ĐẠI HỌC QUỐC GIA TP HCM TRƯỜNG ĐẠI HỌC BÁCH KHOA O VŨ TIẾN DŨNG MÔ PHỎNG VÀ TỐI ƯU HÓA THIẾT BỊ PHẢN ỨNG TỔNG HỢP AMONIẮC Chuyên ngành: Kỹ thuật hóa dầu Mã số: 60520330 LUẬN VĂN THẠC SĨ Tp HCM, tháng 01 năm 2018 CƠNG TRÌNH ĐƯỢC HOÀN THÀNH TẠI TRƯỜNG ĐẠI HỌC BÁCH KHOA – ĐHQG - HCM Cán hướng dẫn khoa học: TS Nguyễn Tuấn Anh ThS Nguyễn Kim Trung Cán chấm nhận xét 1: TS Nguyễn Thành Duy Quang Cán chấm nhận xét 2: TS Lưu Xuân Cường Luận văn thạc sĩ bảo vệ trường Đại học Bách khoa – ĐHQG thành phố Hồ Chí Minh tháng 01 năm 2018 Thành phần Hội đồng đánh giá luận văn thác sĩ gồm: (Ghi rõ họ, tên, học hàm, học vị hội đồng chấm bảo vệ luận văn thạc sĩ) PGS.TS Huỳnh Kỳ Phương Hạ TS Nguyễn Thành Duy Quang TS Lưu Xuân Cường TS Võ Thành Phước TK TS Phạm Hồ Mỹ Phương CHỦ TỊCH HỘI ĐỒNG PGS.TS Huỳnh Kỳ Phương Hạ TRƯỞNG KHOA KỸ THUẬT HÓA HỌC ĐẠI HỌC QUỐC GIA TP.HCM TRƯỜNG ĐẠI HỌC BÁCH KHOA CỘNG HÒA XÃ HỘI CHỦ NGHĨA VIỆT NAM Độc lập - Tự - Hạnh phúc NHIỆM VỤ LUẬN VĂN THẠC SĨ Họ tên học viên: Vũ Tiến Dũng MSHV: 13401157 Ngày, tháng, năm sinh: 15/03/1969 Nơi sinh: Nam Định Chuyên ngành: Kỹ thuật Hóa dầu Mã số: 60520330 I TÊN ĐỀ TÀI: MÔ PHỎNG VÀ TỐI ƯU HÓA THIẾT BỊ PHẢN ỨNG TỔNG HỢP AMONIẮC II NHIỆM VỤ VÀ NỘI DUNG: - Khảo sát trình tổng hợp NH3 dựa phản ứng kết hợp H2 với N2 thiết bị phản ứng có mặt xúc tác, điều kiện nhiệt độ áp suất cao - Xây dựng mơ hình tốn, dựa cân vật chất, lượng, điều kiện ban đầu yếu tố ràng buộc Lập giải hệ phương trình vi phân mơ tả hệ thống, kèm theo điều kiện ràng buộc ban đầu giới hạn kỹ thuật q trình thiết bị, tính tốn hàm mục tiêu - Giải toán tối ưu hàm nhiều biến (khác với nghiên cứu trước) phương pháp: sử dụng phương pháp luân phiên biến kết hợp lát cắt vàng sử dụng phương pháp giải thuật di truyền III NGÀY GIAO NHIỆM VỤ : 06/2016 IV NGÀY HOÀN THÀNH NHIỆM VỤ : 01/2018 V CÁN BỘ HƯỚNG DẪN : TS NGUYỄN TUẤN ANH Tp HCM, ngày 20 tháng 01 năm 2018 CÁN BỘ HƯỚNG DẪN CHỦ NHIỆM BỘ MÔN ĐÀO TẠO TRƯỞNG KHOA KỸ THUẬT HĨA HỌC LỜI CÁM ƠN - Trước tiên, tơi xin chân thành cảm ơn TS Nguyễn Tuấn Anh, ThS Nguyễn Kim Trung, TS Đào Thị Kim Thoa – trưởng mơn Kỹ thuật Hóa dầu, người trực tiếp hướng dẫn, hỗ trợ động viên suốt q trình thực luận văn Nhờ có hướng dẫn giúp đỡ tận tình thầy nên tơi hồn thành luận văn - Tiếp theo, xin trân trọng cảm ơn thầy Khoa Kỹ Thuật Hóa Học – Trường Đại học Bách Khoa – Đại học Quốc gia thành phố Hồ Chí Minh tận tình giảng dạy trang bị cho kiến thức quý báu năm học vừa qua, mà kiến thức giúp tơi vận dụng q trình thực luận văn công việc - Và cuối cùng, tơi xin chân thành cảm ơn gia đình, đồng nghiệp người bạn động viên, chia sẻ, giúp đỡ nhiệt tình đóng góp nhiều ý kiến q báu giúp tơi có động lực hồn thành nhiệm vụ học tập Tp Hồ Chí Minh, ngày 20 tháng 01 năm 2018 Học viên thực luận văn Vũ Tiến Dũng TÓM TẮT - Việt Nam nước nông nghiệp, 70% dân số sông dựa vào nơng nghiệp, phân bón mặt hàng thiết yếu đáp ứng nhu cầu trồng, góp phần quan trọng cho phát triển kinh tế nước nhà, từ năm đầu thập niên trước, từ quốc gia nhập phân bón, đến sản xuất đủ đáp ứng nhu cầu nước thừa để xuất khẩu, đặc biệt phân đạm ure Đạt kỳ tích này, nhờ vào cơng cơng nghiệp hóa, đại hóa đem lại - Amoniắc sản phẩm cho sản xuất đạm ure, vịng 20 năm qua tăng công suất sản xuất đạm ure từ 180 nghìn (nhà máy đạm Hà Bắc) lên triệu (thêm nhà máy đạm Phú Mỹ, Cà Mau Ninh Bình), đồng nghĩa với việc tăng sản lượng amoniắc Như việc nâng cao hiệu sản xuất amoniắc vô quan trọng, góp phần giảm giá sản phẩm đạm ure, góp phần tích cực giảm chi phí sản xuất nơng nghiệp, thúc đẩy xuất nông sản sang nước khu vực, đưa Việt nam trở thành quốc gia phát triển nơng nghiệp bền vững, riêng lúa gạo nước đứng số giới xuất sản phẩm truyền thống - Nguyên liệu sản xuất amoniắc từ lượng than đá, dầu mỏ khí, việc sử dụng hiệu nguồn lượng hóa thạch có ý nghĩa lớn khơng kinh tế mà cịn mơi trường phát triển bền vững hành tinh chúng ta, tính tốn chi phí sản xuất thấp khơng đem lại hiệu cho doanh nghiệp mà đảm bảo phát triển lâu bền cho nhà sản xuất Kể từ khoa học máy tính đời, đem đến cho nhà khoa học nhiều tiến áp dụng tính tốn xử lý tốn khơng kỹ thuật mà giải tốn kinh tế, áp dụng phát triển phần mềm chuyên dụng để mô tối ưu hóa q trình sản xuất Trong luận văn tác giả áp dụng giải toán tối ưu hóa dựa phần mềm Matlab số thuật tốn cho hiệu đầu tư, chi phí sản xuất thấp ABSTRACT - Vietnam is an agricultural country, with more than 70% of its population relying on agriculture Fertilizers are an essential commodity to meet the needs of the crop, contributing significantly to the economic development of the country, from the early years In the past decade, we have come from a fertilizer importing country that has produced enough to meet domestic demand and surplus for export, especially urea fertilizer Achieving this feat, thanks to the industrialization and modernization brought - Ammonia is the main product for urea fertilizer In the last 20 years, we have increased the production capacity of urea fertilizer from 180 thousand tons (Ha Bac Fertilizer Plant) to over million tons (Phu My Fertilizer Plant, Ca Mau and Ninh Binh), which means increased production of ammonia Thus raising the efficiency of production of ammonia is extremely important, contributing to the reduction of urea nitrogen products, contributing to the reduction of agricultural production costs, promoting the export of agricultural products to countries and regions, Making Vietnam a sustainable agricultural developing country, especially rice, we are the number one country in exporting this traditional product - The production of ammonia is from energy such as coal, oil and gas, and the efficient use of fossil fuels is not only an economic one but also an environmental and sustainable development Calculating the cost of production is not only effective for the enterprise, but also guarantees durable development for the manufacturer Since the introduction of computer science, scientists have made many advances in the application of computing to solve not only technical problems but also economic problems Develop specialized software to simulate and optimize production processes In this thesis, the author has applied optimization problem based on matlab software and some algorithms such that the efficiency of investment, production cost is the lowest LỜI CAM ĐOAN Tôi xin cam đoan luận văn thực số liệu, kết luận văn trung thực, xác Tp Hồ Chí Minh, ngày 20 tháng 01 năm 2018 Vũ Tiến Dũng MỤC LỤC TÓM TẮT I ABSTRACT II MỤC LỤC III DANH MỤC BẢNG V DANH MỤC HÌNH VI TỔNG QUAN 1.1 Amoniắc 1.2 Lịch sử ngành công nghiệp sản xuất amoniắc 1.3 Tình hình nghiên cứu 1.4 Mục tiêu nhiệm vụ nghiên cứu 1.4.1 Mục tiêu 1.4.2 Nhiệm vụ CƠ SỞ LÝ THUYẾT 2.1 Tính chất vật lý hoá học NH3 2.1.1 Tính chất vật lý 2.1.2 Tính chất hóa học 2.2 Phương pháp tổng hợp NH3 11 2.2.1 Các phương pháp tổng hợp NH3 11 2.2.2 Tổng hợp NH3 từ phản ứng trực tiếp H2 với N2 11 2.3 Công nghệ sản xuất NH3 từ phản ứng trực tiếp cho H2 kết hợp với N2 12 2.3.1 Công nghệ tổng hợp NH3 áp suất cao hãng Kellogg 12 2.3.2 Công nghệ tổng hợp NH3 áp suất trung bình hãng Krupp Uhde 13 2.3.3 Công nghệ tổng hợp NH3 áp suất thấp hãng Haldor Topsoe 15 2.4 Lựa chọn công nghệ sản xuất NH3: 17 2.5 Một số ưu điểm bật Công nghệ Haldor Topsoe 17 2.6 Cấu tạo nguyên lý hoạt động thiết bị phản ứng tổng hợp amoniắc 18 2.6.1 Cấu tạo thiết bị 18 2.6.2 Nguyên lý hoạt động 19 2.7 Giải hệ phương trình vi phân phương pháp Runge – Kutta bậc 20 iii 2.8 Giải toán tối ưu nhiều biến phương pháp luân phiên biến (cyclic coordinate method) 20 2.9 Phương pháp hàm phạt (penalty method) 22 2.10 Giải toán tối ưu phương pháp lát cắt vàng (giải toán tối ưu hàm biến) 22 2.11 Giải thuât di truyền 23 2.11.1 Tìm hiểu chung GAs 23 2.11.2 Các toán tử giải thuật di truyền 26 2.11.3 Các tham số giải thuật di truyền 27 2.11.4 Công thức Giải thuật Di truyền 27 2.11.5 Các thành phần thuật giải di truyền 28 THIẾT LẬP VẤN ĐỀ 31 3.1 Mô thiết bị phản ứng tổng hợp amoniắc 31 3.2 Hàm mục tiêu 32 3.3 Các ràng buộc đẳng thức 33 3.4 Các ràng buộc bất đẳng thức 35 3.5 Sơ đồ thuật toán 36 KẾT QUẢ VÀ BÀN LUẬN 40 4.1 Kết mô thiết bị phản ứng 40 4.2 Kết tính tốn hàm mục tiêu 43 4.3 Kết tối ưu sử dụng phương pháp luân phiên biến 44 4.3.1 Kết tối ưu ứng với nhiệt độ đỉnh 694K 44 4.3.2 Kết tối ưu đồng thời hai biến nhiệt độ đỉnh chiều dài thiết bị 45 4.4 Kết tối ưu sử dụng phương pháp giải thuật di truyền 45 KẾT LUẬN 47 TÀI LIỆU THAM KHẢO 48 iv DANH MỤC BẢNG Bảng 1.1 Nhu cầu sử dụng NH3 giới [1] Bảng 2.1 Các thông số vật lý đặc trưng NH3 Bảng 4.1 Kết tối ưu nhiệt độ đỉnh 694K 44 Bảng 4.2 Kết tối ưu đồng thời hai biến nhiệt độ đỉnh chiều dài thiết bị 45 Bảng 4.3 Kết tối ưu 46 v 29th Symposium of Malaysian Chemical Engineers (SOMChE) 2016 IOP Publishing IOP Conf Series: Materials Science and Engineering 206 (2017) 012059 doi:10.1088/1757-899X/206/1/012059 1234567890 simulation, and optimization of an auto-thermal ammonia synthesis reactor Some of them can be mentioned here as in Babu and Angira [2], Babu et al [3], Carvalho et al [4], Edgar et al [5], Ksasy et al [6], Murase et al [7], Upreti and Deb [8], Yusup et al [9] However, in the studies of Edgar et al [5], Murase et al [7], the model used has some uncorrected points and have been modified in Upreti and Deb [8] Furthermore, the studies mainly focus on the optimization of reactor length corresponding to a particular reactor top temperature, usually of 694 K [3, 4], or in only several temperatures [6] In this study, not only the reactor length but also the reactor top temperature is included in the optimization variables for finding the maximum profit of the process The coupled differential equations which simulate the synthesis reactor are solved using Runge-Kutta 4th order method Cyclic coordinate search method was applied for the multivariate optimization problem In each coordinate axis search, the problem becomes single variable optimization and the golden section search was employed to find the maximum of the profit The box-constraints of the parameters were guaranteed by adding the penalty to the objective function when any of the limits is violated The results from the study are also compared to the other reports found in literature Problem formulation The problem formulation in this work is similar to the model in Murase et al [7] and includes the modifications mentioned in Babu and Angira [2], Upreti and Deb [8] The heat released by the reaction is used to heat the incoming gas mixture in counter current flow The production of ammonia depends on the temperature of feed gas at the entrance of the reaction zone (top temperature), the partial pressures of the reactants (nitrogen and hydrogen), and the reactor length The optimal design problem aims to obtain the optimal parameters yielding maximum economic return from the reactor operation 2.1 Objective function The objective function for the reactor optimization is the profit of the process based on the difference between the value of the product gas (heating value and the ammonia value) and the value of feed gas (as a source of heat only) less the amortization of reactor capital costs Other operating cost are neglected      F  1.3356  107  1.708  104 N N  704.09 Tg  T0  699.27 T f  T0  3.4566 107  1.9837  109 x  (2) 2.2 Equality constraints The model of ammonia reactor is obtained considering the energy balance for feed gas and reacting gas, and the mass balance for nitrogen, respectively dT f dx dT f dx   US1 Tg  T f WC pf    H  S2 US1 Tg  T f  WC pg WC pg  dN f dx  (3)  dN    dx     p N p1.5 pNH H  k1  k2 1.5  pNH pH  3     (4) (5) in which  20800  k1  1.78954  104 exp    RTg     47400  k2  2.5714 1016 exp    RTg    286 N N pN  2.598 N N0  N N 2 2 (6) (7) (8) 29th Symposium of Malaysian Chemical Engineers (SOMChE) 2016 IOP Publishing IOP Conf Series: Materials Science and Engineering 206 (2017) 012059 doi:10.1088/1757-899X/206/1/012059 1234567890 pH  p N pNH   286 2.23 N N0  N N 2.598 N N (9)  (10)  2NN The notations T f0 , Tg0 , and N N0 denote the initial value at x=0 for Tf, Tg, and N N , respectively The 2 initial values are given by T f0  Tg0  T0 , N N0  701.2 kmol/hm (11) 2.3 Box constraints As usual in industry, the following physical restrictions are imposed over the variables:  x  10, 400  T f  800,  N N  3220 (12) From the system model, it can be obtained that the length of the reactor and the top temperature can be chosen as the independent variables The remaining variables (Tf, Tg, and N N ) can be calculated from the three differential equations From that, the objective function is estimated and is considered as a function of two variables T0 and x From the constraints, the variable T0 is also set to be within 400 and 800 The optimal design problem is summarized as follows max F  x, T0   dT f US1  Tg  T f   dx WC pf  dT H  S2  f   US1 Tg  T f    dx WC pg WC pg    pN p1.5 pNH  s.t  dN H    k1 2  k2 1.53  f  dx  pNH pH    T  T  T , N  701.2 g N2  f 400  T  800,  N  3220 f N2  0  x  10, 400  T0  800      dN    dx    (13) Optimization strategy The procedure to solve problem (13) consists of obtaining approximate solutions of differential equation system (3), (4) and (5), with initial conditions (11) through the fourth-order Runge–Kutta method The initial condition is clearly defined when the top temperature (T0), which is also a variable, is assigned The interval of integration is defined when the reactor length is assigned From these computed values, the objective function is evaluated and the procedure above is repeated until an optimal solution is found Therefore, the problem can be considered as two-variable optimization and the simple cyclic coordinate search can be employed In order to guaranty the constraints, the objective function is forced to assume an undesired value whenever any of variable limits is violated during the optimization process Such approach consists of defining a penalty or barrier to the objective function when any of the limits is violated In each direction search of cyclic coordinate method, a single-variable optimization has to be performed and a derivative-free algorithm, the golden search method, is chosen The proposed strategy is detailed as follows 3.1 Cyclic coordinate search Often in the solution of multivariable optimization problems it is desired to be done with a gradient-free algorithm This may be the case when gradient evaluations are difficult, or in fact gradients of the 29th Symposium of Malaysian Chemical Engineers (SOMChE) 2016 IOP Publishing IOP Conf Series: Materials Science and Engineering 206 (2017) 012059 doi:10.1088/1757-899X/206/1/012059 1234567890 underlying optimization method not exist Such a method that offers this feature is the method of the cyclic coordinate search, the simplest method for nonlinear optimization [10] The minimization problem considered is: optimize f  x  x n The method in its basic form uses the coordinate axes as the search directions Therefore, along each search direction i  1: n , the corresponding variable xi is changed only, with all remaining variables being kept constant to their previous values The optimization is carried out in order over all variables with indices 1,…,n at each iteration of the algorithm The task is repeated until the convergence condition satisfied, such as no significant improvement after one cycle Step Initialization Select a tolerance ε > 0, to be used in the termination criterion Select an initial point x(0) and initialize by setting z(1) ←x(0) Set k = and i = 1, where k indicates the number of iterations, i is the pointer variable for the direction Step Main iteration Search the optimal solution f(z*)=opt f(x) , which is the single-variable optimization of variable xi Update z(i+1)=z* If j < n, then increase i to i +1 and repeat step Otherwise, if j = n, then go to step Step Termination check Set x(k+1) = z(n) If the termination criterion is satisfied, for example abs(x(k+1) - x(k)) < ε, then stop Else, set z(1) = x(k+1) Increase k to k + 1, set i = and repeat step 3.2 Barrier method for constrained optimization In barrier or penalty method, a constrained optimization problem is replaced by an unconstrained problem The solution will favour satisfaction of the constraints by adding to the objective function a term that produces a high cost for violation of the limits Therefore, the objective function can be redefined as  F if 400  T f  800,  N N  3220 F  10 otherwise (14) 3.3 Golden section search The golden section search is a technique for finding the optimum point of a function by iteratively narrowing the interval containing the extremum similar to bisection brackets the zero of a function The algorithm determining the maximum of a function F is briefly described below Step Let [xl,xu] be an interval containing the maximum, ε > be a tolerance Set k=0  x1  xu    xu  xl  where  =  (15)   x2  xl    xu  xl    Step Evaluate F(x1) and F(x2) If F(x1) ≥ F(x2), set xu=x2, x2=x1, x1=xu−ϕ(xu-xl) Else, set xl=x1, x1=x2, x2=xl+ϕ(xu-xl) Step If xu – xl < ε, then the maximum occurs at (xl + xu)/2 and stop iterating, else go to Step 3.4 Parameters In this work, the parameters were obtained from the literature and summarized in Table 29th Symposium of Malaysian Chemical Engineers (SOMChE) 2016 IOP Publishing IOP Conf Series: Materials Science and Engineering 206 (2017) 012059 doi:10.1088/1757-899X/206/1/012059 1234567890 Table Used parameters Parameter Cpf Cpg f ΔH R S1 S2 U W Value 0.707 0.719 1.0 −26000 1.987 10 0.78 500 26400 Unit kcal/kg K kcal/kg K kcal/kmol kcal/kmol K m m2 kcal/h m2 K kg/h RESULTS AND DISCUSSIONS 4.1 Temperature and flow rate profiles In order to simulate and optimize the reactor, several Matlab programing files was developed based on the discussed algorithm Figure shows the profiles obtained at different top temperature (T0) It is evident from the graph that the profiles are smooth and well agree with the others found in literature It is also obtained that the proposed numerical method is stable even at the top temperature as high as 800 K, which is different from the conclusions from [8] (a) (b) (c) (d) Figure The profiles at different top temperatures (a) T0=600 K (b) T0=650 K (c) T0=694 K (d) T0=800 K 29th Symposium of Malaysian Chemical Engineers (SOMChE) 2016 IOP Publishing IOP Conf Series: Materials Science and Engineering 206 (2017) 012059 doi:10.1088/1757-899X/206/1/012059 1234567890 Figure Objective function at different top temperatures 4.2 Optimization of the profit function Figure shows the variation of objective function with reactor length at different top temperatures It can be obtained that the objective function has single maximum point at each top temperature Therefore, the golden section search can be applied for optimization of the profit The optimum objective function at the top temperature of 694 K is usually found in literature [2-4, 8] Therefore, the optimum profit at the top temperature of 694 K was also conducted and compared to the other reports The results are showed in Table Table Optimum length at top temperature of 694 K Parameters x (m) Tf (K) F (106$/year) Babu and Angira [2] 6.586 406.55 5.014 Yusup et al [11] 6.695 399.85 5.017 Ksasy et al [6] 6.425 308.36 5.664 Carvalho et al [4] 6.694 400.00 5.016 Current study 6.695 400.02 5.016 Table Optimum results Variables x (m) T0 (K) Tf (K) Tg (K) NN2 F (106$/year) Interval [0,10] [600,800] [400,800] [0,3220] Optimal solution 6.724 700.27 400.00 629.94 490.68 5.018 The profit return from the process depends not only the length of the reactor but also the top temperature Therefore, the cyclic coordinate search was used for optimization the objective function It was found that the optimum reactor length is 6.724 m and the top temperature should be operated at 700.27 K The profit obtained from the process is 5.018  106 $ per year The other parameters of the process are shown in Table The profit value is higher than the others found in literature The result suggests that the temperature of the feed entering the catalyst zone should be slightly higher and the reactor length is also slightly longer the other found in literature 29th Symposium of Malaysian Chemical Engineers (SOMChE) 2016 IOP Publishing IOP Conf Series: Materials Science and Engineering 206 (2017) 012059 doi:10.1088/1757-899X/206/1/012059 1234567890 Conclusions In this study, we presented a Runge-Kutta 4th order method for solving system of differential equation modeling the ammonia synthesis reactor The maximum profit return was considered as multivariable optimization problem The optimization strategy included cyclic coordinate search method for the top temperature and reactor length, golden section search for each coordinate search and barrier function for the constraints Numerical results suggested the accuracy and efficiency of the method The optimum solution satisfied all the constraints and higher than other reports The synthesis system should be operated at top temperature of 700.27 K with the reactor length of 6.724 m The corresponding economic return is 5.018  106 $ / year Acknowledgement The authors would like to thank Associate Professor Yoshikawa Shiro and Tokyo Institute of Technology, Tokyo, Japan for the kind support during the preparation of the manuscript References [1] Appl M 1999 Ammonia: principles and industrial practice (Weinheim: Wiley-VCH) [2] Babu B V and Angira R 2005 Optimal design of an auto-thermal ammonia synthesis reactor Computers & Chemical Engineering 29 1041-1045 [3] Babu B V, Angira R and Nilekar A 2004 Optimal design of an auto-thermal ammonia synthesis reactor using differential evolution in The Eighth World Multi-Conf on Systemics, Cybernetics and Informatics (Orlando, Florida, USA) [4] Carvalho E P, Borges C, Andrade D, Yuan J Y and Ravagnani M A S S 2014 Modeling and optimization of an ammonia reactor using a penalty-like method Applied Mathematics and Computation 237 330-339 [5] Edgar T F, Himmelblau D M and Lasdon L S 2001 Optimization of Chemical Processes (McGraw-Hill) [6] Ksasy M S M, Areed F, Saraya S and Khalik M A 2010 Optimal Reactor Length of an AutoThermal Ammonia Synthesis Reactor International Journal of Electrical & Computer Sciences 10 6-15 [7] Murase A, Roberts H L and Converse A O 1970 Optimal Thermal Design of an Autothermal Ammonia Synthesis Reactor Industrial & Engineering Chemistry Process Design and Development 503-513 [8] Upreti S R and Deb K 1997 Optimal design of an ammonia synthesis reactor using genetic algorithms Computers & Chemical Engineering 21 87-92 [9] Yusup S, Zabiri H, Yusoff N and Yew Y C 2006 Modeling and optimization of Ammonia reactor using shooting methods, in Proc of the 5th WSEAS Int Conf on Data networks, Communications and Computers 2006, World Scientific and Engineering Academy and Society (WSEAS): Bucharest, Romania p 258-268 [10] Floudas C A and Pardalos P M 2008 Encyclopedia of Optimization (Springer US) [11] Yusup S, Zabiri H, Yusoff N and Yew Y C 2006 Modeling and optimization of Ammonia reactor using shooting methods, in Proceedings of the 5th WSEAS international conference on Data networks, communications and computers 2006: Bucharest, Romania p 258-268 Multivariable optimization of an auto-thermal ammonia synthesis reactor using genetic algorithm Nguyen T Anh-Nga, Nguyen Tuan-Anh, Vu Tien-Dung, and Nguyen Kim-Trung Citation: AIP Conference Proceedings 1878, 020024 (2017); doi: 10.1063/1.5000192 View online: http://dx.doi.org/10.1063/1.5000192 View Table of Contents: http://aip.scitation.org/toc/apc/1878/1 Published by the American Institute of Physics Articles you may be interested in Proliferation and ajmalicine biosynthesis of Catharanthus roseus (L) G Don adventitious roots in self-built temporary immersion system AIP Conference Proceedings 1878, 020018 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Tien-Dung2, Nguyen KimTrung2 Faculty of Applied Sciences, Ton Duc Thang University, District 7, Ho Chi Minh City, Vietnam Faculty of Chemical Engineering, Ho Chi Minh City University of Technology - VNUHCM, District 10, Ho Chi Minh City, Vietnam a) anh.nguyen@hcmut.edu.vn nguyenthianhnga@tdt.edu.vn b) Abstract.The ammonia synthesis system is an important chemical process used in the manufacture of fertilizers, chemicals, explosives, fibers, plastics, refrigeration In the literature, many works approaching the modeling, simulation and optimization of an auto-thermal ammonia synthesis reactor can be found However, they just focus on the optimization of the reactor length while keeping the others parameters constant In this study, the other parameters are also considered in the optimization problem such as the temperature of feed gas enters the catalyst zone The optimal problem requires the maximization of a multivariable objective function which subjects to a number of equality constraints involving the solution of coupled differential equations and also inequality constraints The solution of an optimization problem can be found through, among others, deterministic or stochastic approaches The stochastic methods, such as evolutionary algorithm (EA), which is based on natural phenomenon, can overcome the drawbackssuch as the requirement of the derivatives of the objective function and/or constraints, or being not efficient in nondifferentiable or discontinuous problems Genetic algorithm (GA) which is a class of EA, exceptionally simple, robust at numerical optimization and is more likely to find a true global optimum.In this study, the genetic algorithm is employed to find the optimum profit of the process.The inequality constraints were treated using penalty method The coupled differential equations system was solved using Runge-Kutta 4th order method The results showed that the presented numerical method could be applied to model the ammonia synthesis reactor The optimum economic profit obtained from this study are also compared to the results from the literature It suggests that the process should be operated at higher temperature of feed gas in catalyst zone and the reactor length is slightly longer INTRODUCTION Ammonia is one among the largest volume inorganicchemicals in the chemical process industries[1] Most of the commercially produced ammonia is used in fertilizers with the remainder used in a variety of applications such as plastics, synthetic fibers and resins, pharmaceuticals, explosives, papers and refrigeration[2] Therefore, modelling and optimization of ammonia synthesis have received a considerable attention by industries and researcher Most of the world consumption is manufactured from the elements nitrogen and hydrogen in a catalytic process originally developed by Haber and Bosch using a promoted iron catalyst as follows[2]: ZZX N  3H YZ Z NH (1) The reaction is reversible and exothermic with considerable release of heat Therefore, the reaction is usually carried out in an auto-thermal synthesis reactor, which utilizes the heat of reaction to pre-heat the feed gas and maintain the appropriate temperature inside The production of ammonia depends on several factors such as the reactor length, temperature of feed gas, temperature of the reacted gas mixture at the exit of the reactor, and the mass International Conference on Chemical Engineering, Food and Biotechnology (ICCFB2017) AIP Conf Proc 1878, 020024-1–020024-8; doi: 10.1063/1.5000192 Published by AIP Publishing 978-0-7354-1558-4/$30.00 020024-1 flow rate of nitrogen The optimization problem consists of maximizing the economic return from the process There are many study discussing the modelling, simulation, and optimization of an auto-thermal ammonia synthesis reactor Some of them can be mentioned here as in Babu and Angira [3], Babu et al [4], Carvalho et al [5], Edgar et al [6], Ksasy et al [7], Murase et al [8], Upreti and Deb [9], Yusup et al [10] However, in the studies of Edgar et al [6], Murase et al [8], the model used has some uncorrected points and have been modified in Upreti and Deb [9] Furthermore, the studies mainly focus on the optimization of reactor length corresponding to a particular reactor top temperature, usually of 694 K ([4, 5], or in only several temperatures ([7]) However, the production of ammonia depends not only the reactor length but also the temperature of feed gas at the entrance of the reaction zone (top temperature) Therefore, the optimization problem should be considered as the multivariable problem rather than the single variable problem of reactor length Our previous study[11], not only the reactor length but also the reactor top temperature is included in the optimization variables for finding the maximum profit of the process The coupled differential equations which describes the synthesis reactor are solved using Runge-Kutta 4th order method Cyclic coordinate search method was applied for the multivariate optimization problem The golden section search was employed to solve the single variable maximum problem for each coordinate search The box-constraints of the parameters were guaranteed by adding the penalty to the objective function when any of the limits is violated However, classical search approaches tend to be vulnerable to getting stuck in local optima The population based approaches, such as evolutionary algorithm (EA), genetic algorithm (GA) can overcome the drawbacks such as the requirement of the derivatives of the objective function and/or constraints and are more likely to find a true global optimum In this study, the genetic algorithm is employed to find the optimum profit of the process.The inequality constraints were guaranteed by adding the penalty to the objective function when any of the limits is violated PROBLEM FORMULATION The problem formulation in this work is similar to the model in [8] and includes the modifications of the objective function mentioned in [3, 9] Feed gas contains 21.75 mole% nitrogen, 65.25 mole% hydrogen, 5.0 mole% ammonia, 4.0 mole% methane and 4.0 mole% argon In a typical ammoniareactor, feed gas enters from the bottom of the reactor The reaction is carried out at 500 oC and 200 atm of pressure.The heat released by the reaction is used to heat the incoming gas mixture in counter current flow Figure shows the schematic diagram of an ammonia synthesis reactor The production of ammonia depends on the temperature of feed gas at the entrance of the reaction zone (top temperature), the partial pressures of the reactants (nitrogen and hydrogen), and the reactor length The optimal design problem aims to obtain the optimal parameters yielding maximum economic return from the reactor operation 020024-2 FIGURE Schematic diagram of an ammonia reactor [12] Objective function The objective function for the reactor optimization is the profit of the process based on the difference between the value of the product gas (heating value and the ammonia value) and the value of feed gas (as a source of heat only) less the amortization of reactor capital costs Other operating cost are neglected F 1.3356 u107  1.708 u 104 N N  704.09 Tg  T0  699.27 T f  T0  3.4566 u 107  1.9837 u109 x (2) Equality Constraints The model of ammonia reactor is obtained considering the energy balance for feed gas and reacting gas, and the mass balance for nitrogen, respectively dT f US1 Tg  T f (3) dx WC pf dT f dx  'H S2 § dN2 · US1 Tg  T f   WC pg WC pg ăâ dx áạ ... thuật Hóa dầu Mã số: 60520330 I TÊN ĐỀ TÀI: MƠ PHỎNG VÀ TỐI ƯU HĨA THIẾT BỊ PHẢN ỨNG TỔNG HỢP AMONIẮC II NHIỆM VỤ VÀ NỘI DUNG: - Khảo sát trình tổng hợp NH3 dựa phản ứng kết hợp H2 với N2 thiết bị. .. metan hố - Khí tổng hợp nén tới áp suất khoảng 140 - 220 kg/cm2, sau chuyển hóa thành amoniắc chu trình tổng hợp nhờ thiết bị tổng hợp với thiết kế dịng chảy xun tâm Các thiết bị thiết bị hai tầng... thiết bị phản ứng tổng hợp amoniắc 2.6.1 Cấu tạo thiết bị Hình 2.4 Tháp tổng hợp NH3 hãng Haldor Topsoe S – 200 - Tháp tổng hợp amoniắc thiết bị quan trọng toàn hệ thống công nghệ tổng hợp NH3 Cấu