Modern methods of igneous petrology: understanding magmatic processes. by J. Nicholls and J.K. Russell, editors

Principles Of Thermodynamic Modeling Of Igneous Processes --thermodynamic Properties Of Silicate Liquids With Emphasis On Density, Thermal Expansion And Compressibility -- Simulation Of Igneous Differentiation Processes -- The Mathematics Of Fluid Flow And A Simple Application To Problems Of Magma Transport -- Physical Processes In The Evolution Of Magmas -- Magma Mixing Processes: Insights And Constraints From Thermodynamic Calculations --the Effect Of Oxygen Fugacity On The Redox State Of Natural Liquids And Their Crystallizing Phases --dynamics Of Eruptive Phenomena -- Melt Fraction Diagrams: The Link Between Chemical And Transport Models -- Textural Constraints On The Kinetics Of Crystallization Of Igneous Rocks. J. Nicholls & J.k. Russell, Editors. Includes Bibliographies. Page 1 Titles REVIEWS IN MINERALOGY VOLUME 24 J. NICHOLLS & J. K. RUSSELL, editors Page 1 Titles COPYRIGHT: 1990 MINERALOGICAL SOCIETY of AMERICA Printed by BookCrafters, Inc., Chelsea, Michigan 48118 REVIEWS in MINERALOGY ISSN 0275-0279 MODERN METHODS OF IGNEOUS PETROLOGY: UNDERSTANDING MAGMATIC PROCESSES ISBN 0-939950-29-4 Tables Table 1 Page 1 Titles VOLUME 24 MODERN METHODS OF IGNEOUS PETROLOGY: UNDERSTANDING MAGMATIC PROCESSES iii Page 1 Page 2 Page 3 Titles Chapter 6 J.K. Russell MAGMA MIXING PROCESSES: INSIGHTS AND CONSTRAINTS Chapter 7 I.S.E. Carmichael & M.S. Ghiorso THE EFFECT OF OXYGEN FUGACITY ON THE REDOX STATE OF NATURAL LIQUIDS AND THEIR CRYSTALLIZING PHASES Page 4 Titles Chapter 8 C. Jaupart & S. Tait 213 Dimensions of volcanic systems 214 Velocity and mass flux of eruptions 215 Eruption triggering 216 Effect of eruptions on the magma chamber 217 Physical properties oflava 217 The viscosity of silicate melts 218 The viscosity of bubbly liquids 219 The temperature dependence of viscosity 219 The solubility of gas species of silicate melts 219 The density of magmatic gases 220 The fragmentation process 221 Conclusions 222 Basic principles and equations 223 The mass flux of an eruption 224 Constant conduit radius 225 Variable conduit radius 227 Conclusion 227 Laminar regime and variable properties 228 Choking conditions 231 Conduit flow in explosive eruption regimes 231 Generalized momentum balance 232 Conclusion 232 Separated flow 233 The physics of bubble growth 234 Bubble nucleation 234 Bubble expansion 235 Chemical diffusion 235 Conclusion vii Page 5 Titles Chapter 9 G.W. Bergantz MELT FRACTION DIAGRAMS: THE LINK BETWEEN CHEMICAL Chapter 10 K.V. Cashman TEXTURAL CONSTRAINTS ON THE KINETICS OF CRYSTALLIZATION OF IGNEOUS ROCKS 266 Crystallization without a change in composition 268 Crystallization in multicomponent systems 287 Theory 291 Isobaric cooling 295 Isothermal depressurization 297 Crystallization caused by change in supersaturation 297 Residence times 299 Effect of physical processes 300 Further potential applications of CSDs viii Page 1 Titles PRINCIPLES OF THERMODYNAMIC MODELING OF IGNEOUS PROCESSES F=c-cp+2 (1) Page 2 Titles 2 Page 3 Titles 3 Page 4 Titles 4 c Page 5 Titles 5 Page 6 Titles 6 CALCULATION OF CRYSTALLIZATION PATHS. Page 7 Titles A 7 A Calculate the saturation temperature for all possible phases. The primary (24) x = YA exp(- ~μA°!RT) (25) Tables Table 1 Page 8 Titles 8 Page 9 Titles 9 Saturalion Temperatures DCV045 T C (32) Tables Table 1 Page 10 Titles 10 Page 11 Titles 11 Page 12 Titles 12 Tables Table 1 Page 13 Titles 13 B '-. I --- .- \A ..., ~ .. .. '" Page 14 Titles 14 Page 15 Titles 15 (F dy, + Yi dF)IF = dn/Sn Page 16 Titles 16 Page 17 Titles 17 B A T / ~ = !M =r:«; = " .. Tables Table 1 Page 18 Titles 18 Page 19 Titles 19 Page 20 Titles 20 APPENDIX: DERIVATION OF FRACTIONATION EQUATION AT CONSTANT Hnlelt (AI) Page 21 Titles 21 Page 22 Page 23 Titles 23 Page 24 Page 1 Titles CHAPTER 2 R.L. LANGE & I.S.E. CARMICHAEL Page 2 Titles 26 Page 3 Titles 27 Page 4 Titles 28 Page 5 Titles 29 (8) Page 6 Titles 30 Page 7 Titles 31 (9) Page 8 Titles 32 Page 9 Titles 33 Tables Table 1 Table 2 Table 3 Page 10 Titles 34 Page 11 Titles 35 Tables Table 1 Page 12 Titles 36 Tables Table 1 Page 13 Tables Table 1 Page 14 Titles Andesite Peralkaline rhyolite Tables Table 1 Table 2 Table 3 Page 15 Titles 39 Basaltic Andesite 1000 1100 1200 1300 1400 2.30 -t----.--.--,..----;r--r---r-.....--r----,.---~ 900 Tables Table 1 Page 16 Tables Table 1 Page 17 Titles 41 Page 18 Titles 42 Page 19 Titles 43 Page 20 Titles 44 Page 21 Titles 45 Page 22 Titles 46 K Tables Table 1 Table 2 Page 23 Titles 47 Page 24 Titles 48 Page 25 Titles 49 Page 26 Titles 50 Page 27 Titles 51 ~ • • • ......---. Page 28 Titles 52 Tables Table 1 Page 29 Titles 53 Tables Table 1 Page 30 Titles 54 Melilite-nephelinite ..... . - ~ ___'---------:y Page 31 Titles 55 Page 32 Titles 56 Page 33 Titles 57 Page 34 Titles 58 Feo.947D Tables Table 1 Page 35 Titles 59 Page 36 Titles 60 Page 37 Titles 61 Page 38 Titles 62 Page 39 Titles 63 Page 40 Titles 64 Page 1 Titles CHAPTER 3 SIMULATION OF IGNEOUS R.L. NIELSEN Page 2 Titles 66 Page 3 Titles • ; • . : 10000/T(K) • • . :. • • • • • • • • • .~, .. • ... o o Tables Table 1 Table 2 Page 4 Titles AUGITE OLIVINE Tables Table 1 Page 5 Titles 69 Page 6 Titles 70 Page 7 Tables Table 1 Page 8 Titles 72 Tables Table 1 Page 9 Titles 73 Tables Table 1 Page 10 Titles 74 2~------~------~ D D 1 5 Page 11 Titles MgO .-:. o o 5 5 AI203 Tables Table 1 Page 12 Titles 76 Page 13 Titles 77 8 +.'--+--+--+---+--+--+---+_+--1 MgO Tables Table 1 Page 14 Titles 78 Page 15 Titles 79 :a: o •• • • • • o • • • • o • • o ~ e ... • o o • o ...- m cO ...- ...­ z; Page 16 Titles 80 Page 17 Titles 81 .., • • ~ Si02 MgO I • ~ .. I • ~ . a K20 Tables Table 1 Page 18 Tables Table 1 Page 19 Titles 83 co o o co o ::: o • • co • • • • 0 • o co • o • U") C U") C') U') CO • • . '. C. C. c; • o • o o ~ 0 ... o N C. • • • • • • '" (J) o o co o M II) T r-, • o o· o • o· If> 0 • ~ .2 o. .£: o. '" o .... • Page 20 Titles 84 o 6 8 • Page 21 Titles 85 Page 22 Titles 86 Tables Table 1 Table 2 Table 3 Page 23 Titles 87 100 50 1020 60 Tables Table 1 Table 2 Page 24 Titles 88 Page 25 Titles 89 • • •• • • 2.·. • • • .~ -.~ ./PI:'; • ~. . "". "",,.. Tables Table 1 Table 2 Page 26 Titles 90 Page 27 Titles 91 .. '. • • Tables Table 1 Page 28 Titles 92 Page 29 Titles 93 Page 30 Titles 94 ".' ..... .-{.l(·",·~.:'/.);. ... r.)'I[O) 0 o.o~o,~~ __ :o:-~~ __ +- __ +- __ ~ -< ... ' . ~ o 0 00 ".tH. ;, ,,,,","''',, Tables Table 1 Table 2 Table 3 Page 31 Titles 95 Page 32 Tables Table 1 Table 2 Page 33 Titles 97 Page 34 Tables Table 1 Page 35 Titles 99 • • o "0\000 00 0 0 .: . . • • • Page 36 Titles 100 Page 37 Titles 101 :E '" o '" • o • o • "' • o • o o o • o o • • • 0 o ev '" '" o o ~ ~ o o "' o o o o o "' '" o o o o • -e­ Q ~ • o '" o o o o Page 38 Titles 102 Ni Sr Tables Table 1 Page 39 Titles 103 Page 40 Titles 104 Page 41 Titles 105 Page 42 Page 1 Titles CHAPTER 4 J. NICHOLLS THE MATHEMATICS OF FLUID FLOW AND A SIMPLE V2 = a2 /ax2 + a2 /a'{2 + a2 /Z2 Page 2 Titles 108 x D /Dt = a/at + u a/ax + v a laY + w a /az Tables Table 1 Page 3 Titles 109 au/ax + av/aY + aw/az = 0 V = a/ax i + a laY j + a /az k (8) Page 4 Titles 110 = 11 {2[(au/aX)2 + (av/aY)2 + (aw/aZ)2] + (au/aY + av/aX)2 + (av/az + aw/aY)2 + (aw/ax + au/aZ)2} (17) Page 5 Titles 111 aw/az = 0 P Dw/Dt = - pg - ap/az + 11 [a2w/ax2 + aZw/a'{2 + aZw/z2] (19) paw/at = - pg - ap/az + 11 [aZw/ax2 + aZw/ay2] pcp(aT/at + w aT/aZ) - ap/at - w ap/az = K V2T + 11 [(aw/ax)2 + (aw/aY)2] (20) paw/at = - pg - ap/az + 11 aZw/ax2 pcp(aT/at + W aT/aZ) - ap/at - w ap/az = Page 6 Titles 112 z -b b x x o pg + ap/az = 11 a2w/ax2 Page 7 Titles 113 Z (km) Depth, o a(pg)/az + a2p/az2 = 11 (a2/aX2) aw/az = 0 a2p/az2 = 0 (pg -13)/11 = a2w/ax2 Tables Table 1 Page 8 Titles 114 X (rn ) Tables Table 1 Page 9 Titles 115 (aT/aX)i=-Q/K i atX=b (aT/aX)i= Q/K i atX=-b aT/az = a Page 10 Titles 116 Page 11 Titles 117 X (m) Page 12 Titles 118 , X (rn ) Page 13 Titles 119 C2 = f3 - pg > 0 (aT/ap)H = [T (av/aT)p - v]/cp (aT/ap)G = vis Tables Table 1 Page 14 Titles 120 C2 pg > 0 Tables Table 1 Page 15 Titles 121 Page 16 Titles 122 - ap/az = 13 = pgu(l - u) Page 17 Titles 123 REFERENCES CITED Page 18 Page 1 Titles S. TAIT & C. JAUPART IN THE EVOLUTION OF MAGMAS Page 2 Titles 126 Tables Table 1 Page 3 Titles 127 ) Page 4 Titles 128 Page 5 Titles a) b) c) Upper- crystallised 129 h, Lower. Page 6 Titles 130 Page 7 Titles 131 o .. iii .. E (6) or o2T Page 8 Titles 132 aT Page 9 Tables Table 1 Page 10 Titles 134 'dx+dy+Tz= Tables Table 1 Page 11 Titles 135 dT da [dT] Page 12 Titles 136 a ... b o o I I I I I I I I .Ct.«) _/ J_M _ z Page 13 Titles 137 Page 14 Titles 138 I o COMPOSITION LIQUID SOLID Tables Table 1 Page 15 Titles 139 dh EdT] rOT] dh [dC] = 0 Page 16 Titles 140 or d2T sr d2T d . z ........ bet) Page 17 Titles 141 Page 18 Tables Table 1 Page 19 Titles 143 Page 20 Titles 144 Page 21 Titles 145 a) r';-------- b) ~--- ~ 01 Page 22 Titles 146 Page 23 Titles 147 Page 24 Titles 148 Page 25 Titles 149 c) Dense input Tables Table 1 Page 26 Titles 150 a) . .- -v b) Page 27 Titles 151 Page 28 Titles 152 Page 1 Titles MAGMA MIXING PROCESSES: INSIGHTS AND Page 2 Titles 154 Page 3 Titles 155 Page 4 Page 5 Titles 157 Page 6 Titles 158 Tables Table 1 Table 2 Page 7 Titles 159 Page 8 Titles 160 1.16 -,----.-----,----,.----,-------, 1.14 1.12 1.10 1.0 0.4 0.6 O.B MOLE X MAGMA B 0.2 0.0 o Page 9 Page 10 Titles 162 Page 11 Titles 163 1.12 1.10 1.04 1.02 1.0 0.4 0.6 O.B MOLE X MAGMA B O.G 0.0 - - -- S ~ .._.. P::: ___ Linear -_ Mingled (Ideal) 1.0 0.4 0.6' 0.8 MOLE X MAGMA B O.G 0.0 Page 12 Titles 164 -.. ...... MOLE X DACITE Page 13 Titles 165 Mixing of Hydrous Melts Linear Mingled (Ideal) 1.0 0.4 0.6 0.8 MOLE X DACITE 0.2 1120+---~--,--,---.---,---.--~--~--~~ 0.0 Tables Table 1 Page 14 Titles 166 Page 15 Titles 167 1.0 0.4 0.6 O.B MOLE X DACITE 1000+---~--~--~--,,---,,---~--~--~--~--~ 0.0 0.2 u ~90 μ.. .._., . ...... SYSTEM ENTHALPY Moles of SW-02 Added to SG-05 Tables Table 1 Page 28 Titles 180 .- ~ ..... .__.. Moles of SW-02 Added to SG-05 00000 Moles of Olivine u: H ...j..) O.B S cd cd ~ (1)0.4 ..... :> o 1.0 -x------,-----,-------,-----,----, Moles of SW-02 Added to SG-05 Page 29 Titles 181 Tables Table 1 Page 30 Titles 182 Page 31 Titles 183 ..... E- - ...... S 00000 Equilibrium Temp. Liquidus Temp. Moles of SG-05 Added to SW-02 '"' S Enthalpy (kJjmole) Page 34 Titles 186 Page 35 Titles 187 Page 36 Titles 188 Page 37 Titles 189 Page 38 Titles 190 Page 1 Page 2 Titles 192 Page 3 Titles 193 (4) Page 4 Titles 194 Q * ;;; o nlm- t Tables Table 1 Page 5 Titles 195 Page 6 Tables Table 1 Page 7 Titles 197 Page 8 Tables Table 1 Table 2 Table 3 Page 9 Titles 199 ..... Page 10 Titles 200 Page 11 Titles 0.50 0.10 Tables Table 1 Table 2 Page 12 Titles 202 Page 13 Titles 203 m o eo o eo o '" o o ""'_oocor--.. OaluiNO .... ~, ex:> , '" o o I'­ o o o ..... · . · . . . . . . . . . COONLl),.....,....O