Explicit algebraic equations are derived to determine approximate maximum pumping rates or minimum injection rates to limit sea water intrusion to a prespecified distance from the coastline. The equations are based on Strack's (1976) single-potential solution. The maximum pumping rates and minimum injection rates applied at wells with uniform spacing to control the inland movement of the fresh water-salt water interface in a coastal aquifer could be calculated from Strack's (1976) solution without the need of a numerical optimization algorithm. When wells are distributed in a simple fashion, the maximum intrusion location can be identified precisely for pumping cases and approximately for injection cases. For pumping cases, critical points are the limit of allowable salt water intrusion, whereas no such limit exists for injection cases. Once an application site is identified, a series of design curves for pumping and injection rates can be developed for arbitrary intrusion limits. When a user is interested only in the largest pumping rates associated with critical points, one design curve can yield complete information.
Biochar as a soil amendment can influence the physical and solute transport properties of soils and, thus, provide a means to improve soil fertility. However, the use of different sized biochar particles down to the nano‐scale has revealed inconsistent results, with the mechanisms poorly understood owing to a lack of experimental data. This study investigated the effects and mechanisms of nano‐sized biochar particles (NBC) applied to a sandy loam soil with regard to impacts on the hydraulic characteristics and soil structure. Column experiments were carried out with NBC application rates of 0.0%, 0.3%, 0.5%, 0.7% and 1.0% (by weight). It was found that the NBC changed the distribution of the soil pore structure and affected the degrees of anisotropy, fractal dimension, soil porosity and stability of soil aggregates. NBC applications also increased the water repellency of the soil and reduced the surface energy of soil particles. Regarding soil hydraulic properties, NBC applications increased the saturated hydraulic conductivity of the soil and decreased soil water retention. Increasing the amount of NBC applied to the mixing‐layer decreased cumulative infiltration values (reduced by 3.75%–13.75%). The above results reveal how NBC affects the soil pore structure and soil hydraulic characteristics, which provides a theoretical basis for the systematic evaluation of soil improvement and environmental effects of nano‐sized biochar.
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