Beneficiation of phosphate ore

170 Pages·7.465 MB·English

by  S K Kawatra

Beneficiation of
B
e
n
Beneficiation of e
fi
Phosphate Ore
c
Phosphate Ore ia
t
i
o
n

o
by S. Komar Kawatra and J.T. Carlson f
P by S. Komar Kawatra and J.T. Carlson
h
o
s
Beneficiation of Phosphate Ore examines various methods for p
h
a
processing phosphate rock, an important mineral commodity used t
e

O
in the production of phosphoric acid. The majority of phosphoric
r
e

acid is produced by the wet process, in which phosphate rock
is reacted with sulfuric acid to produce phosphoric acid and
gypsum (calcium sulfate dihydrate). This wet process demands
a phosphate rock feed that meets certain specifications to produce
K
phosphoric acid efficiently and economically. a
w
a
t
r
a
Beneficiation of Phosphate Ore thoroughly explains the methods a
n
d
C
used in beneficiation of different types of phosphate ores for a
r
ls
o
use in the wet process. The mineralogical properties of the two n
major types of phosphate deposits, sedimentary and igneous,
are described along with the processing methods. The benefits
and disadvantages of each process are discussed in detail.
The Society for Mining, Metallurgy & Exploration (SME),
advances the worldwide mining and minerals community
through information exchange and professional development.
SME is the world’s largest association of mining and
minerals professionals.
!SME_BenePhosOre_FullCV_F1.indd 1 11/19/13 7:08 AM
Beneficiation of
Phosphate Ore
by S. Komar Kawatra and J.T. Carlson
Published by the
Society for Mining, Metallurgy & Exploration
!SME_BenePhosOre_TitlePg_L2.indd 1 11/5/13 10:27 AM
Society for Mining, Metallurgy & Exploration (SME)
12999 E. Adam Aircraft Circle
Englewood, Colorado, USA 80112
(303) 948‑4200 / (800) 763‑3132
www.smenet.org
SME advances the worldwide mining and minerals community through information
exchange and professional development. SME is the world’s largest association of mining
and minerals professionals.
Copyright © 2014 Society for Mining, Metallurgy, & Exploration Inc.
Electronic edition published 2014.
All Rights Reserved. Printed in the United States of America.
Information contained in this work has been obtained by SME from sources believed to be
reliable. However, neither SME nor its authors and editors guarantee the accuracy or com‑
pleteness of any information published herein, and neither SME nor its authors and editors
shall be responsible for any errors, omissions, or damages arising out of use of this information.
This work is published with the understanding that SME and its authors and editors are sup‑
plying information but are not attempting to render engineering or other professional services.
Any statement or views presented herein are those of individual authors and editors and are
not necessarily those of SME. The mention of trade names for commercial products does not
imply the approval or endorsement of SME.
No part of this publication may be reproduced, stored in a retrieval system, or transmitted
in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise,
without the prior written permission of the publisher.
ISBN 978‑0‑87335‑391‑5
Ebook 978‑0‑87335‑392‑2
Library of Congress Cataloging-in-Publication Data has been applied for.
Contents
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .vii
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xiii
1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
1.1 Feed Requirements for Phosphoric Acid Production . . . . . . . . . . . . . . . . . . . . . . . .2
1.2 Phosphate Rock Production Statistics and Reserves . . . . . . . . . . . . . . . . . . . . . . .5
2 SOURCES OF PHOSPHATE ROCK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9
2.1 Common Phosphate Minerals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9
2.1.1 Apatite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9
2.1.2 Francolite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10
2.1.3 Collophane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.4 Dahllite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11
2.2 Common Gangue Minerals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12
2.1.1 Clays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12
2.2.2 Quartz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12
2.2.3 Dolomite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12
2.2.4 Calcite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13
2.3 Mineralogy of Sedimentary Phosphates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13
2.4 Mineralogy of Igneous Phosphates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13
2.5 Mineralogy of Biogenic (Island) Deposits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14
3 BENEFICIATION OF SILICEOUS SEDIMENTARY PHOSPHATE ORES . . . .17
3.1 Flotation Feed Preparation—Washing, Sizing, and Desliming . . . . . . . . . . . . . . .17
3.1.1 Industrial Phosphate Washing Plant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20
iii
3.2 Theory of Phosphate Flotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20
3.2.1 Froth Flotation Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
3.2.2 Contact Angle Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30
3.2.3 Entrainment Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36
3.2.4 Surface Properties and Water Chemistry of Siliceous Phosphates . . . . .40
3.3 Crago Double Float Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .44
3.3.1 Stage 1—Anionic Fatty Acid/Fuel Oil Phosphate Flotation . . . . . . . . . . . . .44
3.3.2 Stage 2—Cationic Amine Silica Flotation . . . . . . . . . . . . . . . . . . . . . . . . . . .47
3.3.3 Industrial Flotation Plant for Siliceous Sedimentary Phosphate Ores . . .47
3.4 Proposed Alternatives to the Crago Double Float Process . . . . . . . . . . . . . . . . . .49
3.4.1 Reverse Crago Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49
3.4.2 All-Anionic (Fatty Acid/Fuel Oil Collector) Process . . . . . . . . . . . . . . . . . . .51
3.4.3 All-Cationic (Amine) Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52
3.5 Conclusions from Siliceous Sedimentary Phosphate Ore Processing . . . . . . . .54
4 BENEFICIATION OF HIGH-MgO SEDIMENTARY PHOSPHATE ORES . . . .57
4.1 Mineralogy of High-MgO Sedimentary Phosphate Ores . . . . . . . . . . . . . . . . . . . .57
4.2 Acid Leaching of Carbonaceous Phosphate Ores . . . . . . . . . . . . . . . . . . . . . . . . .58
4.2.1 Strong Acid Leaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58
4.2.2 Organic Acid Leaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .59
4.2.3 Summary of Acid Leaching for the Removal of MgO (Dolomite,
CaMg(CO)) from Phosphate Ores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .66
32
4.3 Thermal Decomposition (Calcination) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .67
4.3.1 Calcination Reactions and Decomposition Temperatures . . . . . . . . . . . . .67
4.3.2 Quenching and Desliming of Calcined Phosphate Ore . . . . . . . . . . . . . . . .70
4.3.3 Effects of Calcination on the Reactivity of Phosphate Products . . . . . . . .70
4.3.4 Process Considerations for Calcination of Carbonaceous
Sedimentary Phosphate Ores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .71
4.3.5 Calcination as a Method for the Removal of MgO from
Phosphate Ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .72
4.4 Beneficiation of Phosphate Ore by Physical Separation Methods . . . . . . . . . . .73
4.4.1 Desliming, Attrition Scrubbing, and Sizing . . . . . . . . . . . . . . . . . . . . . . . . . .73
4.4.2 Sizing and Selective Crushing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .76
4.4.3 Heavy-Media Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .77
4.4.4 Jigging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .84
4.4.5 Summary of Physical Separation Methods for Removal of MgO
from Phosphate Ores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .99
iv
4.5 Flotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .99
4.5.1 University of Florida Two-Stage Conditioning Process . . . . . . . . . . . . . . .101
4.5.2 Tennessee Valley Authority Diphosphonic Acid Depressant
Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .102
4.5.3 U.S. Bureau of Mines Anionic Flotation Process . . . . . . . . . . . . . . . . . . . .104
4.5.4 IMC Cationic Flotation Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .106
4.5.5 IMC Anionic Flotation Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .107
4.5.6 Summary of Flotation for Removal of Dolomite from
Phosphate Ores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .108
4.6 Selective Flocculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .109
4.6.1 Flocculants for the Apatite/Dolomite/Silica System . . . . . . . . . . . . . . . . .111
4.6.2 Factors Affecting Selectivity of Flocculation Processes . . . . . . . . . . . . .112
4.6.3 Selective Flocculation for the Removal of Dolomite from
Phosphate Ores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .114
4.7 Conclusions from Beneficiation of High-MgO Phosphate Ores . . . . . . . . . . . . .115
5 BENEFICIATION OF IGNEOUS PHOSPHATE ORES . . . . . . . . . . . . . . . . . .121
5.1 Flotation of Igneous Phosphate Ores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .121
5.1.1 Collectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
5.1.2 Depressants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .123
5.2 Beneficiation of Major Igneous Phosphate Reserves . . . . . . . . . . . . . . . . . . . . .123
5.1.1 Barreiro Carbonatite Complex, Araxá, MG, Brazil . . . . . . . . . . . . . . . . . . .123
5.2.2 Processing Finnish Igneous Deposits . . . . . . . . . . . . . . . . . . . . . . . . . . . . .125
5.2.3 Processing Phosphates of the Kola Peninsula, Russia . . . . . . . . . . . . . . .126
5.2.4 Processing South African Igneous Phosphate Ores . . . . . . . . . . . . . . . . .127
5.3 Summary of Igneous Phosphate Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . .129
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .131
INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .145
ABOUT THE AUTHORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .153
v

List of Figures
1.1 Simplified process flow diagram for production of phosphoric acid . . . . . . . .2
1.2 World phosphate rock production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6
1.3 Estimated phosphate rock reserves in 2012 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6
2.1 World phosphate reserves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10
2.2 Florida sedimentary phosphate ore sample . . . . . . . . . . . . . . . . . . . . . . . . . . . .14
3.1 Trommel screen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18
3.2 Log washer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18
3.3 Hydrocyclone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19
3.4 Simplified process flow diagram of washing plant at IMC Four
Corners mine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.5 Sodium oleate is an anionic collector that can be used to render
apatite hydrophobic in alkaline environments . . . . . . . . . . . . . . . . . . . . . . . . . .22
3.6 Flotation system with three interrelating subsystems: chemistry,
equipment, and operation components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
3.7 Mechanical flotation cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24
3.8 Schematic of a typical flotation column . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26
3.9 Comparison of axial mixing in unbaffled, baffled, and packed columns . . . .28
3.10 Comparison of bubble growth in unbaffled and baffled columns . . . . . . . . . .29
3.11 Rougher−scavenger−cleaner flotation circuit . . . . . . . . . . . . . . . . . . . . . . . . . .30
3.12 Low surface energies in solids tend to make water bead up (larger
contact angle), whereas high surface energies result in wetting (low
contact angle) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31
3.13 Surface energies and contact angle for a liquid drop on a solid surface . . .31
3.14 Surface energies and contact angle for an air bubble attached to a
solid surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31
3.15 Hydrophobic surfactants can be used to treat glass surfaces and make
water bead up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
vii
3.16 Tantec Cam-Plus Micro contact angle meter . . . . . . . . . . . . . . . . . . . . . . . . . . .34
3.17 Example showing contact angle measurement using the half-angle
method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35
3.18 True flotation versus entrainment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36
3.19 Effects of particle size and hydrophobicity on recovery versus water
recovery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.20 Simplified diagram of electrical double-layer model . . . . . . . . . . . . . . . . . . . . .41
3.21 Effects of various salt solutions on the zeta potential of natural apatite . . . .42
3.22 Zeta potential of francolite and quartz in deionized (D.I.) water and
plant water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .43
3.23 Simplified process flow diagram for the Crago process . . . . . . . . . . . . . . . . . .44
3.24 Simplified process flow diagram of flotation plant at IMC Four Corners
mine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .48
3.25 Spiral concentrator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49
3.26 Simplified process flow diagram for reverse Crago process . . . . . . . . . . . . . .50
3.27 Simplified process flow diagram for FIPR/SAPR all-anionic process . . . . . .52
3.28 Simplified process flow diagram for the all-cationic process . . . . . . . . . . . . .53
4.1 Simplified process flow diagram for acid leaching process . . . . . . . . . . . . . .59
4.2 Simplified process flow diagram of an organic acid leaching process . . . . .64
4.3 Simplified process flow diagram of thermal decomposition process for
beneficiation of carbonaceous sedimentary phosphates . . . . . . . . . . . . . . . .67
4.4 Simplified process flow diagram for attrition scrubbing-flotation
process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .74
4.5 Simplified process flow diagram for scrubbing, sizing, grinding, and
desliming for preparation of flotation feed . . . . . . . . . . . . . . . . . . . . . . . . . . . . .76
4.6 Diagram of high-pressure roll mill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .77
4.7 Simplified process flow diagram of heavy-media separation . . . . . . . . . . . . .78
4.8 Heavy-medium rotating drum separator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .79
4.9 Simplified diagram of a heavy-medium cyclone . . . . . . . . . . . . . . . . . . . . . . . .80
4.10 Particle separation in a heavy-medium cyclone . . . . . . . . . . . . . . . . . . . . . . . .81
4.11 Simplified process flow diagram of a heavy-media flotation process for
beneficiation of phosphate ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .82
4.12 Simplified diagram of a Harz-style jig . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .84
4.13 Mechanisms of particle stratification occurring during the jigging
process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .86
4.14 Particle settling in a fluid under “free settling” conditions . . . . . . . . . . . . . . .87
4.15 Hindered settling and consolidation trickling . . . . . . . . . . . . . . . . . . . . . . . . . . .88
viii
4.16 List of variables involved in the jigging process . . . . . . . . . . . . . . . . . . . . . . . . .89
4.17 Simple harmonic motion can be used to describe the fluid flow
during the jigging cycle for a plunger-style jig . . . . . . . . . . . . . . . . . . . . . . . . . .90
4.18 Effects of water addition on fluid flow velocity throughout the jigging
cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .91
4.19 “Over the screen” versus “through the screen” jigging . . . . . . . . . . . . . . . . .92
4.20 Potential flotation/jigging process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .94
4.21 Grade versus recovery curve for experiments using higher-MgO
phosphate feed sample 1 from mine A that was sized to −5/+20 mesh
(−3.35/+0.85 mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .96
4.22 Grade versus recovery curve for experiments using a crushed
higher-MgO phosphate sample 2 from mine A that was sized to
−6/+20 mesh (−3.35/+0.85 mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .97
4.23 Simplified process flow diagram for University of Florida two-stage
conditioning process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .101
4.24 Chemical formula for hydroxyethylidene diphosphonic acid (CPOH) . . .103
2 2 7 8
4.25 Simplified process flow diagram for TVA diphosphonic acid
depressant process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .104
4.26 Simplified process flow diagram for USBM process for the anionic
flotation of dolomite from phosphate ores . . . . . . . . . . . . . . . . . . . . . . . . . . . .105
4.27 Simplified process flow diagram for IMC cationic flotation process . . . . . .106
4.28 Simplified process flow diagram for IMC anionic flotation process . . . . . . .108
4.29 General structure of anionic collector (sodium salt of sulfonated
oleic acid) used in IMC anionic flotation process . . . . . . . . . . . . . . . . . . . . . .109
4.30 Selective flocculation using a polymeric flocculant . . . . . . . . . . . . . . . . . . . .110
4.31 Molecular structures of PAA and PEO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .112
5.1 Chemical structure of oleic acid C H O and linoleic acid C H O . . . . .122
18 34 2 18 32 2
5.2 Simplified process flow diagram for processing of Brazilian igneous
phosphate reserves that contain barite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .124
5.3 Simplified process flow diagram for Siilinjärvi (Finland) phosphate
concentrator plant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .126
5.4 Simplified structure for the N-sarcosine collector used in the flotation
of Finnish phosphates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .126
5.5 Simplified process flow diagram for beneficiation of Kola Peninsula
(Russia) igneous phosphate ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .127
5.6 Simplified process flow diagram for beneficiation of Phalaborwa
igneous phosphate ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .128
ix