(N-45) Identification of segments of computed reactive three-phase lines to be included in the heterogeneous region of phase diagrams of reactive systems (R234-2)

Abstract

For reactive systems, equations of state (EoS) may predict the existence of (reactive) three-phase lines (R-3PLs). In general, only a part of a specific R-3PL contributes to the heterogeneous region (HR) of a reactive phase diagram of specified initial global composition z0 (also named ?reactive isopleth? (R-IP)). In this work, we propose a method for detecting the segments, of an already computed R-3PL, that should contribute to the HR of a yet to be computed R-IP (of already specified z0). The method consists of solving, for each point of the R-3PL (R-3PP), a system of equations related to reactive two-phase constant phase fraction lines that originate at the R-3PP. The R-3PP contributes to the R-IP if the solution of such system satisfies a number of restrictions. The graphical abstract (GA) shows three R-IPs for the methanol(M) + dimethyl ether(DME) + water(W) reactive system (DME + W ⟷ 2M), calculated using the Peng-Robinson EoS, at varying initial DME/W ratio (RDME-W, mole basis), i.e., at varying initial global component-mole-fraction vector z0. In all three cases M is initially absent. The GA also includes a complete computed R-3PL (green line) which starts, for the T range of the GA, at point A and ends at a reactive critical end point (R-CEP). The R-IPI at RDMEW=2.33 (𝑧𝑀 0 = 0.0, 𝑧𝐷𝑀𝐸0 = 0.7, 𝑧𝑊 0 = 0.3) is made of a single reactive saturation segment and the entire R-3PL is compatible with the global initial composition of this R-IP (z0I). The R-IPII at RDME-W=3.5 (𝑧𝑀 0 = 0.0, 𝑧𝐷𝑀𝐸0 = 0.7778, 𝑧𝑊 0 = 0.2222) is made of a reactive phase envelope (R-PE) made of two dew points (red) segments, a bubble points (blue) segment and a cloud (liquid-liquid) points (violet) segment, all of them reactive, and of a segment of a R-3PL compatible with z0II which extends from point A to point E. Finally, the R-IPIII at RDME-W=15 (𝑧𝑀 0 = 0.0, 𝑧𝐷𝑀𝐸0 = 0.9375, 𝑧𝑊 0 = 0.0625) is qualitatively similar to the R-IPII, but now the R-3PL segment compatible with z0III extends from point A to point C.