Fasa Terkondensasi (Kf)
3
Va lidated Computing Approach for High-Pressure Chemical and Multiphase Equilibrium Abstract For the comput at ion of chemic al and phase equi li br iu m at cons ta nt temper ature and pressure, there have bee n propos ed a wid e var iet y of proble m formulations and numerical solution procedures, involving both direct minimization of the Gibbs energy and the solution of equivalent nonlinear equation systems. Still, with very few exceptions, these methodologies may fail to solve the chemical and phase equilibrium problem correctly . Nevertheless, there are many existing solution methods that are extremely reliable in general and fail only occasionally. o ta!e good advant age of thi s wea lth of avai lable tec hni que s, we demonstrate her e an approach in which such techniques can be combined with procedures that have the power to validate results that are correct, and to identify results that are incorrect. Furthermore, in the latter case, corrective feedbac! can be provided until a result that can be validated as correct is found. he validation procedure is deterministic, and provides a mathematical an d computational guarantee that the global minimum in the Gibbs energy has been found. o demonstr ate this valid ated computing approach to the chemical and phase equilibrium problem, we present several examples involving reactive and nonreactive components at high pressure, using cubic equation"of"state models. #eywords $ %hase equilibrium& 'hemical equilibri um& Stability analysis& (nterval analysis& ) alidated computing& *quation of state.
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Transcript of Fasa Terkondensasi (Kf)
Validated Computing Approach for High-Pressure Chemical and Multiphase Equilibrium
Validated Computing Approach for High-Pressure Chemical and Multiphase Equilibrium
Abstract
For the computation of chemical and phase equilibrium at constant temperature and pressure, there have been proposed a wide variety of problem formulations and numerical solution procedures, involving both direct minimization of the Gibbs energy and the solution of equivalent nonlinear equation systems. Still, with very few exceptions, these methodologies may fail to solve the chemical and phase equilibrium problem correctly. Nevertheless, there are many existing solution methods that are extremely reliable in general and fail only occasionally. To take good advantage of this wealth of available techniques, we demonstrate here an approach in which such techniques can be combined with procedures that have the power to validate results that are correct, and to identify results that are incorrect. Furthermore, in the latter case, corrective feedback can be provided until a result that can be validated as correct is found. The validation procedure is deterministic, and provides a mathematical and computational guarantee that the global minimum in the Gibbs energy has been found. To demonstrate this validated computing approach to the chemical and phase equilibrium problem, we present several examples involving reactive and nonreactive components at high pressure, using cubic equation-of-state models.Keywords : Phase equilibrium; Chemical equilibrium; Stability analysis; Interval analysis; Validated computing; Equation of state.
Kebenaran Perhitungan dari Bahan Kimia Bertekanan Tinggi dan Kesetimbangan Fasa Banyak
Abstrak
Untuk menghitung bahan kimia yang terkandung dan kesetimbangan fasa pada temperature dan tekanan yang tetap, harus diketahui selisih dari jumlah bahan yang akan diteliti dengan bahan contoh, atau setidaknya energi Gibbs dan hasil dari pembagian pada kesetimbangan. Tapi pada beberapa kasus, metode ini tidak bisa memecahkan bahan kimia apa yang terkandung dan kesetimbangan fasa secara pasti. Sebenarnya banyak sekali metode yang biasa digunakan dengan tingkat kesalahan yang kecil. Untuk mendapatkan hasil yang baik kami mencoba menggabungkan teknik yang tersedia, dengan teknik yang kami gunakan dalam prosedur, agar kekuatan untuk menganalisa hasil yang benar dan tidak benar lebih valid. Dalam kondisi yang lain, dan dengan kasus yang berbeda pula, koreksi balik dapat dilakukan, sampai hasil yang valid dan benar didapatkan. Penentuan dari kevalidan suatu hasil dikontrol, dan dibuktikan dari perhitungan matematik, dengan catatan bahwa energi Gibbs minimum sudah diketahui. Untuk membuktikan kebenaran perhitungan dari banyaknya bahan kimia dan kesetimbangan fasa, kami memberikan contoh-contoh umum berkaitan dengan reaktif dan tidak reaktifnya suatu komponen pada tekanan tinggi, menggunakan model yang sesuai dengan bentuk aslinya.Kata kunci : Kesetimbangan fasa, Kesetimbangan kimia, Kestabilan analisis, Interval analisis, Kebenaran perhitungan, Kesetaraan. Tugas Kimia Fisika IIAbstrak Kesetimbangan Fasa Terkondensasi
Nama : Ratih Indah Mutiara PermataNIM : H 311 04 015
JURUSAN KIMIA
FAKULTAS MATEMATIKA DAN ILMU PENGETAHUAN ALAM
UNIVERSITAS HASANUDDIN
MAKASSAR
2006
