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<oai_dc:dc xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
  <dc:contributor>Allen M. Shapiro</dc:contributor>
  <dc:creator>V.D. Cvetkovic</dc:creator>
  <dc:date>1992</dc:date>
  <dc:description>&lt;p&gt;&lt;span&gt;It is common to represent solute tranport in heterogeneous formations in terms of the resident concentration&amp;nbsp;&lt;/span&gt;&lt;i&gt;C&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;/i&gt;&lt;span&gt;(x, t), regarded as a random space function. The present study investigates the alternative representation by&amp;nbsp;&lt;/span&gt;&lt;i&gt;q&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;/i&gt;&lt;span&gt;, the solute mass flux at a point of a control plane normal to the mean flow. This representation is appropriate for many field applications in which the variable of interest is the mass of solute discharged through a control surface. A general framework to compute the statistical moments of&amp;nbsp;&lt;/span&gt;&lt;i&gt;q&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;/i&gt;&lt;span&gt;and of the associated total solute discharge&amp;nbsp;&lt;/span&gt;&lt;i&gt;Q&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;/i&gt;&lt;span&gt;and mass&amp;nbsp;&lt;/span&gt;&lt;i&gt;M&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;/i&gt;&lt;span&gt;is established. With&amp;nbsp;&lt;/span&gt;&lt;i&gt;x&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;/i&gt;&lt;span&gt;the direction of the mean flow, a solute particle is crossing the control plane at&amp;nbsp;&lt;/span&gt;&lt;i&gt;y&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;/i&gt;&lt;span&gt;= η,&amp;nbsp;&lt;/span&gt;&lt;i&gt;z&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;/i&gt;&lt;span&gt;= ζ and at the travel (arrival) time τ. The associated expected solute flux value is proportional to the joint probability density function (pdf)&amp;nbsp;&lt;/span&gt;&lt;i&gt;g&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;span&gt;&amp;nbsp;of η, ζ and τ, whereas the variance of&amp;nbsp;&lt;/span&gt;&lt;i&gt;q&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;/i&gt;&lt;span&gt;is shown to depend on the joint pdf&amp;nbsp;&lt;/span&gt;&lt;i&gt;g&lt;span&gt;&amp;nbsp;&lt;/span&gt;&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;span&gt;&amp;nbsp;of the same variables for two particles. In turn, the statistical moments of η, ζ and τ depend on those of the velocity components through a system of stochastic ordinary differential equations. For a steady velocity field and neglecting the effect of pore‐scale dispersion, a major simplification of the problem results in the independence of the random variables η, ζ and τ. As a consequence, the pdf of η and ζ can be derived independently of τ. A few approximate approaches to derive the statistical moments of η, ζ and τ are outlined. These methods will be explored in paper 2 in order to effectively derive the variances of the total solute discharge and mass, while paper 3 will deal with the nonlinear effect of the velocity variance upon the moments of η, ζ and τ&lt;/span&gt;&lt;/p&gt;</dc:description>
  <dc:format>application/pdf</dc:format>
  <dc:identifier>10.1029/91WR03086</dc:identifier>
  <dc:language>en</dc:language>
  <dc:publisher>American Geophysical Union</dc:publisher>
  <dc:title>A solute flux approach to transport in heterogeneous formations: 1. The general framework</dc:title>
  <dc:type>article</dc:type>
</oai_dc:dc>