Method of modeling cloud point of a mixture of fatty acid methyl esters using a modified UNIFAC model and a system therefor

摘要

A method for predicting onset of liquid phase to solid phase transition of a mixture including a plurality of fatty acid methyl esters components. The method includes identifying chemical and molecular structure of each component of the mixture, calculating activity coefficients for each component in a liquid phase and a solid phase, calculating chemical potential for each component in the liquid phase and in the solid phase at a predetermined temperature and a predetermined pressure, and calculating the cloud point of the mixture. A system for carrying out the method is also disclosed.

主权项

1. A method for predicting onset of liquid phase to solid phase transition of a mixture including a plurality of fatty acid methyl esters (FAME) components, the FAME components are subdivided into a plurality of groups, comprising:
identifying chemical and molecular structure of each component of the mixture using data collected with a mass spectrometer and using a computing device containing a library of information of the chemical and molecular structure of each component; calculating, using the computing device, activity coefficients for each component in a solid phase and a liquid phase according toln⁢⁢γiGS=1-Vi′+ln⁢⁢Vi′-5⁢qi⁡(1-ViFi+ln⁡(ViFi))andln⁢⁢γiGL=∑k⁢υki⁡(ln⁢⁢ηk-ln⁢⁢ηki), wherein:
γiGS is the effect of group interaction on the activity coefficient of component i in the solid phase;i is the ith component in the mixture;
V′i=ri3/4/Σjχjrj3/4, wherein:ri=Σiνkiδi is the volume parameter for component i;νk, is the number of a kth group in component i;δi is a volume parameter of component i;rj=Σjνkjδj, is the volume parameter for component j;νkj is the number of the kth group in component j;δj is a volume parameter of component j;χi is the mole fraction of component j;
qi=ΣiνkiQi is the area parameter, wherein:νki is the number of the kth group in component iQi: is the surface area parameter of component i;
Vi=ri/Σjχjrj;Fi=qi/Σχiqi;γiGL is the effect of group interaction on the activity coefficient of component i in the liquid phase;ln ηk is the kth group contribution on the activity coefficient through the group interaction;ln ηk is the kth group contribution on the activity coefficient through the group interaction in the pure component i; calculating, using the computing device, chemical potential (μ) for each component in the liquid phase (L) and in the solid phase (S) at a predetermined temperature (T) and a predetermined pressure (P) according to
μiL=μi0,L(T,P)+RT ln(γiGLχiL) andμiS=μi0,S(T,P)+RT ln(γiGSχiS), wherein μiL is the chemical potential of component i in the liquid phase; μi0,L is the chemical potential of component i in the liquid phase at temperature T and pressure P; R is the ideal gas constant; γiGL is the effect of group interaction on the activity coefficient of component i in the liquid phase; χiL is the mole fraction of component i in the liquid phase; μiS is the chemical potential of component i in the solid phase; μi0,S is the chemical potential of component i in the solid phase at temperature T and pressure P; γiGS is the effect of group interaction on the activity coefficient of component i in the solid phase; χiS is the mole fraction of component i in the solid phase; and calculating, using the computing device, the cloud point of the mixture, wherein the cloud point is used to characterize cold flow properties of FAME, according toRT⁢⁢ln⁡(γiGS⁢xiSγiGL⁢xiL)=μi0,L⁡(T,P)-μi0,S⁡(T,P), wherein
qi=ΣνkiQk, wherein Qk is the surface area parameter of the kth group,ln⁢⁢ηk=zQk2⁢{-ln⁡(∑m⁢θm⁢τmk)+1-∑l⁢θl⁢τkl∑j⁢θj⁢τjl},wherein⁢⁢z⁢⁢is⁢⁢the⁢⁢charge⁢⁢of⁢⁢the⁢⁢kth⁢⁢group,⁢ln⁢⁢ηki=zQk2⁢{-ln⁡(Σm⁢θm⁢τmk)+1-Σl⁢θl⁢τklΣj⁢θj⁢τjl},θm=Qm⁢Xm∑n⁢Qn⁢Xn,θl=Ql⁢XlΣj⁢Qn⁢Xn,θj=Qj⁢XjΣj⁢Qn⁢Xn, wherein Qm is the surface area parameter of the mth group, Qn is the surface area of the nth group, Ql is the surface area parameter of the lth group, and Qj is the surface area parameter of component j,Xm=Σj⁢vmj⁢xjΣn⁢Σj⁢vnj⁢xj,wherein:⁢vmj⁢⁢is⁢⁢the⁢⁢number⁢⁢of⁢⁢a⁢⁢m⁢⁢th⁢⁢group⁢⁢in⁢⁢component⁢⁢j;and⁢⁢vnj⁢⁢is⁢⁢the⁢⁢number⁢⁢of⁢⁢a⁢⁢n⁢⁢th⁢⁢group⁢⁢in⁢⁢component⁢⁢j;Xn=Σj⁢vnj⁢xjΣn⁢Σj⁢vnj⁢xj,wherein⁢:Xl=Σj⁢vlj⁢xjΣl⁢Σj⁢vlj⁢xj,wherein⁢:vlj⁢⁢is⁢⁢the⁢⁢number⁢⁢of⁢⁢a⁢⁢l⁢⁢th⁢⁢group⁢⁢in⁢⁢component⁢⁢j;Xj=Σn⁢vnj⁢xjΣj⁢Σj⁢vnj⁢xj;andτmk=exp⁡(-AmkT-Bmk-Cmk⁢T);τkl=exp⁡(-AklT-Bkl-Ckl⁢T);τjl=exp⁡(-AjlT-Bjl-Cjl⁢T),and wherein group shape parameters δk and Qk and group interaction parameters A, B, and C are determined from the library of information for each type of bond for each component of the mixture.