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it <br /> 0 <br /> 300 HYDROCARBON CONTAMINATED SOILS AND GROUNDWATER GROUNDWATER REMEDIATION LIMITS 301 <br /> >, �t of the seven c.haracteristi(. data sets using only its first five data points then its - <br /> M' first six data points [lien its fm st seven data points, etc This comparison is equiva- <br /> y lent to evaluating the data sets fol trendlessness as the data are being c.ollcoed <br /> Ci E L N 0 0 0 t) W N m p m " H <br /> E zzz � } } � zr � r <br /> � o <br /> 0 <br /> CL RESULTS PHASEI <br /> u (A <br /> Summarizing results presented in detail elsewhere,' 2 the linear asymptotic <br /> 0 <br /> method was superior to the exponential method for most of the seven charac- <br /> teristic data sets evaluated in Phase 1, 1 e , it identified an asymptotic condition <br /> u a- o o I I I I o I I ! with less data than the exponential regression method The exponential method <br /> HjX <br /> assumes a zero asymptote, while most of the data sets clearly exhibited a <br /> LU nonzero asymptote Presence of a nonzero asymptote has been interpreted to <br /> indicate that two distinct processes combine to produce the characteristic con- <br /> s r .. centration time patterns ' 2 The initial decline represents the active removal of <br /> m0 M m — m n 0 cm N contamination from the contaminated groundwater, while the asymptotic region <br /> uCL 0 o 0 0 0 0 o 0 o i represents slow release from residual hydrocarbon contaminated soils or a con- <br /> n �° <br /> ' tinumg slow leak <br /> C <br /> It was also shown'z that statistical variability in data in the asymptotic region <br /> 0 <br /> 0 could be explained, in large part,by sampling and analyttc.al variability, and that <br /> these sources of variability obscure precise determination of trends in the asymp- <br /> v+ 0 Rf­ o 0 to ao Un a) w W 0 <br /> oma oto cv o N a tv a n o totic region The effect of analytical variations on definition of the trend were <br /> 3 a i o 0 0 o a o o i cv w analyzed and are predictable ' Z <br /> 0 <br /> J <br /> PHASE 2 ADDITION OF NONLINEAR METHOD <br /> o a <br /> Vi Results of Phase I suggested that an alternative nonlinear method representing <br /> w 15 cc N N - — - - co 0 0 an exponential decay with a nonzero asymptote may be useful Regression anal- <br /> 0 0 0 0 0 0 o 0 0 0 0 <br /> v ,0 E g ysts is used to fit a function of the form <br /> :° <br /> N W <br /> 2 C = Coe-kt + Ci <br /> d <br /> ir <br /> ro The nonlinear regression procedure uses an iterative Gauss Newton method 6 <br /> ° E a R N ioN 00 (D to N o The initial estimates of C„ and k are determined by the exponential regression <br /> a W0 ,12 to o i) Ln to Lo a tv o rn <br /> cit a o a o 0 0 0 0 o i i i procedure while the initial estimate of Cf is zero By an iterative process, more <br /> 0 g realistic values of C., k, and Ci are determined that minimize the sum of squared <br /> residuals <br /> V <br /> 0 <br /> Development of PC Software <br /> 1= r <br /> 4 � a <br /> F o o c . N Ln v N h The nonlinear, linear asymptotic, and exponential methods are supported by <br /> 0 <br /> N w a r a user-friendly PC software package to be released by API in 1991 The pro- <br /> Fa " grain is written in "C" with graphics displays and plotting created with the <br />