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fixed some links
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cneyens committed Jan 24, 2025
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9 changes: 5 additions & 4 deletions doc/examples/03_uniform_3D.ipynb
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"\n",
"The `adepy.uniform.point3` algorithm can be used to solve 3D solute transport originating from a continuous point source in an infinite aquifer. A third-type boundary is applied at the point source whereby water with a known, constant concentration is injected at a constant rate. It is assumed that the injection rate is small so that the flow field remains uniform.\n",
"\n",
"As an example, a natural gradient tracer test is simulated, where a pulse injection of chloride was applied in three wells during a one-day period. The wells were screened across a small interval in the aquifer. Superposition in time and space is applied to simulate this problem (see also the [00_uniform_overview.ipynb](00_uniform_overview.ipynb) notebook for more information about superpositioning). This example corresponds to sample problem 9 in [Wexler (1992)](https://doi.org/10.3133/twri03B7)."
"As an example, a natural gradient tracer test is simulated, where a pulse injection of chloride was applied in three wells during a one-day period. The wells were screened across a small interval in the aquifer. Superposition in time and space is applied to simulate this problem (see also the [00_uniform_overview.ipynb](./00_uniform_overview.ipynb) notebook for more information about superpositioning). This example corresponds to sample problem 9 in [Wexler (1992)](https://doi.org/10.3133/twri03B7)."
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"t = 400 # output time, d\n",
"dt = 1 # pulse duration, d\n",
"\n",
"# to simulate a pulse injection of 1 day, simulate a continuous source for t = total time and subtract the solution for t = total time - 1 day\n",
"# to simulate a pulse injection of 1 day, simulate a continuous source for t = total time and\n",
"# subtract the solution for t = total time - 1 day\n",
"cw1 = point3(c0, x, y, z, t, v, n, al, ah, av, Q, w1[0], w1[1], w1[2]) - point3(\n",
" c0, x, y, z, t - dt, v, n, al, ah, av, Q, w1[0], w1[1], w1[2]\n",
")\n",
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"\n",
"The `adepy.uniform.patchf` algorithm can be used to simulate 3D solute transport originating from a patch source at `x = 0` in a bounded aquifer. The aquifer is finite in the y- and z-directions, and semi-infinite in the x-direction (no solution for negative x-values, i.e. upstream from the source). Impermeable boundaries are placed at the finite ends of the aquifer's y and z-extents, where the concentration gradient across the boundary is fixed at zero so the solute can not pass through. This solution may be valid for aquifers with a limited width, for example embedded in less-permeable or impermeable sediments which are close enough to the source as to affect its spread. \n",
"\n",
"As an example, chloride migration from a landfill leachate in a gravel pit in a narrow valley-infill aquifer is simulated, corresponding to sample problem 10 in [Wexler (1992)](https://doi.org/10.3133/twri03B7). Note the effect of the impermeable aquifer boundary at `y = 0`. Comparison with [the 2D solution](02_uniform_2D.ipynb) shows the effect of the vertical concentration spread on the plume shape and the resulting concentrations, illustrating the errors that can occur when simulating 2D solute transport when a 3D solution is more appropriate."
"As an example, chloride migration from a landfill leachate in a gravel pit in a narrow valley-infill aquifer is simulated, corresponding to sample problem 10 in [Wexler (1992)](https://doi.org/10.3133/twri03B7). Note the effect of the impermeable aquifer boundary at `y = 0`. Comparison with [the 2D solution](./02_uniform_2D.ipynb) shows the effect of the vertical concentration spread on the plume shape and the resulting concentrations, illustrating the errors that can occur when simulating 2D solute transport when a 3D solution is more appropriate."
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"\n",
"The resulting 3D concentration field from a patch source placed at `x = 0` in a semi-infinite aquifer can be simulated using `adepy.uniform.patchi`. The aquifer is infinite in the y- and z-directions and in the positive x-direction. For locations upstream of the source (i.e. negative x-values), the solution is undefined. \n",
"\n",
"For this problem, [Domenico & Robbins (1985)](https://doi.org/10.1111/j.1745-6584.1985.tb01497.x) and later [Domenico (1987)](https://doi.org/10.1016/0022-1694(87)90127-2) provided a popular closed-form solution. Due to the relatively straightforward computation, it has seen widespread use in screening tools, e.g. the BIOCHLOR and BIOSCREEN models of the EPA. However, as shown by i.a. [Srinivasan et al. (2007)](https://doi.org/10.1111/j.1745-6584.2006.00281.x) and [West et al. (2007)](https://doi.org/10.1111/j.1745-6584.2006.00280.x), the Domenico & Robbins solution was derived using an approximate approach and is therefore not accurate for non-zero longitudinal dispersivities. An exact solution for simulating a patch source in a semi-infinite aquifer was derived by [Wexler (1992)](https://doi.org/10.3133/twri03B7) and is implemented here in `adepy.uniform.patchi`.\n",
"For this problem, [Domenico & Robbins (1985)](https://doi.org/10.1111/j.1745-6584.1985.tb01497.x) and later [Domenico (1987)](https://doi.org/10.1016/0022-1694%2887%2990127-2) provided a popular closed-form solution. Due to the relatively straightforward computation, it has seen widespread use in screening tools, e.g. the BIOCHLOR and BIOSCREEN models of the EPA. However, as shown by i.a. [Srinivasan et al. (2007)](https://doi.org/10.1111/j.1745-6584.2006.00281.x) and [West et al. (2007)](https://doi.org/10.1111/j.1745-6584.2006.00280.x), the Domenico & Robbins solution was derived using an approximate approach and is therefore not accurate for non-zero longitudinal dispersivities. An exact solution for simulating a patch source in a semi-infinite aquifer was derived by [Wexler (1992)](https://doi.org/10.3133/twri03B7) and is implemented here in `adepy.uniform.patchi`.\n",
"\n",
"The example below simulates the fate of a contaminant containing strontium-90 originating from a deep, subterranean radioactive-waste storage facility as it migrates through a thick, confined aquifer (sample problem 11 in [Wexler (1992)](https://doi.org/10.3133/twri03B7)). The species is subjected to first-order radioactive decay."
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