{"id":1709,"date":"2026-02-14T04:24:40","date_gmt":"2026-02-14T04:24:40","guid":{"rendered":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/chapter\/ch053-xhtml\/"},"modified":"2026-08-01T10:48:20","modified_gmt":"2026-08-01T10:48:20","slug":"using-superposition-to-represent-simple-boundary-conditions","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/chapter\/using-superposition-to-represent-simple-boundary-conditions\/","title":{"raw":"11.2 Using Superposition to Represent Simple Boundary Conditions","rendered":"11.2 Using Superposition to Represent Simple Boundary Conditions"},"content":{"raw":"
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\r\n\r\nOne of the basic assumptions used to develop analytical solutions to predict drawdown in wells penetrating unconfined, confined, leaky confined, and unconfined units, and associated confining beds is that the set of geologic units being represented are infinite in lateral extent and no boundaries are present in the portion of the aquifer being stressed. In an extensive groundwater system, where boundaries are located tens of kilometers from the test site and the cone of depression of the hydraulic test may only extend a few kilometers, the assumption of an infinite water\u2011bearing unit is reasonable (Figure 71<\/a>, Well A).\r\n\r\n<\/div>\r\n
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\r\n
\r\n
\r\n\r\nFigure 71 \u2011<\/strong> Schematic map view of a shallow isotropic and homogeneous confined aquifer (tan) that is bordered by impermeable granite bed rock, a well\u2011connected large lake, and mountain ranges that allow some flow into the aquifer. Cones of depression are plotted for three wells that are pumping at similar rates. Red represents more drawdown and blue less drawdown. Black lines represent drawdown contours that have larger magnitude near the center of the cone of depression. At Well A, the cone of depression is symmetrical, as pumping has not encountered boundaries that limit the expansion of the cone. At this site, for analytical purposes, the aquifer can be assumed to represent a system that is infinite in extent. At Well B, the cone of depression encountered the impermeable bedrock and began to expand along the boundary and deepen. The equipotential lines indicate flow is parallel to the boundary converging toward the position of the well where flow lines turn to flow to the well. Well C, is near a large lake that is in communication with the aquifer. The lake provides water to the pumping well through lateral aquifer recharge so drawdown slows and eventually the cone no longer grows when inflow from the lake equals the pumping rate. The equipotential lines indicate flow across the boundary.<\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
\r\n\r\nHydraulic testing can identify boundary conditions that alter drawdown at observation wells or production wells. When boundaries are encountered the trend in drawdown will change as pumping continues. The rate of drawdown will decrease if a recharge boundary (Figure 71<\/a>, Well C) is encountered, and the rate of drawdown will increase if an impermeable boundary (Figure 71<\/a>, Well B) is contacted. The effect of boundaries on drawdown trends for pumping or observation wells in an aquifer behaving as a Theis system (i.e., totally confined) are shown in Figure 72<\/a>. Figure 73<\/a> illustrates the effect of boundaries on the shape of Cooper\u2011Jacob semi\u2011log time\u2011drawdown plots.\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 72 \u2011<\/strong> A log\u2011log plot of drawdown versus time for a pumping well penetrating a confined aquifer. The blue line represents the drawdown expected if the aquifer behaves as a Theis system and is unbounded. The time\u2011drawdown curve also shows the response of the theoretical Theis conditions if the cone of depression encounters a no\u2011flow boundary (upper black dashed line). The lower dashed curve indicates that the drawdown would be less if recharge or leakage from a boundary is encountered (Cherry, 2022).<\/span>\r\n\r\n<\/div><\/blockquote>\r\n<\/div>\r\n
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\r\n\r\nFigure 73 \u2011<\/strong> Examples of boundary condition influences on time\u2011drawdown data collected during a constant\u2011discharge pumping test of a confined unit. Plots are semi\u2011log graphs. Drawdown changes occur in both pumping and observation wells. a) The theorical response of a totally confined aquifer that is not affected by boundary conditions, the aquifer is infinite in extent. b) The deviation in the time\u2011drawdown data (red dashed line) that shows the slope of the drawdown trend is decreasing and reaching equilibrium as a recharge boundary is encountered. c) The deviation in the time\u2011drawdown data when an impermeable boundary is encountered as shown by the red dashed line. Drawdown increases with time.<\/span>\r\n\r\n<\/div><\/blockquote>\r\n<\/div>\r\n
\r\n\r\nCare must be taken to determine the likely source of the observed drawdown response when assessing the presence or absence of aquifer boundaries. In this section, we discuss lateral recharge boundaries in contrast to recharge from local confining beds and overlying aquifers as discussed in Section\u00a09 (i.e., Hantush\u2011Jacob and Hantush Equations). Leaky aquifer settings will cause drawdown curve slopes to decrease without the cone of depression encountering an adjacent physical boundary. Unconfined aquifers with delayed yield also exhibit a period of decreased slope and a period of increasing drawdown that are not related to a lateral recharge boundary.\r\n\r\n<\/div>\r\n
\r\n\r\nAs stated, at some test sites physical boundaries adjacent to the groundwater system may be close enough to affect hydraulic testing and\/or planned production rates. When the configurations of boundaries are relatively simple, e.g., a linear boundary, the effect of the boundary on the predicted drawdown can be addressed using image well theory based on superposition of analytical solutions. As boundary conditions become less geometrically linear and more complex, other techniques such as numerical modeling are more appropriate because analytical models cannot easily address complex boundaries (e.g., Anderson et al., 2015).\r\n\r\n<\/div>\r\n
\r\n

Image Well Methodology<\/h3>\r\n
\r\n\r\nImage well methodology generates the drawdown distribution that would result when pumping near a boundary. It applies standard analytical models developed in previous sections. The method involves first replacing the bounded confined or unconfined system with an infinite aquifer, then placing one or more image wells on the other side of the boundary at the same distance the pumping well is located from the identified boundary. Depending on the boundary being simulated, image wells are either pumped or water is injected at the same rate as the actual pumping well. The resulting image\u2011well and operating\u2011well drawdown cones are superimposed to generate a distribution of drawdown in the portion of the aquifer in which the pumping well is located.\r\n\r\n<\/div>\r\n
\r\n\r\nThe image well methodology is described by Ferris and others (1962). Their work is featured in numerous textbooks (e.g., Freeze & Cherry, 1979; Fetter, 2001; Schwartz & Zhang, 2003), state and federal agency documents (e.g., Lohman, 1972), and professional handbooks (e.g., Sterrett, 2007). Basically, image well methodology uses superposition to represent a boundary by either creating a condition where head does not change along the boundary by using an image well with Q<\/em> of opposite sign as the pumping well, or a condition where the gradient across the boundary is zero using an image well with a Q<\/em> having the same sign as the pumping well.\r\n\r\n<\/div>\r\n<\/div>\r\n
\r\n

Linear Impermeable and Recharge Boundaries<\/h3>\r\n
\r\n\r\nFerris and others (1962) present the image well method to determine the water table map and profile for a pumping well in an unconfined groundwater system near an impermeable linear boundary that is infinite in extent (Figure 74<\/a>). The methodology can also be used to represent confined and leaky confined systems.\r\n\r\n<\/div>\r\n
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\r\n
\r\n
\r\n\r\nFigure 74 \u2011<\/strong> Illustration of the application of image well methodology to generate the cone of depression for a well in an unconfined system that is pumping next to an impermeable boundary (from Ferris, et al., 1962.<\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
\r\n
a) Cross section of the unconfined unit and impermeable boundary material. The dashed red line represents the boundary which approximates the position of the field feature that is of irregular shape. The final resultant drawdown profile is plotted in blue.<\/blockquote>\r\n<\/div>\r\n
\r\n
b) The application of image well methodology (hydraulic counterpart of the real system). The boundary is created mathematically by placing a continuous infinite aquifer with properties equal to the field aquifer (yellow) in the white area with a pumping well (image well) positioned an equal distance from the boundary as the original well. To generate the drawdown profile and cone of depression resulting from the presence of the impermeable boundary, both wells are started at the same time at the original pumping well rate. This results in the mathematical water level being the same at the boundary and decreasing away from the boundary on both sides such that the gradient is zero, thus there is no flow and an impermeable boundary is created. The composite drawdown profile and cone of depression are derived for a specified time by superposing the original pumping well drawdown, sp<\/sub><\/em>, and the image well drawdown, si<\/sub><\/em>, as shown by the blue drawdown profile.<\/blockquote>\r\n<\/div>\r\n
\r\n
c) A map view of the composite cone of depression. Only the yellow shaded portion of the diagram is used to represent conditions at the site because the image well is not physically present at the site. The area shaded in yellow shows dashed black streamlines (groundwater flow directions) and solid black composite contour lines of hydraulic head that mirror drawdown. Water levels decline and drawdown increases toward the well.<\/blockquote>\r\n<\/div>\r\n
\r\n\r\nFigure 74<\/a> explains the application of image well theory to represent a linear impermeable boundary. The cone of depression in the aquifer is not symmetrical because no water is available to flow from the impermeable bedrock on the right into the aquifer. As a result, the cone of depression needs to expand to the top and bottom and left side of the map view to capture water from storage in order to supply the volume of water pumped from the well. As the water level contours are at right angles to the boundary, groundwater flow is parallel to the impermeable boundary (e.g., Woessner & Poeter, 2020).\r\n\r\n<\/div>\r\n
\r\n\r\nA constant flux or recharge boundary is simulated by using the same process with the opposite sign on Q<\/em> to simulate a linear boundary that is infinite in extent as shown in Figure 75<\/a> (Ferris et al., 1962).\r\n\r\n<\/div>\r\n
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\r\n
\r\n
\r\n\r\nFigure 75 \u2011<\/strong> Illustration of the application of image well methodology to generate the cone of depression of a well in an unconfined system with a well pumping next to a connected recharge boundary (Ferris, et al., 1962). The recharge boundary is represented by a fully penetrating stream. This condition could also be thought of as a boundary where any amount of pumping near the boundary would not alter the head at the boundary (constant head boundary).<\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
\r\n
a) Cross section of the unconfined aquifer and recharge boundary. The dashed red line represents the boundary which approximates the position of the field feature that is of irregular shape. The final resultant drawdown profile is plotted in blue.<\/blockquote>\r\n<\/div>\r\n
\r\n
b) The application of image well methodology (hydraulic counterpart of the real system). The boundary is created mathematically by placing a continuous infinite system with properties equal to the field setting (yellow area) in the white area with an injection well (image well) positioned an equal distance from the boundary as the original well. The image well injects water at the same rate that water is pumped from the original well. The injection well creates a cone of impression (water levels rise above the background water level, negative drawdown). This results in the mathematical water level being the same at the boundary and decreasing away from the boundary on the field side of the boundary and increasing on the image side creating a flow across the boundary. To generate the drawdown profile both wells are started at the same time with equal pumping and injection rates. The composite drawdown profile and cone of depression at a specified time are derived by superposing the pumping well drawdown, sp<\/sub><\/em>, and the image well water level rise (negative drawdown), si<\/sub><\/em>, as shown by the blue drawdown profile. It represents the pumping of the original well with a recharge boundary present.<\/blockquote>\r\n<\/div>\r\n
\r\n
c) A map view of the composite cone of depression. Only the yellow shaded portion of the diagram is used to represent conditions at the site because the image well is not physically present. The area shaded in yellow shows dashed black streamlines (groundwater flow directions) and solid black composite contour lines of hydraulic head that mirrors drawdown. Water levels do not change at the boundary and drawdown increases toward the pumping well.<\/blockquote>\r\n<\/div>\r\n
\r\n\r\nFigure 75<\/a> explains how to apply image well theory in the presence of a linear recharge boundary. The cone of depression in the aquifer is not symmetrical because water is contributed by flow from the recharge boundary. Drawdown is less to the right of the pumping well and greater to the left of the well. The groundwater elevation contours are parallel to the recharge boundary and decrease towards the well. Water is flowing at right angles from the boundary to the well (e.g., Woessner & Poeter, 2022).\r\n\r\n<\/div>\r\n
\r\n\r\nIf the drawdown at an observation well located near an impermeable linear boundary needs to be predicted, the composite drawdown from both the pumping well and image well are computed at the observation well location (Figure 76<\/a>). When a recharge boundary is present, the drawdown at an observation well is derived by combining the effect of the pumping well and the drawup (negative drawdown) from the image well. Again, both pumping and image well values are added to generate the total drawdown at the observation well.\r\n\r\n<\/div>\r\n
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\r\n
\r\n
\r\n\r\nFigure 76 \u2011<\/strong> Map view of a pumping well (red dot) and corresponding image well (open red dot) in a setting with a single linear impermeable boundary. To compute the drawdown in an observation well the radial distances are determined from both the pumping well and image well, then the resulting drawdowns at that location are calculated and added together.<\/span>\r\n\r\n<\/div><\/blockquote>\r\n<\/div>\r\n
\r\n\r\nFerris and others (1962) also presented how image well methods could be used to simulate systems with dual linear boundaries of infinite extent and more complex boundary configurations using image well theory. An example of using image well theory to represent the presence of both a linear impermeable boundary and recharge boundary near a pumping well is presented in Box 3<\/a><\/span>.\r\n\r\n<\/div>\r\n
\r\n\r\nImage well methods are easily applied to simple single linear boundaries. Image well theory uses superposition and is based on computing drawdown and drawup by solving analytical equations (e.g., Theis, Jacob, Hantush). As boundaries become more complex, image well methods are not adequate to represent conditions. Typically, numerical groundwater modeling techniques are used to represent complex boundaries (e.g., Anderson et al., 2015; Woessner & Poeter, 2020).\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"
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One of the basic assumptions used to develop analytical solutions to predict drawdown in wells penetrating unconfined, confined, leaky confined, and unconfined units, and associated confining beds is that the set of geologic units being represented are infinite in lateral extent and no boundaries are present in the portion of the aquifer being stressed. In an extensive groundwater system, where boundaries are located tens of kilometers from the test site and the cone of depression of the hydraulic test may only extend a few kilometers, the assumption of an infinite water\u2011bearing unit is reasonable (Figure 71<\/a>, Well A).<\/p>\n<\/div>\n

\n

\"\"<\/p>\n

\n
\n
\n

Figure 71 \u2011<\/strong> Schematic map view of a shallow isotropic and homogeneous confined aquifer (tan) that is bordered by impermeable granite bed rock, a well\u2011connected large lake, and mountain ranges that allow some flow into the aquifer. Cones of depression are plotted for three wells that are pumping at similar rates. Red represents more drawdown and blue less drawdown. Black lines represent drawdown contours that have larger magnitude near the center of the cone of depression. At Well A, the cone of depression is symmetrical, as pumping has not encountered boundaries that limit the expansion of the cone. At this site, for analytical purposes, the aquifer can be assumed to represent a system that is infinite in extent. At Well B, the cone of depression encountered the impermeable bedrock and began to expand along the boundary and deepen. The equipotential lines indicate flow is parallel to the boundary converging toward the position of the well where flow lines turn to flow to the well. Well C, is near a large lake that is in communication with the aquifer. The lake provides water to the pumping well through lateral aquifer recharge so drawdown slows and eventually the cone no longer grows when inflow from the lake equals the pumping rate. The equipotential lines indicate flow across the boundary.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n

\n

Hydraulic testing can identify boundary conditions that alter drawdown at observation wells or production wells. When boundaries are encountered the trend in drawdown will change as pumping continues. The rate of drawdown will decrease if a recharge boundary (Figure 71<\/a>, Well C) is encountered, and the rate of drawdown will increase if an impermeable boundary (Figure 71<\/a>, Well B) is contacted. The effect of boundaries on drawdown trends for pumping or observation wells in an aquifer behaving as a Theis system (i.e., totally confined) are shown in Figure 72<\/a>. Figure 73<\/a> illustrates the effect of boundaries on the shape of Cooper\u2011Jacob semi\u2011log time\u2011drawdown plots.<\/p>\n<\/div>\n

\n

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

\n
\n
\n

Figure 72 \u2011<\/strong> A log\u2011log plot of drawdown versus time for a pumping well penetrating a confined aquifer. The blue line represents the drawdown expected if the aquifer behaves as a Theis system and is unbounded. The time\u2011drawdown curve also shows the response of the theoretical Theis conditions if the cone of depression encounters a no\u2011flow boundary (upper black dashed line). The lower dashed curve indicates that the drawdown would be less if recharge or leakage from a boundary is encountered (Cherry, 2022).<\/span><\/p>\n<\/div>\n<\/blockquote>\n<\/div>\n

\n

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

\n
\n
\n

Figure 73 \u2011<\/strong> Examples of boundary condition influences on time\u2011drawdown data collected during a constant\u2011discharge pumping test of a confined unit. Plots are semi\u2011log graphs. Drawdown changes occur in both pumping and observation wells. a) The theorical response of a totally confined aquifer that is not affected by boundary conditions, the aquifer is infinite in extent. b) The deviation in the time\u2011drawdown data (red dashed line) that shows the slope of the drawdown trend is decreasing and reaching equilibrium as a recharge boundary is encountered. c) The deviation in the time\u2011drawdown data when an impermeable boundary is encountered as shown by the red dashed line. Drawdown increases with time.<\/span><\/p>\n<\/div>\n<\/blockquote>\n<\/div>\n

\n

Care must be taken to determine the likely source of the observed drawdown response when assessing the presence or absence of aquifer boundaries. In this section, we discuss lateral recharge boundaries in contrast to recharge from local confining beds and overlying aquifers as discussed in Section\u00a09 (i.e., Hantush\u2011Jacob and Hantush Equations). Leaky aquifer settings will cause drawdown curve slopes to decrease without the cone of depression encountering an adjacent physical boundary. Unconfined aquifers with delayed yield also exhibit a period of decreased slope and a period of increasing drawdown that are not related to a lateral recharge boundary.<\/p>\n<\/div>\n

\n

As stated, at some test sites physical boundaries adjacent to the groundwater system may be close enough to affect hydraulic testing and\/or planned production rates. When the configurations of boundaries are relatively simple, e.g., a linear boundary, the effect of the boundary on the predicted drawdown can be addressed using image well theory based on superposition of analytical solutions. As boundary conditions become less geometrically linear and more complex, other techniques such as numerical modeling are more appropriate because analytical models cannot easily address complex boundaries (e.g., Anderson et al., 2015).<\/p>\n<\/div>\n

\n

Image Well Methodology<\/h3>\n
\n

Image well methodology generates the drawdown distribution that would result when pumping near a boundary. It applies standard analytical models developed in previous sections. The method involves first replacing the bounded confined or unconfined system with an infinite aquifer, then placing one or more image wells on the other side of the boundary at the same distance the pumping well is located from the identified boundary. Depending on the boundary being simulated, image wells are either pumped or water is injected at the same rate as the actual pumping well. The resulting image\u2011well and operating\u2011well drawdown cones are superimposed to generate a distribution of drawdown in the portion of the aquifer in which the pumping well is located.<\/p>\n<\/div>\n

\n

The image well methodology is described by Ferris and others (1962). Their work is featured in numerous textbooks (e.g., Freeze & Cherry, 1979; Fetter, 2001; Schwartz & Zhang, 2003), state and federal agency documents (e.g., Lohman, 1972), and professional handbooks (e.g., Sterrett, 2007). Basically, image well methodology uses superposition to represent a boundary by either creating a condition where head does not change along the boundary by using an image well with Q<\/em> of opposite sign as the pumping well, or a condition where the gradient across the boundary is zero using an image well with a Q<\/em> having the same sign as the pumping well.<\/p>\n<\/div>\n<\/div>\n

\n

Linear Impermeable and Recharge Boundaries<\/h3>\n
\n

Ferris and others (1962) present the image well method to determine the water table map and profile for a pumping well in an unconfined groundwater system near an impermeable linear boundary that is infinite in extent (Figure 74<\/a>). The methodology can also be used to represent confined and leaky confined systems.<\/p>\n<\/div>\n

\n

\"\"<\/p>\n

\n
\n
\n

Figure 74 \u2011<\/strong> Illustration of the application of image well methodology to generate the cone of depression for a well in an unconfined system that is pumping next to an impermeable boundary (from Ferris, et al., 1962.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n

\n

a) Cross section of the unconfined unit and impermeable boundary material. The dashed red line represents the boundary which approximates the position of the field feature that is of irregular shape. The final resultant drawdown profile is plotted in blue.<\/p><\/blockquote>\n<\/div>\n

\n

b) The application of image well methodology (hydraulic counterpart of the real system). The boundary is created mathematically by placing a continuous infinite aquifer with properties equal to the field aquifer (yellow) in the white area with a pumping well (image well) positioned an equal distance from the boundary as the original well. To generate the drawdown profile and cone of depression resulting from the presence of the impermeable boundary, both wells are started at the same time at the original pumping well rate. This results in the mathematical water level being the same at the boundary and decreasing away from the boundary on both sides such that the gradient is zero, thus there is no flow and an impermeable boundary is created. The composite drawdown profile and cone of depression are derived for a specified time by superposing the original pumping well drawdown, sp<\/sub><\/em>, and the image well drawdown, si<\/sub><\/em>, as shown by the blue drawdown profile.<\/p><\/blockquote>\n<\/div>\n

\n

c) A map view of the composite cone of depression. Only the yellow shaded portion of the diagram is used to represent conditions at the site because the image well is not physically present at the site. The area shaded in yellow shows dashed black streamlines (groundwater flow directions) and solid black composite contour lines of hydraulic head that mirror drawdown. Water levels decline and drawdown increases toward the well.<\/p><\/blockquote>\n<\/div>\n

\n

Figure 74<\/a> explains the application of image well theory to represent a linear impermeable boundary. The cone of depression in the aquifer is not symmetrical because no water is available to flow from the impermeable bedrock on the right into the aquifer. As a result, the cone of depression needs to expand to the top and bottom and left side of the map view to capture water from storage in order to supply the volume of water pumped from the well. As the water level contours are at right angles to the boundary, groundwater flow is parallel to the impermeable boundary (e.g., Woessner & Poeter, 2020).<\/p>\n<\/div>\n

\n

A constant flux or recharge boundary is simulated by using the same process with the opposite sign on Q<\/em> to simulate a linear boundary that is infinite in extent as shown in Figure 75<\/a> (Ferris et al., 1962).<\/p>\n<\/div>\n

\n

\"\"<\/p>\n

\n
\n
\n

Figure 75 \u2011<\/strong> Illustration of the application of image well methodology to generate the cone of depression of a well in an unconfined system with a well pumping next to a connected recharge boundary (Ferris, et al., 1962). The recharge boundary is represented by a fully penetrating stream. This condition could also be thought of as a boundary where any amount of pumping near the boundary would not alter the head at the boundary (constant head boundary).<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n

\n

a) Cross section of the unconfined aquifer and recharge boundary. The dashed red line represents the boundary which approximates the position of the field feature that is of irregular shape. The final resultant drawdown profile is plotted in blue.<\/p><\/blockquote>\n<\/div>\n

\n

b) The application of image well methodology (hydraulic counterpart of the real system). The boundary is created mathematically by placing a continuous infinite system with properties equal to the field setting (yellow area) in the white area with an injection well (image well) positioned an equal distance from the boundary as the original well. The image well injects water at the same rate that water is pumped from the original well. The injection well creates a cone of impression (water levels rise above the background water level, negative drawdown). This results in the mathematical water level being the same at the boundary and decreasing away from the boundary on the field side of the boundary and increasing on the image side creating a flow across the boundary. To generate the drawdown profile both wells are started at the same time with equal pumping and injection rates. The composite drawdown profile and cone of depression at a specified time are derived by superposing the pumping well drawdown, sp<\/sub><\/em>, and the image well water level rise (negative drawdown), si<\/sub><\/em>, as shown by the blue drawdown profile. It represents the pumping of the original well with a recharge boundary present.<\/p><\/blockquote>\n<\/div>\n

\n

c) A map view of the composite cone of depression. Only the yellow shaded portion of the diagram is used to represent conditions at the site because the image well is not physically present. The area shaded in yellow shows dashed black streamlines (groundwater flow directions) and solid black composite contour lines of hydraulic head that mirrors drawdown. Water levels do not change at the boundary and drawdown increases toward the pumping well.<\/p><\/blockquote>\n<\/div>\n

\n

Figure 75<\/a> explains how to apply image well theory in the presence of a linear recharge boundary. The cone of depression in the aquifer is not symmetrical because water is contributed by flow from the recharge boundary. Drawdown is less to the right of the pumping well and greater to the left of the well. The groundwater elevation contours are parallel to the recharge boundary and decrease towards the well. Water is flowing at right angles from the boundary to the well (e.g., Woessner & Poeter, 2022).<\/p>\n<\/div>\n

\n

If the drawdown at an observation well located near an impermeable linear boundary needs to be predicted, the composite drawdown from both the pumping well and image well are computed at the observation well location (Figure 76<\/a>). When a recharge boundary is present, the drawdown at an observation well is derived by combining the effect of the pumping well and the drawup (negative drawdown) from the image well. Again, both pumping and image well values are added to generate the total drawdown at the observation well.<\/p>\n<\/div>\n

\n

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

\n
\n
\n

Figure 76 \u2011<\/strong> Map view of a pumping well (red dot) and corresponding image well (open red dot) in a setting with a single linear impermeable boundary. To compute the drawdown in an observation well the radial distances are determined from both the pumping well and image well, then the resulting drawdowns at that location are calculated and added together.<\/span><\/p>\n<\/div>\n<\/blockquote>\n<\/div>\n

\n

Ferris and others (1962) also presented how image well methods could be used to simulate systems with dual linear boundaries of infinite extent and more complex boundary configurations using image well theory. An example of using image well theory to represent the presence of both a linear impermeable boundary and recharge boundary near a pumping well is presented in Box 3<\/a><\/span>.<\/p>\n<\/div>\n

\n

Image well methods are easily applied to simple single linear boundaries. Image well theory uses superposition and is based on computing drawdown and drawup by solving analytical equations (e.g., Theis, Jacob, Hantush). As boundaries become more complex, image well methods are not adequate to represent conditions. Typically, numerical groundwater modeling techniques are used to represent complex boundaries (e.g., Anderson et al., 2015; Woessner & Poeter, 2020).<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":8,"menu_order":46,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1709","chapter","type-chapter","status-publish","hentry"],"part":579,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/pressbooks\/v2\/chapters\/1709","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/wp\/v2\/users\/8"}],"version-history":[{"count":5,"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/pressbooks\/v2\/chapters\/1709\/revisions"}],"predecessor-version":[{"id":3760,"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/pressbooks\/v2\/chapters\/1709\/revisions\/3760"}],"part":[{"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/pressbooks\/v2\/parts\/579"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/pressbooks\/v2\/chapters\/1709\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/wp\/v2\/media?parent=1709"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/pressbooks\/v2\/chapter-type?post=1709"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/wp\/v2\/contributor?post=1709"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/an-introduction-to-hydraulic-testing-in-hydrogeology\/wp-json\/wp\/v2\/license?post=1709"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}