Development of Simplified Models of Water Quality in Lignite Mining Areas

NOT FOR QUOTATION WITHOUT PERMISSION OF THE AUTHOR

DEXELOPMENT OF SEMPLIETED MODELS OF WATER

QUALITY

IN

LIGNITE MINING

AREAS

L. Luckner J. Hummel R. Fischer S. Kaaen

May 1985 CP-85-26

CoLLaborative P a p e r s r e p o r t work which h a s not been performed solely at t h e International Institute f o r Applied Systems Analysis and which h a s received oniy limited review. Views o r opinions e x p r e s s e d h e r e i n d o not necessarily r e p r e s e n t those of t h e Insti- t u t e , i t s National Member Organizations, o r o t h e r organizations supporting t h e work.

INTERNATIONAL INSTITUTE FOR APPLIED SYSTENS AKALYSIS 2361 Laxenburg, Austria

PREFACE

The Regional Water Poticies p r o j e c t of IIASA focuses on intensively developed regions where both groundwater and s u r f a c e water a r e integrat- ing eiements of t h e environment. Our r e s e a r c h i s d i r e c t e d towards t h e development of methods and models t o s u p p o r t t h e resolution of conflicts within such socio-economic environmental systems. For t h a t r e a s o n compiex decision s u p p o r t model systems a r e under development f o r important test a r e a s . One of t h e s e test a r e a s i s a n open-pit lignite mining area in t h e GDR.

A fundamental presumption f o r t h e development of such systems a r e a p p r o p r i a t e submodels of t h e basic environmental p r o c e s s e s t o be con- sidered. These submodels have t o r e f l e c t t h e p r o c e s s e s sufficiently accu- r a t e l y but should b e on t h e o t h e r hand simple enough f o r t h e i r integration in complex model systems.

The p a p e r deals with water quality processes. I t p r e s e n t s a methodol- ogy f o r t h e development of simplified models with special r e g a r d t o lignite mining areas.

The r e s e a r c h h a s been done in t h e Joint R e s e a r c h Group "Open-pit Mine Dewatering Problems" of t h e Grossr%schen Institute f o r Lignite Mining and t h e Dresden University of Technology. This r e s e a r c h i s p a r t of a colla- borative agreement between IIASA and t h e Institute f o r Water Management in Berlin. This p a p e r i s t h e final r e p o r t f o r t h e second s t a g e of collabora- tion.

Although t h e methodology h a s been developed with special r e g a r d t o open-pit lignite mining areas t h e given a p p r o a c h e s a r e intended t o be more generally applicable.

S e r g e i Orlovski P r o j e c t Leader

Regional Water Policies P r o j e c t

ABSTRACT

The development of complex decision s u p p o r t model systems f o r t h e analysis of regional water policies f o r regions with intense socio-economic development effecting and being a f f e c t e d by t h e water r e s o u r c e s system i s of increasing importance. One of t h e most illustrative examples are regions with open-pit lignite mining.

Such model systems have t o b e based on a p p r o p r i a t e submodels e.g. f o r water quality p r o c e s s e s . The p a p e r d e s c r i b e s submodel f o r groundwater and s u r f a c e water quality with special r e g a r d t o open-pit lignite mining regions.

W e consider t h e d i s c h a r g e of acid f e r r u g i n o u s water into r i v e r s as having t h e most important impact on water quality in open-pit lignite mining areas. One goal of t h e model system is t h e c h o i c e of t h e n e c e s s a r y d e g r e e of purification f o r mine water t r e a t m e n t plants, taking into account self- purification in r i v e r s and remaining p i t s as well as t h e water quality demand of down-stream water u s e r s .

Based on comprehensive water quaiity models, t h e development of which is d e s c r i b e d in t h e p a p e r , t h e possibilities f o r t h e derivation of r e d u c e d models are described. Those model have been e l a b o r a t e d f o r groundwater, as t h e s o u r c e of pollution, mine water treatment plants as c o n t r o l units, r i v e r sections with a n intake of acid f e r r u g i n o u s water, and remaining pits, which c a n a l s o s e r v e as effective c o n t r o l units.

Related with e a c h o t h e r , t h e s e models form t h e complex system model, a system of differential equations. They were numerically solved. The com- p u t e r p r o g r a m i s included in t h e p a p e r .

CONTENTS

1. Introduction

2. Comprehensive Water Quality Models 2.1 Components

2.2 Single P r o c e s s e s 2.2.1 Transportation 2.2.2 S t o r a g e

2.2.3 Reactions 2.2.4 Exchange

2.3 Comprehensive Complex Model 3. Model Reduction

3.1 General Methods

3.2 Submodel "Groundwater"

3.3 Basis of t h e S u r f a c e Water Models 3.4 Submodel "Mine Water Treatment Plant"

3.5 Submodel "River"

3.6 Submodel "Remaining Pit"

4. Complex Model 4.1 Bases

4.2 P r o g r a m Description R e f e r e n c e s

Appendix 1: FEMO

-

Reduced Models f o r Water Quality by Oxida- tion of Fe(I1) in Mine Water Treatment Plants, R i v e r s and Remaining P i t s

Appendix 2: Test Results of t h e Model FEMO

D J W E L O P ~ N T OF SIMPLIFIED MODELS OF WATER

QUALITY

IN LIGNITE MINING AREAS

L. ~ u c k n e r ' , J. ~ u m m e l ' , R. ~ i s c h e r ' a n d S.

ad en^

1.

Introduction

Lignite mining l e a d s t o significant w a t e r quality problems , L u c k n e r a n d Hum- me1 1982. Frequently t h e quality of mine d r a i n a g e w a t e r i s s t r o n g l y a f f e c t e d by t h e oxidation of f e r r o u s d i s u l p h i d e minerals ( p y r i t e , m a r c a s i t e ) in t h e d r a i n e d ground.

This r e s u l t s f r o m t h e a e r a t i o n in t h e subsoil of t h e c o n e of d e p r e s s i o n of o n e or s e v e r a l mines. With t h e r e c h a r g e of t h e n a t u r a l g r o u n d w a t e r , t h e oxidation pro- d u c t s are flushed o u t , a n d t h e p e r c o l a t e d w a t e r becomes v e r y a c i d i c . Conse- quently, t h e a c i d i t y of t h e g r o u n d w a t e r i n c r e a s e s . In t h e post-mining p e r i o d , t h e same e f f e c t o c c u r s c a u s e d by t h e r a i s i n g of t h e g r o u n d w a t e r t a b l e a n d t h e leaching of a l l a c i d p r o d u c t s . Especially t h e pH-value in s p o i l s i s v e r y low, if t h e spoil m a t e r i a l h a s n o t enough n e u t r a l i z a t i o n c a p a c i t y . T h e r e are typically high sulphate-, iron(I1)- a n d p r o t o n - c o n c e n t r a t i o n s in t h e g r o u n d w a t e r in s u c h a r e a s , S t a r k e 1980. The d i s c h a r g e of s u c h polluted mine d r a i n a g e w a t e r i n t o s t r e a m s also l e a d s t o t h e acidification of t h e s e s u r f a c e w a t e r r e s o u r c e s in mining r e g i o n s , a n d may significantly e f f e c t down-stream w a t e r yields, see Kaden et.al. 1985.

The design of w a t e r management policies a n d w a t e r u s e technologies as well as t h a t of mine d r a i n a g e c a n only b e done p r o p e r l y when i t i s based o n a p p r o p r i a t e mathematical models, Kaden a n d L u c k n e r 1984. These models h a v e t o b e built u p as submodels f o r a complex model system; t h i s implies t h a t t h e y h a v e t o b e as simple as possible, Kaden et.al. 1985. On t h e o t h e r hand, t h e y a l s o h a v e t o reflect t h e r e a l w a t e r quality p r o c e s s e s in mining r e g i o n s with t h e r e q u i r e d a c c u r a c y for t h e planned model-supported decision making.

' ) ~ e s e a r c h Croup f o r Open-Pit D e w a t e r i n g Problems o f t h e Crossritschen I n s t i t u t e f o r L i g n i t e Nln- ipg and t h e Dresden U n i v e r s i t y o f Technology

2 t ~ n t e r n a t l o n a l I n s t i t u t e f o r Applied S y s t e m s A n a l y s i s Laxenburg, A u s t r i a

This collaborative p a p e r d e s c r i b e s t h e methodology used t o obtain such sim- plified models of groundwater and s u r f a c e water quality p r o c e s s e s suitable f o r decision s u p p o r t model systems f o r regional water policies in open-pit lignite min- ing a r e a s , based on comprehensive water quality models. This methodology, t o g e t h e r with t h e included modular software package, should also b e applicable t o similar regional studies.

2. Comprehensive Water Quality Models

2.1.

Components

The most comprehensive water quality models a r e t h e s y s t e m s d e s c r i p t i v e models of t h e dynamic water quality p r o c e s s e s in t h e underground with distributed p a r a m e t e r s , s e e Luckner and Mucha 1984. In comparison with water quantity prob- lems (water flow problems), which a r e well-based from t h e methodological point of view, s e e e.g. Kaden et.al. 1985, difficulties of developing groundwater quality models f o r mining regions are tremendous.

The underground, t h e soilwater zone as well as groundwater zone, is a three level m u l t i p h a s e s y s t e m (see Luckner and Schestakow, 1986):

The components of t h e mixed phases "soilair", "soilwater o r groundwater", and "soil o r r o c k " a r e in t h e lowest level. Under t h i s consideration, t h e mixed phase "soilair" i s composed of t h e gaseous components N 2 , 0 2 , C 0 2 , Ar, HzO, SO2,

.. . .

One considers t h e main component of t h e a i r (nitrogen N 2 ) as t h e solvent and t h e o t h e r components as solutes. The same situation i s given f o r t h e mixed phase

"groundwater". H e r e water i s t h e solvent, and t h e cations (e.g. H), ~e 2 + , CU"

+,....),

anions (e.g. SO:-,

SO^'-,

CL-, HCO;, ~ 0 : - , O H

,...

), gases (e.g. 0 2 , C 0 2 , k t

,...

^),

complexes and suspended gaseous, liquid o r solid p a r t i c l e s a r e t h e solutes. One can a l s o consider t h e r o c k material in a similar way. In t h e loose-rock clay e.g. t h e SiO,

-

t e t r a h e d r o n s and AL(OH),

-

octahedrons a r e t h e solvents, in which t h e cations and anions a r e embedded (dispersed) as solutes.

Those solvents at t h e c e n t e r of o u r consideration a r e called " m i g r a n t s " . A migrant, t h e r e f o r e , c a n e x i s t in e a c h of t h e t h r e e mixed phases of t h e "under- ground". W e distinguish s i n g l e - m i g r a n t models of water quality from m u l t i - m i g r a n t models.

The t h r e e mixed p h a s e s "soilair", "soil

-

o r groundwater", and "soil o r r o c k "

in t h e middle level form t o g e t h e r in t h e highest h i e r a r c h i c a l level t h e multiphase system "underground". The fluid mixed p h a s e s "soilair" and "soilwater o r ground- water" especially cause t h e mobility of t h e migrants in t h e "underground"! On t h e o t h e r hand t h e immobile mixed phase "rock" i s often responsible f o r t h e signifi- c a n t migrant s t o r a g e capability.

The multiphase system "underground" stands in t h e highest level. The smallest considerable p a r t of such a system i s t h e r e p r e s e n t a t i v e e l e m e n t a r y volume (REV), and t h e l e a s t considerable time s t e p i s t h e s o called r e p r e s e n t a t i v e elemen- t a r y time (RET), see Luckner and Schestakow 1986. Figure 1 shows t h e h i e r a r c h i - c a l scheme of t h e t h r e e level multiphase system described above.

Only two h i e r a r c h i c a l levels consist in s u r f a c e water bodies. We c a n t h e r e f o r e con- s i d e r s u r f a c e water quality models as special c a s e s of underground water quality models, and need no f u r t h e r s e p a r a t e description h e r e f o r t h e s u r f a c e water qual- ity models.

MLILTIPHASE SYSTEMS "UNDERGROUND ^"

Figure 1: H i e r a r c h i c a l scheme of t h e three-level multiphase system "underground"

for migration r e s e a r c h p u r p o s e s 2.2.

Single

Processes

The f o u r main p r o c e s s e s in which t h e migrants are subjugated are

-

t r a n s p o r t a t i o n

-

s t o r a g e

-

r e a c t i o n s and

-

e z c h a n g e .

We have to consider, t h e r e f o r e , t h e t r a n s p o r t a t i o n phenomena in e a c h and with e a c h of t h e fluid mixed p h a s e s , t h e s t o r a g e and t h e i n t e r n a l physic-chemical and bio-chemical r e a c t i o n s in e a c h of t h e mixed p h a s e s and, l a s t but not least, t h e exchange between t h e mixed p h a s e s of t h e multiphase system "underground" a n d t h e e x t e r n a l exchange with o t h e r systems.

2.2.1.

Transportation

The t r a n s p o r t of migrants in t h e "underground" t a k e s place (besides t h e pur- posive self-movement of some organisms) by means of:

-

molecular d i m s i o n

-

convection and

-

h y d r o d y n a m i c a l d i s p e r s i o n .

Molecular d n s i o n is based on

Brown

's molecular motion in solid, liquid and gaseous materials. This t r a n s p o r t p r o c e s s is only important in t h e "soilair"-phase.

In t h e "soil- o r groundwaterH-phase i t i s significant, when p r a c t i c a l l y no convec- tion e x i s t s (e.g. in clays).

The t r a n s p o r t a t i o n of O2 o r C 0 2 e.g. in t h e "soilair"-phase is mainly caused by molecular diffusion. This p r o c e s s c a n practically be stopped by s a t u r a t i o n of t h e p o r e s with water, b e c a u s e t h e diffusion coefficient in water is about one hundred thousand times less t h a n in a i r . This f a c t can b e used, e.g. t o r e d u c e t h e acidifica- tion of t h e mine water. The oxygen migrates t o t h e sulphuric materials (e.g.

p y r i t e ) , from t h e atmosphere t o t h e coal-seams and o t h e r l a y e r s , in which t h e p y r i t e is embedded, t h r o u g h t h e "soilair"-phase by molecular diffusion. If w e flood t h e s e l a y e r s or if w e c o v e r t h e s e l a y e r s by low permeable materials (e.g. silty materials), which are p r a c t i c a l l y always water s a t u r a t e d , t h e n t h e oxidation rate and t h e r e f o r e t h e acidification rate c a n b e markedly reduced.

Convective t r a n s p o r t and h y d r o d y n a m i c d i s p e r s i o n are always coupled with t h e movement of a mobile mixed phase in t h e underground. The convection d e s c r i b e s bulk movement of a mobile mixed phase. That means, t h e s t a t i s t i c a l a v e r a g e d movement of all t h e i r components

-

t h e hydrodynamic dispersion

-

r e f l e c t s a l l t h e deviations from t h i s a v e r a g e .

The convective t r a n s p o r t i n t e g r a t e s in t h i s way t h e flow p r o c e s s of water in t h e migration p r o c e s s . T h e r e f o r e , one also often s p e a k s of "coupled w a t e r q u a n - t i t y a n d q u a l i t y models", see e.g. Luckner and Gutt 1981. Without sufficient knowledge a b o u t t h e flow p r o c e s s e s in t h e area u n d e r consideration, no water quality model c a n b e quantified. Special difficulties a r i s e in t h o s e cases, when more t h a n one mobile immiscible p h a s e e x i s t s in t h e underground, e.g. water and a i r in t h e u n s a t u r a t e d zone of a cone of depression. The convective t r a n s p o r t model i s t h e n significantly more complex, see Luckner and Schestakow 1986. How- e v e r , t h e t r a n s p o r t of oxygen, f o r instance, in t h e u n s a t u r a t e d soil-water zone cannot b e modeled with only a single moving phase.

The real velocities of migrants digress, of c o u r s e , about t h e a v e r a g e bulk- movement of t h e mixed mobile phase. I t is often supposed t h a t t h e s e deviations a r e normally d i s t r i b u t e d about t h e convection movement. The values of t h e h y d r o - d y n a m i c d i s p e r s i o n depend on t h e convection (in t h e case of zero-convection no hydrodynamic dispersion a p p e a r s ) a n d on t h e g r a d i e n t of t h e migrant- concentration. One distinguishes t h e longitudinal (in t h e direction of t h e bulk- movement) from t h e t r a n s v e r s a l hydrodynamic dispersion (perpendicular t o t h e direction of t h e bulk-movement). The m o s t difficult problem is t h e mathematical description of t h e scale-dependency of t h e dynamic dispersion, f o r d e t a i l s see Luckner and Schestakow 1986.

The total t r a n s p o r t a t i o n process of t h e migrants in t h e underground is approximated by t h e superposition of t h e single p r o c e s s e s described. This includes t h e assumption t h a t t h e s e p r o c e s s e s are l i n e a r . This assumption c o r r e s p o n d s t o t h e state-of-the-art in groundwater quality modeling.

2.2.2.

Storage

Each mixed phase of t h e multiphase system "underground" i s c a p a b l e of s t o r - ing migrants. The s p e c ~ c storage s i i s defined a s t h e s t o r e d quantity of t h e migrant i in t h e considered mixed phase divided by t h e volume of t h e multiphase system. I t depends on a storage c o e m c i e n t ca, and a n i n t e n s i v e s t a t e v a r i a b l e P , , with s ,

=

c a , . P , . The s t o r a g e - r a t e t h e r e f o r e amounts t o

d s / d t

=

(2 ( c a . P ) / d t .

The e a s i e s t measurable intensive s t a t e v a r i a b l e of t h e mixed p h a s e s in t h e underground i s t h e concentration c{ of t h e considered migrant i in t h e mobile fluid phase a f t e r i t s e x t r a c t i o n (separation). This v a r i a b l e c{ is, in w a t e r o r a i r , a well- known function of t h e chemical potential &, see Luckner and Schestakow 1986.

Because i t is a l s o known t h a t in t h e thermodynamic state of equilibrium in a multi phase system t h e chemical potential p i s equal in e a c h of t h e mixed p h a s e s p 1

=

p2

= -

, t h e mathematical formulation i s mostly based on c ( .

Generally t h e s o called Henry-storage-isotherm, t h e F r e u n d l i c h - s t o r a g e - isotherm a n d t h e Langmui~storage-isotherm are used as mathematical models of t h e s t o r a g e p r o c e s s e s in t h e multiphase system "underground". The f i r s t model i s suitable t o d e s c r i b e t h e s t o r a g e p r o c e s s in w a t e r o r a i r f o r low concentrations of migrants, t h e second e.g. f o r adsorption of sulphate, cadmium o r h e r b i c i d e s on t h e solid phase, and t h e t h i r d when e.g. gases, cadmium o r phosphate are a d s o r b e d on t h e soil o r r o c k . At t h i s t h e H e n r y s t o r a g e - i s o t h e r m i s a n asymptote t o t h e LangmuiF-storage-isotherm in t h e case of low concentrations. Up till now w e found t h e b e s t r e s u l t s with t h e

Langmui~storage-isotherm,

because i t gives r e a s o n a b l e s t o r a g e - r a t e s in t h e case of v e r y low as well as in t h e case of v e r y high concentra- tions.

2.2.3.

R e a c t i o n s

In e a c h of t h e mixed p h a s e s i n t e r n a l r e a c t i o n s may o c c u r . The most important forms (see Luckner and Schestakow 1986) a r e :

-

association/dissociation p r o c e s s e s (complex formation, aggregation, dissolu- tion, and precipitation with co-precipitation),

-

oxidation/reduction p r o c e s s e s ,

-

a c i d / b a s e r e a c t i o n s and

-

biological metabolizing.

The mathematical r e a c t i o n model h a s t o d e s c r i b e t h e stoichiometric balance as well as t h e r e a c t i o n - r a t e s of t h e migrants. The t o t a l r e a c t i o n - r a t e r is formed by t h e forward rate r' describing t h e transformation velocity of t h e initial s u b s t a n c e s IS t o t h e r e a c t i o n p r o d u c t s RP a n d t h e backward rate r" t h e back transformation:

v ,

=

a , b , c , d are stoichiometric coefficients and A , B ,

C, D

substances. The thermodynamically-based r e a c t i o n - r a t e i s approximately

r

=

r '

-

r" k '

.x

v j ' p , - k " . x v { ' k

=

-k.ARG

IS RP (1)

with

ARC

-

free r e a c t i o n enthalpy k

-

velocity coefficient.

With t h e symbol. [i] f o r t h e concentration of t h e migrant i (substance i ) in a mixed p h a s e t h e e a s i e s t mathematical r e a c t i o n model can b e formulated a s :

This model holds only t r u e , when t h e concentrations of t h e initial substances are significantly h i g h e r t h a n t h o s e of t h e r e a c t i o n products. Otherwise w e have t o f o r - mulate:

But t h e s e models d o n o t r e f l e c t t h e thermodynamic equilibrium. This is only possi- ble by introduction of t h e thermodynamic equilibrium constant given as

KT

" x [ i ] / n [ j ]

=

k ' / k " :

Often i t is a l s o useful t o r e s t r i c t t h e maximal r e a c t i o n - r a t e t o r,,. This is possible e.g. by means of Eq.(5), Luckner and Schestakow 1986:

With r *

=

k *-[i ]

=

( r

, , ,

/ k ,ax ).[i ] a p p r o p r i a t e t o Eq. (2) t h e Eq. (5) r e p r e s e n t s e.g. t h e important

Michaelis-Menten-kinetics.

All t h e s e r e a c t i o n models ignore t h e necessity of a n a c t i v a t i o n e n e r g y respectively enthalpy t o start t h e r e a c t i o n

-

^see Figure 2. B i o - c a t a l y z e r s c a n r e d u c e t h i s activation e n e r g y . These c a t a l y z e r s a r e produced by microorganisms.

They often enormously i n c r e a s e t h e velocity constant k and by t h i s means t h e r e a c t i o n - r a t e . On t h e o t h e r hand t h e variation of t h e equilibrium state k ' / k " i s t h e r e b y negligible.

Consequently a n important possibility t o r e d u c e t h e acidification of groundwater in mining areas i s t h e development-stunting of microorganisms which are involved in t h e oxidation p r o c e s s of t h e sulphuric materials, see Luckner and Hummel 1982. In t h e r a n g e of pH>4 t h e activity of t h e most interesting microorganisms thioba- c i l l u s f e r r o o z i d a n s and f e r r o b a c i l l u s f e r r o o z i d a n s are negligible. Two ways are useful t o i n c r e a s e t h e pH-values, by liming or t o use a s h e s of coal-fired power- plants, which are s p r e a d o u t on t h e t o p of t h e ground s u r f a c e and are mixed by t h e work of e x c a v a t o r s . In such mixed spoils p r a c t i c a l l y n o acidification of groundwa- ter t a k e s p l a c e , only t h e sulphate concentration i n c r e a s e s , s e e Fischer et.al. 1985.

2.2.4.

Exchnnge

The most important forms of exchange between t h e p h a s e s a r e , s e e Luckner and Schestakow 1986:

-

t h e anion and cation exchange

-

t h e adsorption and desorption of migrants and

G A

-- ---

+ARH

- -

energy

a)

-ARH

- --

- +

Direction of the change of system state

Figure 2: Scheme of e n e r g y respectively enthalpy change in chemical systems a ) migrants are in a metastable equilibrium b) migrants are in a n instable equilibrium c ) migrants are for a n exothermal r e a c t i o n in a s t a b l e equili- brium

-

t h e e x t e r n a l exchange e.g. d u e to a b s t r a c t i o n of t h e r o o t system.

The mathematical formulation of t h e s e p r o c e s s e s in a multiphase system h a s to t a k e into account, t h a t t h e exchange models d o not c o n t r a d i c t with t h e used s t o r a g e - p r o c e s s models. I t i s t h e r e f o r e recommended t o u s e coupled exchange-storage models, which t u r n o v e r in t h e equilibrium state to t h e above mentioned s t o r a g e models, s e e Luckner and Schestakow 1986. This holds t r u e for t h e s t o r a g e of t h e considered migrant in t h e mixed phase 11 exchanging migrants with t h e mixed p h a s e I. Typical models are:

-

t h e r e v e r s i b l e l i n e a r k i n e t i c model of-t o r d e r

f o r follows

-

t h e r e v e r s i b l e n o n l i n e a r k i n e t i c model

ds ^fl

f o r

-

_{d t} ^{+ 0 follows}

sfl

=

( k j / k,).[i];

=

K.[i], 0 ⁽ F r e u n d l i c h s t o r a g e -isotherm),

-

t h e b i l i n e a r k i n e t i c model

d s ,

f o r

-

_{d t} ^{+ 0} follows with kl/ k ,

= K'

F o r p r a c t i c a l p u r p o s e s t h e same recommendations hold as f o r t h e s t o r a g e - process-models.

2.3.

Comprehensive Complex Model

The mathematical model of t h e complex dynamic water quality p r o c e s s , t h e complez c o m p r e h e n s i v e w a t e r q u a l i t y model, should b e developed based on figurative models. The elaboration of a chain of t h e s e models with g r a d u a t e d approximation-levels i s o f t e n useful, see Luckner and Schestakow 1986.

Let us c o n s i d e r such a chain with t h r e e levels as shown in t h e u p p e r p a r t of Figure 3.

The first f i g u r a t i v e model in t h i s f i g u r e r e f l e c t s t h e r e a l distribution of t h e vari- ous mixed p h a s e s in a r e p r e s e n t a t i v e volume of t h e multiphase system "under- ground". T h r e e mixed p h a s e s are considered:

-

t h e mobile fluid p h a s e marked by f l o w arrows, i.e. t h e mobile p a r t of t h e groundwater,

-

t h e immobile fluid p h a s e a d s o r b e d in thin films a r o u n d t h e solid p a r t i c l e s and e n t r a p p e d in t h e small p o r e s , t h e s o called dead-end p o r e s , and

-

t h e solid skeleton (e.g. sand g r a i n s ) marked by crosshatching.

The second f i g u r a t i v e model r e f l e c t s t h e o r d e r e d r e p r e s e n t a t i v e s t a t i s t i c a l a v e r - a g e distribution of t h e t h r e e p h a s e s in t h e elementary volume. The s t o r a g e symbols mark t h e storage-capability of e a c h p h a s e , a n d t h e exchange symbols mark t h e possible exchange-paths equivalent t o t h e f i r s t figurative m o d e l .

Finally in t h e t h i r d f i g u r a t i v e model t h e approximation is t a k e n still f u r t h e r . The nodal points of t h e models c h a r a c t e r i z e t h e mixed phases. Their number i s r e d u c e d t o two

-

t o t h e mobile p h a s e as b e f o r e , a n d t o a n immobile p h a s e formed by t h e solid p h a s e and t h e immobile p a r t of t h e liquid phase. Between both of them t h e e z c h a n g e t a k e s place. The v e r t i c a l arrows on t h e l e f t nodal point, which c h a r a c t e r i z e s t h e mobile phase, symbolizes t h e t r a n s p o r t a t i o n p r o c e s s and t h e diagonal arrows t h e r e a c t i o n in r e s p e c t t o t h e considered migrant. Such a model must b e developed for e a c h migrant. In o u r example t h r e e migrants M , , M 2 , M , are considered, t h e r e f o r e t h e Figure 3 contains t h e s e t h r e e models. These models are t h e b a s e for t h e mathematical formulation of t h e complex p r o c e s s .

A s t h e n e x t model t h e s t o i c h i o m e t r i c balance of t h e considered migrants h a s t o b e formulated. From t h i s model w e calculate t h e r e l a t i o n s between t h e formation-rates a n d t h e d e c a y - r a t e s of t h e considered migrants. If w e consider t h e t h r e e migrants Fe '+, 0, a n d Fe (OH)= and t h e well-known stoichiometric balance model r e l a t i o n of i r o n oxidation , compare Figure 3:

irn

-

irn

r n : T R = S + irn: TR = S +

r n : T R = S + irn: TR = S +

Figure 3: Scheme of a typical comprehensive systems-descriptive groundwater quality model

t h e n w e c a n easily find t h a t e.g. t h e j ' o r m a t i o n - r a t e of o n e mole Fe (OH), is equal to t h e d e c a y - r a t e of o n e m o l e F e 2 + and f o u r times as much as t h e d e c a y - r a t e of one mole disolved oxygen in t h e mobile groundwater phase.

The complex mathematical model consists finally of a n equation system of n*m equations ( n

-

number of t h e considered p h a s e s and m

-

number of t h e considered migrants). Let u s r e g a r d only t h e f i r s t equation in t h e Figure 3 r e f l e c t i n g t h e migration p r o c e s s of t h e migrant M , in t h e mobile phase. In t h i s equation, TR sym- bolizes t h e t r a n s p o r t a t i o n p r o c e s s , S t h e s t o r a g e p r o c e s s , EX t h e e x c h a n g e p r o - cess,

IR

a r e a c t i o n p r o c e s s i n t e r n a l of a p h a s e , and S/S a source/sink-term reflecting a n e x t e r n a l r e a c t i o n , e.g. t h e e x t r a c t i o n of a migrant from t h e con- s i d e r e d phase by t h e roots of plants, o r in o u r case e.g. t h e intake of oxygen o r lime h y d r a t e in a mine water t r e a t m e n t plant or remaining pit.

The equations of t h e system are coupled with e a c h o t h e r by t h e exchange pro- cess and i n t e r n a l r e a c t i o n s , s e e Figure 3. Of c o u r s e , t h e e x t e r n a l r e a c t i o n c a n a l s o have a couple e f f e c t , t h i s will not b e considered h e r e ( s e v e r a l typical examples are d e s c r i b e d in Luckner and Schestakow 1986).

Last but not least i t i s n e c e s s a r y t o complete t h e equation system by i n i t i a l and b o u n d a r y c o n d i t i o n s . This problem is d e s c r i b e d in more d e t a i l s in Luckner and Schestakow 1986. F o r e a c h derivation of e a c h of t h e dependent state- v a r i a b l e s of t h e equation system one o r two of t h o s e conditions a p p r o p r i a t e t o t h e

o r d e r of t h e derivation h a v e t o b e formulate 3. Model Reduction

3.1. General Methods

The reduction of t h e comprehensive systems d e s c r i p t i v e w a t e r quality models t o box-models i s possible in d i f f e r e n t ways. The following methods h a v e been stu- died:

-

f i t t i n g of a black-box model by means of k n o w n (measured) i n p u t

-

^{a n d}

o u t p u t - s i g n a l s , e.g. a deterministic trend-model, a convolution i n t e g r a l o r a n influence matrix, see Luckner and Mucha 1984,

-

use of a n a l y t i c a l s o l u t i o n s of approximated systems d e s c r i p t i v e water qual- ity m o d e l s as t r a n s i t i o n - f u n c t i o n s of box-models,

-

m i n i m i z a t i o n of t h e mixed p h a s e s of t h e multiphase system e.g. t o a two- o r t o a one-single-phase model,

-

m i n i m i z a t i o n of t h e considered m i g r a n t s , e.g. t o ~ eand ~

@,

+ which h a v e often t h e g r e a t e s t importance in coal mining d i s t r i c t s ,

-

p a r a m e t e r - l u m p i n g by averaging of t h e p a r a m e t e r s in s p a c e as w e l l as in time,

-

s p a c e - l u m p i n g leading t o t h e neglect of all t h e t r a n s p o r t a t i o n p r o c e s s e s , t h i s a l s o includes parameter-lumping,

-

time-lumping leading t o t h e neglect of all s t o r a g e p r o c e s s e s and t h e con- sideration of equilibrium exchange p r o c e s s e s and r e a c t i o n p r o c e s s e s (this method a l s o includes parameter-lumping).

For r e a l situations i t i s usually n e c e s s a r y t o u s e s e v e r a l of t h e s e a p p r o a c h e s t o g e t h e r .

In t h e following t h e development of r e d u c e d conceptual water quality models f o r typical subsystems in r e g i o n s with open-cast lignite mines, which are coupled with e a c h o t h e r will b e demonstrated:

-

t h e groundwater as t h e s o u r c e of pollution,

-

a mine w a t e r t r e a t m e n t plant as t h e c o n t r o l unit,

-

_a r i v e r section with a n intake of a c i d ferruginous w a t e r , and

-

a remaining p i t , which c a n a l s o b e used as a n effective c o n t r o l unit in mining areas.

These models may b e used t o estimate t h e n e c e s s a r y d e g r e e of purification f o r t h e acid f e r r u g i n o u s mine d r a i n a g e water in t h e mine w a t e r t r e a t m e n t plant and t h e remaining pit, taking into account t h e self-purification p r o c e s s in r i v e r s and remaining p i t s , as well as t h e water quality requirements of down- stream u s e r s .

To c h a r a c t e r i z e t h e model r e d u c t i o n p r o c e d u r e in a uniform way f o r e a c h of t h e f o u r above mentioned subsystems, w e a r e using a box-symbol reflecting t h e system under consideration with a h e a d l i n e marking t h e system's name. Around t h e box are symbolized a l l t h e i n p u t s a n d o u t p u t s as w e l l as t h e considered migrants (left and r i g h t ) e.g. Fee+ and

P,

a n d a l s o t h e chemical c o n t r o l s u b s t a n c e s (on t h e top), e.g. lime h y d r a t e o r oxygen.

Figure 4 shows t h e connections between t h e f o u r subsystems respectively t h e connections between t h e i r water quality models in mining areas with acid f e r r u g i - nous mine water. The c h a r a c t e r i s t i c chemical s p e c i e s (migrants) in t h e whole sys- t e m a r e Fee+ and

@.

In t h e following t h e single models will b e discussed in more detail.

SUBMODEL Input

I

Output substances MODEL REDUCTION REDUCED MODEL I I BOUNDARY CONDITION lFe2*]< 2mg/l

1

Mech. Operation C02 O2

.

Ca(OH12 MINE WATER TREATMENT PLANT

-

@Fe2*, H*, 02, Ca(OH12

I

Fe2*, H*, Fe10H13, ca2* @2M, 1Ph

I

T. S, EX.

@ . @

@Balance model with

@

,

@

UNDERGROUND FeS2. O2

I

Fe2*, H*, SO:- 2M.lPh

I

T,S,EX,IR,SS Stochastic trend-madel

[ Fe2*1

,

IH*I [ Fe2*]

1

o-~.~G

[H*]

<

1 o-~.~ rnol/l O2

1

Ca(OH12 [H*]

RIVER Fe2*, H*, O2

1

Fe10H13, Fe2', H*

REMAINING PIT Fe2*, H*, O2 , Ca10H12

I

Fe2*, H*, Fe(OH13, ca2* )@ 2M, 1Ph

I

T, @.EX.

@ re

*Balance model with@,

@

,

@

4

-

IH+I [Fe2*1 with

0, @

2M, 1Ph

I @.s.Ex.

@,SS Parameter lumped dynamic model with

'

n

In t h e second l i n e a r e marked l e f t t h e number of t h e considered migrants and t h e considered phases, and on t h e r i g h t hand side are specially marked t h e con- sidered processes.

In t h e t h i r d l i n e t h e names of t h e reduced models a r e given, e.g. "balance model with source/sink t e r m and reaction" in t h e case of t h e mine water treatment plant.

3.2. S u b m o d e l

"

G r o u n d w a t e f '

A s t o c h a s t i c t r e n d model f o r t h e prognosis of groundwater quality w a s developed based on t h e stoichiometric Eq.(lO) and yearly s e r i e s of measurements of t h e Fe 2+-and I?-concentration in t h e drained mine water.

The t r e n d models have t h e form, see Kaden et.al. 1985:

The coefficients a h , b&, U R , ~ and a ~ , b H , U R , H e.g. a r e tabulated f o r t h e GDR min- ing t e s t a r e a in Kaden et.al. 1985. Figure 5 shows t h e s e t r e n d s f o r t h e mine water of t h e mine A in this test a r e a .

The o x y g e n - r a t e diffusing v e r t i c a l through t h e dewatered zone depends on t h e oxygen concentration in soil-air and groundwater (see t r a n s p o r t a t i o n ) , t h e content of b u f f e r i o n s , especially CO:-, HCOg and O H (see reactions), and biotoxic sub- s t a n c e s to r e t a r d effectively t h e activity of microorganisms. The oxygenation pro- cess may b e controlled by a l l t h e s e f a c t o r s as i t is usually done worldwide. The use of coal-fire power-plant-ashes i s a p a r t i c u l a r l y effective method of buffering t h e system and t o p r e v e n t pH-falldown, Fischer 1985.

3.3.

Bases

o f the Surface Water M o d e l s

The submodels reflecting t h e water quality p r o c e s s e s in t h e mine water t r e a t - ment plant, t h e r i v e r system and t h e remaining pit are developed under t h e follow- ing assumptions:

-

^The chemical r e a c t i o n s in t h e water bodies a r e considered as non-equilibrium r e a c t i o n s with complete stoichiometric t u r n o v e r of t h e initial substances.

-

_The d i s s o l v e d c a r b o n i c a c i d of t h e drained groundwater i s removed in t h e mine water t r e a t m e n t plant by mechanical de-acidification and in t h e r i v e r s by d e gasification during t h e flow p r o c e s s e s . Similar r e a c t i o n s a r e a l s o given in t h e remaining pit. These p r o c e s s e s are not considered h e r e .

-

^The b u f f e r c a p a c i t y of water with r e f e r e n c e t o hydrogen c a r b o n a t e i s neglected. This is only allowable f o r water with low c a r b o n a t e hardness. Such conditions a r e typical f o r t h e GDR test area.

-

In t h e s u r f a c e water bodies i s enough o x y g e n for o x i d a t i o n p r o c e s s e s , and t h e p a r t i a l p r e s s u r e i s constant (po2

=

0.21 b a r ) .

-

_The t r a n s p o r t processes a r e one-dimensional.

UNDERGROUND FeS2, O2

1

~ e ~ ' , H', SO:- 2 M . l P h

I

T , S , E X , I R , S S l Stochastic trend-model

Figure 5: Scheme of t h e r e d u c e d model f o r t h e ground water pumped from a n open-pit mine

-

All t h e f e r r o u s hydroxide formed is sedimented within t h e r e a c t i o n time; n o mathematical modeling i s t h e r e f o r e n e c e s s a r y t o reflect t h e s e d i m e n t a t i o n p r o c e s s .

-

Biochemical a n d chemical c a t a l y s i s of formed f e r r o u s hydroxide a n d oxi- d e h y d r a t e s are not considered in t h e coefficient k of t h e r e a c t i o n rate m o d e l

( s e e r e a c t i o n s ) .

The c h a r a c t e r i s t i c chemical r e a c t i o n s f o r

all

f u r t h e r submodels in t h e one-phase- system "water" are t h e o x y g e n a t i o n r e a c t i o n s of F e ( I I ) and t h e h y d r o l y s i s of Fe (III),

Eq.

(13). The p r o t o n s formed will b e neutralized in t h e mine water treat- ment plant, and, if n e c e s s a r y and possible, in t h e remaining p i t by means of t h e t r e a t m e n t with lime h y d r a t ,

Eq.

(14). The total r e a c t i o n is defined by

Eq.

(15).

1 1

Fe2+

+ -

^0,

+

Ca (OH).

+

He0 -r Pe (OH)S

+ cae+.

4

The k i n e t i c s of ferrous-ion oxygenation in l a b o r a t o r y systems h a s been previously

studied a n d t h e g e n e r a l rate law was fdund t o be ( s e e a l s o Eq. (2)).

w h e r e k i s t h e velocity c o n s t a n t in m ~ l - ~ 1' min-' bar-'. [ O r ] d e n o t e s t h e concen- t r a t i o n of h y d r o x y l ions, a n d [Fee+] d e n o t e s t h e c o n c e n t r a t i o n of f e r r o u s ions. In Table 1 t h e velocity c o n s t a n t i s given from t h e l i t e r a t u r e . A t c o n s t a n t p o 2 Eq.(16) r e d u c e s t o a r e a c t i o n rate model of pseudo-first-order kinetics:

with

k

,

h a s t h e unit of i n v e r s e time.

Table 1: Velocity c o e f f i c i e n t s f o r t h e oxygenation k i n e t i c s of f e r r o u s ions

(

I n v e s t i g a t o r s

)

Velocity c o e f f i c i e n t k

1

T e m p e r a t u r e

(

1 I

^{[mol - 2 . ~} 2.atm-1.min-1]

I roc] 1

I I I I

I Stumm, L e e (1961) 1 (8.0

*

^{2.5).1013 20.5 OC I}

F o r a water t e m p e r a t u r e of a b o u t 10°C a n d a oxygen p a r t i a l p r e s s u r e n e a r p o 2

=

0 . 2 1 b a r k 'will b e in t h e r a n g e of k *

=

1 . 6

- .

13.6.10-" in mo12 m-'s-'.

I Morgan, B i r k n e r (1966) S c h e n k , Weber (1968) Theis (1972)

The weathering of p y r i t e or marcasite forms protons. They c a n b e neutralized by a c o r r e s p o n d i n g quantity C U ( O H ) ~ . The neutralization c a p a c i t y KKc i s stoichiometrical:

2.0-1013

(2.1

*

0 . 5 ) . 1 0 ~ ~ 1.36.10"

F o r a technical lime h y d r a t e t h e c o n s t a n t

KIP

is in t h e r a n g e of 0.015

- .

0.025 m o l p / g C U ( O H ) ~ . The e x a c t value h a s t o b e determined in t h e l a b o r a t o r y . This means t h e e f f e c t i v e s u b s t a n c e of t e c h n i c a l lime h y d r a t e amounts t o between 56% a n d 93%.

2 5 2 5 2 5

In t h e t r a n s p o s i t i o n of F e (11) i n t o F e (111)-hydroxide, t h e s t o i c h i o m e t r i c ratio between p r o t o n s - a n d f e r r o u s mass-formation rate

Kn

is:

- ⁼

^{3.58-10-~ mol}

^HC

Kfi -

_{[Fe 2+] g F e 2 +}

'

The shown connections are a n important b a s e f o r t h e development of t h e following submodels. By optimal d o s a g e of C U ( O H ) ~ , t h e t r e a t e d mine w a t e r p r a c t i c a l l y d o e s not contain F e e + a n d h a s a pH-value of 7.

3.4. S u b m o d e l "Mine Water T r e a t m e n t P l a n t "

In t h e mine water t r e a t m e n t plant t h e precipitation of Fe (111) o c c u r s by simul- taneous neutralization through dosage of lime h y d r a t e . The redilced model aliows t o simulate t h e output concentration and dosage of Ca (OH),. The m a s s t r a n s p o r t i s neglected.

I n t e r n a l r e a c t i o n p r o c e s s e s (Eq.(16)) and t h e e x t e r n a l s i n k f o r protons (S/S) through a neutralization substance have t o b e considered. Under t h e s e assumptions t h e r e d u c e d model h a s t h e form:

d H+ d F e 2 +

I?: _{d t}

=

Kfi _{d t}

+ K H

[Cd (OH).]

+ c

^QA-[I?I

^-

^{Qz.[fllz. (ZOb)}

An u n d e r d o s a g e of lime h y d r a t e r e s u l t s in incomplete neutralization of p r o t o n s , t h a t means only a p a r t i a l precipitation of t h e ion o c c u r s and t h e pH-values remain l e s s than 7.

The alkalinization s u b s t a n c e Ca (OH)e g u a r a n t e e s a definite s a t u r a t i o n pH- value of 12.6 f o r 20' C in t h e case of overdosage because Ca (OH)e h a s a relatively low water solubility (1.6 g / 1 in t h e case of 20' C). In a c c o r d a n c e with t h e limits for d i s c h a r g e of water into public s u r f a c e water systems t h e pH-value should b e held in t h e r a n g e of 6.5 <pH<8.5, which i s equivalent t o 10-5.5 5

[I?]

^S if

[I?]

i s given in rnol / m5. In mine water t r e a t m e n t plants t h e r e s i d e n c e time i s usually in t h e r a n g e of 2.0

...

2.5 h o u r s . Typically in t h e

GDR

e.g. are sedimentation t a n k s with a capacity of 3 m '/ s a n d a volume of 27000 m 3.

Figure 6 shows t h e r e s u l t s of t h e submodel Eq. (20).

The g r a p h in Figure 6 shows t h e r e q u i r e d demand of calcium hydroxide in t h e case of a r e f e r e n c e pH-value of 7.0 in t h e d i s c h a r g e depending on t h e input pH-value and on t h e change of t h e Fe(II)-concentration. For t h e g r a p h a neutralization capacity of t h e lime h y d r a t e ( a s technical product) of 0.025 mol

HC

p e r g Ca(OH), i s presumed. Figure 6 shows a l s o t h a t at pH-values l e s s t h a n 4 a substantially i n c r e a s e d amount of lime h y d r a t i s r e q u i r e d for neutralization.

3.5. S u b m o d e l " R i v e i '

An intensive a e r a t i o n of t h e r i v e r water provides enough oxygen t o t h e i r o n p r e c i p i t a t i o n according to Eq.(13). The formed p r o t o n s will b e neutralized up t o t h e exhaustion of t h e b u f f e r capacity of t h e c a r b o n a t e and hydrogencarbonate ions. A pH-change o c c u r s at about 3.58.10-e rnol

I?

p e r e a c h g F e 2 + if all CO:-- and HCO; -ions are c o n v e r t e d .

The r i v e r water e.g. in t h e Lusatian lignite mining d i s t r i c t ( t h e

GDR

test a r e a , see Kaden et.al., 1985) h a s a low buffer c a p a c i t y , s o t h a t i t c a n b e neglected in o r d e r t o simplify t h e r i v e r submodels. In t h e opposite way t o Baumert et.al. 1 9 8 1 in t h e submodel "River" t h e hydrodynamic dispersion and diffusion is also neglected.

The r i v e r system i s subdivided into b a l a n c e profiles and r i v e r s e g m e n t s between them. E x t e r n a l sinks and s o u r c e s (water diversion and intake) are a r r a n g e d on t h e balance points (junctions). S t o r a g e changes will b e neglected. The variation of t h e Fe2+-concentration in t h e r i v e r by oxidation and hydrolysis is approximated as a r e a c t i o n of t h e 1 s t o r d e r , and t h e variation of t h e I?- concentration i s r e g a r d e d as a r e a c t i o n of t h e 0th o r d e r .

MINE WATER TREATMENT PLANT

eFe2', H', 02, Ca(OH12

( _I

^Fe2', T , 5 , EX, ^H', Fe(OH13, ca2'

@ . @ It t

^{500 400}

I e ~ a l a n r e model with

@

,

@ I I

Figure 6: Demand of lime h y d r a t e in dependency on t h e input pH-value and t h e difference of Fe 2+-input and -output concentration

d c d c

Based on t h e assumption t h a t v-

= -

holds t r u e in t h e r i v e r segments, t h e d z d t

submodel "River" h a s t h e form:

d Fee+

mD+: ,-"a =-m ^-

^k

d z d t

[ P I

^{[Fe 2+]}

On t h e junction t h e Fee+ o r t h e I? concentration in t h e r i v e r water will be d e t e r - mined under t h e assumption t h a t p e r f e c t mixing exists:

Figure 7 shows typical r e s u l t s of t h e submodel "river".

Obviously t h e o x i d a t i o n r a t e depends on t h e input p H values. I t i n c r e a s e s by h i g h e r pH. Figure 7 shows f u r t h e r low changes of Fe(II)-concentrations (Sl g / m3) f o r long r e s i d e n c e times. The formed protons v a r y between pH-values of 5.9.. .and 6.0. For p H < 5.9 t o 6.0 no important oxidation r a t e exists. In r e a l i t y , h i g h e r oxidation rates often t a k e place. This i s caused by t h e neglected buffer capacity and catalyzes of formed f e r r o u s hydroxides.

RIVER

2+ H+

~ e ? ' , H',

o2 1

Fe(OH)3. Fe , l 2M, 1Ph

I

@ , s . E x .

@

^,SS

Parameter lumped dynamic model with with

@

^,

@

Figure 7: Changes of t h e f e r r o u s ion concentration by oxygenation with air-oxygen without neutralization in t h e r i v e r

3.6. Submodel "Remaining Pit"

In remaining p i t s t h e o z i d a t i o n of F e 2 + by air-originated oxygen t a k e s p l a c e as well as a n additional h y d r o l y s i s of t h e produced Fe3+. The r e a c t i o n s depend o n t h e p H value. F o r p H less t h a n 6.0 n o important oxidation rate ( s e e Figure 7 ) exists. By adding Lime h y d r a t e t o t h e water body of a remaining p i t , p r o t o n s which are in t h e water and are formed by Fee+

-

oxidation will b e neutralized. If t h e p H value i s less t h a n 4.0 a l a r g e amount of lime h y d r a t e is needed to neutralize t h e water (see Figure 6). Under t h o s e conditions t h i s method is uneconomical. Another possibility for neutralization is t h e flooding of t h e remaining p i t with s u r f a c e water, which h a s a h i g h e r p H value.

All t r a n s p o r t a t i o n p r o c e s s e s are neglected in t h e submodel " R e m a i n i n g pit".

Only t h e following p r o c e s s e s are t a k e n into account:

-

s t o r a g e p r o c e s s e s ,

-

r e a c t i o n p r o c e s s e s with

.

r e a c t i o n kinetics of 1st o r d e r for Fe2+-oxidation

.

r e a c t i o n kinetics of 0th o r d e r for t h e neutralization p r o c e s s ,

-

e x t e r n a l inputs and outputs (external exchange).

Based on t h a t w e obtain:

Fe2+ : 0

=

d (V. [Fe e+]) k *

d t ⁺

-'v.

[Fe

2+1 + z

^{QA. [Fe 2+]}

^- z

^{QZ-[Fe 2'1} ( ~ 3 ~ )

[ P I

H t :

o =

+ K R e V

d t

-

KKCU (0H)22V

+

d t

+ C Q A . [ ~ I - C Q Z . [ ~ I Z

.

With d (V [i I)/ d t = V d [i

I /

^{d t}

+

AV/ At t h e following differential/difference equa- tions c a n b e formulated based on Eq.(23):

k *

2+ d [Fee+]

-

Fe : AV ~ Q A

[H'12

^[Fee+]

-

^[Fe e+]. (-

d t At.V ⁺

-

^{V > +}

Figure 8 shows r e s u l t s of t h i s model f o r a n example with t h e following conditions:

The conditions f o r a n example a r e :

-

V = 1 0 ? m 3 ,

-

input pH- and input Fe2+-concentration a r e equal t o t h e initial pH=pHo and initial Fe e+-concentration,

-

t h e capacity of technical lime h y d r a t e is 0.02 moL P / g Ca(OH), (tech.),

-

r e a c t i o n coefficient k *

=

2 . l 0 - ~ ~ in mole m-' s-',

-

lime h y d r a t e dosage 100 g / s

=

8.6 t ^/ d

.

Independent of t h e input p H , if i t i s g r e a t e r t h e n 4.0, t h e equilibrium pH-value i s in t h e r a n g e of 6.2

...

6.3. Under such conditions 5 0 I of t h e ~ e ' + will b e oxidized within 1 0 days.

The influence of t h e s t o r a g e change r a t e

crN/

d t which couples t h e water quantity model with t h e dynamic water quality model of a remaining pit o r o t h e r big s u r f a c e water r e s e r v o i r s c a n b e significant.

4. C o m p u t e r M o d e l

4.1.

B a s e s

The last t h r e e r e d u c e d submodels c a n b e described in a g e n e r a l form with z

=

[ ~ e ~ ' ] , y

=

[ P I :

The finite difference analogou of t h e s e equations is:

REMAINING P I T

~ e ~ + , H', O2 , Ca(OH12

1

~ e ~ + , H', Fe(OH)3, ca2+

2M, 1Ph

I

^{T , @,EX,}

@

^,

@

@Balance model with@,

@

^,

@

Figure 8: The change of t h e Fe2+- and l?- concentration in a remaining pit From Eq. (26a) we obtain:

A polynomial function of 3 r d o r d e r r e s u l t s if w e i n s e r t Eq.(27) into (26b). The solu- tion i s t o b e found in t h e r a n g e of

<

^y

<

1 0 , t h i s means in t h e r a n g e of 2 < p H

<lo.

4.2. P r o g r a m D e s c r i p t i o n

The computer program FEMO h a s been developed for t h e numerical solution of t h e generalized mathematical model f o r t h e t h r e e subsystems r e f l e c t e d by Eq.(28).

The solution of t h e polynomial function i s executed with Newtonsapproximation method for a given r a n g e . If n o solution with t h e assumed time s t e p i s possible, t h a n i t i s c o r r e c t e d . The time s t e p will b e a l s o c o r r e c t e d , when t h e change of p H is g r e a t e r as a given value. The program s t o p s if

-

t h e changes of p H a r e l e s s than 0.01 p H units,

-

_{t h e ~e} '+-concentrations a r e l e s s than 0.1 g / m ',

-

t h e end of residence time i s r e a c h e d , and

-

in t h e submodel "Mine Water Treatment Plant" t h e p H limits are exceeded.

An expansion of t h e model about pH-buffer r e a c t i o n s and catalytic r e a c t i o n s is possible.

The program s o u r c e code i s given in t h e Appendix 1. In Figure 9 a simplified flow c h a r t of t h e program i s depicted. In Appendix 2 t e s t r e s u l t s a r e given.

The input d a t a needed in applying t h e model a r e listed in Table 2. In Figure 1 0 t h e input d a t a format i s shown.

Data input Control prints

h

Computation of parameters for differential equation

L -

w-

Computation of parameters for polynom

+

Computation of initial value with function KUDl

+

Computation for maximal

60 iterations

!

Correction of time step A

Y

Computation of discriminant D Y

Computation [Felt + At

and [H+] ⁺ At

Computation of extrem values with their function values

A

Selection of start value for polynomal solution

Figure 9: Flow c h a r t of t h e model

Table 2: List of input data

r h k

t

d h

V

a

reaction constant k H final time maximum change of pH in one t i m e step

volume

reaction constant k*

outflow

' Description

text f o r heading number of values

number of model ( 1 12 13)

print after k time steps Record

1

^Symbol

1

^inflow

1 2

6 -

cj'ez concentration [Fee+]-input text

n irn

, k ,

7 ^{P ~ Z}

I

^{p~ input}

8

1

^ck demand of lime hydrate

, I

I

⁹

1

^cj'eO initial [Fee+] concentration

j

¹⁰

1

^{p h 0 I}

ⁱ

initial pH-value

Unit

mol h?/ g Ca ( O H ) z sec.

-

rn9

rnol e . r n - 6 - ~ e ~ - 1 rn sec.

rn = / sec.

g / sec.

Figure 10: Input data format

REFERENCES

Baumert, H. et al. 1981. A generalized program p a c k a g e f o r t h e simultaneous simu- lation of t r a n s i e n t flow and matter t r a n s p o r t problems in r i v e r networks.

Intern. c o n f e r e n c e on Numerical Modelling, Bratislava, Czechoslovakia, May 4-8, 1981, Section 2.2, p . 7.

Fischer, R. et al. 1985. The problem of weathering of markasite and p y r i t (in Ger- man), Leipzig , Neue Bergbautechnik (forthcoming).

Kaden, S., Luckner, L. 1984. Groundwater management in open-pit lignite mining areas. Intern. Symposium Canada, May 21-23, P r o c . , Vol. I, pp. 69-78.

Kaden, S. et a l . 1985a. Water Policies: Regions with Open-Pit Lignite Mining (Intro- duction t o t h e IIASA Study), IIASA, WP-85-04, p. 67.

Kaden, S. et al. 1985b. Decision s u p p o r t model systems for regional water policies in open-pit lignite mining areas, Intern. Journal of Mine Water, (forthcoming).

Luckner, L. 1982. Actual problems of groundwater r e s o u r c e s protection in t h e GDR in connection with t h e i r intensified utilization (in German), WWT Berlin, 32(1982), No. 1, pp. 20-23.

Luckner, L., Hummel, J . 1982. Modelling and predictions of t h e quality of mine d r a i n a g e water used f o r t h e drinking water supply in t h e GDR. 1st Interna- tional Mine Water Congress of t h e IMWA, Budapest, Hungary, P r o c . D , pp. 25- 36.

Luckner, L., Mucha, I. 1984. Theory and methods of hydrogeological modeling in connection with t h e solution of major p r a c t i c a l problems on regional and local scales, 27th i n t e r n . Geological Congress, P r o c . Vol. 1 6 (Hydrogeology), pp.

91-106, VNU S c i e n c e P r e s s , U t r e c h t , The Netherlands.

Luckner, L., Schestakow, W.M. 1986. Migration p r o c e s s e s in t h e soil- and groundwa- t e r zone (in German and in Russian), VEB Deutscher Verlag f u r Grundstoffin- d u s t r i e , Leipzig and Isdatelstvo Nedra Moscow, planned f o r 1986.

Morgan, J. J., Birkner, F.B. 1966. F e r r o u s oxidation kinetics, Journal of S u n . Eng.

Dev. C i v i l Eng., 1 6 , pp. 137-143.

Schenk, J.E., Weber, W.J. 1968. Chemical interactions of dissolved silica with iron(I1) and (111), J. A m e r i c a n Water Works A s s . , 60, pp. 199-212.

S t a r k e , W. 1980. Utilization of mine water of open-cast lignite mines f o r drinking water supply (in German), WWT Berlin, 30(1980), No. 7 , pp. 219-222.

Stumm, W., Lee,

G.F.

1961. Oxygenation of f e r r o u s ion, Ind. E n g . C h e m i s t r y , 53, pp. 143-146.

Theis, T.L. 1972.

Ph.D.

Dissertation, Notre Dame University, Notre Dame, Ind., USA.

Appendix

1

c

S C S t W W t Y Y Y Y Y w - Y Y Y Y Y Y Y Y Y Y Y Y - -

c

2educed Models +or dater Quai itv by Oxidarion oi Fe(I1)

in c

Mine Water Treatment Plants, Rivers and Remaininq Fits

program + e m ~

a - reaction constant K* CmoiH2

mmt-6

s-11 1.6 ... ^13.6 * ^10-13

b - ^In(I0) T

b1..4 - parameters +or ~oiynom

b s ~ b b - variabie +or ~ i i W + t ~ p W ( t + d t )

cah - required dosage o+ lime hydrates Cg/sl c+ez - concentration ZFeZ+l-input Cg/m*33 c+eO - inital concentration CFeZtI Cg/m*3?

chz - concentrarion CHtl-input Cmoi/m*31 ck - demand o+ lime hydrate Cg/sl

d - reaction constant kfe

=

0.OJ58 Cmol

Ht

/(g Fe2t) I

dh - maximum change o+ pH in one time step (0.25 . . . 0.3) dt - time step is]

dta - inintai time step Csl

e)+)g - parameters for difierentiai equation 1 2 - function values +or extreme values

i m - number oi modei i m = 1 river

im

=

2 mine water treatment piant im = 3 remaining

^pit

k - print after k time steps

~ u d

i

- function to estimate start vaiues o+ solution poiynom

n

- number oi values (max.lD)

ph

²

- pH- i npur pho - inital pH

sa - out+low Cmw3/s2 qz - in? low Cm*3/s!

rhk - reaction constant kH(0.015 . . . 0.025) imol

Ht

/(q Ca(OH)2)1

t

- iinai time Csl

text - text +or heading ti - ^{actua i time is1}

vjvp - volume Cm*31

xO - concentration i F e 2 W t l Cg/m*31

Y

0 - concentration

CISfJtntl

Cmol/m*31 y l ~ y 2 - extreme vaiues

ydl~yd2 - approximate values +or YO

dimension ~ i e 0 ( 1 0 ) ~ p h 0 ( 1 ~ ) , v p ( l l ) , ~ k ( 1 n ) ~ q a ( 1 0 ) ~

* qz(1O)~phz(1U),c+ez(10)

realM

a ~ b ~ a ~ d l 0 ~ e ~ i ~ g ~ c h z ~ ~ d 1 ~ y a 2 ~ ~ 1 ~ ~ 2 ~

*

b l ~ b ~ ~ b 3 , b 4 , ~ 5 ~ b b ~ x f ~ y O , t , t i , d t

reaim Kudi

character*Z rext

data i i n ~ i o u / 5 , 6 / ~ a , d 1 o / 3 . ~ d - ~ 2 ~ 1 . ~ d - ~ l / c *

^{i in}

- standard input

E M

iou - standard output

c

* IIASA-subroutine +or assignment of input/outpur u n ~ t s ,

c * has to be replaced

i v

adaqute statements, e.9. cpen-statement

if data input/output is not done via standard i / c .

c a l

I

usearg

data input

read(iinjJ(a72)') text w r i t e ( i o u ~ Z 0 0 0 ) text

f o r m a t ( Z x r J P R

0 G R A

M

F E M

O J / /

)ax) 'Reduced Water Quality Models By Fe(II)-Oxidation'

/ / ~ 3 x ~ a 7 Z , d ~ 3 ~ ) 5 8 ( ' * ~ ) / )

UP( l)=u

do 10 i=2)n+l

vp(i)=vp(i-l>+t*(qz(i-1)-qa(i-i))

cont

i

nue b=dlog(dlG) dta-t

computation