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wr . . � --3' -.F-, y. <br /> T"* <br /> h, <br /> A <br /> 5 <br /> r FLOW MODELING FOR y <br /> ` VAPOR EnRACI" ON SYMMS <br /> by Dcnro,t_Lfauldin <br /> sacrantentn, CA <br /> I� <br /> Q G flow rate <br /> 1,36,empirical correction factor <br /> INTRODUCTION K intrirGsic permeability <br /> 1. b = length of screen in vapor <br /> } 'the task of modeling air flow through soil was <br /> extraction well <br /> undertaken to provide a more sign Parameters of u z dynamic viscosity of air <br /> i 3 in unSerstwiding the basic designsoil venting PV absolute pressure in vapor <br /> a vapor extraction system• extraction well(vacuum) <br /> ' applications,it is important to know the amount <br /> quired P = atmospheric ambient air , <br /> ff of vacuum in the vapor extraction well repressure <br /> to produce t desed flow rate theoretitcalumtthe ethod for R = radius of influence <br /> This paper P r = radius of vapor extraction <br /> modeling air flow through soil. Viand data well <br /> I <br /> compared to the theoreticadl onthod� theoretical <br /> an empirical figure bas f the equation values <br /> �l which was adjusted by the field data. Additionally,xssumptions sensitivity analysis of <br /> mctho con tete ao <br /> were made to p <br /> €i parameters: <br /> y TI[G(1tiCTICAI.M�"l[IUD certain. <br /> Nttmcrov presented an u 6.325f)x109, (ft2f[b x rain) <br /> In 1965, Aravin and which blft2 <br /> Dare's law. p =2116.224, U ) <br /> equation adapted fro h a Porous media. R 100, (ft) <br /> modeled air flaw through L r 0.1667, (ft) <br /> uatiun l was <br /> e: log(Rif) The value for viscosityereAmbient eair pressure,was <br /> Q = 136 Kblu i(Pf`�j t'� ! S l Passunted tobeI atmospher& Due to R being <br /> Q = {low rate buried in the to function, it was <br /> found to bee <br /> non-sensitive to the flow rate; therefore,a value <br /> 1.36=empirical correction factor witich corresponds to an <br /> K = intrinsic permeability of iW feet was use value <br /> average long-term Heid nteasuretttent A <br /> b = thickness of Porous media tens of 0.1667 <br /> u = dynamic viscosity of fluid typically used in sail venting v <br /> apor <br /> Pf = pressure of fluid feet was used as a radion of thee vdividing <br /> P = absolute pressure well. Substituting the assumed and ssitnplifying <br /> R = length of strata both sides of the equation by"b, <br /> r = radius of induction point yields: <br /> To adapt the Aravin and Numerov equation so nation3 <br /> it venting applications. <br /> that it relates to snthe <br /> uatiun Parameters were = 7.7397x10 ((Pv21P)-p) <br /> detinitiuns of the eq q K <br /> redefined to yield: <br /> Equation 3 determines the th.;oretical f10- <br /> wn a vrate <br /> of <br /> Pled flow rate)dependent on <br /> l=c+u�►ti<tn 2 per fact of screen (` e uatiun is depe <br /> t extraction well. The q <br /> Q = 1.36 Kblu t(p,2lP)-Pj !tog{Rlr) the intrinsic permeability and the amount of <br /> i <br />