 
 
 3. Initial solution characteristics and results of the 
 
 hypothetical simulations with from zero to five coal mines 
 discharging at half-mile intervals. 16 
 
 4. Simulated stream characteristics resulting from the 
 
 sensitivity analyses with five coal mines discharging 
 at half-mile intervals. 21 
 
 FACTORS FOR CONVERTING INCH-POUND UNITS TO METRIC 
 (INTERNATIONAL SYSTEM) UNITS 
 
 Multiply inch-pound unit 
 
 by_ 
 
 To obtain Metric units 
 
 foot (ft) 
 
 0.3048 
 
 meter (m) 
 
 square foot (ft 2 ) 
 
 0.0929 
 
 square meter (n£) 
 
 mile (mi) 
 
 1.609 
 
 kilometer (km) 
 
 cubic foot per second (ft 3 /s) 
 
 0.0283 
 
 cubic meter per second 
 
 (m 3 /s) 
 
 To convert degree Fahrenheit (°F) to degree Celsius (°C) 
 
 (0.556) (°F - 32°) = °C 
 
 To convert degree Celsius (°C) to degree Kelvin (°K) 
 
 °C + 273.16 = °K 
 
 USE OF TRADE NAMES 
 
 Use of brand and firm trade names in this report is for identification 
 purposes only and does not constitute endorsement by the U. S. Geological 
 Survey. 
 
 -iv- 
 
THEORETICAL TECHNIQUE FOR PREDICTING THE CUMULATIVE IMPACT 
 OF IRON AND MANGANESE OXIDATION IN STREAMS RECEIVING 
 DISCHARGE FROM COAL MINES 
 
 By Keith E. Bobay 
 
 ABSTRACT 
 
 Two U. S. Geological Survey computer programs are modified and linked to 
 predict the cumulative impact of iron and manganese oxidation in coal-mine 
 discharge water on the dissolved-chemical quality of a receiving stream. The 
 coupled programs calculate the changes in dissolved-iron, dissolved-manganese, 
 and dissolved-oxygen concentrations; alkalinity; and, pH of surface water 
 downstream from the point of discharge. First, the one-dimensional, steady- 
 state stream, water-quality program uses a dissolved-oxygen model to calculate 
 the changes in concentration of elements as a function of the chemical reac¬ 
 tion rates and time-of-travel. Second, a program (PHREEQE) combining pH, 
 reduction-oxidation potential, and equilibrium equations uses an aqueous-ion 
 association model to determine the saturation indices and to calculate pH; it 
 then mixes the discharge with a receiving stream. The kinetic processes of 
 the first program dominate the system, whereas the equilibrium thermodynamics 
 of the second define the limits of the reactions. 
 
 A comprehensive test of the technique was not possible because a complete 
 set of data was unavailable. However, the cumulative impact of representative 
 discharges from several coal mines on stream quality in a small watershed in 
 southwestern Indiana was simulated to illustrate the operation of the tech¬ 
 nique and to determine its sensitivity to changes in physical, chemical, and 
 kinetic parameters. Mine discharges averaged 2 cubic feet per second, with a 
 pH of 6.0, and concentrations of 7.0 milligrams per liter (mg/L) dissolved 
 iron, 4.0 mg/L dissolved manganese, and 8.08 mg/L dissolved oxygen. The 
 receiving stream discharge was 2 cubic feet per second, with a pH of 7.0, and 
 concentrations of 0.1 mg/L dissolved iron, 0.1 mg/L dissolved manganese, and 
 8.70 mg/L dissolved oxygen. Results of the simulations indicated the follow¬ 
 ing cumulative impact on the receiving stream from five discharges as compared 
 with the effect from one discharge: 0.30 unit decrease in pH, 1.82 mg/L 
 increase in dissolved-iron, 1.50 mg/L increase in dissolved-manganese, and 
 0.24 mg/L decrease In dissolved-oxygen concentration. 
 
 -1- 
 
INTRODUCTION 
 
 Background 
 
 The Surface Mining Control and Reclamation Act requires that before a 
 permit to mine is issued, an assessment must "be made by the regulatory au¬ 
 thority of the probable cumulative impacts of all anticipated mining upon the 
 hydrology of the area (Public Law 95-87, 1977, Sec. 507 (b)(ll)) 
 
 The cumulative impact area is defined as "the area in which there would be 
 an interaction between the hydrologic impacts of the proposed mine and all 
 other anticipated mining." (Federal Register, 1983, p. 43957) 
 
 The section on background and legislative intent further states "if any 
 material damage would result to the hydrologic balance from the cumulative 
 impacts of a newly proposed and any previously permitted operation, the new 
 operation could not be permitted." (Federal Register, 1983, p. 43957) 
 
 Therefore, the regulatory authority is required to make a cumulative 
 assessment of every permit, prior to issuance, as to whether material damage 
 will occur. But the regulations and statements of intent allow a wide lati¬ 
 tude and do not specify the analytical technique to make the assessment. 
 Currently, the most common cumulative hydrologic impact assessment (CHIA) 
 performed by regulatory authorities is based on a qualitative analysis. Many 
 assessments simply state 'No Impact' by summing the determinations in the 
 probable hydrologic consequence (PHC) sections of the permit applications 
 (Nadolski and others, 1983, p. 210). 
 
 Purpose and Scope 
 
 This report presents a quantitative, reproducible technique for assessing 
 the cumulative impact on a receiving stream from the oxidation of dissolved 
 ferrous iron and dissolved manganous manganese in coal-mine discharges. The 
 technique predicts dissolved-oxygen, dissolved-iron, dissolved-manganese, and 
 alkalinity concentrations and pH of the receiving stream. Although criteria 
 such as depositional and biological effects, and changes in suspended sediment 
 loads are needed to make a thorough judgment of material damage, the present 
 technique is limited to impacts to the chemistry of the water column. 
 
 The proposed technique does not require chemical equilibrium; it explic¬ 
 itly solves the nonlinear effects of the kinetically modeled oxidation on the 
 general chemistry of the receiving stream. The technique uses two existing 
 public-domain U.S. Geological Survey computer programs, making availability 
 easy to regulatory authorities. Although the technique is theoretically 
 applicable to a wide range of hydrologic settings, simulations were performed 
 with representative data from a small watershed in southwestern Indiana. 
 
 -2- 
 
Approach 
 
 The simple stoichiometry of ferrous iron and manganous manganese oxidation 
 and precipitation forms the basis of this theoretical technique: 
 
 and 
 
 Fe(II) + 1/4 0 2 + 5/2 1L0 = Fe(OH) 3 + 2 H+ 
 
 (Singer and Stumm, 1968, p. 12), 
 
 Mn(II) + 1/2 0 2 + 1^0 = Mn0 2 + 2 H + 
 
 (Hera and Lind, 1983, p. 2037). 
 
 ( 1 ) 
 
 ( 2 ) 
 
 As one mole of Fe(II) is oxidized to Fe(III) and precipitated as ferric 
 hydroxide, one-quarter mole of oxygen is consumed and two moles of hydrogen 
 ion are produced. Similarly, as one mole of Mn(II) is oxidized to Mn(IV) and 
 precipitated as Mn0 2 , one-half mole of oxygen is consumed and two moles of 
 hydrogen ion are produced. 
 
 Therefore, to determine the cumulative impact on a receiving stream as a 
 result of these chemical reactions, the following questions must be addressed: 
 
 1) How many moles of the reduced forms of the metals are 
 
 oxidized, given thermodynamic and kinetic constraints? 
 
 2) How much of the oxygen which has been consumed is 
 
 replaced by reaeration? 
 
 3) Of the total hydrogen ions produced, how many moles are 
 
 free, thus able to reduce pH? 
 
 4) What are the effects from mass balance when two waters 
 
 are combined? 
 
 The kinetics of oxidation and reaeration in the one-dimensional, steady- 
 state stream, water-quality program (Bauer and others, 1979) are combined with 
 the equilibrium thermodynamic, pH, and mass-balance calculations in the 
 PHREEQE (acronym for pH, redox, and equilibrium equations) program (Parkhurst 
 and others, 1980) to simulate the reactions and answer these questions. 
 
 Chapman (1982) constructed a complex program, RIVEQL II, to similarly 
 combine a chemical equilibrium model with a physical transport model which 
 included a pseudo-kinetic treatment of redissolution. However, chemical reac¬ 
 tions other than redissolution of precipitates and dissociation of surface 
 species were treated as equilibrium reactions. Bencala (1983) coupled a phys¬ 
 ical mass transport model and a kinetic model to simulate solute transport 
 processes in a mountain pool-and-riffle stream. This strictly deterministic 
 model was applied primarily to understand the physical and chemical processes 
 in the system. Lumb (1982) presented a procedure for the assessment of cumu¬ 
 lative impacts from coal mining based on a qualitative matrix to determine the 
 magnitude of the impact. Then, techniques ranging from simple mass balance to 
 data-intensive hydrologic models were used to quantify the impacts. 
 
 -3- 
 
The theoretical technique presented here is a more simplified effort which 
 combines many of the physical, chemical, and biological processes into lumped 
 parameters. However, it has the advantage of not requiring intensive data 
 collection. Most chemical and physical parameters are available in coal-mine 
 permit applications (Nadolski and others, 1983, p. 209). Kinetic rates, if 
 not determined empirically, must be estimated from a range of values in the 
 literature. In order to determine the maximum potential damage, a worst case 
 scenario could be represented by fast oxidation and slow reaeration. 
 
 DESCRIPTION OF TECHNIQUE 
 
 Two U. S. Geological Survey computer programs are modified and coupled to 
 perform the calculations in the technique. In addition, 11 subprograms are 
 used to enter and reformat the data, and to perform simple calculations. A 
 Command Procedure Language (CPL) program combines the two primary FORTRAN 
 programs and 11 subprograms into one system. Simplifying assumptions, program 
 options, and program interactions are presented below. 
 
 Computer Programs Used 
 
 One-dimensional, Steady-state Stream, Water-quality Program 
 
 The one-dimensional, steady-state stream, water-quality program predicts 
 the receiving stream response to waste inputs, such as coal-mine discharge or 
 sewage effluent. It calculates the response of dissolved oxygen, biochemical 
 oxygen demand (BOD), nitrogen, phosphorus, coliform bacteria, and three user- 
 defined conservative constituents (Bauer and others, 1979, p. 1). 
 
 The one-dimensional analysis is ideally applied to narrow, low-order 
 streams. Some accuracy is lost when it is used on wide, turbulent rivers. 
 The steady-state assumption requires that the receiving stream is divided into 
 subreaches defined by the location of inflows. Therefore, the flow remains 
 constant through each subreach of the system (Bauer and others, 1979, 
 p. 2-15). 
 
 The framework for this FORTRAN IV program is derived from a dissolved- 
 oxygen (DO) model based on a modified Streeter-Phelps oxygen-sag equation. 
 The DO deficit is calculated as a function of the initial deficit, oxygen 
 sources (atmospheric reaeration and photosynthesis), and oxygen sinks (BOD, 
 algal respiration, and sediment oxygen demand). The deficit is computed for 
 the time-of-travel through each subreach. The DO concentration at any point 
 in the subreach is equal to the saturated DO concentration minus the DO 
 deficit (Bauer and others, 1979, p. 9-11). 
 
 -A- 
 
Figure 1 is a diagram showing the location of three coal-mine discharges 
 into a receiving stream. The discharges are modeled from the sediment ponds 
 to the confluence and then mixed with the stream. The stream is divided into 
 three subreaches (R^ -R 2 , Rg-R^ , Rg-R^); each begins at the confluence with a 
 discharge. The mixed solution is modeled for each subreach. The final solu¬ 
 tion is shown as at an arbitrary point downstream from the last inflow. 
 The mine discharges are assumed to be the only inflows to the stream between 
 Rq and Rg. 
 
 EXPLANATION 
 
 MD Mine discharge 
 
 R 0 Or iginal receiving water 
 
 R-j-q Resulting mixed receiving waters 
 
 Figure 1.-* Hypothetical inflows and subreaches 
 of a receiving stream. 
 
 -5- 
 
pH, Redox, and Equilibrium Equations (PHREEQE) Program 
 
 PHREEQE is a FORTRAN IV computer program designed to simulate geochemical 
 reactions. The program is similar to the Survey’s WATEQ family of programs 
 based on aqueous-ion association models; yet, the functions and capabilities 
 of PHREEQE are much broader and more sophisticated. It can calculate pH, pE, 
 alkalinity, total concentration of elements, amounts of minerals exchanging 
 with aqueous phases, the distribution of aqueous species, and the saturation 
 state of the aqueous phase with respect to specified mineral phases (Parkhurst 
 and others, 1980, p. 1-3). 
 
 The thermodynamic data base of the aqueous model includes 120 aqueous 
 species from 19 elements, and 38 minerals. The model is completely user- 
 definable. The program uses equilibrium equations based on five fundamental 
 concepts: electrical neutrality, conservation of electrons, mass balance, 
 mineral equilibrium, and mass action. Iteration techniques are used to solve 
 a set of nonlinear equations. Several types of reactions can be simulated, 
 including mixing, titration, evaporation, and equilibration. The reactions 
 can also be used in various combinations (Parkhurst and others, 1980, p. 1-7, 
 42). 
 
 Assumptions and Modifications of the Programs 
 
 Specific assumptions are made prior to running either program (PHREEQE or 
 water-quality program). The one-dimensional analysis requires complete mixing 
 of constituents within any cross-section. The steady-state assumption re¬ 
 quires constant flow rate through each subreach. Constant stream morphometry 
 is also assumed through each subreach. Thus, major changes in hydraulic 
 characteristics, stream temperature, or reaction coefficients require a new 
 subreach division (Bauer and others, 1979, p. 1-2). Additional assumptions 
 and modifications to the primary subprograms are made with oxygen sources and 
 sinks, reaction rates, reduction-oxidation potential, nonequilibrium, and 
 kinetic dominance. 
 
 The technique addresses only the reduced states of iron and manganese as 
 the dominant dissolved forms in most natural waters (Hem, 1963, p. A8; Hem 
 and Cropper, 1959, p. 10). Because the technique is concerned with the 
 maximum potential effects from the oxidation of these reduced forms, decreases 
 in concentrations of the metals owing to complexation and adsorption are 
 assumed to be insignificant. As the reduced states are oxidized to iron (III) 
 and manganese (IV) and then precipitated, oxygen is consumed and the pH is 
 lowered. Precipitation of the aqueous phase to the solid phase is modeled in 
 the technique as an equilibrium process. The oxidation and precipitation of 
 iron is shown in two steps (Singer and Stumm, 1968, p. 12): 
 
 Fe(II) + 1/4 0 2 + H + = Fe(III) + 1/2 H 2 0 (oxidation), (3) 
 
 and 
 
 Fe(III) + 3 H 2 0 = Fe(0H) 3 + 3 H+ (precipitation). (4) 
 
 -6- 
 
In the laboratory, Hera and Lind (1983, p. 2037) have shown that the oxida¬ 
 tion of Mn(II) results in the formation of metastable intermediate products* 
 Two possible intermediates are hausmannite (Mn 3 0 4 ) and feitknechtite (BMnOOH). 
 The pyrolusite (Mn0 2 ) end-product results from the disproportionation of the 
 intermediates. The following stoichiometry shows this two-step process for 
 hausmannite: 
 
 3 Mn(II) + 1/2 0 2 + 3 ^0 = Mn 3 0 4 + 6 H + (oxidation), (5) 
 
 and 
 
 Mn 3 0^ + 4 H+ = Mn0 2 + 2 Mn(II) + 2 ^0 (6) 
 
 (disproportionation and precipitation). 
 
 The modified Streeter-Phelps equation in the DO model has been simplified 
 for the technique. The sum of effects from photosynthesis, respiration, sedi¬ 
 ment oxygen demand, and biochemical oxygen demand (BOD) are assumed to be 
 zero. This could occur in a low-order stream receiving little sunlight where 
 a minimum amount of algae and sludge deposits are present. Biochemical oxygen 
 demand is a measure of the dissolved oxygen required by microorganisms in the 
 biochemical oxidation of organic matter. In the theoretical technique, the 
 BOD terms are replaced by ferrous oxygen demand (FOD) and manganous oxygen 
 demand (MOD). The following equation describes the dissolved oxygen sources 
 and sinks: 
 
 dD/dT = - 1/A d(QD) /dx - K a D + 1/4 KfF + 1/2 KJM, 
 
 (7) 
 
 where 
 
 D 
 
 is 
 
 T 
 
 is 
 
 X 
 
 is 
 
 A 
 
 is 
 
 Q 
 
 is 
 
 K 
 
 is 
 
 a 
 
 K f 
 
 K 
 
 is 
 
 is 
 
 m 
 
 F 
 
 is 
 
 M 
 
 is 
 
 and 1/4 
 
 and 
 
 dissolved oxygen deficit, in milligrams per liter; 
 time-of-travel, in days; 
 downstream distance, in feet; 
 cross-sectional area, in square feet; 
 discharge, in cubic feet per second; 
 atmospheric reaeration rate, in day -1 ; 
 ferrous deoxygenation rate, in day -1 ; 
 manganous deoxygenation rate, in day -1 ; 
 
 dissolved-iron (II) concentration, in milligrams per liter; 
 dissolved-manganese (II) concentration, in milligrams per liter; 
 1/2 are the stoichiometric mole ratios from equations 1 and 2. 
 
 At steady-state conditions, dD/dT=0. Upon integration with boundary con¬ 
 ditions, C=C Q (any solute concentration) at x=0, 
 
 D = D 0 (e" K a T ) + 1/4 K f F Q /(K a -K f ) (e" K f T -e _K a T ) 
 
 + 1/2 K m M 0 /(K a -K m ) (e" K m T - e " K a T ). (8) 
 
 This equation is used in the model calculations. It can be simplified to show 
 the effects of FOD and MOD without reaeration by setting K equal to zero: 
 
 D = D q + 1/4 F q (1 - e” K f T ) + 1/2 M Q (1 - e~ K m T ). (9) 
 
 The results of the two equations can be compared to show the relative impor¬ 
 tance of atmospheric reaeration. 
 
 -7- 
 
The theoretical rate of reaction for ferrous iron oxidation can be calculated 
 using values for DO, pH, a constant (kl) from the literature, and adjustment 
 for calibration ( Stumm and Lee, 1961, p. 145; Singer and Stumm, 1970, p. 
 1122; Stumm and Morgan, 1970, p. 534; Sung and Morgan, 1980, p. 562). The 
 following equation defines the kinetic relationship for iron in the pH range 5 
 to 8 (Stumm and Lee, 1961, p. 145): 
 
 -d[Fe(II)]/dT = kl[Fe(II)]p0 2 [0H"1 2 , (10) 
 
 where [] denotes activity, p0 2 is the partial pressure of oxygen, and kl is a 
 constant. 
 
 Equation 10 shows that the reaction rate is first order with respect to 
 the partial pressure of oxygen and second order with respect to the hydroxyl 
 ion activity. Because the pH is directly proportional to the activity of the 
 hydroxyl ion, the reaction rate increases two orders of magnitude for every 
 unit increase in pH. At constant DO and pH, the entire rate becomes first 
 order (Singer and Stumm, 1968, p. 13): 
 
 -d[Fe(II)]/dT = k[Fe(II)]. (11) 
 
 Manganese is not so easily removed from water as iron; the kinetics of 
 the reaction are much slower. Also, the oxidation reaction is much more 
 complex than iron and not fully understood because Mn(II) can be oxidized to 
 Mn(III) or Mn(IV) (Hem, 1963, p. 2, 54). However, the reaction is similarly 
 second-order dependent upon [OH - ] and first-order dependent on Q, (Morgan, 
 1967, p. 606-618; Stumm and Morgan, 1970, p. 536). Manganese has been shown 
 to precipitate with other elements and compounds, but coprecipitation with 
 ferric hydroxide does not normally occur at pH less than 6.7 (Hem, 1963, p. 
 59-61). Although the oxidation of reduced manganese is autocatalytic (Morgan, 
 1967, p. 613-614; Stumm and Morgan, 1970, p. 535), pseudo first-order kinet¬ 
 ics can be assumed if a substantial area of oxide surface is available (Lewis, 
 1976, p. 139-144; Hem, 1981, p. 1373). Because substantial oxidation of Mn 
 (II) does not occur at pH much less than 8.0 (Coughlin and Matsui, 1976, p. 
 108), and in order to simplify the kinetics for the water-quality program, 
 manganese oxidation is assumed to be pseudo first-order in the technique. The 
 rate law takes the same form as iron in equations 10 and 11. 
 
 Whereas substantial oxidation of ferrous iron in natural waters will 
 normally occur in minutes to hours, manganese (II) requires hours to days 
 (Pankow and Morgan, 1981a, p. 1157-1158; Sung and Morgan, 1981, p. 2377). 
 The constant (k) in equation 11 will normally differ one-to-three orders of 
 magnitude between the two metals. 
 
 Reaeration rates can be calculated within the water-quality program or 
 entered directly. Eight reaeration equations, including the Bennett-Rathbun 
 and Tsivoglou-Wallace equations, are available. The user enters the equation 
 number and stream parameters that are required. All reaction coefficients are 
 adjusted for water temperatures other than 20 degrees Celsius (Bauer and 
 others, 1979, p. 14; Terry and others, 1983, p. 49). 
 
 According to Stumm and Lee (1961, p. 144), fifty percent of the acidity in 
 acid-mine drainage originates from the oxidation of ferrous iron. This oxida¬ 
 tion is accompanied by the release of protons (H+) which tend to reduce the pH 
 
 -8- 
 
of the solution. The iron, manganese, and oxygen lost in the reaction are 
 removed from the solution in PHREEQE by a negative reaction. The resulting pH 
 reflects the change owing to oxidation and precipitation as shown in equations 
 1 and 2. 
 
 The concept of reduction-oxidation (redox) potential is addressed in 
 PHREEQE as pE (negative logarithm of the electron activity). The redox condi¬ 
 tions in the initial solution must be specified for PHREEQE calculations to 
 begin (Parkhurst and others, 1980, p. 32). Because the absolute value of the 
 pE is meaningless (Thorstenson, 1984, p. 34-38) and usually unknown, a high 
 positive number is input as pE to indicate nearly saturated oxidation condi¬ 
 tions in flowing waters. Only a relative value is required because dissolved 
 oxygen is explicitly solved in the water-quality program. 
 
 The chemical composition of a solution is influenced significantly by the 
 dissolution and precipitation of mineral phases interacting with the solution. 
 Therefore, the chemical model must be tailored to characterize the particular 
 geologic setting, such as including calcite to reflect the buffering potential 
 of a carbonate bearing terrane. These phase interactions are affected by 
 kinetic processes and geochemical equilibrium. While the equilibrium thermo¬ 
 dynamics determine the direction of the reaction and what the equilibrium 
 concentration will be under given conditions, the kinetics indicate how fast 
 the reaction will proceed or how much time is required. If the kinetics are 
 fast enough, the reaction can be treated as an equilibrium process. If the 
 reaction proceeds at a slow rate, then kinetics is the controlling process 
 (Stumm and Morgan, 1970, p. 12; Hoffman, 1981, p. 352). In the theoretical 
 technique proposed here, the kinetics of the reactions dominate the system and 
 the equilibrium thermodynamics define the limits of the reaction. 
 
 Coupling of the Programs 
 
 A CPL (Command Procedure Language) utility program was written to link the 
 water-quality and PHREEQE programs that form the basis of this technique. The 
 CPL program is currently on the PRIME computer system of the Indiana District 
 of the U. S. Geological Survey. Figure 2 schematically shows the physical 
 interactions of these two programs for three coal-mine discharges. The mine 
 discharge solution (MD) is modeled from the point of discharge (see figure 1) 
 to its confluence with the receiving stream. The water-quality program (Q.W.) 
 calculates downstream values for dissolved oxygen, iron, and manganese. The 
 changes in concentrations are entered into PHREEQE as a negative reaction and 
 removed from solution. The moles of oxygen lost due to ferrous and manganous 
 oxidation (X^q) are calculated in a subprogram. The calculations within 
 PHREEQE are performed as stated in the previous section. The output solution 
 from PHREEQE, including pH, pE, and alkalinity, is combined in a subprogram 
 with the downstream concentrations of dissolved iron, dissolved manganese, and 
 dissolved oxygen from the water-quality program. These solution characteris¬ 
 tics of the discharge channel are mixed in PHREEQE with the solution charac¬ 
 teristics of the receiving stream (R q ). This mixed solution is returned to 
 the water-quality program while treating the total metals as reduced because 
 PHREEQE ’oxidizes' the reduced forms if the solution conditions are oxidizing. 
 
 -9- 
 
This does not affect any characteristic of the solution except the meaningless 
 variable, pE. This solution is entered into the water-quality program and the 
 cycle is repeated. 
 
 R-j-g Resulting mixed receiving waters 
 
 Figure 2.** Interaction of the primary programs. 
 
 In addition to the two primary programs, the CPL program includes three 
 data-entry subprograms and eight data-handling subprograms. The subprogram 
 called PHRQINPT sets up the input file for PHREEQE by prompting the user for 
 parameter values (G.W. Fleming and L.N. Plummer, written commun., 1984). The 
 CPL program includes two other data-entry subprograms to set up the input file 
 for the water-quality program. 
 
 -10- 
 
c 
 
 o 
 
 o 
 
 09 
 
 E 
 
 (0 
 
 9 
 
 CO 
 
 c 
 
 * 
 
 O 
 
 O 
 
 Figure 3.-- Flowchart of the primary programs. 
 
 Figure 3 is a flowchart of the program inputs, outputs, operations, and 
 decisions. As shown in figure 2, the coal-mine discharge (MD) is modeled 
 initially in PHREEQE and the water-quality program. A subprogram accesses the 
 solubility indices in PHREEQE to determine whether precipitation conditions 
 exist (SI > 0) for Fe(0H) 3 A (amorphous) and Mn0 2 • If dissolution conditions 
 exist (SI < 0) or if the calculated concentrations in solution are less than 
 the equilibrium concentrations, then the user must re-enter PHREEQE and obtain 
 the equilibrium value for the species. The concentration in the water-quality 
 program must be replaced by this equilibrium or limiting value before the 
 
 -11- 
 
program can continue. Another data-handling subprogram compares the output 
 from the two primary programs and merges the data into a PHREEQE input file so 
 that the mine-discharge solution can be mixed with the headwater solution 
 (R q ). When the output solutions from the two primary programs are compared, 
 they should be equal, except for dissolved oxygen; PHREEQE only lowers the pE 
 when oxygen is removed. The mixed downstream solution (R) is entered into the 
 programs, modeled over the reach, and mixed with the next mine discharge. 
 This cycle continues until the final downstream solution (R^) is obtained. 
 
 Physical and Chemical Options of the Programs 
 
 The coupling of the programs provides a variety of options for the user. 
 These include the general hydrologic configuration, the types of aqueous 
 species in solution, and the use of different mineral phases as oxidation 
 products. 
 
 A typical hydrologic configuration is shown in figure 1 where three coal¬ 
 mine discharges are modeled. Several discharges or inflows can be included in 
 the model. Any distance between inflows is acceptable as long as the steady- 
 state assumption is not violated. If the hydrologic setting includes two or 
 more watersheds, the watersheds must be modeled separately, and then mixed at 
 the point of confluence. 
 
 Although the technique addresses the kinetics of only ferrous and manga¬ 
 nous oxidation, PHREEQE can solve initial solutions of up to 120 aqueous 
 species. At present, though, the CPL program is capable of treating only two 
 other species as non-conservative, and three species as conservative constit¬ 
 uents chosen by the user. This limitation is imposed by the capacity of the 
 water-quality program's data-input file. A mass-balance approach is used in 
 the program to calculate the downstream concentrations after mixing. There¬ 
 fore, inaccurate results will occur if non-conservative species are input as 
 conservative constituents. 
 
 Thirty-eight mineral phases are available in the pre-constructed PHREEQE 
 data base. Pyrolusite, Mn0 2 , has been added from the data base in WATEQF 
 (Plummer and others, 1976, p. 13, 60) as the final oxidation product of 
 Mn(II). Although intermediate oxidation products from Fe(II) and Mn(II) are 
 possible (eg. MnC0 3 , Mn 3 0 4 , Mn(0H)2» Fe(0H) 2 , Fe 3 0 4 , and FeOOH), pyrolusite 
 and amorphous ferric hydroxide are the most likely oxidation end products. 
 Therefore, their equilibrium thermodynamics are used in the calculations. 
 
 -12- 
 
SIMULATIONS OF CUMULATIVE IMPACTS OF IRON AND MANGANESE OXIDATION USING 
 
 REPRESENTATIVE DATA FROM A SMALL WATERSHED, SOUTHWESTERN INDIANA 
 
 Characteristics of the Data 
 
 The validity of the theoretical technique could not be tested because a 
 complete set of data was not available. However, simulations were run with 
 data representative of a small watershed in southwestern Indiana to illustrate 
 the operation of the technique and to determine its sensitivity to changes in 
 parameters, such as reaction rates, initial water quality, discharge quantity, 
 and distances. 
 
 Stream morphometric characteristics are available from previous studies 
 and topographic maps (Peters, 1981; Renn, 1983). The stream characteristics 
 used in the simulations are shown in table 1. A range of values is given for 
 the receiving-stream data because certain parameters increase in the down¬ 
 stream direction. For example, the quantity of each succeeding stream reach 
 increases by 2.0 cubic feet per second (ft 3 /s) at the confluence with each 
 mine discharge. Coal-mine discharge and receiving-stream data are available 
 from permit applications for many areas in southwestern Indiana (SIECO, Inc., 
 1982, p. 38-40; Geosciences Research Associates, Inc., 1983, p. A3-A4). 
 Commonly collected parameters in permit applications include iron, pH, alka¬ 
 linity, sulfate, total dissolved solids, total suspended solids, and major 
 cations and anions (Nadolski and others, 1983, p. 209). 
 
 The initial quality and chemical characteristics of the coal-mine dis¬ 
 charges and receiving stream used in the simulations are shown in table 2. A 
 range of values is given for the rates of reactions in the receiving stream. 
 The rates decrease downstream as pH and dissolved-oxygen concentration de¬ 
 crease. The remaining receiving-stream data represent the water quality 
 before mixing with the first mine discharge. 
 
 Simulations were run as worst case scenarios; the discharge quality was 
 assumed to be the poorest permissable under the laws. The maximum daily legal 
 discharge concentrations of total iron and total manganese from a coal-mine 
 sediment pond are 7.0 milligrams per liter (mg/L) and 4.0 mg/L, respectively. 
 The pH must remain between 6.0 and 9.0 with minor exceptions (Federal 
 Register, 1982, p. 45395). In order to determine the maximum impact from 
 oxidation, the metals are assumed to be in the reduced, dissolved state. This 
 assumption requires that the original coal-mine discharge be in a state of 
 nonequilibrium. 
 
 -13- 
 
Table 1.—Morphometric characteristics of the simulated streams and mine discharges 
 
 
 
 
 
 
 
 
 rH 
 
 <u 
 
 > 
 
 CO 
 
 )-i 
 
 ^ 4_» ^ 
 
 O 1 1-1 
 
 
 3 
 
 s total 
 
 CO 
 
 6 
 
 c0 
 
 CU 
 
 5-4 
 
 Atmospheric 
 
 reaeration 
 
 rate (day -1 
 
 23.2 
 
 CO 
 
 . 
 
 CM 
 
 CO CM -d 
 
 £ f w 
 
 cu 
 
 e 
 
 •H 
 
 m 
 
 • 
 
 r» h 
 • -d 
 
 m 
 
 . 
 
 CO 
 
 4J 
 
 CO 
 
 TO 
 
 <U 
 
 4-1 
 
 CO 
 
 /—V 
 
 cu CM 
 
 CO o >> 
 
 CU ^-4 co 
 
 C 4-> TO 
 
 c0 co 
 
 CM 
 
 • 
 
 o 
 
 • 
 
 »—H 
 
 <U 
 
 cx 
 
 o 
 
 
 
 E 
 
 •H 
 
 bC TO 
 d *H CU 
 
 $ X t! 
 
 o 
 
 1 
 
 CM 
 
 »— 1 ,d 
 
 0) O W 
 
 o 
 
 m 
 
 in 
 
 o 
 
 CO 
 
 fa O CO 
 
 5-1 
 
 
 • 
 
 CO M-i 
 
 OJ CJV. 
 bC >-i 4J 
 
 CO 14-1 
 
 5-1 14-4 
 
 a) o 
 
 o 
 
 o 
 
 • 
 
 o 
 
 o 
 
 o 
 
 . 
 
 cu 
 
 -C 
 
 4-1 
 
 IM 
 
 O 
 
 CO 
 
 o 
 
 r—4 
 
 c L 
 
 O tn 
 
 C -H CO 
 
 O 4-4 TO 
 
 5-4 CO 
 
 M TO 
 
 o 
 
 • 
 
 o 
 
 - 50.0 
 
 1 cO ^ 
 
 CO CUcM 
 
 CO 5-4 -l- 1 
 
 O cO 144 
 
 
 
 •H 
 
 4-4 
 
 CO 
 
 •H CO 
 
 •H <U 
 
 X •*■> 
 
 O co 
 
 5-1 
 
 
 0 *01 
 
 l-i w 
 
 O 
 
 cO -d 
 
 a; c v 
 bO o ^ 
 
 2.0 
 
 1-12.0 
 
 M ^ 
 
 (U *30 
 
 4-1 >-< 
 
 o CO 
 
 CO -C 
 
 P-/-V 
 
 E O 
 
 CU o 
 
 H 
 
 25.0 
 
 22.0 
 
 co i-i cu 
 
 * V-I 4-» V-I 
 
 <U O 
 
 > <U *4-4 
 
 < CO O 
 
 
 4.0 
 
 5-4 C-) 
 
 CO CO 
 
 O TO 
 
 r— | CU 
 
 >■> 
 
 4-4 
 
 •H CO ^ 
 d CO co 
 •H O 
 
 o 
 
 • 
 
 o 
 
 • 
 
 -d 
 
 4-1 
 
 a 
 
 cu x 
 
 TO o 
 
 
 m 
 
 c0 d 
 o *H 
 •H £ 
 
 E _ 
 
 <U TO 
 
 Alkal 
 
 (mg/L 
 
 CaC 
 
 o 
 
 Id 
 
 o 
 
 in 
 
 rH 
 
 rage 
 f rea 
 (ft) 
 
 0.50 
 
 50-.7 
 
 4- d 
 
 O cO 
 
 TO 
 
 d 
 
 PH 
 
 6.0 
 
 7.0 
 
 0 ) o 
 
 
 • 
 
 
 1—1 N 
 
 eg i-3 
 
 4- ^ 
 
 o 
 
 r— < 
 
 Reach 
 
 length 
 
 (mi) 
 
 o 
 
 in 
 
 50 
 
 •H 
 
 t—i 
 
 c0 
 
 d bC 
 
 s e 
 ‘— 1 
 
 • 
 
 • 
 
 • 
 
 o 
 
 • 
 
 3 
 
 cr 
 
 ,_l 
 
 1-- 
 
 04 hJ 
 
 o 
 
 f—H 
 
 tn 
 
 4J z'-' 
 
 •H CO 
 
 
 o 
 
 • 
 
 CM 
 
 c0 
 
 •H 
 
 4-1 
 
 CU bO 
 
 fa E 
 >—1 
 
 • 
 
 • 
 
 4-) "i 
 d co 
 
 CO J-> 
 
 2.0 
 
 — 
 
 2.0-1 
 
 •H 
 
 3 
 
 M 
 
 1 
 
 1 
 
 Di ssolved 
 oxygen 
 (nig/h) 
 
 00 
 
 o 
 
 . 
 
 o 
 
 r-- 
 
 . 
 
 d 
 
 o 
 
 •H 
 
 cu 
 
 bO 
 
 d 
 
 <U co 
 
 Receiving 
 
 stream 
 
 CM 
 
 <U 
 
 i—! 
 
 00 
 
 00 
 
 4-4 
 
 3 
 
 H 
 
 O 
 
 CO 
 
 c -d 
 
 S CO 
 •H 
 TO 
 
 -d 
 
 CO 
 
 H 
 
 d 
 
 o 
 
 i-i 
 
 4-4 
 
 d 
 
 rH 
 
 Mine 
 
 scharge 
 
 bO 
 
 d 
 
 •H E 
 > co 
 
 •H 0) 
 
 <U 5-4 
 
 O 4-4 
 
 
 
 
 
 o 
 
 CO 
 
 •H 
 
 T3 
 
 CU CO 
 fa 
 
 -14- 
 
The reaction rate for iron was calculated by means of equation 10. At 25 
 degrees Celsius, pH of 6, 8.08 mg/L dissolved oxygen (saturation), and kl of 
 14 (±5) x 10 13 (L 2 mole -2 atm -1 min -1 ) (Stumm and Lee, 1961, p. 145; Singer and 
 Stumm, 1968, p. 13; Stumm and Morgan, 1970, p. 534), the iron reaction rate 
 for the mine discharge is approximately 10 per day. In the case of manganese, 
 however, similar reaction constants are not available for pseudo first-order 
 rates. Instead, reaction rates measured in near-neutral waters were obtained 
 from the literature. Reported values for pseudo first-order reaction rates 
 range from 0.7 to 0.9 per day (Lewis, 1976, p. 152; Hera, 1981, p. 1373). 
 These rates were adjusted in the simulations owing to differences in pH and 
 temperature. At pH 6.5 and 23.5 degrees, a value of 1.0 per day was assigned 
 to k. At pH 6.0 and 25 degrees, a value of 0.2 per day was used in the simu¬ 
 lations. The Tsivoglou-Wallace equation was used to calculate the atmospheric 
 reaeration rate (Bauer and others, 1979, p. 17; Terry and others, 1983, p. 
 49). The rate for the mine discharge is 23.2 per day. The reaeration rate 
 for the receiving stream is an order of magnitude less owing to the difference 
 in slope. 
 
 The maximum effect from the complete oxidation and precipitation of 7 mg/L 
 dissolved ferrous iron and 4 mg/L dissolved manganous manganese can be calcu¬ 
 lated using the stoichiometry in equations 1 and 2. First, the units are 
 converted to moles per liter (M): 
 
 7 mg/L Fe(II)/55847(mg/mole) = 1.25 x 1(T 4 M Fe(II), (12) 
 
 and 4 mg/L Mn(II)/54938(mg/mole) = 7.28 x 10” 5 M Mn(II). (13) 
 
 Then, to determine the amount of oxygen consumed as a result of the complete 
 oxidation, the mole ratios must be introduced: 
 
 1.25 x 1CT 4 M Fe(II) x 1/4 = 3.13 x 1CT 5 M 0 2 , (14) 
 
 and 7.28 x 10" 5 M Mn(II) x 1/2 = 3.64 x 1CT 5 M 0 2 . (15) 
 
 Therefore, the concentration of dissolved oxygen depleted owing to the com¬ 
 plete oxidation of 7 mg/L Fe(II) and 4 mg/L Mn(II) is 6.77 x 10 -5 moles/L or 
 2.17 mg/L. It is interesting to note that the dissolved manganese has a 
 greater potential for depleting the oxygen than does dissolved iron. 
 
 Similarly, to determine the amount of hydrogen ions produced as a result 
 of the complete oxidation and precipitation of the iron and manganese, differ¬ 
 ent mole ratios are applied: 
 
 1.25 x 10 -4 M Fe(II) x 2 = 2.50 x 10" 4 M H+, (16) 
 and 7.28 x 10 -5 M Mn(II) x 2 = 1.46 x 10 -4 M H + . (17) 
 
 Therefore, 3.96 x 10” 4 moles/L hydrogen ions are produced. In a dilute solu¬ 
 tion with no buffering capacity, these would all be free protons resulting in 
 a pH of 3.40. 
 
 However, complete oxidation of the reduced forms may or may not occur in 
 natural waters. As stated earlier, other factors, such as kinetics, thermo¬ 
 dynamics, reaeration, buffering capacity, and mass balance are included in the 
 theoretical technique to determine the cumulative impact of iron and manganese 
 oxidation on the receiving stream. 
 
 -15- 
 
Simulations With Discharges from Zero to Five Coal Mines 
 
 The coal-mine water was modeled from its point of discharge to its mouth 
 one-half mile downstream. The solution characteristics are shown in table 3 
 as the original mine discharge and discharge at the mouth. As shown in the 
 table, very little change occurred over the reach because not enough time was 
 available for the reactions to proceed. Dissolved-oxygen concentration de¬ 
 creased 0.10 mg/L and dissolved-iron concentration decreased 0.99 mg/L. These 
 solution characteristics were used for all of the mine discharges in the sub¬ 
 sequent simulations. 
 
 Table 3.—Initial solution characteristics and results of the hypothetical 
 simulations with from zero to five coal mines discharging at half-mile 
 
 intervals 1 
 
 Number of 
 discharges 
 
 Dissolved 
 
 oxygen 2 
 
 Di ssolved 
 iron (II) 
 
 Dissolved 
 manganese (II) 
 
 pH 
 
 Alkalinity 
 as CaC0 3 
 
 Temp 
 
 (°C) 
 
 Discharge 
 (ft 3 /s) 
 
 0 
 
 8.64 
 
 0.001 
 
 0.09 
 
 7.00 
 
 150 
 
 22.0 
 
 2 
 
 1 
 
 7.96 
 
 .004 
 
 1.76 
 
 6.42 
 
 101 
 
 23.5 
 
 4 
 
 2 
 
 7.74 
 
 .11 
 
 2.49 
 
 6.26 
 
 86 
 
 24.0 
 
 6 
 
 3 
 
 7.69 
 
 .60 
 
 2.87 
 
 6.19 
 
 78 
 
 24.2 
 
 8 
 
 4 
 
 7.70 
 
 1.30 
 
 3.11 
 
 6.15 
 
 74 
 
 24.4 
 
 10 
 
 5 
 
 7.72 
 
 1.82 
 
 3.26 
 
 6.12 
 
 71 
 
 24.5 
 
 12 
 
 Original 
 
 receiving 
 
 stream (Rq) 8.70 
 
 .10 
 
 .10 
 
 7.00 
 
 150 
 
 22.0 
 
 2 
 
 Original 
 
 mine 
 
 discharge 
 
 8.08 
 
 7.00 
 
 4.00 
 
 6.00 
 
 60 
 
 25.0 
 
 2 
 
 Mine 
 
 discharge 
 
 at mouth 
 
 7.98 
 
 6.01 
 
 3.99 
 
 5.99 
 
 59 
 
 25.0 
 
 2 
 
 Results are shown for the furthest downstream point for 0-5 discharges 
 (RM 0.0 in figures 6, 7, and 8). 
 
 2 A11 units in milligrams per liter unless otherwise specified. 
 
 -16- 
 
The oxidation of iron and manganese in a stream not receiving coal-mine 
 discharge was simulated to establish baseline water quality. The stream was 
 modeled under steady-state conditions for 2.5 miles. Downstream water quality 
 is summarized in table 3 and in figures 4 and 5. As shown in the figures, 
 very little change occurs over the reach. Compared to the original receiving- 
 stream quality in table 3, dissolved iron decreased 0.099 mg/L to equilibrium, 
 dissolved manganese decreased 0.01 mg/L, dissolved-oxygen concentration 
 remained near saturation, and the pH remained at 7.00. 
 
 < 
 a: 
 
 o 
 
 2 
 
 O 
 
 o 
 
 RIVER MILE 
 
 EXPLANATION 
 
 X Zero coal-mine discharges A One coal-mine discharge 
 
 O Two coal-mine discharges V Three coal-mine discharges 
 
 O Four coal-mine discharges □ Five coal-mine discharges 
 
 Figure 4. — Simulated cumulative impact of iron and manganese 
 oxidation on concentrations of dissolved iron (II) and dissolved 
 manganese (II) in streams receiving discharge from zero—to- 
 five coal mines at half-mile intervals. 
 
 -17- 
 
z* 
 
 o 
 
 < 
 
 ce 
 
 LxJ 
 
 O 
 
 Z 
 
 o 
 
 o 
 
 o 
 
 o 
 
 RIVER MILE 
 
 EXPLANATION 
 
 X Zero coal-mine discharges A One coal-mine discharge 
 
 O Two coal-mine discharges V Three coal-mine discharges 
 
 O Four coal-mine discharges □ Five coal-mine discharges 
 
 Figure 6. -- Simulated cumulative impact of iron and manganese 
 oxidation on concentrations of dissolved oxygen (DO) and pH 
 in streams receiving discharge from zero—to—five coal mines 
 at half-mile intervals. 
 
 Simulations were run to determine the effect on a stream receiving 
 identical discharges from one to five coal mines. The discharges flowed into 
 the stream beginning at river mile (RM) 2.5 and at half-mile intervals there¬ 
 after, depending on the number of coal mines modeled. For example, with three 
 coal mines, discharges would enter the receiving stream at RM 2.5, RM 2.0, and 
 RM 1.5, then the stream would be modeled under steady-state conditions to 
 
 -18- 
 
RM 0.0. Results at the furthest downstream point are shown in table 3 and in 
 figures 4 and 5. After the initial rises from mixing, a logarithmic decay of 
 dissolved iron is shown in figure 4 for each of the simulations. Dissolved 
 manganese increases initially upon mixing, then decreases linearly owing to 
 the extremely slow kinetics. The first discharge accounts for 53 percent of 
 the total increase in dissolved manganese between the initial concentration 
 and the concentration resulting from five discharges. 
 
 The dissolved-oxygen concentration at the upstream site (R Q ) drops 
 sharply after mixing with the first mine discharge at RM 2.5, then slowly 
 decreases as the oxygen is lost to FOD and MOD. The results obtained from 
 simulating one discharge is unique; oxygen concentration begins to increase 
 after RM 1.5. Reaeration is greater than oxidation because almost all of the 
 iron has been oxidized and very little MOD has taken place. The first dis¬ 
 charge accounts for 74 percent of the total decrease in dissolved oxygen be¬ 
 tween zero and five coal-mine discharges. The remaining four discharges 
 account for only 26 percent of the decrease at RM 0.0 • Similar results are 
 shown for the pH. The first discharge accounts for nearly two-thirds of the 
 total decrease in pH. 
 
 In general, the curves show that for relatively conservative species 
 (Mn(II)), as well as oxygen and pH, the cumulative impacts of iron and manga¬ 
 nese oxidation from additional discharges is degressive. That is, as more 
 coal mines discharge to a receiving stream, the incremental change in concen¬ 
 tration at a point downstream becomes less. In these simulations, the first 
 discharge accounted for 50 to 75 percent of the change in concentration. For 
 reactive species, such as dissolved ferrous iron, the first few discharges may 
 result in equilibrium concentrations at the furthest downstream point (RM 
 0.0), depending on the magnitude of the oxidation rate. Additional discharges 
 increase the downstream concentration in fairly uniform increments once equi¬ 
 librium is achieved. 
 
 Comparing the downstream values from only one coal-mine discharge with the 
 values from five discharges shows that dissolved iron increased 1.82 mg/L, 
 dissolved manganese increased 1.50 mg/L, dissolved-oxygen concentration de¬ 
 creased 0.24 mg/L, and pH decreased 0.30 units. Compared with the baseline 
 simulation, dissolved iron from five discharges increased the same, 1.82 mg/L, 
 whereas, dissolved manganese increased 3.17 mg/L, dissolved-oxygen concentra¬ 
 tion decreased 0.92 mg/L, and pH decreased 0.88 units. 
 
 Comparing the downstream values from five discharges with the representa¬ 
 tive mine discharge characteristics in table 3 shows that nearly 75 percent of 
 the dissolved ferrous iron from all five discharges oxidized to ferric iron 
 and precipitated theoretically. Only 19 percent of the dissolved manganese 
 (II) oxidized. Therefore, manganese builds up in the receiving stream. 
 
 - 19 - 
 
Sensitivity Analyses 
 
 Several simulations were run in order to determine the sensitivity of the 
 technique to changes in parameter values. The simulations were grouped 
 according to the parameter types: chemical, physical, and kinetic. Results 
 of these simulations are shown in table 4 and in figures 6, 7, and 8. All of 
 these simulations were run with five coal mines discharging into the receiving 
 stream and, therefore, can be compared to the original simulation with five 
 discharges. The pH is relatively insensitive to the parameter changes shown, 
 except alkalinity and dilution. Therefore, pH has not been included in the 
 figures. 
 
 Effects from varying certain chemical parameters are shown in table 4 and 
 in figure 6. Dissolved-oxygen concentration in the discharge was set to 0.0 
 mg/L in one simulation. Consequently, the oxidation rate was initialized at 0 
 per day, then gradually increased as oxygen was produced from reaeration. 
 This anaerobic state could result from discharges originating at or near the 
 bottom of a stagnant sedimentation pond. Dissolved-iron concentration was 
 thirty percent greater as a result of the low oxygen and the slow oxidation. 
 Dissolved oxygen was 2.65 mg/L lower at RM 0.0 than the original simulation 
 (see table 4) owing to the lower initial concentrations and less FOD and MOD. 
 This is a significant decrease in oxygen in the receiving stream and implies 
 that these discharges should be aerated. Oxygen concentrations could be 
 increased by installing splash blocks to aerate the solution below the point 
 of discharge or by discharging from the pond surface. 
 
 The regulated 30-day averages for total iron and total manganese (3.5 mg/L 
 and 2.0 mg/L, respectively) were input as discharge concentrations (Federal 
 Register, 1982, p. 45395). As shown in table 4, values at RM 0.0 are 0.91 
 mg/L and 1.63 mg/L, respectively, or exactly half of the final concentrations 
 in the original simulation. In the next simulation, the alkalinities of the 
 discharge and the receiving stream were decreased an order of magnitude. 
 Although the equilibrium concentrations of iron (II) and manganese (II) are 
 normally affected by the alkalinity of a solution, the simulated iron and 
 manganese concentrations at RM 0.0 did not change. The pH of the stream 
 dropped from 6.12 to 5.74 as a result of the reduced capacity of the stream to 
 buffer the increased hydrogen ion activity. 
 
 The amount of discharge and the distance were varied as the physical 
 parameters of the sensitivity analyses. Additionally, a simple mass balance 
 was calculated and included in figure 7. In the first simulation, the results 
 for the reactive species, dissolved iron, are much higher because mass balance 
 treats all elements as strictly conservative. The mass balance approximation 
 for a relatively conservative species, such as dissolved manganese, is fairly 
 accurate. Results for dissolved oxygen are only 0.46 mg/L greater (see table 
 4). Although not shown, the pH is within one percent of the value produced 
 with the theoretical technique. 
 
 The receiving stream was increased to 20 ft 3 /s in the next simulation. 
 The iron and manganese concentrations in figure 7 show the effects from this 
 dilution. The oxidation rates in the receiving stream were increased as a 
 
 - 20 - 
 
result of the higher pH and oxygen concentration. At RM 0.0, the dissolved- 
 iron concentration is near equilibrium, whereas dissolved manganese is less 
 than one-third of the concentration of the original simulation. 
 
 The distance from the point of discharge to the receiving stream (see 
 figure 1) was decreased from 0.5 miles to 0.05 miles or 264 feet. Very little 
 change is seen in the results at RM 0.0. Coal-mine discharges were located at 
 0.1 mile intervals instead of 0.5 miles in the next simulation. As shown in 
 figure 7, the increase in dissolved iron and dissolved manganese in the first 
 half-mile was very large. But after reaching a peak concentration of 4.09 
 mg/L, the iron decreased to a value 0.69 mg/L below the original simulation 
 owing to the long time-of-travel available for oxidation. Manganese concen¬ 
 trations peaked after the last discharge at RM 2.1, then oxidized very slowly 
 and decreased nearly to the original concentration. 
 
 Table 4.—Simulated stream characteristics resulting from the sensitivity 
 analyses with five coal mines discharging at half-mile intervals 1 
 
 Parameter changes 
 
 Dissolved 
 
 oxygen 2 
 
 Di ssolved 
 iron (II) 
 
 Di ssolved 
 manganese (II) 
 
 PH 
 
 Alkalinity 
 as CaC0 3 
 
 Original simulation 
 
 7.72 
 
 1.82 
 
 3.26 
 
 6.12 
 
 71 
 
 D0=0.0 mg/L 3 
 
 5.07 
 
 2.37 
 
 3.28 
 
 6.13 
 
 72 
 
 Fe=3.5 mg/L; Mn=2.0 mg/L 3 
 
 7.95 
 
 .91 
 
 1.63 
 
 6.14 
 
 73 
 
 Alkalinity decreased 10X 
 
 7.72 
 
 1.82 
 
 3.25 
 
 5.74 
 
 4 
 
 Flow at Rq= 20 cfs 
 
 8.13 
 
 .03 
 
 1.05 
 
 6.58 
 
 117 
 
 Distance=0.05 miles 3 
 
 7.71 
 
 2.09 
 
 3.25 
 
 6.12 
 
 71 
 
 Discharge interval=0.1 mile 
 
 7.66 
 
 1.13 
 
 3.24 
 
 6.11 
 
 71 
 
 Mass balance 
 
 8.18 
 
 5.85 
 
 3.35 
 
 6.17 
 
 75 
 
 Oxidation rate decrease 10X 
 
 8.10 
 
 5.02 
 
 3.34 
 
 6.15 
 
 74 
 
 Oxidation rate increase 10X 
 
 7.48 
 
 .01 
 
 2.49 
 
 6.09 
 
 68 
 
 Reaeration rate decrease 10X 
 
 7.59 
 
 1.82 
 
 3.26 
 
 6.12 
 
 71 
 
 Reaeration rate increase 10X 
 
 8.08 
 
 1.82 
 
 3.26 
 
 6.12 
 
 71 
 
 Results are shown for the furthest downstream point (RM 0.0 in figures 6, 7, 
 and 8). 
 
 2 A11 units are in milligrams per liter except pH. 
 
 3 These parameter changes pertain to the coal-mine discharge only. 
 
 - 21 - 
 
GC 
 
 Ul 
 
 h; 
 
 2 - 1 
 o a: 
 
 lZ Uf 
 £ °- 
 Od V) 
 
 £ 1 
 
 Ui 
 
 o 
 
 ad 
 
 o 3 
 a — 
 
 o 2 
 
 Q 2 
 
 or 
 
 £ " 
 2 z? 
 
 < a: 
 
 £ £ 
 
 Ul 
 
 o 
 
 </) 
 
 < 
 
 o § 
 a —, 
 
 £ 2 
 
 . a: 
 
 11 
 
 * * 
 ad lu 
 
 h- a. 
 
 u W 
 O 2 
 
 z < 
 o 
 
 o 2 
 
 c 
 
 2 2 
 
 9.0 
 
 8.0 - 
 
 7.0 - 
 
 <2 6.0 - 
 
 5.0 
 
 4.0 
 
 3.0 - 
 
 2.0 - 
 
 1.0 - 
 
 0.0 
 
 RIVER MILE 
 
 EXPLANATION 
 
 □ Original simulation O Alkalinity decreased by 10X 
 
 A Fe= 3.5 mg/L; Mn = 2.0 mg/L at point of discharge 
 X Dissolved oxygen = 0.0 mg/L at point of discharge 
 
 Figure 8. -- Results of the chemical sensitivity analyses on 
 concentrations of dissolved oxygen (DO), dissolved iron (II), 
 and dissolved manganese (II) in streams receiving discharge 
 from five coal mines at half-mile intervals. 
 
 - 22 - 
 
an 
 
 LlJ 
 
 2 - 1 
 o an 
 
 an (/) 
 
 o 
 
 < 
 
 an 
 
 o 
 
 o ^ 
 o — 
 
 o 2 
 
 Q 2 
 
 OC 
 
 t “ 
 
 9 . =i 
 < an 
 £ £ 
 3 3 
 2 < 
 8 § 
 
 )( ^*~*H*K - - X K 
 
 □ Original Simulation 
 A Distance = .05 miles 
 O Mass balance 
 
 RIVER MILE 
 
 EXPLANATION 
 
 X Flow at Ro = 20 cfs 
 O Discharges at 0.1 mile intervals 
 
 Figure 7. -- Results of the physical sensitivity analyses on 
 concentrations of dissolved oxygen (DO), dissolved iron (II), 
 and dissolved manganese (II) in streams receiving discharge 
 from five coal mines at half-mile intervals. 
 
 - 23 - 
 
< 
 
 or 
 
 Ld 
 
 o 
 
 o 
 
 o 
 
 o 
 
 Q 
 
 < 
 
 a: 
 
 UJ 
 
 o 
 
 o 
 
 o 
 
 RIVER MILE 
 
 EXPLANATION 
 
 □ Original simulation X Oxidation rate decrease by 10X 
 
 A Oxidation rate increase by 10X O Reaeration rate decrease by 10X 
 O Reaeration rate increase by 10X 
 
 Figure 8. — Results of the kinetic sensitivity analyses on 
 concentrations of dissolved oxygen (DO), dissolved iron (II), 
 and dissolved manganese (II) in streams receiving discharge 
 from five coal mines at half-mile intervals. 
 
 - 24 - 
 
The oxidation and reaeration rates were varied by an order of magnitude in 
 the final group of sensitivity analyses. The ferrous and manganous oxidation 
 rates were decreased by a factor of 10 in the first of these simulations. The 
 results in figure 8 show dissolved iron as a fairly conservative species with 
 little oxidation taking place. The final concentration is 3.20 mg/L greater 
 than the original simulation (see table 4). When the rates were increased an 
 order of magnitude, the dissolved iron decreased nearly to the equilibrium 
 concentration. Dissolved manganese decreased approximately 25 percent com¬ 
 pared with the original simulation. Iron and manganese concentrations were 
 not affected by changes in the reaeration rate. Increased reaeration and 
 decreased oxidation rates resulted in similar dissolved-oxygen concentrations 
 at RM 0.0. Increased oxidation and decreased reaeration also resulted in 
 similar oxygen concentrations. In these simulations though, the net change in 
 dissolved oxygen was less than 0.4 mg/L. 
 
 In summary, iron oxidation rate, dilution, and low initial concentrations 
 of the dissolved constituents in the mine water had the most pronounced effect 
 on stream quality at RM 0.0. Dissolved iron was fairly sensitive to direct 
 changes in the oxidation rate and indirectly through decreased oxygen concen¬ 
 trations. Changes in the reaeration rate had a negligible effect on all down¬ 
 stream constituents. As long as some oxygen was available, iron and manganese 
 were not affected. Mass balance calculations gave a good approximation for 
 concentrations of oxygen and manganese. pH was relatively insensitive to 
 parameter changes. 
 
 SUMMARY AND CONCLUSIONS 
 
 A theoretical technique is proposed for predicting the maximum cumulative 
 impact from the oxidation of iron and manganese on the dissolved-chemical 
 quality of streams receiving discharge from coal mines. Regulatory agencies 
 are required to consider the probable cumulative impact of anticipated coal 
 mining before granting a permit. Although this includes chemical, physical, 
 and biological impacts on the hydrology of the area, the technique is limited 
 to the theoretical chemical effects of iron and manganese oxidation. 
 
 The technique is based on the stoichiometry of ferrous iron and manganous 
 manganese oxidation and precipitation. As one mole of Fe (II) is converted to 
 Fe (III) and as one mole of Mn (II) is converted to Mn (IV), three-quarters of 
 one mole of oxygen is consumed and four moles of hydrogen ion are produced. 
 The amount of metals oxidized and precipitated, the effects on pH and dis¬ 
 solved oxygen, and the changes in concentration of elements owing to mass 
 balance and chemical reactions are calculated in the technique. 
 
 A coupling program dynamically links two existing U. S. Geological Survey 
 computer programs: the one-dimensional, steady-state stream, water-quality 
 program and the pH, redox, and equilibrium equations (PHREEQE) program. The 
 water-quality program calculates concentration changes in iron, manganese, and 
 dissolved oxygen as a function of reaction rates and time-of-travel. PHREEQE 
 simulates geochemical reactions; calculates saturation indices, alkalinity, 
 and pH; and mixes two solutions. The reaction kinetics drive the system, 
 whereas thermodynamics provide the limiting situation. 
 
 - 25 - 
 
Although data were not available to test the technique, simulations with 
 data representative of southwestern Indiana were run to illustrate the opera¬ 
 tion of the technique and to determine its sensitivity to changes in chemical, 
 physical, and kinetic parameters. The theoretical impact on streams receiving 
 identical discharges from zero to five coal mines was simulated. Results 
 showed that the discharge from the first coal mine accounted for 50 to 75 
 percent of the total changes in pH, dissolved oxygen, and dissolved manganese 
 for the entire system of five coal mines. For dissolved iron, additional 
 discharges resulted in fairly uniform increases above equilibrium in concen¬ 
 trations downstream. Comparing the results from five coal-mine discharges 
 with the ambient water quality shows a decrease of almost 1 rag/L in dissolved 
 oxygen and 1 pH unit due to ferrous and manganous oxidation and mass balance. 
 
 In general, the simulations showed that the oxidation of the maximum legal 
 concentrations of iron and manganese (assuming the reduced, dissolved state) 
 in the discharge from five coal mines does not have a dramatic cumulative 
 impact on downstream concentrations of dissolved oxygen or pH. Enough oxygen 
 is transferred into solution as a result of atmospheric reaeration to offset 
 most of the oxygen lost to ferrous and manganous oxidation. The carbonate 
 system in solution provides enough alkalinity to minimize pH effects. Approx¬ 
 imately 75 percent of the ferrous iron in the mine discharge oxidized to 
 ferric iron and precipitated theoretically as amorphous ferric hydroxide. On 
 the other hand, over 80 percent of the dissolved manganese remained in solu¬ 
 tion as a result of the slow kinetics. Therefore, manganese builds up in the 
 receiving stream. 
 
 The technique is most sensitive to changes in iron oxidation rate, amount 
 of flow in the receiving stream, and low initial constituent concentrations in 
 the mine discharge. Changes in atmospheric reaeration rate had a negligible 
 effect on water quality at RM 0.0 because oxygen was never limiting. Mass 
 balance approximations for dissolved oxygen and dissolved manganese were close 
 to the original results of the simulations. pH was relatively insensitive to 
 changes in parameters. 
 
 This theoretical technique is readily available and is flexible enough to 
 be used by any regulatory agency. Although the technique is presented on a 
 theoretical basis, reasonable results have been produced with various 
 simulations. However, validation is required in order to apply the technique 
 to real systems. This should be accomplished in subsequent work. 
 
 - 26 - 
 
SELECTED REFERENCES 
 
 Bauer, D. P. , Jennings, M. E. , and Miller, J. E. , 1979, One-dimensional, 
 steady-state stream, water-quality model: U.S. Geological Survey Water 
 
 Resources Investigations Report 79-45, 219 p. 
 
 Bencala, K. E., 1983j Simulation of solute transport in a mountain pool-and- 
 riffle stream with a kinetic mass transfer model for sorption: Water 
 
 Resources Research, v. 19, no. 3, p. 732-738. 
 
 Chapman, B. M., 1982, Numerical simulation of the transport and speciation of 
 nonconservative chemical reactants in rivers: Water Resources Research, 
 v. 18, no. 1, p. 155-167. 
 
 Coughlin, R. W., and Matsui, Iwao, 1976, Catalytic oxidation of aqueous 
 Mn(II): Journal of Catalysis, v. 14, p. 108-123. 
 
 Diem, Dieter and Stumm, Werner, 1984, Is dissolved Mn +2 being oxidized by 0 2 
 in the absence of Mn-bacteria or surface catalysts?: Geochimica et 
 
 Cosmochimica Acta, v. 48, no. 7, p. 1571-1573. 
 
 Federal Register, 1982, Coal mining point source category; Effluent limita¬ 
 tions guidelines for existing sources and standards of performance for new 
 sources; Final rule: U.S. Environmental Protection Agency, Wednesday, 
 
 October 13, 1982, v. 147, no. 198, p. 45382-45399. 
 
 Federal Register, 1983, Surface coal mining and reclamation operations; Per¬ 
 manent regulatory program hydrology permitting and performance stan¬ 
 dards; Geology permitting: U.S. Department of Interior, Office of Surface 
 Mining Reclamation and Enforcement, Monday, September 26, 1983, v. 48, no. 
 187, p. 43956-43985. 
 
 Geosciences Research Associates, Inc., 1983, Final report, Part A: Determina¬ 
 tion of probable hydrologic consequences for J, H & L Coal Co., Inc., Vigo 
 County, Indiana Permit No. S-00086: Bloomington, IN. 
 
 Hem, J. D., 1963, Chemical equilibria and rates of manganese oxidation: U.S. 
 
 Geological Survey Water-Supply Paper 1667-A, 64 p. 
 
 - 1964, Deposition and solution of manganese oxides: U.S. Geological 
 
 Survey Water-Supply Paper 1667-B, 42 p. 
 
 - 1981, Rates of manganese oxidation in aqueous systems: Geochimica et 
 
 Cosmochimica Acta, v. 45, no. 8, p. 1369-1374. 
 
 Hem, J. D. , and Cropper, W. H. , 1959, Survey of ferrous-ferric chemical 
 
 equilibria and redox potential: U.S. Geological Survey Water-Supply Paper 
 1459A, 30 p. 
 
 Hem, J. D. , and Lind, C. J., 1983, Nonequilibrium models for predicting forms 
 of precipitated manganese oxides: Geochimica et Cosmochimica Acta, v. 47, 
 no. 11, p. 2037-2046. 
 
 - 27 - 
 
SELECTED REFERENCES—Continued 
 
 Hoffman, M. R., 1981, Thermodynamic, kinetic, and extrathermodynamic consid¬ 
 
 erations in the development of equilibrium models for aquatic systems: 
 Environmental Science and Technology, v. 15, no. 3, p. 345-353. 
 
 Jaynes, D. B., Ragowski, A. S., and Pionke, H. B., 1984, Acid mine drainage 
 from reclaimed coal strip mines: 1, Model description: Water Resources 
 
 Research, v. 20, no. 2, p. 233-242. 
 
 Jaynes, D. B., Pionke, H. B., and Ragowski, A. S., 1984, Acid mine drainage 
 from reclaimed coal strip mines: 2, Simulation results of model: Water 
 
 Resources Research v. 20, no. 2, p. 243-250. 
 
 Lewis, D. M., 1976, The Geochemistry of manganese, iron, uranium, lead 210, 
 
 and major ions in the Susquehanna River: PhD Dissertation, Yale Univer¬ 
 sity, New Haven, CT., 272 p. 
 
 Lumb, A. M., 1982, Procedures for assessment of cumulative impacts of surface 
 mining on the hydrologic balance: U.S. Geological Survey Open-File Report 
 82-334, 50 p. 
 
 Morgan, J. J. , 1967, Chemical equilibria and kinetic properties of manganese 
 in natural waters: in Faust, S. D. and Hunter, J. V., eds., Principles 
 
 and applications of water chemistry: New York, Wiley, P. 561-624. 
 
 Nadolski, J. A., Pike, T. J. , and Frickel, D. G. , 1983, Approaches for con¬ 
 ducting cumulative hydrologic impact assessments for surface coal mining 
 operators: Symposium on Surface Mining, Hydrology, Sedimentology, and 
 
 Reclamation, Lexington, Ky., Proceedings, 1983, p. 207-210. 
 
 Pankow, J. F., and Morgan, J. J., 1981a, Kinetics for the aquatic environment: 
 Part I: Environmental Science and Technology, v. 15, no. 10, p. 1155— 
 
 1162. 
 
 - 1981b, Kinetics for the aquatic environment: Part II: Environmental 
 
 Science and Technology, v. 15, no. 11, p. 1306-1313. 
 
 Parkhurst, D. L. , Thorstenson, D. C., and Plummer, L. N., 1980, PHREEQE - A 
 computer program for geochemical calculations: U. S. Geological Survey 
 
 Water Resources Investigations Report 80-96, 216 p. 
 
 Peters, J. G. , 1981, Effects of surface mining on water quality in a small 
 
 watershed, Sullivan County, Indiana: U. S. Geological Survey Open-File 
 
 Report 81-543, 61 p.. 
 
 Plummer, L. N. , Jones, B. F., and Truesdell, A. H. , 1976, WATEQF - A FORTRAN 
 IV version of WATEQ, A computer program for calculating chemical equilib¬ 
 rium of natural waters: U.S. Geological Survey Water Resources Investi¬ 
 gations Report 76-13, 61 p. 
 
 - 28 - 
 
SELECTED REFERENCES—Continued 
 
 Public Law 95-87, 1977, Surface raining control and reclamation act of 1977, in 
 United States Statutes at Large 91: Washington, D.C., Government Printing 
 Office, Statute 445. 
 
 Renn, D. E., 1983, Quality of surface water in the coal-mining region. South¬ 
 western Indiana, October 1979 to September 1980: U.S. Geological Survey 
 Open-File Report 83-680, 95 p. 
 
 Singer, P. C. and Stumm, Werner, 1968, Kinetics of the oxidation of ferrous 
 iron: Second Symposium on Coal Mine Drainage Research, Pittsburgh, Pa., 
 
 Proceedings, 1968, p. 12-34. 
 
 - 1970, Acid mine drainage: The rate determining step: Science, v. 167, 
 
 p. 1121-1123. 
 
 Stumm, Werner and Lee, G. F., 1961, Oxygenation of ferrous iron: Industrial 
 and Engineering Chemistry, v. 53, no. 2, p. 143-146. 
 
 Stumm, Werner and Morgan, J. J. , 1970, Aquatic chemistry: New York, Wiley- 
 Interscience, 583 p. 
 
 Sung, Windsor and Morgan, J. J. , 1980, Kinetics and products of ferrous iron 
 oxygenation in aqueous systems: Environmental Science and Technology, v. 
 14, no. 5, p. 561-568. 
 
 - 1981, Oxidative removal of Mn(II) from solutions catalysed by the 
 
 y-FeOOH (lepidocrocite) surface: Geochimica et Cosmochimica Acta, v. 45, 
 p. 2377-2383. 
 
 SIECO, Inc., 1982, Final report, Part A: The determination of probable hydro- 
 logic consequences for J & J Coal Company Inc., Warrick County, Indiana, 
 Permit no., 81-183: Columbus, Ind., 64 p. 
 
 Terry, J. E., Morris E. E. , and Bryant, C. T. , 1983, Water-quality assessment 
 of White River between Lake Sequoyah and Beaver Reservoir, Washington 
 County, Arkansas: U. S. Geological Survey Water Resources Investigations 
 Report 83-4092, 263 p. 
 
 Tetra Tech, Inc., 1985, Rates, constants, and kinetics formulations in surface 
 water quality modeling (2d ed.): Prepared for the Environmental Research 
 Laboratory, U.S. EPA, Athens, Georgia, EPA-600/3-78-105, 335 p. 
 
 Thorstenson, D. C., 1984, The concept of electron activity and its relation to 
 redox potentials in aqueous geochemical systems: U.S. Geological Survey 
 Open-File Report 84-072, 45 p. 
 
 ☆ U.S. GOVERNMENT PRINTING OFFICE: 1986-642-960/728 
 

 
 
 
 
 
 
 
 
 
 
 
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