Читать книгу Numerical Simulation, An Art of Prediction, Volume 2 - Jean-François Sigrist - Страница 18

Many physical processes are modeled by equations that form the basis of the models used in the simulations of changes in chemical species concentrations. These include the laws established in the 19th Century by the French physicist Jean-Baptiste Biot (1774–1862), the French engineer Henry Darcy (1803–1858) and the German physiologist Adolf Fick (1829–1901). They relate the flow of a physical quantity to a variation of another quantity:

 – the law described by Fourier and formulated by Biot reflects the diffusion of heat. It is written as follows φ = –λ∇T and stipulates that the heat flux (φ) flows from hot areas to cold areas (∇T), all the more easily as the medium in question is conductive (λ);

 – Darcy’s law expresses the flow rate of an incompressible fluid filtering through a porous medium. It is written as follows φ = K∇H and indicates that the flow of a fluid between two points, made by its flow (φ), is all the easier as the medium is porous (K) and that the resistance to its flow, expressed by the hydraulic pressure losses (∇H), is low;

 – Fick’s law accounts for the diffusion of matter. It is written as follows φ = –ρD∇c and indicates that a chemical species spreads from areas where it is highly concentrated to areas where it is less concentrated. The mass flow of a component (φ) is inversely proportional to changes in its concentration (∇c) and depends on its density (ρ) and its propensity to spread (D).

The calculation algorithms consist of solving these equations, to which are added, on the one hand, those of the physicochemical equilibria between the different species in play present in the gaseous, aqueous state, or adsorbed on clays and organic matter of the soil (highly dependent on temperature, soil moisture and its acidity), and, on the other hand, those making consumption and/or production effects by biological reactions linked to the presence of microorganisms. Physicochemical models make it possible to calculate the evolution of chemical concentrations in the different soil layers, and in particular at the surface. Volatilization is then calculated by using equations describing the convection and diffusion effects of gaseous ammonia from the ground surface to the atmosphere based on the effects of wind conditions and stability of the lower atmospheric layers.

A set of simulations, aggregated for different plots and taking into account composition differences as well as meteorological factors, allows data to be reproduced on larger scales – typically a small agricultural region.

“It is possible to scale up, for a country, with the same principle: by performing as many simulations as necessary to describe an entire region and synthesize the results of the calculations. No less than 150,000 simulations are needed to represent the use of mineral and organic fertilizers during the soil fertilization phase (in the fall and then from February to late spring) and estimate their effects on the scale of a country like France. Two days of calculation on about forty cores are necessary to realize it!”.

Figure 1.16. From the use of nitrogen fertilizers to ammonia emissions in France [HAM 14]

COMMENT ON FIGURE 1.16.– The figure on the left represents the quantities of nitrogen used in agriculture in France during the 2005–2006 crop year in the form of ammonia and urea and therefore susceptible to volatilization (the values are expressed in thousands of tons of ammoniacal nitrogen). The figure on the right shows the resulting ammonia emissions (values are expressed in thousands of tons of ammonia, NH3). The choice is made here to present the results of the calculations for the entire season, according to the different regions of the country and for the two main categories of fertilizers: synthetic fertilizers (in gray) and organic waste products (in black).

The difficulty of the calculation lies in the reliability of the data required to inform the model: composition of the fertilizers used, types of fertilized soil, crop species and the fertilization routes preferred by farmers, including dates, doses and forms of fertilizer applied and methods of application.

“Simulations allow us to identify interesting trends. Their quality depends very much on the quality of the data on which they are based. Soil type, range of inputs, emission data and field surveys are the preferred sources for researchers to inform their models. The validation of the calculations continues to pose problems: although the simulations are able to report the concentration of ammonia in the air with good spatial and temporal resolution, we do not currently have such an accurate measurement network to directly compare the results of our calculations with field observations – this is a current area of research involving different teams in France”.

The researchers’ calculations tend to reflect the variability of the situations encountered through sensitivity studies: their analyses are being refined and are providing decision-makers with tangible evidence for assessing the risks associated with the massive use of fertilizers and, in the near future, phyto-pharmaceuticals.

NOTE.– At the heart of the matter to understand soil chemistry.

For the American physicist Richard Feynman (1918–1988), simulating the world asks us to account for the mechanics of the infinitely small: “Nature isn’t classical, damnit, and if you want to make a simulation of nature, you’d better make it quantum mechanical, and by golly it’s a wonderful problem, because it doesn’t look so easy” (quoted by [BAI 16]). This idea was followed by two researchers in theoretical physico-chemistry, Fabienne Bessac and Sophie Hoyau, in order to study the mechanisms of pollutant adsorption in soils [BEL 17a, BEL 17b]:

“Atrazine is an herbicide whose marketing and use have been banned in France since September 2002 and June 2003, respectively. However, they are still found in groundwater in some regions today. Our research aims to understand the physico-chemical mechanisms that would explain how the soils exposed to it release it into the water…”.

Figure 1.17. 3D representation of atrazine (source: www.commons.wikimedia.org). For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 1.17.– C8H14ClN5 is the raw chemical formula for atrazine, the active ingredient of a pesticide, also listed, according to the International Union of Pure and Applied Chemistry nomenclature, as 2-chloro-4-(ethylamine)-6-(isopropylamine)-s-thiazine. The figure represents a 3D view of the molecule and highlights the atomic bonds between hydrogen (H, in white), carbon (C, in black), nitrogen (N, in blue) and chlorine (Cl, in green). Atrazine is a powerful herbicide that has long been appreciated by some farmers because it is inexpensive and quite powerful. It was banned in France in 2003 and in the European Union because of its adverse effects on health and the environment, but is still used today in some countries, such as the United States.

It is at the atomic scale that scientists are trying to understand the desorption phenomena – the mechanism by which molecules adsorbed on a substrate detach themselves from it. The model used is gradually being built to describe soil composition, including water and pesticide.

“We built a model by taking into account the pesticide alone and then the pesticide in interaction with different elements present in the soil, such as sodium Na⁺ and calcium Ca²⁺. Then we added clay and finally water. At each step, we were able to observe the differences in interactions and understand the phenomena involved, in particular how the binding sites between the pesticide and the clay involved in absorption or desorption change at the molecular scale”.

Simulations consist of solving the Schrödinger equation (Chapter 1, Volume 1) and can be used to achieve thermodynamic quantities for the chemical species being modeled. This is one of the most accurate models imaginable for this type of problem – and it is also one of the most time-consuming.

The calculations provide access to two types of information:

 – Absorption energies and the position of atoms in the corresponding structures: the lower the total energy of the calculated structure, the more likely it is to exist;

 – Changes in the spatial organization of atoms over time, over very short periods of time, in the order of the femtosecond to the nanosecond (10–12 and 10–9 s, respectively), can provide thermodynamic information on the studied system.

Figure 1.18. Example of calculation at the atomic scale [BEL 17b]. For a color version of this figure, see www.iste.co.uk/sigrist/simulation2.zip

COMMENT ON FIGURE 1.18.– The figure represents a molecular structure calculated for the interaction between atrazine and clay. The soil is modeled here by an infinite crystal lattice: in practice, it is a cell, on the edge of which are applied conditions of repetitiveness, reflecting an infinite extension. The calculation shows how the atrazine molecule behaves in this environment and what the associated energies are. The simulation allows us to find the most probable structures after the adsorption of the pesticide on the clay.

“Due to the complexity and size of the models, we used HPC calculation methods. Simulating the desorption of the pesticide in water requires, for example, nearly two million hours of calculation – spread over the thousands of cores of a supercomputer!”

Calculation at the atomic scale is a first step in research: it serves as a reference for validating models that introduce simplifications and lend themselves to faster calculations. The objective is to carry out simulations under environmental conditions, with the data collected in the fields. Calculations using these models, in which accuracy is demonstrated by comparison with the atomic scale calculation, should determine the pesticide partition constants between the liquid and mineral phases – and answer the initial question. It is a wonderful problem, because it is far from simple!