Jos_von_Asmuth_Thesis.pdf - repository

_~ÅâÖêçìåÇ=~åÇ=íÜÉçêó=d h d − hS = + r(2.45)dtc=fí=áë=åçíÉÇ=íÜ~í=Éèì~íáçå=EOKQRF=ÇçÉë=åçí=Åçåí~áå=~åó=êÉÑÉêÉåÅÉ=íç=~=ëé~íá~ä=ÇáãÉåëáçåK=qÜÉ=áåíÉêå~ä=ÜÉ~Ç=çÑ=íÜÉ=ëóëíÉã=áë=ìåáÑçêãI=~åÇ=çåäó=~=ÇáÑÑÉêÉåÅÉ=áå=ÜÉ~Ç=ïáíÜ=íÜÉ=çìíëáÇÉ=ïçêäÇ=áë=ëéÉÅáÑáÉÇI=ïáíÜçìí=~=ÇáêÉÅíáçåK=dê~éÜáÅ~ääó=E~ë=áå=ÑáÖìêÉ=OKNUF=~åÇ=áåíìáíáîÉäóI=ÜçïÉîÉêI=áí=ã~ó=ÄÉ=ÅçåîÉåáÉåí=íç=éáÅíìêÉ=íÜÉ=ÜÉ~Ç=ÇáÑÑÉêÉåÅÉ=~ë=~=îÉêíáÅ~ä=Åçäìãå=çÑ=ï~íÉêI=ïÜáÅÜ=çÑ=ÅçìêëÉ=êÉèìáêÉë=íÜÉ=îÉêíáÅ~ä=ÇáãÉåëáçåK=fÑ=ïÉ=ëçäîÉ=EOKQRF=Ñçê=~å=áãéìäëÉ=çÑ=êÉÅÜ~êÖÉ=~åÇ=ìëÉ=EOKPQF=I=ïÉ=ÑáåÇ=íÜ~í=íÜÉ=áãéìäëÉ=êÉëéçåëÉ=ÑìåÅíáçå=xJz=áë=~å=ÉñéçåÉåíá~ä=~åÇ=Éèì~äë=íÜ~í=çÑ=~=ëáåÖäÉI=äáåÉ~ê=êÉëÉêîçáê=EëÉÉ=~äëç=ëÉÅíáçå=OKPKNFW==θ 1 t( t) = exp( )S− cS(2.46)=^ë=Ñçê=~åó=äáåÉ~ê=ëóëíÉãI=~äëç=áå=íÜáë=Å~ëÉ=íÜÉ=ÖêçìåÇï~íÉê=äÉîÉä=ÑäìÅíì~íáçåë=Å~å=åçï=ÄÉ=ÑçìåÇ=íÜêçìÖÜ=ÅçåîçäìíáçåK=qÜÉ=äáåÉ~ê=êÉëÉêîçáêI=ÜçïÉîÉêI=Ü~ë=íÜÉ=êÉã~êâ~ÄäÉ=~åÇ=ìëÉÑìä=éêçéÉêíó=íÜ~í=íÜÉ=ÑäìÅíì~íáçåë=áå=äÉîÉä=ã~ó=~äëç=ÄÉ=ÅçãéìíÉÇ=êÉÅìêëáîÉäóK=få=çíÜÉê=ïçêÇëI=íÜÉ=î~äìÉ=çÑ= h( t ) =~í=~åó=íáãÉ=ëíÉé=ã~ó=ÄÉ=ÅçãéìíÉÇ=Ñêçã= h( t − ∆ t)=~åÇ=íÜÉ=íçí~ä=áåéìí=çîÉê=íÜÉ=íáãÉ=ëíÉé R tI=~ë=xaÉ=wÉÉìï=~åÇ=eÉääáåÖ~I=NVRUzW==∆t∆th( t) = { h( t − ∆t) − d}exp( − ) + Rtc{1 − exp( − )} + d(2.47)cScS=bèì~íáçå=EOKQTF=áë=Éèìáî~äÉåí=íç=~å=^ouENF=ãçÇÉä=EÉèì~íáçå=EOKQF=F=áå=ÇáëÅêÉíÉ=íáãÉ=xhåçííÉêë=~åÇ=_áÉêâÉåëI=OMMMzK=qÜÉ=Ñ~Åí=íÜ~í= h Å~å=ÄÉ=ÅçãéìíÉÇ=êÉÅìêëáîÉäóI=~ääçïë=íÜÉ=êÉëéçåëÉ=é~ê~ãÉíÉêë=x c,S z=íç=ÅÜ~åÖÉ=éáÉÅÉïáëÉ=çîÉê=íáãÉK=`çåëÉèìÉåíäóI=Éèì~íáçå=EOKQTF=Å~å=~äëç=ÄÉ=~ééäáÉÇ=íç=åçåJëí~ÄäÉ=çê=åçåJäáåÉ~ê=ëóëíÉãë=EïÜÉêÉ= c =~åÇLçê= S ~êÉ=~=ÑìåÅíáçå=çÑ= h FK==1/Sresponse factor (−)cS = 0.05cS = 0.1cS = 0.2cS = 0.40 50 100 150 200time (days)figure 2.19: Example IR functions of the reservoirsystem of figure 2.18 for different values of cS .==== RN=2.3.5.2 Recharge on a system with a one-dimensional head gradientfå=~=ëóëíÉã=ïáíÜ=~=çåÉJÇáãÉåëáçå~äI=Üçêáòçåí~ä=ÜÉ~Ç=Öê~ÇáÉåíI=íÜÉ=ï~íÉê=Ä~ä~åÅÉ=Éèì~íáçå=áë=ÖáîÉå=ÄóW==∂qx∂h− = S − r(2.48)∂x∂tKKÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁKÁK