{"id":1183,"date":"2026-05-12T21:46:50","date_gmt":"2026-05-12T21:46:50","guid":{"rendered":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/chapter\/aquifer-test-analysis\/"},"modified":"2026-05-13T16:30:13","modified_gmt":"2026-05-13T16:30:13","slug":"aquifer-test-analysis","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/chapter\/aquifer-test-analysis\/","title":{"raw":"8.4 Aquifer Test Analysis","rendered":"8.4 Aquifer Test Analysis"},"content":{"raw":"
\r\n
\r\n\r\nThe following is a general, simplified discussion of the analysis of aquifer test data. A detailed and comprehensive overview of aquifer testing procedures and data analysis methods is provided in An Introduction to Hydraulic Testing in Hydrogeology: Basic Pumping, Slug, and Packer Methods<\/em><\/span><\/a>\u2197 by Woessner and others (2020), which is available as a free download from The Groundwater Project. Professionals and students who are interested in aquifer testing are encouraged to download and review that book.\r\n\r\n<\/div>\r\n
\r\n

The Theis Curve\u2011Matching Method for Non\u2011Leaky (i.e., fully confined) Aquifers<\/h3>\r\n
\r\n\r\nThe data set produced by a multi\u2011well aquifer test with a single observation well includes a pumping rate, a distance from the pumping well to the observation well, and a set of time\u2011drawdown data\u2014that is, values for drawdown at various times after the start of pumping. Analyzing the data using the traditional Theis curve\u2011matching method requires the following steps.\r\n\r\n<\/div>\r\n
    \r\n \t
  1. Obtain a Theis equilibrium type curve graph and a blank log\u2011log graph that has the same scale as the Theis type curve. A blank log\u2011log graph is provided as Figure\u00a043<\/span><\/a> and the type curve with the same scale is provided as Figure\u00a044<\/span><\/a>.<\/li>\r\n \t
  2. Plot the time\u2011drawdown data on the blank log\u2011log graph. An example is shown in Figure\u00a045<\/span><\/a>a.<\/li>\r\n \t
  3. Overlay the time\u2011drawdown data graph on the type curve\u2014it is best to use a light table or tape the type curve on a window or white computer screen\u2014and move the graph until the data line up with the type curve. It is essential that the axes on both graphs are parallel during the matching procedure; otherwise, the match will not be correct. An example is shown in Figure\u00a046<\/span><\/a>a<\/li>\r\n \t
  4. Select a corresponding point on each graph and determine the values of u<\/em> and W(u<\/em>) for that point on the time\u2011drawdown graph. The point does not have to fall on the Theis curve; it only needs to be in an area where both graphs overlap so a common match point can be determined. An example is provided in Figure\u00a046<\/span><\/a>b.<\/li>\r\n \t
  5. Re\u2011arrange the Theis equation\u2014Equation\u00a0(73)<\/span><\/a>\u2014to solve for [latex]T[\/latex] and substitute the values of [latex]s [\/latex]and [latex]W(u)[\/latex] from the curve match point to determine [latex]T[\/latex]. The re\u2011arranged equation is shown as Equation (76)<\/span><\/a>.<\/li>\r\n<\/ol>\r\n<\/colgroup>\r\n\r\n\r\n
    <\/th>\r\n[latex]T = \\frac{Q}{4\\pi s}W(u)[\/latex]<\/th>\r\n(76)<\/span><\/th>\r\n<\/tr>\r\n<\/thead>\r\n<\/table>\r\n
      \r\n \t
    1. Re\u2011arrange the equation for [latex]u[\/latex] shown as Equation\u00a0(74)<\/span><\/a> to solve for [latex]S[\/latex] and substitute the values of [latex]t[\/latex] and u from the curve match point, and the value of [latex]T[\/latex] determined in step 5, to calculate [latex]S[\/latex]. The re\u2011arranged equation is shown as Equation\u00a0(77)<\/span><\/a>.<\/li>\r\n<\/ol>\r\n<\/colgroup>\r\n\r\n\r\n
      <\/th>\r\n[latex]S = \\frac{4Ttu}{r^{2}}[\/latex]<\/th>\r\n(77)<\/span><\/th>\r\n<\/tr>\r\n<\/thead>\r\n<\/table>\r\n
      \r\n\r\nFigure\u00a046<\/span><\/a> shows an example of a time\u2011drawdown data set with a correct curve match. Figure\u00a046<\/span><\/a>a shows the data plotted on a log\u2011log graph with a type curve plotted to the same scale. In Figure\u00a046<\/span><\/a>b the data graph has been overlain on the type curve such that the axes are parallel and the data form a best fit to the drawdown curve. Note that the data do not exactly fall on the type curve; there will always be some \u201cnoise\u201d in a time\u2011drawdown data set due to measurement limitations and variations in water level related to barometric pressure changes, surface stresses (e.g., vehicular traffic), and distant wells pumping the aquifer. In Figure\u00a046<\/span><\/a>b match point [latex]t[\/latex]\u00a0(time)\u00a0=\u00a01 and [latex]s[\/latex]\u00a0(drawdown)\u00a0=\u00a01 results in [latex]u[\/latex]\u00a0=\u00a00.31 and [latex]W(u)[\/latex]\u00a0=\u00a07. Figure\u00a047<\/span><\/a> shows an example of an incorrect curve match with non\u2011parallel axes (Exerc<\/u><\/span>ise\u00a0<\/u><\/span><\/span><\/a>10<\/u>\u2ba7 and Exercis<\/span>e\u00a01<\/span><\/span><\/a>1\u2ba7).\r\n\r\n<\/div>\r\n
      \r\n\r\n\"\"\r\n\r\n<\/div>\r\n
      \r\n
      \r\n\r\nFigure\u00a043\u00a0\u2011\u00a0<\/strong>Blank log\u2011log graph paper with same scale and extent as type curve shown in Figure\u00a044<\/span><\/a> for curve\u2011matching.<\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n
      \r\n\r\n\"\"\r\n
      \r\n
      \r\n
      \r\n\r\nFigure\u00a044\u00a0\u2011\u00a0<\/strong>Theis non\u2011equilibrium type curve for non\u2011leaky (i.e., fully) confined aquifers.<\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
      \r\n\r\n\"\"\r\n
      \r\n
      \r\n
      \r\n\r\nFigure\u00a045\u00a0\u2011\u00a0<\/strong>Example data for curve\u2011matching method: a) time\u2011drawdown data from an aquifer test; b) Theis non\u2011equilibrium type curve for non\u2011leaky (i.e., fully) confined aquifers.<\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
      \r\n\r\n\"\"\r\n
      \r\n
      \r\n
      \r\n\r\nFigure\u00a046\u00a0\u2011\u00a0<\/strong>Example of curve\u2011matching method: a) plotted data overlain on type curve with best match of the data to the type curve; b) match point t<\/em>\u00a0(time)\u00a0=\u00a01 and s<\/em>\u00a0(drawdown)\u00a0=\u00a01 on data graph corresponds to W(u)<\/em>\u00a0=\u00a07 and u<\/em>\u00a0=\u00a00.31.<\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
      \r\n\r\n\"\"\r\n
      \r\n
      \r\n
      \r\n\r\nFigure\u00a047\u00a0\u2011\u00a0<\/strong>Example of incorrect curve\u2011matching due to failure to properly align the axes.<\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
      \r\n

      Leaky Confined and Unconfined Methods<\/h3>\r\n
      \r\n\r\nAs shown in Figure\u00a040<\/span><\/a>, the drawdown curve for a leaky confined aquifer will not follow the same shape as a non\u2011leaky confined aquifer; therefore, drawdowns from a leaky confined aquifer will not match the Theis non\u2011leaky type curve due to reduced drawdowns caused by the addition of water to the aquifer through the leaky confining layer. Hantush and Jacob (1955) and Walton (1960) developed curve\u2011matching methods that are like the Theis method but include additional type curves and an additional term in the well function that accounts for the contribution of interformational leakage. A version of the Walton type curves is provided as Figure\u00a048<\/span><\/a>.\r\n\r\n<\/div>\r\n
      \r\n\r\n\"\"\r\n\r\n<\/div>\r\n
      \r\n
      \r\n
      \r\n\r\nFigure\u00a048\u00a0\u2011\u00a0<\/strong>Theoretical type curves of W(u,r\/B<\/em>) versus 1\/u<\/em> for a leaky aquifer (from Freeze & Cherry, 1979; modified from Walton, 1960).<\/span>\r\n\r\n<\/div><\/blockquote>\r\n<\/div>\r\n
      \r\n\r\nIn an unconfined aquifer, the drawdown response has three separate parts to it which result in a distinctive shape shown in Figure\u00a042<\/span><\/a>. Neuman (1975) developed a similar curve\u2011matching method in which the well function is composed of three separate arguments, one for each of the drawdown stages. A version of the Neuman type curves is presented as Figure\u00a049<\/span><\/a>.\r\n\r\n<\/div>\r\n
      \r\n\r\n\"\"\r\n\r\n<\/div>\r\n
      \r\n
      \r\n
      \r\n\r\nFigure\u00a049\u00a0\u2011\u00a0<\/strong>Theoretical type curves of W(uA, uB, \u03b7<\/em>) versus 1\/uA<\/em> and 1\/uB<\/em> for an unconfined aquifer (from Freeze & Cherry, 1979; modified from Neuman 1975).<\/span>\r\n\r\n<\/div><\/blockquote>\r\n<\/div>\r\n
      \r\n\r\nThe leaky and unconfined methods are discussed in more detail in sections 9 and 10 of An Introduction to Hydraulic Testing in Hydrogeology: Basic Pumping, Slug, and Packer Methods<\/em><\/span><\/a>\u2197 by Woessner and others (2020), as well as in Analysis and Evaluation of Pumping Test Data (2nd edition<\/span><\/a>)<\/em>\u2197 by Kruseman and others (2000). Both books are available as free downloads from The Groundwater Project. Readers are encouraged to review these books for more information.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"
      \n
      \n

      The following is a general, simplified discussion of the analysis of aquifer test data. A detailed and comprehensive overview of aquifer testing procedures and data analysis methods is provided in An Introduction to Hydraulic Testing in Hydrogeology: Basic Pumping, Slug, and Packer Methods<\/em><\/span><\/a>\u2197 by Woessner and others (2020), which is available as a free download from The Groundwater Project. Professionals and students who are interested in aquifer testing are encouraged to download and review that book.<\/p>\n<\/div>\n

      \n

      The Theis Curve\u2011Matching Method for Non\u2011Leaky (i.e., fully confined) Aquifers<\/h3>\n
      \n

      The data set produced by a multi\u2011well aquifer test with a single observation well includes a pumping rate, a distance from the pumping well to the observation well, and a set of time\u2011drawdown data\u2014that is, values for drawdown at various times after the start of pumping. Analyzing the data using the traditional Theis curve\u2011matching method requires the following steps.<\/p>\n<\/div>\n

        \n
      1. Obtain a Theis equilibrium type curve graph and a blank log\u2011log graph that has the same scale as the Theis type curve. A blank log\u2011log graph is provided as Figure\u00a043<\/span><\/a> and the type curve with the same scale is provided as Figure\u00a044<\/span><\/a>.<\/li>\n
      2. Plot the time\u2011drawdown data on the blank log\u2011log graph. An example is shown in Figure\u00a045<\/span><\/a>a.<\/li>\n
      3. Overlay the time\u2011drawdown data graph on the type curve\u2014it is best to use a light table or tape the type curve on a window or white computer screen\u2014and move the graph until the data line up with the type curve. It is essential that the axes on both graphs are parallel during the matching procedure; otherwise, the match will not be correct. An example is shown in Figure\u00a046<\/span><\/a>a<\/li>\n
      4. Select a corresponding point on each graph and determine the values of u<\/em> and W(u<\/em>) for that point on the time\u2011drawdown graph. The point does not have to fall on the Theis curve; it only needs to be in an area where both graphs overlap so a common match point can be determined. An example is provided in Figure\u00a046<\/span><\/a>b.<\/li>\n
      5. Re\u2011arrange the Theis equation\u2014Equation\u00a0(73)<\/span><\/a>\u2014to solve for [latex]T[\/latex] and substitute the values of [latex]s[\/latex]and [latex]W(u)[\/latex] from the curve match point to determine [latex]T[\/latex]. The re\u2011arranged equation is shown as Equation (76)<\/span><\/a>.<\/li>\n<\/ol>\n\n\n\n\n<\/colgroup>\n\n\n
        <\/th>\n[latex]T = \\frac{Q}{4\\pi s}W(u)[\/latex]<\/th>\n(76)<\/span><\/th>\n<\/tr>\n<\/thead>\n<\/table>\n
          \n
        1. Re\u2011arrange the equation for [latex]u[\/latex] shown as Equation\u00a0(74)<\/span><\/a> to solve for [latex]S[\/latex] and substitute the values of [latex]t[\/latex] and u from the curve match point, and the value of [latex]T[\/latex] determined in step 5, to calculate [latex]S[\/latex]. The re\u2011arranged equation is shown as Equation\u00a0(77)<\/span><\/a>.<\/li>\n<\/ol>\n\n\n\n\n<\/colgroup>\n\n\n
          <\/th>\n[latex]S = \\frac{4Ttu}{r^{2}}[\/latex]<\/th>\n(77)<\/span><\/th>\n<\/tr>\n<\/thead>\n<\/table>\n
          \n

          Figure\u00a046<\/span><\/a> shows an example of a time\u2011drawdown data set with a correct curve match. Figure\u00a046<\/span><\/a>a shows the data plotted on a log\u2011log graph with a type curve plotted to the same scale. In Figure\u00a046<\/span><\/a>b the data graph has been overlain on the type curve such that the axes are parallel and the data form a best fit to the drawdown curve. Note that the data do not exactly fall on the type curve; there will always be some \u201cnoise\u201d in a time\u2011drawdown data set due to measurement limitations and variations in water level related to barometric pressure changes, surface stresses (e.g., vehicular traffic), and distant wells pumping the aquifer. In Figure\u00a046<\/span><\/a>b match point [latex]t[\/latex]\u00a0(time)\u00a0=\u00a01 and [latex]s[\/latex]\u00a0(drawdown)\u00a0=\u00a01 results in [latex]u[\/latex]\u00a0=\u00a00.31 and [latex]W(u)[\/latex]\u00a0=\u00a07. Figure\u00a047<\/span><\/a> shows an example of an incorrect curve match with non\u2011parallel axes (Exerc<\/u><\/span>ise\u00a0<\/u><\/span><\/span><\/a>10<\/u>\u2ba7 and Exercis<\/span>e\u00a01<\/span><\/span><\/a>1\u2ba7).<\/p>\n<\/div>\n

          \n

          \"\"<\/p>\n<\/div>\n

          \n
          \n

          Figure\u00a043\u00a0\u2011\u00a0<\/strong>Blank log\u2011log graph paper with same scale and extent as type curve shown in Figure\u00a044<\/span><\/a> for curve\u2011matching.<\/span><\/p>\n<\/div>\n<\/div>\n

          \n

          \"\"<\/p>\n

          \n
          \n
          \n

          Figure\u00a044\u00a0\u2011\u00a0<\/strong>Theis non\u2011equilibrium type curve for non\u2011leaky (i.e., fully) confined aquifers.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n

          \n

          \"\"<\/p>\n

          \n
          \n
          \n

          Figure\u00a045\u00a0\u2011\u00a0<\/strong>Example data for curve\u2011matching method: a) time\u2011drawdown data from an aquifer test; b) Theis non\u2011equilibrium type curve for non\u2011leaky (i.e., fully) confined aquifers.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n

          \n

          \"\"<\/p>\n

          \n
          \n
          \n

          Figure\u00a046\u00a0\u2011\u00a0<\/strong>Example of curve\u2011matching method: a) plotted data overlain on type curve with best match of the data to the type curve; b) match point t<\/em>\u00a0(time)\u00a0=\u00a01 and s<\/em>\u00a0(drawdown)\u00a0=\u00a01 on data graph corresponds to W(u)<\/em>\u00a0=\u00a07 and u<\/em>\u00a0=\u00a00.31.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n

          \n

          \"\"<\/p>\n

          \n
          \n
          \n

          Figure\u00a047\u00a0\u2011\u00a0<\/strong>Example of incorrect curve\u2011matching due to failure to properly align the axes.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n

          \n

          Leaky Confined and Unconfined Methods<\/h3>\n
          \n

          As shown in Figure\u00a040<\/span><\/a>, the drawdown curve for a leaky confined aquifer will not follow the same shape as a non\u2011leaky confined aquifer; therefore, drawdowns from a leaky confined aquifer will not match the Theis non\u2011leaky type curve due to reduced drawdowns caused by the addition of water to the aquifer through the leaky confining layer. Hantush and Jacob (1955) and Walton (1960) developed curve\u2011matching methods that are like the Theis method but include additional type curves and an additional term in the well function that accounts for the contribution of interformational leakage. A version of the Walton type curves is provided as Figure\u00a048<\/span><\/a>.<\/p>\n<\/div>\n

          \n

          \"\"<\/p>\n<\/div>\n

          \n
          \n
          \n

          Figure\u00a048\u00a0\u2011\u00a0<\/strong>Theoretical type curves of W(u,r\/B<\/em>) versus 1\/u<\/em> for a leaky aquifer (from Freeze & Cherry, 1979; modified from Walton, 1960).<\/span><\/p>\n<\/div>\n<\/blockquote>\n<\/div>\n

          \n

          In an unconfined aquifer, the drawdown response has three separate parts to it which result in a distinctive shape shown in Figure\u00a042<\/span><\/a>. Neuman (1975) developed a similar curve\u2011matching method in which the well function is composed of three separate arguments, one for each of the drawdown stages. A version of the Neuman type curves is presented as Figure\u00a049<\/span><\/a>.<\/p>\n<\/div>\n

          \n

          \"\"<\/p>\n<\/div>\n

          \n
          \n
          \n

          Figure\u00a049\u00a0\u2011\u00a0<\/strong>Theoretical type curves of W(uA, uB, \u03b7<\/em>) versus 1\/uA<\/em> and 1\/uB<\/em> for an unconfined aquifer (from Freeze & Cherry, 1979; modified from Neuman 1975).<\/span><\/p>\n<\/div>\n<\/blockquote>\n<\/div>\n

          \n

          The leaky and unconfined methods are discussed in more detail in sections 9 and 10 of An Introduction to Hydraulic Testing in Hydrogeology: Basic Pumping, Slug, and Packer Methods<\/em><\/span><\/a>\u2197 by Woessner and others (2020), as well as in Analysis and Evaluation of Pumping Test Data (2nd edition<\/span><\/a>)<\/em>\u2197 by Kruseman and others (2000). Both books are available as free downloads from The Groundwater Project. Readers are encouraged to review these books for more information.<\/p>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":8,"menu_order":27,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1183","chapter","type-chapter","status-publish","hentry"],"part":1489,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters\/1183","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/users\/8"}],"version-history":[{"count":3,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters\/1183\/revisions"}],"predecessor-version":[{"id":1860,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters\/1183\/revisions\/1860"}],"part":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/parts\/1489"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters\/1183\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/media?parent=1183"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapter-type?post=1183"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/contributor?post=1183"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/license?post=1183"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}