See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/334454536 Modeling and Simulation of a Water Gas Shift Reactor operating at a low pressure Article - July 2019 CITATIONS 3 3 authors: Wail El Bazi ENSA khouribga Maroc 14 PUBLICATIONS 33 CITATIONS SEE PROFILE M.S. KADIRI Ecole Nationale des Sciences Appliquées de Khouribga, Morocco 21 PUBLICATIONS 318 CITATIONS SEE PROFILE All content following this page was uploaded by Wail El Bazi on 12 January 2021. The user has requested enhancement of the downloaded file. READS 4,020 ResearchGate A. El Abidi Cadi Ayyad University - Ecole Nationale des Sciences Appliquées - Safi - Morocco 19 PUBLICATIONS 77 CITATIONS SEE PROFILE JOURNAL INTERNATIONAL LOF ENGINERING BESR International Journal of Innovation Engineering and Science Research AND SO INOVATION SCIENCE R SEARCH Modeling and Simulation of a Water Gas Shift Reactor operating at a low pressure Wail El Bazi¹*, Abderrahim El-Abidi²,³, Moulay Saddik Kadiri¹, Said Yadir²,3 ¹ Laboratory of Process Engineering and Industrial Systems Optimization (LIPOSI) ENSA Khouribga, Sultan Moulay Slimane University, Béni Mellal, Morocco *corresponding author: w.elbazi@usms.ma ² Laboratory of Materials, Processes, Environment and Quality (LMPEQ), ENSA Safi, Cadi Ayyad University, Marrakech, Morocco 3 Laboratory of Electronics, Instrumentation and Energy (LEIE), Faculty of Science, Chouaib Doukkali University, El Jadida, Morocco Open Access ABSTRACT In order to study the WGS on an industrial scale at a low pressure, the modeling and simulation of a WGS reactor operating at a pressure close to Patm and processing an industrial charge in the presence of a high temperature shift catalyst (Fe2O3/Cr2O3) were performed. The Profiles of the carbon monoxide conversion, temperature and pressure along the reactor were obtained. The effect of several operating parameters (inlet temperature, H₂O/CO ratio) on the conversion of carbon monoxide along the reactor has been determined. The estimated catalytic mass to convert 60.5% of the carbon monoxide contained in the inlet is 170.76 t. The pressure drops in the reactor are not negligible and the maximum temperature reached is without any harmful effect on the catalyst. The choice of an optimal inlet temperature and a high H₂O/CO ratio improves the conversion of carbon monoxide. Keywords- Packed bed reactor, catalyst, water gas shift reaction I. INTRODUCTION Hydrogen is an important source of energy and is involved in various industrial processes such as: ammonia synthesis, methanol synthesis, etc. [1]. The production of this molecule can be carried out through several ways: Production from methane [2], biological production [3], water electrolysis [4], chemical production of aluminum and sodium hydroxide [5], or WGS (water gas shift reaction) which is a chemical reaction converting a mixture of carbon monoxide (CO) and water vapor (H₂O) into a mixture of carbon dioxide (CO₂) and hydrogen (H₂): CO+H2O = CO2 + H2 AHR (298K) This slightly exothermic reaction discovered by the Italian physicist Felice Fontana in 1780 [1] can occur in the presence of catalysts based on several metals such as Cu, Fe, Ni, Pd, PT, Rh, Ru [6] or even metal oxide [7]. At high temperatures (350-450°C) catalysts based on iron oxides and chromium oxide III (Cr2O3) can be used [7]. At low temperatures (120-240°C) copper or copper oxide catalysts can be used with promoters of alumina oxide (Al2O3) [7] and zinc oxide (ZnO) [8]. WGS can occur at pressures ranging from 1 to 83.75 bars [ 7-10]. but often industrial reactors operate at high pressures [ 8,11-12]. Numerous models of the water gas shift reactors have been published to date. Elnashaie et al developed a steady-state one-dimensional heterogeneous model to study the behavior of industrial reactors operating at high temperatures [11]. Their work also focused on the effect of temperature on the conversion of carbon monoxide. Adams et al used a dynamic two-dimensional heterogeneous model to study the behavior of reactors operating at both high and low temperatures [13]. Adams was also Volume 2 Issue 6 November - December 2018 == 41.2 KJ/mol 47 | Wail El Bazi et al. "International Journal of Innovation Engineering and Science Research" interested in the effect of important parameters on Xco (H₂O/CO - temperature ratio). Falleiros Barbosa Lima et al investigated an industrial reactor operating at high temperatures, using different one- dimensional pseudo homogeneous models [14]. The effect of catalyst deactivation on reactor performance was also investigated. A steady-state one-dimensional pseudo-homogeneous model was also used by Shokry et al to predict the evolution of molar flow rate along and at the outlet of an industrial WGS reactor operating at low temperatures [12]. These authors also studied the effect of pressure, inlet temperature, H₂O/CO ratio on Xco. The major disadvantage of operating at high pressures is the enormous energy costs that it would be interesting to reduce them by carrying out the WGS at low pressures. In addition, the operating life of the catalyst can reach 15 years if the reactor operates at a low pressure [15]. Indeed, several papers have been carried out to study this reaction and to determine its kinetic expressions in the presence of catalysts allowing its activation at pressures close to the atmospheric pressure [8,16-23]. It would therefore be interesting to use these expressions in the simulation and study of the behaviour of reactors operating at pressures on the order of 1 atm. In fact, the work of Maklavany et al has been interested in this topic. These authors used the kinetic expression of WGS in the presence of a low temperature shift catalyst (CuO/ZnO/Al₂O3) to simulate a laboratory reactor operating at 1.2 bar. Two models were used: a steady state 2D homogeneous isothermal model [24] and a 1D homogeneous isothermal model with axial dispersion [25]. The effect of temperature on the variation of several parameters along the reactor (CO concentration, pressure, reaction rate, superficial velocity) was also studied. In our study, we also carried out the simulation of a reactor operating at a low pressure. But in our case, it is in the presence of a high temperature shift catalyst (Fe2O3 /Cr₂O3) and for a large reactor. This will allow the industrial-scale study of the reaction at a low pressure and clarified the strengths and weaknesses of the realization of WGS under this condition. The model we used to simulate the fixed catalytic bed is the steady state one-dimensional pseudo homogeneous model that is widely used in the study of the behaviour of industrial catalytic convertors, sites of the WGS [12,14,26] or other gas phase reactions [27,28,29]. In the first part of this study, we used the kinetic rate expression corresponding to this catalyst in the modeling and simulation of an industrial WGS reactor. This allowed the prediction of profiles of the carbon monoxide conversion, temperature and pressure along the reactor. Then, the work was continued by studying the effects of the operating parameters (inlet temperatures, H₂O/CO ratios) on the conversion of carbon monoxide in order to define the optimal conditions of the reaction realization. II. DESCRIPTION A. Description of the studied catalyst and the operating conditions for establishing the kinetic rate expression The kinetic rate expression corresponding to the chosen catalyst was carried out by Keiski et al [18]. The characteristics of the catalyst, as well as the operating conditions under which the kinetic rate expression was established, are presented in Table I [7,13,18]. TABLE I. Catalyst CCE C12 Ref: [7,13,18] CATALYST CHARACTERISTICS AND OPERATING CONDITIONS FOR THE ESTABLISHMENT OF THE WGS KINETICS [7,13,18] Equivalent spherical diameter, dp (μm) Composition Fe₂O3/Cr₂O3 (89/9%) Operating conditions for the establishment of WGS kinetics T: [575-675 K], P : 1 atm H₂O/CO (molar) : [2.4-12.1] Gas mixture of different fractions of: CO, CO2, H2O, Hz, Nz 2800 Volume 2 Issue 6 November December 2018 Shape Cylinder Catalyst density, Pc (kg/m³) B. Description of the reactor and the operating conditions considered in the simulation The characteristics of the simulated reactor are presented in Table II. 3730 48 | Wail El Bazi et al. "International Journal of Innovation Engineering and Science Research" Packed bed diameter D (m) 0.09 Packed bed length, L (m) 2.2 TABLE II. REACTOR CHARACTERISTICS Number of packed beds (tubes) 6000 The first simulations were run to predict the profiles of carbon monoxide conversion, temperature and pressure along the reactor operating at a low pressure and for a feed flow of an industrial nature. We ran these Simulations under the operating conditions presented in Table III. TABLE III. OPERATING CONDITIONS USED FOR THE PREDICTION OF X(Z), T(Z) AND P(Z) Molar flow rate of the feed gas mixture, F₁,0 Inlet pressure, Po Inlet temperature, To (mol. s-¹) (atm) (K) CO: 23.28 CO₂: 94.19 H₂ : 364.149 H₂O: 228.93 N₂: 134.354 Keq III. EQUATIONS Thermal property of the packed bed Adiabatic The compositions and the inlet pressure of the gas mixture of table 3 are close to those studied when establishing the kinetic rate expression of the WGS [18]. The temperatures remain within the temperature range of the kinetic study [18]. At the same time, in order to evaluate the WGS at low pressures in a situation close to an industrial case, each partial molar flow rate of WGS reagent (CO, CO2, H₂O, H₂) presented in Table 3 is equal to 30% of the actual partial molar flow rate of the same reagent feeding the high pressure WGS reactor of the Alexandria Fertilizers Company (AlexFert) [12]. The molar flow rate of nitrogen shown in this table is equal to 30% of the real molar flow rate of the inerts feeding the company's reactor. A. kinetic expression The kinetic expression used is a simple power-law model [7,18]: -rco (mol.kg cata¯¹. h¯¹) = 2623447 exp -79759 RT В = ex p To study the effect of temperature on the carbon monoxide conversion along the reactor, other simulations were performed for other inlet temperatures (575 K, 605 K, 620 K) while keeping the other operating conditions (Table 3) and the same reactor characteristics (Table 2). Finally, the study of the effect of the H₂O/CO ratio on the Xco profile along the reactor required further simulations for [H₂O]/[CO] = 3 which corresponds to Fo(H₂O) = 69.84 mol.s-¹ and Fo(CO) = 23.28 mol.s 1 and for [H₂O]/[CO] = 5 which corresponds to Fo(H₂O) = 116.4 mol.s-¹ and Fo(CO)= 23.28 mol.s-1. These last simulations were established by varying only the molar flow rate of the water vapor. While the other operating conditions (Table III) and reactor characteristics (Table II) have not been changed. 1.12 Volume 2 Issue 6 November December 2018 Сco2 CH2 1 Ссо Снчо Ке void fraction in the packed bed The equilibrium constant, Keq, is given by the equation 2 [7,18]: 4577.8 4.33) T Where -rco is the CO conversion rate, Ci is the molar concentration of species i (mol.dm-³) and ß is the reversibility factor: દ 0.4 590 0.74 C047C0218[1 − B] (2) (1) 49 | Wail El Bazi et al. "International Journal of Innovation Engineering and Science Research" B. Process modeling and numerical solution The following assumptions were made to develop the used mathematical model for the packed bed reactor simulation: Adiabatic reactor. ● ● Steady state condition. Axial dispersion is neglected, because the flow rate is sufficiently high to create a turbulent flow G.dp (Re: = > 40) and (L/dp>150) [30]. Where Re is the Reynolds number, G is the superficial mass velocity (kg.m-². s-¹) and µ is the dynamic viscosity of the mixture (Pa.s). μl Radial dispersion is neglected, because the tube diameter is narrow, the reactor is adiabatic and the WGS is a moderately exothermic. Under these conditions, radial gradients of concentrations and temperatures are not important [30,31,32]. The system of differential equations used is as follows [14]: dXco -coFPresPBS Fco,0 dz The heat and mass transfer as well as the diffusion in the catalyst were lumped in the rate constant. ● ● dT ΣFiCpi dz For the reagent: dp dz C₁ is expressed using the perfect gas equation: Pi RT For the product: For the inert: C₁ = -f² = Where Pi is the partial pressure (Pa), expressed as follows: P₁ = -fPgu ²³ dp - AHRTCO FPresPBS With yi is the molar fraction of the species i The expression of the molar flow rate, Fi (mol. s-1), of each component depends on its nature, be it a reagent, a product or an inert: F₁ = F₁,0 — Fco,o * Xco F₁ = F₁,0 + Fco,o * Xco F₁ = F₁,0 (3) Volume 2 Issue 6 November December 2018 (4) (5) (6) F₁. P = y₁.P i=n Σ=0 Fi (7) (8) (9) 50 |

1. Coal is valued by its heat value. Order the following coal types from poor heat value to rich heat value: bituminous, sub bituminous,anthracite and lignite. (2%)

35. Supercritical CO2 turbine driver is dependingthat is commonly qualify as: (1%)on the thermal process a) Rankine cycle b) Brayton cycle c) Carnot cycled) Lenoir cycle

Q.1 [14 marks] = Figure Q1 shows a vertical pressure vessel consisting of a cylindrical shell (radius r = 0.50 m, and length, L 20 m) and two hemispherical heads with the same radius as the shell. The vessel is pressurised to 125 bar. It is constructed of carbon steel with a density of p = 8000 kg m-³ and a yield strength of Oy = 800 MPa. support Part A head B shell CP303 Materials, Processing, Applications —A- head L Figure Q1: Vertical Pressure Vessel (a) Calculate the thickness, t, of the cylindrical shell and hemispherical heads required to withstand the internal pressure if the maximum allowable stress, Gallow, is one-half of gy. PLEASE TURN OVER [2 marks] Page 2 of 9 [Q1. continued] (b) Calculate the mass (in kg) of the cylindrical section and hemispherical heads. Express the combined head and shell mass as a weight (in N) and calculate the resulting stress, ow, produced in the vessel wall at the point where the lower head and shell meet (position A in the figure). [4 marks] (c) Using the thickness calculated in (a), calculate the hoop and longitudinal stress in the cylindrical shell arising from the internal pressure. Then calculate the combined (total) longitudinal stresses due to the internal pressure and the weight of the shell and upper head at the position A. Also, calculate the total combined stresses in the hoop direction at this position. [4 marks] (d) Similarly, consider position B at the junction between the upper head and shell. Determine the combined longitudinal and hoop stresses at this point. [4 marks] PLEASE TURN OVER CP303 Materials, Processing, Applications Page 3 of 9 Q.2 [11 marks] Consider a pressure vessel with identical dimensions and materials of construction to that in Figure Q1 above but operating at a higher pressure of 180 bar and with an increased shell thickness of t = 2.25 cm. (a) Calculate the hoop and longitudinal stress in the cylindrical section of the revised vessel. [2 marks] (b) Assume that there was uniform internal corrosion in the cylindrical section of the vessel at a rate of 0.8 mmpy. How many years would it take the vessel to become unsafe - i.e. the point at which the hoop stress exceeds the yield strength? (c) The vessel develops a semi-circular crack in the cylindrical shell (size, 2a = 0.2 cm, Y = 0.70) oriented in the hoop (circumferential) direction. Determine whether this crack is stable if the fracture toughness of the carbon steel is KIC = 15 MPa m [3 marks] 112. [2 marks] (d) Demonstrate that for the situation in (c) above, this vessel is not a 'leak before break' design. Hence, calculate the value of Kic that would be required to make this vessel leak before break. PLEASE TURN OVER CP303 Materials, Processing, Applications [4 marks] Page 4 of 9

*Water enters an evaporator with a quality 20% and flow through a vertical pipe with a diameter 20 mm and length 4.5 m. Heat is added uniformly along the pipe length with the gradient of 15 kW/m. The pressure at the pipe inlet was 7 MPa and the mass flux is 600 kg/m².s. Calculate the pressure at the pipe exit and the flow regime at the inlet and exit assuming that the slip ratio is equal to (liquid density/vapor density)^(1/3)

Q.1 [14 marks] = Figure Q1 shows a vertical pressure vessel consisting of a cylindrical shell (radius r = 0.50 m, and length, L 20 m) and two hemispherical heads with the same radius as the shell. The vessel is pressurised to 125 bar. It is constructed of carbon steel with a density of p = 8000 kg m-³ and a yield strength of Oy = 800 MPa. support Part A head B shell CP303 Materials, Processing, Applications —A- head L Figure Q1: Vertical Pressure Vessel (a) Calculate the thickness, t, of the cylindrical shell and hemispherical heads required to withstand the internal pressure if the maximum allowable stress, Gallow, is one-half of gy. PLEASE TURN OVER [2 marks] Page 2 of 9 [Q1. continued] (b) Calculate the mass (in kg) of the cylindrical section and hemispherical heads. Express the combined head and shell mass as a weight (in N) and calculate the resulting stress, ow, produced in the vessel wall at the point where the lower head and shell meet (position A in the figure). [4 marks] (c) Using the thickness calculated in (a), calculate the hoop and longitudinal stress in the cylindrical shell arising from the internal pressure. Then calculate the combined (total) longitudinal stresses due to the internal pressure and the weight of the shell and upper head at the position A. Also, calculate the total combined stresses in the hoop direction at this position. [4 marks] (d) Similarly, consider position B at the junction between the upper head and shell. Determine the combined longitudinal and hoop stresses at this point. [4 marks] PLEASE TURN OVER CP303 Materials, Processing, Applications Page 3 of 9 Q.2 [11 marks] Consider a pressure vessel with identical dimensions and materials of construction to that in Figure Q1 above but operating at a higher pressure of 180 bar and with an increased shell thickness of t = 2.25 cm. (a) Calculate the hoop and longitudinal stress in the cylindrical section of the revised vessel. [2 marks] (b) Assume that there was uniform internal corrosion in the cylindrical section of the vessel at a rate of 0.8 mmpy. How many years would it take the vessel to become unsafe - i.e. the point at which the hoop stress exceeds the yield strength? (c) The vessel develops a semi-circular crack in the cylindrical shell (size, 2a = 0.2 cm, Y = 0.70) oriented in the hoop (circumferential) direction. Determine whether this crack is stable if the fracture toughness of the carbon steel is KIC = 15 MPa m [3 marks] 112. [2 marks] (d) Demonstrate that for the situation in (c) above, this vessel is not a 'leak before break' design. Hence, calculate the value of Kic that would be required to make this vessel leak before break. PLEASE TURN OVER CP303 Materials, Processing, Applications [4 marks] Page 4 of 9

Problem 2. (5 points) A friend is planning her career and thinks she would like to have an income of $10,000 per month for 20 years beginning at age 65. Starting at age 25, how much would she have to invest per month over her 40-year career to achieve her goal? Assume that she will earn 7% per year on her investments (APY).

1.Student has provided general flow and data required for this work. 2.course is more related to Pharmaceutical so please do the necessary and not make it too much like a chemical engineering based to provide- 1.just researching all the required resources for the report 2.want all the resources, data and references to write and do calculations in the report 3.some data is given, others either need to be found or use experimental data from other sources/n Assignment 2-MECH3002 Thermal resistances - Conduction and Convection – Thermal Mug Manufacturing This assessment will be marked out of 10 using the Rubric attached. The assessment is worth 10 % of the total unit mark. This assessment is to be completed in groups of 1-3 individuals. 1. Learning Outcomes: ● Apply theory learned in the lectures in practice Problem solving using engineering skill and analytical thinking Understand the correlation between convection and conduction Determine the importance of convection and conduction for specific projects ● 2. Background: We have studied the mechanism of conduction and convection. We also learned that there is a resistance associated with the traveling of heat in solids (conductive resistance) and in fluids (convective resistance). With this knowledge, it is possible to predict the heat loss in different bodies with different geometries. Particularly, we have studied regular shaped bodies such as walls, cylinders and spheres. Following the design of a thermos in Assignment 1 completed in Week 4, you are to use this knowledge and, as engineers, actually manufacture a thermal cup/mug in Assignment 2, Thermal cup/mugs (also known as travel mugs) are used to keep a beverage warm for a given period by making use of insulating materials and high-performance design. Patents for thermal cups date as far back as 1958. A relatively recent thermal cup patent issued in 2004 defines its invention as: "A thermal cup includes a hollow inner cup body having an inner surrounding wall and an outer surrounding wall that confine an enclosed chamber therebetween, and an outer cup body made of a heat insulating material and disposed to surround the outer surrounding wall of the inner cup body. The inner surrounding wall further confines a space for containing liquid therein. The outer cup body cooperates with the outer surrounding wall of the inner cup body to confine a clearance therebetween. A thermal conductor unit is provided on the outer surrounding wall of the inner cup body, and is disposed in the clearance." (Luo, 2004). 112 111 12 13- FIG. 1 PRIOR ART Figure 1: Patent sketch of a thermal cup from (Luo, 2004) 3. Your specific tasks are to: 1) Add the effect of convection to your previously submitted Assignment 1. Display (or estimate) all the heat transfer coefficients (conductive k and convective h) involved. Calculate the expected heat transfer and the expected energy loss over a 3-h period. 2) Determine the significance of convection in your design and then determine whether your original project will have any alterations before manufacturing. 3) Manufacture the cup/mug you have designed. You are actually going to manufacture (create, build, construct) the product you have designed. You are not allowed to buy a product ready off the shelf and present it as yours. But you are welcome to use off the shelf components or pieces that you may need. The requirements are: a. Total volume (dimension) cannot exceed 1.5 L b. Should hold at least 300 mL of liquid C. Cannot weigh more than 700 g d. Should be "liquid proof", i.e., cannot leak or deteriorate when in contact with liquids. e. Should keep contents at a temperature higher or equal to 55 % of the original temperature for 3 hours. f. Aesthetics will not be marked 4) Record the making of your cup/mug. You are to make a short video (2 min to 5 min) of you making your product. Edits are welcome. You don't have to record every detail, but the overall making of the product. Not all group members need to appear in the video. 4. Deliverables There are three straight forward deliverables for this activity: the project, the product and the video. They are described in more detail hereafter: A short 2-page document addressing all the tasks set in Section 3. It should have an executive summary (also known as an abstract in this case) that condenses to one paragraph what your product is and what it does (max 300 words). It should also contain the convection calculations, your decision on whether to modify the original product or not and what the modifications are (if any). This report should also contain the REFERENCES for everything you used that was created/published by others or previously. You can also reference your Assignment 1. The thermal cup/mug itself. The actual product that will be tested against the requirements given and against a professional cup/mug in the Macquarie workshop later in the semester. A 2 to 5 min long video showcasing your working on your thermal cup/mug. Video link should be in your project written report. 5. Assessment This assignment contributes towards the assessment of MECH3002. You will work for this project and hand in a report. The report will be marked out of 100. ■ Report due at 11:55 PM 29th October 2023. Unless a Special Consideration request has been submitted and approved, a 5% penalty (of the total possible mark) will be applied each day a written assessment is not submitted, up until the 7th day (including weekends). After the 7th day, a grade of '0' will be awarded even if the assessment is submitted. Must reference sources of information and include a complete reference list. The report must be well written, concise and clear. Document must address all aspects outlined in Section 3 Your specific tasks. 6. Rubric Assessed Marks capability (Total 100) Project Product Video 10 10 10 25 25 20 Competencies to be demonstrated for High Distinction Updated calculations for heat loss and energy loss are presented. The estimation for the cup/mug performance still meets the requirement set for the product. Discussion of whether project should be modified or not in light of the convection now being accounted. Delivering a product Product meets geometry, weight and holding content requirements Your product meets the performance requirement Your video is within the time limit, shows at least one member of the group working on your product, shows the final product (result) and is uploaded into a free video hosting website by the assignments due date. 7. Resources You can be creative about your project. Here are some videos to give you some inspiration on how to start your assignment. https://www.youtube.com/watch?v=mPJoCRbnFIE https://www.youtube.com/watch?v=oL86W7GmPWk https://www.youtube.com/watch?v=BRsBwwwoC U https://youtu.be/PY5Kryq62SQ

2. The GE supercritical CO2 turbine generator relies on the following:(1%) a) Supercritical CO2 requires higher temperature. b) Supercritical CO2 requires lower temperature. c) Supercritical CO2 is temperature independent. d) None of the above.

Questions 1- Concentration of the feed 2- Temperature of the chiller 3- How do you determine concentration of Ethanol and Methanol in the ADV FIXTURE. 4- Draw the apparatus and give as much detail as you can. 5- How do you measure the concentration of the samples 6- Something about Fenske equation (make sure you know all the steps on how to calculate the number of stages) 7- VLE stand for 8- How to calculate average volatility? 9- What is the actual number of trays in the distillation in 1954 and ADV?

Problem 1. (6 points) You can deposit up to $6,500 in a Roth Individual Retirement Account (Roth IRA) before the age of 50 and $7,500 if you are 50 or older. In a Roth IRA, taxes are paid on the income in the year it is earned, but the withdrawals from the account after age 65 are not taxed. (a) Assume the maximum investment amount is constant, and that you made the maximum investment from ages 25 until 49, and then you didn't invest another dime after age 49. How much would your account be worth when you were 75 assuming a 7% annual interest rate compounded annually? (b) Now assume that you didn't start investing until you were 50, and you made the maximum investment until age 75. How much would your account be worth when you were 75 assuming a 7% annual interest rate compounded annually?