{"id":131,"date":"2020-11-15T00:31:04","date_gmt":"2020-11-15T00:31:04","guid":{"rendered":"https:\/\/books.gw-project.org\/geologic-frameworks-for-groundwater-flow-models\/?post_type=chapter&p=131"},"modified":"2020-12-12T23:29:14","modified_gmt":"2020-12-12T23:29:14","slug":"exercise-solutions","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/geologic-frameworks-for-groundwater-flow-models\/chapter\/exercise-solutions\/","title":{"raw":"13 Exercise Solutions","rendered":"13 Exercise Solutions"},"content":{"raw":"

<\/a>Exercise 1 \u2013 Solution<\/h1>\r\nIf only the flow of groundwater through the sand is significant, what is the net\/gross ratio of this core?<\/em>\r\n\r\n[latex]\\displaystyle Net\/Gross=\\frac{0.19+0.29}{0.37+0.19+0.14+0.29+0.23}=0.39[\/latex]\r\n

Return to Exercise 1<\/a><\/p>\r\n\r\n

<\/a>Exercise 2 \u2013 Solution<\/h1>\r\nWhat are the calculated bulk vertical and horizontal hydraulic conductivities of the representative volume?<\/em>\r\n\r\n[latex]\\displaystyle Kv=\\frac{0.37+0.19+0.14+0.29+0.23}{\\frac{0.37}{1.0\\times 10^{-6}}+\\frac{0.19}{1.0\\times 10^{-4}}+\\frac{0.14}{2.0\\times 10^{-5}}+\\frac{0.29}{2.0\\times 10^{-4}}+\\frac{0.23}{5.0\\times 10^{-6}}}[\/latex]\r\n\r\nVertical bulk hydraulic conductivity = Kv<\/em> = 2.9 \u00d7 10-6<\/sup>\u00a0m\/s<\/strong>\r\n\r\n[latex]\\displaystyle Kh=\\frac{(1.0\\times 10^{-6}\\times 0.37)+(1.0\\times 10^{-4}\\times 0.19)+(2.0\\times 10^{-5}\\times 0.14)+(2.0\\times 10^{-4}\\times 0.29)+(5.0\\times 10^{-6}\\times 0.23)}{0.37+0.19+0.14+0.29+0.23}[\/latex]\r\n\r\nHorizontal bulk hydraulic conductivity = Kh<\/em> = 6.7 \u00d7 10-5<\/sup> m\/s<\/strong>\r\n

Return to Exercise 2<\/a><\/p>\r\n\r\n

<\/a>Exercise 3 \u2013 Solution<\/h1>\r\nWhat else would you need before using the calculated bulk hydraulic properties for a flow model?<\/em>\r\n\r\nYou would need to know how this core fits within the geological framework of the model. Some key questions to ask: What is the scale of the model compared to the scale of the core? This core would be reasonably representative of flow units that are a few meters thick, but not for units that are tens of meters thick. Are the stratigraphic horizons horizontal, or do they have a measurable dip? If so, it may be necessary to apply a dip correction<\/a>, as in Section 5. Keep in mind that the geology likely varies as much horizontally as it does vertically, so additional cores would be necessary to apply this methodology rigorously.\r\n

Return to Exercise 3<\/a><\/p>","rendered":"

<\/a>Exercise 1 \u2013 Solution<\/h1>\n

If only the flow of groundwater through the sand is significant, what is the net\/gross ratio of this core?<\/em><\/p>\n

\"\displaystyle Net/Gross=\frac{0.19+0.29}{0.37+0.19+0.14+0.29+0.23}=0.39\"<\/p>\n

Return to Exercise 1<\/a><\/p>\n

<\/a>Exercise 2 \u2013 Solution<\/h1>\n

What are the calculated bulk vertical and horizontal hydraulic conductivities of the representative volume?<\/em><\/p>\n

\"\displaystyle Kv=\frac{0.37+0.19+0.14+0.29+0.23}{\frac{0.37}{1.0\times 10^{-6}}+\frac{0.19}{1.0\times 10^{-4}}+\frac{0.14}{2.0\times 10^{-5}}+\frac{0.29}{2.0\times 10^{-4}}+\frac{0.23}{5.0\times 10^{-6}}}\"<\/p>\n

Vertical bulk hydraulic conductivity = Kv<\/em> = 2.9 \u00d7 10-6<\/sup>\u00a0m\/s<\/strong><\/p>\n

\"\displaystyle Kh=\frac{(1.0\times 10^{-6}\times 0.37)+(1.0\times 10^{-4}\times 0.19)+(2.0\times 10^{-5}\times 0.14)+(2.0\times 10^{-4}\times 0.29)+(5.0\times 10^{-6}\times 0.23)}{0.37+0.19+0.14+0.29+0.23}\"<\/p>\n

Horizontal bulk hydraulic conductivity = Kh<\/em> = 6.7 \u00d7 10-5<\/sup> m\/s<\/strong><\/p>\n

Return to Exercise 2<\/a><\/p>\n

<\/a>Exercise 3 \u2013 Solution<\/h1>\n

What else would you need before using the calculated bulk hydraulic properties for a flow model?<\/em><\/p>\n

You would need to know how this core fits within the geological framework of the model. Some key questions to ask: What is the scale of the model compared to the scale of the core? This core would be reasonably representative of flow units that are a few meters thick, but not for units that are tens of meters thick. Are the stratigraphic horizons horizontal, or do they have a measurable dip? If so, it may be necessary to apply a dip correction<\/a>, as in Section 5. Keep in mind that the geology likely varies as much horizontally as it does vertically, so additional cores would be necessary to apply this methodology rigorously.<\/p>\n

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