The Issue of Calculating the Final Temperature of the Products of Rapid Exothermic Chemical Reactions with Significant Energy Release in a Closed Volume

The theoretical problem solved in this article is the calculation of thermodynamic parameters such as final temperature, distribution of the liquid and dry saturated vapour phases of the substance that are considered to be in thermodynamic equilibrium, and pressure of the system of several reaction products after adding to the system a certain amount of heat or the thermal effect released during rapid exothermic reaction in a closed volume that occurs so fast that it can be considered to be adiabatic, and when the volume of liquid reagents is several orders of magnitude less than the volume of the reactor. The general multi-substance problem is reduced to a theoretical problem for one substance of calculation thermodynamic parameters of system after adding a certain amount of heat that gives theoretically rigorous isochoric calculation. In this article, we substantiate our view that isochoric pass of calculation is more robust compared to seemingly more natural isobaric pass of calculation, if the later involves quite not trivial calculation of the adiabatic compression of a two-phase system (liquid – dry saturated vapour) that can pass itself into another kind of state (liquid – wet saturated vapour), which requires, apparently, more complex descriptions compared with isochoric calculation because the specific heat capacity of wet saturated vapour can be negative.

The solved theoretical problem relates to a practical problem that has been a driver for our research as part of a design of the reactor of the titanium reduction from magnesium and titanium tetrachloride supplied into atmosphere of the reactor at high temperatures when both reagents are in gaseous state. The reaction is known to be exothermic with a high thermal effect, and estimate of the final temperature and pressure of the products of reaction, for instance, designing the reactor allows eliminating the possibility of the reaction products to penetrate backwards into supply tracts of the reagents. Using a rigid theoretical approach and heuristics of thermodynamic parameters of reaction products available in the literature, we have presented a graphical dependence of final temperature, pressure ratio of the liquid and vapour state of titanium after the reaction on the initial temperature of the reactor and magnesium in the range of 1200–1800 °K while titanium tetrachloride is injected into reactor at its critical temperature.