Accurate Vaporizing GasDrive Minimum Miscibility Pressure Prediction

SPE SPE 15677 Accurate Vaporizing Gas-Drive Minimum Miscibility Pressure Prediction by E.-H Benmekki and G,A Mansoori, ●SPE ● U of ///inois Member Copyright 19S6, Sociely of Petroleum Engineers This paper was prepared tor presentation at the 61st Annual Technical Conference and Exhibition of the Societ y of Pelroleum Engineers held in New Orfeans, LA October 5-8, 1986 This paper waa selected for presentation by an SPE Program Commiltee following review of information contained in an abatract aubmittad by the author(a) Conlents ot the paper, aa presented, have not been reviewad by the Society of Petrolebm Engineers and are subject to correction by the aulhor(s) The material, as presented, doas not necessarily reflect any position of the Society of Petroleum Engineers, ita officers, or members, Papera presented at SPE meetings are subject to publication review by Editorial Committees of the S@ety of Petroleum Engineers Permission to copy is reetrtcted to an abstract of not more than 3W words Illustration may not be copied, The abstract ahoutd contain conspicuous acknowledgment of where and by whom the paper ia praeenlad Write Publications Manager, SPF, PO Sox 83383S, Richardson, TX 75083.3836 Telex, 7S098S SPEDAL ABSTRACT Prediction of The 14inimum Miscibility Pressure (IMP) of the Vaporizing Gas Drive (VGD) process is of state with different modeled using an ●quation mixing rUle8 joined with ● newly formulated expression for the unlike-three-body interactions ●nd the resarvolr fluid between tha injection gas The comparison of the numericel results with the evailable experimental data indicates that an ●quation of state alone overestimate the MMP However, when tha equation of stata is Joined with the unlike-threa-body interaction term, the MP will be predicted ●ccurately proposed The technique is used to develop a simple and reliable correlation for the accurate vaporizing gas drive MMP prediction INTRODUCTION The Ternary or pseudoternary diagram is a useful way development to visualize the of miscible displacement in enhanced oi I recovery The phasa behavior of a reservoir fluid for which the axact composition is never known can be represented approximately on a triangular diagram by grouping the components of the reservoir fluid into three pseudocomponents, Such diagram is called pseudoternary diagram Tha scopa of this paper involvas the use of the Peng-Robinson equation of atate couplad with coherent mixing and combining rules derivad from statistical mechanical consideration, ●nd the ●ffects in Implementation of the three body the ●valuation of the phaae behavior of ternary systems and tha prediction of the minimum mlacibility TO support prassura of simulatad reservoir fluids, the application of the model, it was preferable to obtain phase bahavior data for true tarnary systems Refareneas ●nd illuatratione at ●nd of papar such ●s carbon dioxide-n-butana-n-deeane ●nd methane-n-butana-n-decane, with are rigorously described by ternary diagrams Moreover, ●xperimental vapor-liquid data for the above ●t pressures ●nd tamperature$ aystama are ●vailable which fall within the range of tha majority of oil reservoirs eqUatlOn The utility of the Peng-Robinson (PR) of state has baen tested’*2 with Iimitad aucce$ in predicting the phasa ●nd minimtm behavior miscibility reservoir pressures of simulated fluids By using the PR equation of stste ●n overprediction of the !4RP of the methane-n-butane●nd it was balaived n-decana system was observed that this was due to the limitations of the PR ●ccurately predict equation which doss not the phasa behavior of the mathana-n-butane-n-decane system In addition tha in the critical region prediction of the vapor-liquid coexi$tenca curves of the carbon dioxida-n-butana-n-decane sytems was not satisfactory in all ranges of presaurea and compositions The ultimate objective of this paper it to show the impact of the mixing and combining rules on the prediction of and the phase envelops tha contribution of the three body-effects on phaae behavior predictions naar the critical ragion THE VAN OER WAALS MIXING From conformal tha statistical machanica it intarmolecular potantial molecules of a mixture potential energy function the following axpresslon: RULES solution theory of can ba ahown that palranergy function of any two can ba ralated to the of a raferenca fluid by ACCURATEVAPORIZING GAS DRIVEMINIMUN RT 1/3 (r) ‘IJ = f;juo(r,thli “ (1) ) hx - ~ ~ n Z =; (4) V (v+b) +b (v-b) where a(T) = a(Tc){l + K(l-T~/2)}2 (5) a(Tc) = 0.4572fI R2T~iPc (6) b u 0.07180 nn ‘Xhx a (T) p.— v-b potential energy In the above equation U is the function of the reference pure fluid, fi is the conformal molecular energy parameter and AiJ1/3 is the conformal molecular length parameter of interactions betwean molecules i and j of the mixture By using Eq.1 in tha statistical mechanical virial or energy equations of state and application of the conformal solution approximation to the radial distribution functions of components of a mixturas it can be shown that SPE 15677 MISCIBILITY PRBSSURRPREDICTION RTc/Pc (7) (2) ‘ixjfijhij the characteristic following relationship: xixjhij constant u is gi~;en by tha (3) i] K - o.37k6k where hx ●nd fx ●re the conformal solution parameters of ● hypothetical pure fluid which represent the mixture ●nd xi, x ●re the mole fractione This means that for]the extension applicability of ● pure fluid equation of state mixtures one has to replace moiecular ●nergy of state with length parameters of tha ●quation above mixing rules of to ●nd the In ordar to apply the van der Waais mixing rules in different equations of state, one has to consider the fol iowing guidelines of the conformal solution theory of statistical machanics: (i) The vander Waals mixing rules are for constants of an equation of stata (ii) Equation ia a mixing rule for parameters that are proportional to (molecuiar length) 3.(moiecuiar energy) and Equation is a mlxlng rula for parameters that are proportional to (molecular Iangth)j In the the Peng-Robinson5 received a wide calculations is parform vapor-liquid Peng-Robinson aquatlon of equation of acceptance in chosen in this equilibrium state - 0.26992Q2 (6) can identical with the mixing Equations and ●re rules which were originally proposed by van der Waals4 for the van der Waals equation of atate as it was applied to simple mixturas Aa an exampie state which has process engineering investigation to calculations + 1.5ii226w It Is customary, for parameters e and b with which ●re known ●a thair nn a = Z the mixture, the following mixing rules to calculate expressions (9) XiXjaij ij b = ! i aij = (lo) xibi (1-4ij)(aiiajj) This set of mixing with the guidelines solution theory of In order correctly we must constants write the foliowlng ’/2 rules is dictated statistical (11) however inconsistent by tha conformal mechanics to apply the van der W&ale mixing in tha Pang-Robinson equation of tharmodynamlc variables separate of etate Thus , of tha ●quation Peng-Robineon equation of stata form: rules atata, from wa can in tha v - v c/RT + d - -—-—- - - - - THEORY (cd/RT) z.— OF THE THREE BOOY FORCES (12) (v+b) v-b where -—.- c = a(Tc) + (1+[)2 (b/v) and In a potential be wri~.ten (v-b) nn c = ~>x.x.c IJIJ ij (13) b = ~~ (lb) xixjbij i.i nn (15) d = ;;xixjdij l/3 b ii bij= (1-l ij)3 [ for that be the unlika ●re corwiatent interaction with the U=!u(ij) i