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A thermodynamic model for plant growth, validated with Pinus sylvestris data

Attorre, F., Sciubba, E., Vitale, M.
Ecological modelling 2019 v.391 pp. 53-62
Pinus sylvestris, carbon dioxide, engineering, environmental factors, equations, evapotranspiration, exergy, genotype, metabolism, primary productivity, soil, thermodynamic models, tree age, tree growth, trees
Plants are open, irreversible and non-equilibrium systems that live via mass- and energy exchanges with the environment, and therefore, are amenable to a thermodynamic treatment: in fact, they may be considered “energy converters”, because their metabolism is nothing else than a controlled ability to transform energy from one form (solar) into another (chemical energy suitable to cell metabolism) and to activate and maintain reactions at cellular- and molecular level -promoting the plant growth. This paper presents an original model based on mass conservation and on the First- and Second Law of Thermodynamics, which results in a set of equations that allow for the calculation of the Primary Productivity (NPP) and consequently lead to a measure of the plant growth. The model is lumped, steady-state and totally deterministic, because no primary process is modelled in detail: the control volume is a portion of the universe that contains the plant and its immediate surroundings (atmosphere and the relevant portion of the soil), and the solution is strongly depending on the imposed boundary conditions. In such a formulation, the tree is considered as a non-equilibrium system evolving at a steady rate, and the only implicit assumption is the local equilibrium hypothesis. The general evolution equations are derived, and their steady-state form is analysed in detail. The approach is based on the calculation of the exergy in- and outflows from the control volume. Based on reasonably accurate empirical data, the exergy budget shows that the overall exergy conversion efficiency is quite low in plants and is very sensitive to even small changes in the environmental condition and to the adopted evapotranspiration model, as it would have been expected. The model is applied to a mature specimen of Pinus sylvestris and the results are compared with some literature data: despite neglecting the real chemo-physical details, the model reproduces the most salient characters of the tree growth. The sensitivity of the results to the tree age as well to the main model parameters is also calculated. The application of the same model to different species may reveal asymmetries in the “adaptability” of certain genotypes to different environments. On the more specific engineering side, the model may see an immediate application in the estimate of CO2 capture by plants.