Natural gas is a clean and abundant fossil fuels. Cooling or liquefying natural gas makes it easier to transmit from sources to consumers. Liquefying gases is used to separate desirable elements or compounds. High thermal efficiency is the most important feature of the equipment that are used in gas treatment and petrochemical industries for cooling or liquefying natural gas. Coldboxes are self-supporting structures, acting as support for enclosed equipment, such as heat exchangers, drums, valves and instrumentation. It is one of the most widely used equipment in this field. The most important part of Coldbox from the standpoint of heat transfer is the set of compact heat exchangers, while the other components increase the cooling load loss. Compact heat exchangers used in colboxes are in the category of multi-stream heat exchangers. Plate-fin heat exchangers (PFHE) due to thermal efficiency and compactness (i.e., heat transfer surface area-to-volume ratio) are one of the best choices for liquefying gases. The design and simulation of the multi-stream heat exchangers are markedly different than those of two-fluid exchanger. Features like bypass heat transfer or crossover in temperature common in multi-stream heat exchangers, have no equivalent in two-stream units. Crossover in temperature, longitudinal conduction, bypass heat transfer, heat transfer in distributors, change in fluid properties, two phase flow and phase change makes the analysis of plate fin heat exchangers more complex than conventional heat exchangers.The aim of this thesis is to analyze the performance of the plate fin heat exchanger of phase 9 and 10 of South Pars Petrochemical Complex with given geometry and input. For this purpose, by using Aspen software and splitting heat exchanger into 6 sections, a layer by layer simulation has been made. The maximum deviation for outlet temperature between the simulation result and South Pars Data is 0.83°C for stream A in the best layer arrangement in each section. Outlet temperature of streams B, C and G match with the South Pars data. Another aim of this thesis is to investigate the effect of the layer arrangement upon heat transfer. Layer arrangement is key problem for design and rating multi-stream heat exchanger. The layer arrangement design was developed for all 6 sections due to the indeterminate layer arrangement in South Pars data. The zigzag curve, which is a criterion for suitability of the layer arrangement in plate fin heat exchanger, drawn for all 6 sections. With an increasing zigzag curve deviation, the difference between the outlet temperature of simulation result and South Pars data increased. Criteria for selecting suitable layer arrangement has suggested by using the zigzag curve results. The highest and lowest zigzag curve deviation for the most appropriate layer arrangement has been obtained 0.3 and 0.072. Excellent agreements with the published simulation have been observed in this part. Due to evaporation, condensation and single phase flow in the exchanger, the effect of the mass flow upon heat transfer coefficient, outlet temperature, outlet vapor mass fraction and pressure drop is investigated. Heat transfer coefficient and pressure drop increased by increasing the mass flow rate. Outlet temperature and outlet vapor mass fraction reduced by increasing the mass flow rate in streams which evaporation occured. The impact of longitudinal conduction and heat transfer in distributors is investigated, the results reflect the impact upon the outlet temperature and pressure drop is negligible. A program provided to calculate the stream outlet temperatures for part of the heat exchanger where supercritical phase change happens. Program results were found to be in agreement with the South Pars phase 9 and 10 data Keywords: Coldbox, Plate fin heat exchanger, Zigzag Curve