Sampling with discrete contamination

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This is an author-deposited version published in :

http://oatao.univ-toulouse.fr/

Eprints ID : 5522

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OATAO is an open access repository that collects the work of Toulouse researchers and

makes it freely available over the web where possible.

To cite this document : Lyman, Geoffrey and Bourgeois, Florent

Sampling with discrete contamination. In: 5th World Conference

on Sampling and Blending (WCSB5), 25-28 Oct 2011, Santiago,

Chile.

Any correspondence concerning this service should be sent to the repository

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23 Geoffrey J. Lyman

Materials Sampling & Consulting, Australia Florent S. Bourgeois

Materials Sampling & Consulting Europe, France

Sampling with discrete contamination

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INTRODUCTION

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Figure 1 Illustration of disposition of samples and slugs of contaminated material

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Table 1 Simulation results for sampling with discrete slugs of contaminant (10 000 simulation)

Case 1 2 3 4 5 6 7 8 V)5,%$@mA ST ST ST ST ST ST ST ST N+/.#'#+2%$@nA PTT STT PTT STT PTT PTT PTT PTT V)5,$%*[#$@uA T=TTTP T=TTTP T=TTTP T=TTTP T=TTTb T=TTbT T=TTQT T=TTP N+/.#'#+2$%*[#$@vA T=TTTb T=TTTb T=TTTP T=TTTP T=TTTP T=TTTP T=TTTP T=TTTP V&'()#$0.&/2*1+$hci b=T PT=T P=T S=T P=T P=T P=T P=T V)5,$/1+/$@((:A PTTT PTTT PTTT PTTT STT ST QQ PTT D-#.&,#$/1+/$@((:A S S S S S S S S

D-$/1+/$@%*'5)&2*1+A S=TP P=ej S=Tk P=ee P=ed P=eP P=ef P=ek

OVI$2"#1.8 T=efT T=dfb P=jPS P=SkP T=efT T=SSS T=QQe T=dbj

(8)

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Figure 2 Histogram of sample concentrations and cumulative distribution from simulation, Case 1

(9)

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(10)

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(11)

where mI *%$2"#$*+/.#'#+2$'&%%$*+$C,?$T *%$2"#$'&%%$413$*+$2("?$w$*%$2"#$&(#.25.#$*+$'#2.#%$ &+9$s *%$2"#$/5R#.$%(##9$*+$'l%=$!"#$.#%5)2$*%^ 5 = 5 = STTT T=TPe Q=d T=b SP=P I m (22) D%%5'#$2"&2$&+$*+/.#'#+2$*%$2&C#+$#-#.8$fT$%#/1+9%$&+9$2"&2$&$%&'()*+,$5+*2?$L, /1..#%(1+9%$ 21$STTT$21++#%$10$,.&*+=$!"#.#$&.#$2"#+$eT$*+/.#'#+2%$2&C#+$95.*+,$2"#$%&'()*+,=$!"#$0.&/2*1+$ 10$2"#$%&'()*+,$5+*2$2&C#+$&%$(.*'&.8$*+/.#'#+2%$*%^ = 5 = 5 = d eT SP=P S=T PT T=TTTeb I nm f L (23) where L, 2"#$#E2#+2$10$2"#$%&'()*+,$5+*2$*%$2&C#+$&%$STTT$21++#%=$!"*%$%&'()*+,$(.121/1)$*%$ 2"#$1+#$9#<+#9$:8$2"#$g&+&9*&+$F.&*+$g1''*%%*1+$01.$3"#&2$%&'()*+,$@g&+&9*&+$F.&*+$ g1''*%%*1+?$STTeA= m#E2?$&%%5'#$2"#$&-#.&,#$)#-#)$10$/1+2&'*+&2*1+$*% c=PT((:$&+9$2"#$&-#.&,#$/1+2&'*+&2*1+$ )#-#)$*+$&$%)5,$*%$c_T=PdTT((:=$n#2$2"#$%)5,$1//5(8$&$-1)5'#$10$2#+$)*2.#%$&+9$3#*,"$j$C,=$ !"#+$2"#$+5':#.$10$%)5,%$'5%2$:#^ = T cL m c u (24) %1^ 5 5 = 5 = d PT S PT PdTT j PbdQ m (25)

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(12)

Figure 10 Histogram of sample concentrations and cumulative distribution from simulation, design study

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Figure 11 Random slugs for one realisation of the design example

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Figure 12 Concentration as a function of time for 22 tonne slugs (portion of data set)

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(13)

VARIOGRAMS OF CONCENTRATION N+$,#+#.&)?$2"#.#$*%$+1$&+&)82*/&)$#E(.#%%*1+$01.$2"#$-&.*1,.&'$10$/1+/#+2.&2*1+=$>13#-#.?$ 3"#+$2"#$%)5,$%*[#$*%$%'&))$&+9$2"#$+5':#.$10$%)5,%$*%$+12$211$)&.,#$@")#''#PA?$2"#.#$3*))$:#$ &)'1%2$+1$1-#.)&($10$2"#$%)5,%$&+9$2"#$%)5,%$01.'$&$\11)#&+$.&+91'$%#2=$N+$%5/"$&$/&%#?$*2$*%$ C+13+$2"&2$2"#$-&.*1,.&'$.*%#%$0.1'$[#.1$21$&$%*))$10^

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CONCLUSIONS

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(14)

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(15)

APPENDIX A – THE VARIANCE OF THE SAMPLE CONCENTRATION

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(16)

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