Reactive transport in porous media with dissolution and precipitation has important applications in oil and gas industry and groundwater remediation. In this work, we present a simulation method for reactive flow in porous media of two salts that share an ion. The method consists of a front-tracking solver that uses the Riemann solutions of the underlying set of hyperbolic partial differential equations. In addition to the discontinuities stemming from the nonlinearities of the flux function, the flux function for the corresponding advection reaction equation also admits discontinuities for a heterogeneous medium. Here, we solve the Riemann problem for the governing nonlinear hyperbolic system with a discontinuous flux function. We use mass balance across the interface and the non-decreasing sequence of velocity of waves to seek the unique solution for this problem. Furthermore, a model is provided for mixing of streamlines at the well to estimate the amount of precipitate. In the use of streamline methods, we have modified the definition of time-of-flight to allow the model to be easily utilised for the heteregeneous case. The simulation method is applied to model dissolution through injection of an unsaturated fluid. It is shown that the first dissolution shock, which causes induced precipitation due to the co-ion effect, results in accumulation of precipitate at the well.

We present a local equilibrium theory for the reactive transport of two salts that share an anion in an ideal solution. We revisit this classic problem using the theory of hyperbolic partial differential equations accounting for the volume of precipitates. We construct analytical solutions for the 2 × 2 system of conservation laws in the absence of hydrodynamic dispersion. The character of the system depends on the saturation of the salts, that is, whether the fluid is saturated with both, either of the two or none of the salts. We provide a comprehensive analysis of the system and its solution. Each primitive variable, the amount of precipitate and the concentration of ions, remains constant along one class of waves that propagate in the system. The analysis of the system allows identification of seven bifurcations with respect to the intermediate state.

Sustainable livestock production requires that animals have a high production potential but are also highly resilient to environmental challenges. The first step to simultaneously improve these traits through genetic selection is to accurately predict their genetic merit. In this paper, we used simulations of sheep populations to assess the effect of genomic data, different genetic evaluation models and phenotyping strategies on prediction accuracies and bias for production potential and resilience. In addition, we also assessed the effect of different selection strategies on the improvement of these traits. Results show that estimation of both traits greatly benefits from taking repeated measurements and from using genomic information. However, the prediction accuracy for production potential is compromised, and resilience estimates tends to be upwards biased, when families are clustered in groups even when genomic information is used. The prediction accuracy was also found to be lower for both traits, resilience and production potential, when the environment challenge levels are unknown. Nevertheless, we observe that genetic gain in both traits can be achieved even in the case of unknown environmental challenge, when families are distributed across a large range of environments. Simultaneous genetic improvement in both traits however greatly benefits from the use of genomic evaluation, reaction norm models and phenotyping in a wide range of environments. Using models without the reaction norm in scenarios where there is a trade-off between resilience and production potential, and phenotypes are collected from a narrow range of environments may result in a loss for one trait. The study demonstrates that genomic selection coupled with reaction-norm models offers great opportunities to simultaneously improve productivity and resilience of farmed animals even in the case of a trade-off.