Maximization of propylene in an industrial FCC unit

Abstract

The FCC riser cracks gas oil into useful fuels such as gasoline, diesel and some lighter products such as ethylene and propylene, which are major building blocks for the polyethylene and polypropylene production. The production objective of the riser is usually the maximization of gasoline and diesel, but it can also be to maximize propylene. The optimization and parameter estimation of a six-lumped catalytic cracking reaction of gas oil in FCC is carried out to maximize the yield of propylene using an optimisation framework developed in gPROMS software 5.0 by optimizing mass flow rates and temperatures of catalyst and gas oil. The optimal values of 290.8 kg/s mass flow rate of catalyst and 53.4 kg/s mass flow rate of gas oil were obtained as propylene yield is maximized to give 8.95 wt%. When compared with the base case simulation value of 4.59 wt% propylene yield, the maximized propylene yield is increased by 95%.

Introduction

The fluid catalytic cracking (FCC) is one of the most important refining processes within an oil refinery [1]. It is a key technology that converts heavy distillates, such as bottoms of vacuum and atmospheric distillation units, into desirable products such as gasoline, diesel and middle distillates, using zeolite-cracking catalyst [2]. These cracking reactions take place in the riser column [3]. The FCC is a type of secondary unit operation and one of the most important processes in a petroleum refinery. The FCC unit is mostly used to increase gasoline and diesel yield to meet high demand of fuel which is due to increase in transportation. However, it is not just to increase gasoline and diesel but middle distillates such as the gas lump as well, which comprises light olefins such as ethylene and propylene; major sources of the raw materials for the polyethylene and polypropylene industries. These light olefins are the most important raw materials for many chemicals such as acrylonitrile, propylene oxide, and other chemicals that are consumed as substitutes for non-plastic materials [4].

In recent times, there has been an increase in the demand for propylene, a petrochemical industry feedstock [5] and it is chiefly sourced from light olefins in the naphtha steam pyrolysis process. Naphtha steam pyrolysis process is a high energy consumption process because it is carried out at about 800 °C and separation of olefins is done at a temperature as low as − 100 °C [5]. This makes the naphtha steam pyrolysis process a more capital intensive one. However, propylene and ethylene are sourced cheaply from the FCC unit due to the abundance and cheapness of the FCC feedstock compared with Naphtha [4, 5], and the recent growth in demand for propylene in the world has maintained focus on the refineries toward FCC technologies for the maximization of propylene production to achieve economic profit [6]. In addition, the FCC operates below 550 °C and does not require extreme ‘cold’ for the separation of propylene from liquefied petroleum gas (LPG) [5]. Therefore, the cost of producing propylene from the FCC is much lower than that from steam pyrolysis [7]. The FCC unit is thus ideally suited for the manufacture of ethylene and propylene from the light products. Currently, there is an increasing interest in maximizing propylene yield of FCC units [7, 8]. The FCC unit has the ability to produce high yields when suitable operating conditions are selected. However, due to changes in quality, nature of the crude oil feedstock, changes in the environment and the desire to achieve maximum profitability, it results in many different operating conditions in the FCC riser unit [5, 9].

According to Almeida and Secchi [10] and John et al. [9], the riser can produce large profits when it runs at maximum capacity with maximum feed rate and power applied to the equipment. Optimization of the design and operation is crucial to facilitate the constantly changing quality and nature of blends of feedstocks while meeting the maximum capacity requirements. Some factors such as the large amount of feed processed, valuable gasoline yield, gas lump yield, the various processes occurring in the riser and its economic operation affects the overall economic performance of the refinery; thus it is vital to improve the performance of the riser through process optimization strategies [9, 11].

The production of propylene is mostly achieved using catalytic reactions with special selectivity for propylene [7, 8, 12, 13]. A number of lumps for catalytic cracking were reported in the literature but most of them lumped the gaseous products in a single lump, thereby making it difficult to optimize or maximize a particular gas, for instance propylene. Usman et al. [14] conducted experiment using three different crudes (Super Light, Extra Light and Arab Light) catalytically cracked to produce light olefins, where they presented propane and propylene as different lumps. They used different catalysts: base-equilibrated catalyst and others; (Z30 and Z1500) which are the base-equilibrated catalyst + MFI Zeolite at varying Si/Al ratio. The results shows that the total weight fraction of the two lumps; propylene and propane has propylene about 80–89% for all the crude oils and catalysts used [14]. This percentage is high, therefore, a combined lump of propylene and propane can be treated as a single lump of propylene and the kinetic model of Ancheyta and Rogelio [15] is suitable for this work. Hence, in this study, the FCC riser is simulated based on a six-lumped kinetic model [15] consisting of vacuum gas oil, gasoline, C₃’s (propane and propene), C₄’s (butane and butene), dry gas (H₂, C₁–C₂) and coke. Vacuum gas oil is the feed whilst gasoline, butylene, propylene and dry gas are products with coke deposited on the catalyst. The yield of the propylene is further enhanced by optimizing the operating conditions of the riser.

The FCC riser is a complex unit that involves strong multi-variable interactions, complex hydrodynamics and operating restrictions, which poses as a major difficulty in the simulation of the process. However, minimal changes due to simulation and optimization can result in higher yield, thus increasing economic benefits. In the FCC unit, the yield of propylene is influenced by the reaction temperature, catalyst-to-oil ratio (C/O), residence time, nature of feed and the catalyst system [16,17,18], and when any of the foregoing variables is optimized, the yield of propylene can considerably increase.

Hence, gPROMS software 5.0 will be utilized for the simulation and optimization of the riser to obtain results showing the effects of changing variables such as temperature and mass flow rates [9] on the yield of propylene. To carry out this optimization, a single objective function was developed and implemented in gPROMS software that uses a successive reduced quadratic programming (SRQPD) optimization technique. This technique is a Sequential Quadratic Programming-based solver imbedded in the gPROMS software. Hence, the aim of this work is to maximize the yield of propylene by varying different sets of riser operational conditions.

Riser model

The FCC unit (Fig. 1) houses the cylindrical vessel called riser, which is the main reactor, where the cracking reaction takes place in the presence of a catalyst. The catalyst, a mixture of crystalline alumina silicates (zeolites) is a sand-like material which is fluidized into a fluid via contact with liquid fed into the FCC unit [2, 9]. A typical configuration of a FCC process consists of two major units; the riser and regenerator.

Fig. 1

A schematic diagram of the FCC unit

This study is focused on the riser unit of the FCC since it is where the products are made. It is modelled as plug flow and the vaporization of gas oil was considered to be instantaneous in the vaporization section. The hot regenerated catalyst from the regenerator meets the feed at the vaporization section and vaporizes the feed with the aid of dispersion steam to move upward into the riser where the gas oil gets cracked on the catalyst and produces desirable products [2]. The riser in this work is of industrial size; 30 m high and 1.0 m diameter, whose simulation and further optimization is carried out using the mathematical models obtained from the literature [2, 19, 20] as presented in Table 1. The choice of the mathematical model is based on the fact that it captures the actual hydrodynamic model of an industrial FCC unit and has been used extensively in the literature. The riser is simulated using a six-lump kinetic model as shown in Fig. 2, and the kinetic data for the various constants in Fig. 2 are estimated using parameter estimation technique. The simulation involves many other parameters such as the feed conditions, catalyst properties and riser dimensions which were obtained from the literature and presented in Appendix Tables 8 and 9. The steady state model is derived from mass, energy and momentum balance equations for the catalyst and gaseous phases of the riser, while assuming that there is no loss of heat from the riser to the surrounding [21]. In addition, it is assumed that the cracking reactions only take place on catalyst surface.

Table 1 Equations and descriptions

Fig. 2

Six-lump model [2, 15]

Equations (1)–(6) represent the overall rates of reaction for gas oil; R_go, gasoline; R_gl, gas; R_C4, butylene; R_C3, propene; R_dg, dry gas, and R_ck, coke; for the six-lump kinetic reactions. Each overall rate of reaction is a function of overall rate constants, defined by the Arrhenius equation given in Eqs. (7)–(18). The rate of heat removal by reaction Q_react is given by Eq. (19), while Eqs. (20)–(25) and Eqs. (26)–(27) result from the material and energy balance of the catalyst and gas phases, respectively. The equations describing the hydrodynamics of the riser are Eqs. (28)–(53) [2, 19]. Equations (28) and (29) describe the catalyst and gas velocity profiles across the riser [2]. Equations (30) and (31) describe the gas volume fraction, ɛ_g, and catalyst volume fraction, ɛ_c; they provide a hydrodynamic constrain such that the summation of the volume fractions is unity. The riser pressure is described by Eq. (37), which is obtained from the simple ideal gas relationship with Z as compressibility factor [22] described in Eq. (47).

gPROMS is a robust software used for solving the set of differential algebraic equations describing the riser. It is an equation-oriented software and all solvers have been designed specifically for large-scale systems such as the FCC unit with no restrictions regarding the size of the differential–algebraic equations other than those imposed by available machine memory [23]. gPROMS is a process modelling software for simulation, optimisation and control (both steady state and dynamic) of highly complex processes such as the FCC unit riser. Due to its robustness, more research work on the FCC unit is being carried out using gPROMS in recent time [9, 20, 24, 25]. These are the first attempts on the FCC unit and gPROMS displayed great capability and reliability. The riser model construction is described in the model section and the parameters are specified in the process section of the gPROMS software 5.0.0.

Riser kinetics and parameter estimation

The kinetic studies on the production of propylene have been carried out and they are mostly based on catalytic pyrolysis. However, catalytic pyrolysis includes catalytic reactions and thermal reactions [26], and the cracking extent of catalytic pyrolysis is more comprehensive than that of catalytic cracking [27]. In addition, catalytic cracking is favoured over thermal cracking for maximum propylene production especially in high severity FCC unit [18]. Moreover, just like the catalytic cracking reactions require the understanding of the kinetics of the reaction involved for reactor design, the design of the catalytic pyrolysis reactor would require the understanding of both the thermal and catalytic reactions involved to design a catalytic pyrolysis reactor. This is true because kinetic study is an essential mean for thorough understanding of reactions and catalysis for any catalysed chemical reaction which helps in the correct design of chemical reactors and determines the progress of the chemical reaction  [28]. In this study, mathematical and kinetic models used are based on the kinetic-lumping approach which catalytic cracking as a form of reaction was employed [2, 9, 19].

One of the kinetic-lumped models for the production of propylene based on catalytic pyrolysis of heavy oils is the eight-lumped model [26] which include ethylene as a lump and a separate propylene lumped with butylene. Where propylene is required as a separate lump, this eight-lumped model may not be useful. Some kinetic models for the propylene production are based on catalytic cracking, such as the four-lumped model which includes propylene as a component of a gas lump [29]; the ten-lumped model with propylene as a distinct lump [30] and six-lumped model with distinct propylene lump [15]. To maximize the yield of propylene in a lumped kinetic model, propylene has to be a separate lump. The gas lump in Hussain et al. [29] is a mixture of propylene, butylene and some dry gas; hence, it is unsuitable for use to maximize propylene because maximizing gas lump would mean maximizing other gases along.

The ten-lumped model of Du et al. [30] and six-lumped model of Ancheyta and Rogelio [15] are most suitable for their ability to have propylene as unique lumps. However, the yields of lumps were obtained at a particular constant temperature; 580 °C [30] and 500 °C [15], instead of progressive temperature profile of the catalyst and vapour phases as it is obtainable in the industrial FCC riser. Specific rate constants for the various cracking reactions and catalyst deactivation in a typical industrial riser also vary along the length of the riser. In this work, the catalyst deactivation is represented by Eq. (33) which as a function of varying temperature of the gas phase of the riser. Since temperature varies in the riser and has effect on some important kinetic variables such as rate constants and catalyst deactivation, it therefore means that heat required at every point in the riser varies. This heat requirement is estimated by heat of reaction of all cracking reactions as shown in Eq. (19).

The riser mathematical model used in this work requires kinetic data that involves activation energy, frequency factor and heat of reaction, and all vary along the riser. Hence, in this work, heats of reactions, frequency factors and activation energies for varying rate constants are estimated using parameter estimation. Where the kinetic parameters to be estimated are numerous and especially with limited laboratory data available, it poses a lot of challenges [31, 32]. For the parameter estimation and simulation of the riser, the six-lumped model [15] is chosen over the ten-lumped model because it predicts propylene as a single lump and has less parameters to be estimated which reduces the complexity of the model.

Parameter estimation

Parameter estimation is carried out for a certain model by optimizing nearly all or some parameters by means of experimental data. The optimized estimated parameters are those best matches between the experimental data and predicted data by the model [33]. There are several techniques used for parameter estimation in chemical and biochemical engineering for systems of dynamic and steady state models [31,32,36]. A technique for parameter estimation is carried out through online optimization where the estimates are taken from minimization of the sum of squared errors of the optimization problem by matching the experimental and calculated results within some given range of constraints [37, 38]. This method has acceptance in the parameter estimation of chemical processes [39] and it is the method used in this work. It uses the Successive Quadratic Programming (SQP) [40] on the optimization framework of gPROMS software [41] and it is proved to be very capable [39].

gPROMS parameter estimation requires the use of experimental data for validation and for the design of experiments on the gPROMS platform. In this work, the experimental results were obtained from the literature [15] for each of the six-lumped models are used as experimental data to generate the predicted results. Ancheyta and Rogelio [15] presented 15 sets of fractional yields for the six lumps obtained at fifteen different weight hourly space velocities (WHSV) from 6 to 48 h⁻¹ and at 773 K. These sets of fractional yields for the six lumps were read with a software called Webplotdigitizer 3.8 and are presented in Table 2. On the gPROMS parameter estimation framework, the fifteen sets of results are used with each set for a single experiment that represents experimental values $y_{i}^{ \exp } .$ Along with the complete riser mathematical model (hydrodynamic, kinetic, mass and energy conservation equations), the calculated values $y_{i}^{cal}$ are obtained and the sum of squared errors (SSE) are minimized.

Table 2 Six-lumps yield used as experimental data

Table 2 presents the experimental data obtained from the literature [15].

There are two approaches here: first, simulation for converging all the equality constraints and satisfying the inequality constraints; second, carrying out the optimization where the objective function is

$${\text{Obj}}({\text{SSE}}) = \mathop \sum \limits_{M = 1}^{{M_{t} }} (y_{i}^{\exp } - y_{i}^{\text{cal}} )^{2} ,$$

(58)

where y is the mass fraction of lumps and i is the various lumps in the riser.

The parameter estimation problem statement can be written as

Given	The fixed riser reactor configuration, feed quality and characteristics, catalyst properties and process operational conditions
Optimize	The kinetic parameters; activation energies E, heat of reactions ΔH and frequency factors ko at given process conditions
So as to minimize	The sum of squared errors (SSE)
Subject to	Equality and inequality constraints

Mathematically,

$$\mathop {{\rm min} }\limits_{{\xi_{i0} , \eta_{i} ,\theta_{i} }} {\text{SSE,}}$$

s. t.

$$f(x,z^{\prime}(x),z(x),u(x),v) = 0\quad ({\text{model equations}},{\text{equality constraints}}),$$

(59)

$$\xi^{l} \le \xi \le \xi^{u} \quad ({\text{inequality constraints}}),$$

(60)

$$\eta^{l} \le \eta \le \eta^{u} \quad ({\text{inequality constraints}}),$$

(61)

$$\theta^{l} \le \theta \le \theta^{u} \quad ({\text{inequality constraints}}),$$

(62)

where $f(x,z^{\prime}(x),z(x),u(x),v) = 0$ is the model equation, x is the height of the riser and the independent variable, u(x) is the decision variable; ξ is the upper and lower limits of the frequency factors k _oi ; η is the upper and lower limits of the activation energies E _i ; θ is the upper and lower limits of the heat of reactions ΔH _i . z(x) is the differential and algebraic equations while z′(x) is their derivative and v is the constant parameters.

Upper and lower limits are set for the decision variables which of course they are the parameters requiring to be estimated. They are set based on the assumption that the kinetic values will be within the range found in the literature for four-, five- and six-lumped models. Moreover, six-lumped model was derived based on the sequential strategy [42]. They assumed that the major reactant and products of the cracking reactions have similar rate constants, hence derived the four-lumped model from the three-lumped model and hence the six-lumped model from the five-lumped model in a sequential strategy. Therefore, it is expected in this work that the upper and lower limits for the activation energy, heat of reaction and frequency factors should be within the existing range. The values from the literature are: activation energy (31,923–57,278.96 kJ/kg mol) [43, 44] and (31,820–66,570 kJ/kg mol) [19], heat of reaction (195–745 kJ/kg) and frequency factor (0.000629–1457.5 s⁻¹) [19]. The upper and lower limits are opened further wide on the gPROMS parameter estimation framework to allow the software make the best estimates. Hence, the upper and lower limits for the following variables are activation energy (0 and 100,000 kJ/kg mol), heat of reaction (0 and1000 kJ/kg), and frequency factors (0 and 2000 s⁻¹). Another reason for opening the limits of the decision variables is to allow for the adjustment of data obtained from the laboratory model to get modified since they are being used on a mathematical model that represents an industrial unit [30].

FCC riser optimization

During optimisation, one tries to minimize or maximize a global characteristic of a process such as cost and time by exploiting the degrees of freedom under a set of constraints [33]. Therefore, it can be said that effective optimisation is needed to achieve the best process possible, in terms of obtaining more of a desired product. Optimisation can be described by a procedure, or set of procedures to find the best optimal solution for a particular problem. Common examples include maximizing the yield from a chemical reaction [9, 33] or minimizing the amount of energy consumed in a particular process [33].

An optimisation study of a FCC unit was carried out using genetic algorithm by [45]. It was a multi-variable-multi-objective optimization technique in which a three-objective function optimisation was carried out. It included the maximization of the gasoline yield, minimisation of the air flow rate and minimisation of CO in the flue gas. This technique works by the principle of a population being generated within the upper and lower limits of the decision variables. Thereafter, an individual is selected from the population depending on their “fitness”. This individual is then copied to formulate a new generation until a global maximum or minimum is found. Results obtained showed good stability but computational times were found to be very long. A dynamic real-time optimisation study of a FCC unit was carried out [10]. They developed a NLP problem and was solved using a simultaneous strategy where a continuous problem was converted into an NLP. The solution included the use of DAE system being converted into a system of algebraic equations. Results obtained matched plant data very closely. A real-time optimisation strategy for an FCC unit controller was presented [10], where a linear model predictive controller was optimized so that it would be able to handle disturbances in the commissioning or load disturbance phases. The objective function in their work was to maximize the production of LPG. Results had shown that the dynamic response of the controller was smooth and fast in the real controller and there were major issues with the controller response. John et al. [9] undertook a study to maximize the gasoline output in a FCC unit using SQP on gPROMS. The objective function was the maximization of the yield of gasoline and the variables being optimized were mass flow rates of catalyst and gas oil and temperatures of catalyst and gas phases. Their results showed a feasible solution, whereby yield of gasoline had increased by 4.51%. Another SQP algorithm was used to maximize propylene yield in a secondary reaction and 16.68 vol% was achieved [46].

With respect to the FCC process, it is obvious that the optimisation of the process can yield significant gains in different areas such as maximizing the yield of the product. Furthermore, optimisation of FCC riser can be undertaken to minimize the operating cost as well as the capital cost if observed from a design standpoint. It can also be used to minimize certain outputs such as carbon dioxide emissions to meet legislations [25]. Due to the complex nature of the FCC process, very few simulation optimisation studies have been carried out and optimisation of FCC units have been primarily through experimental means. However, the optimisation of the process through mathematical models is now gaining grounds in research. As computers become more powerful, it is now becoming possible to undertake rigorous models of the FCC unit through first principle modelling and empirical correlations. The benefit of using these numerical optimisation models is that the costs involved are very small compared to utilising lab scale experiments as well as the speed of computation once a model is built.

There are three main issues called the constraint triangle for maximizing propylene production; the effects of existing FCC technology, operation variables and catalysts on product quality and quantity [47]. Since the alteration of the FCC unit configuration and catalyst development is not the focus of this work, even though they are very important in FCC unit optimization, only the operation variables are manipulated to maximize the yield of propylene lump (C₃’s). Higher propylene production comes at the expense of gasoline. For traditional refiners, maximizing gasoline yield is more important than the propylene yield, while for those interested in petrochemical applications, the target is operating at maximum propylene yield [7].

Optimization problem statement

Optimisation of the yield of propylene.

The optimization problem can be described as

Given	The fixed volume of the riser
Optimize	The mass flow rate of catalyst, mass flow rate of gas oil and temperatures of gas and catalyst phases
So as to maximize	The yield of propylene lump (C3’s) $y_{{{\text{C}}3}}$
Subject to	Constraints on the mass flow rates of catalyst and gas oil, temperatures of gas and catalyst phases, and exit concentration of gasoline

The optimisation problem can be written mathematically as

$${\text{Objective function:}}\quad \mathop {\text{Max}}\limits_{{T_{j} ,{\rm FF}_{j} ,y_{\text{gl}} }} y_{{{\text{C}}3}} .$$

(63)

Subject to

$${\text{Process model:}}\quad f(x,\dot{z}(x), z(x), u(x),v) = 0,$$

(64)

$${\text{Boundary:}}\quad x = x^{ {\rm max} } ,$$

(65)

$${\text{Inequality constraints:}}\quad {\text{FF}}_{\text{g}}^{{\rm min} } \le {\text{FF}}_{\text{g}} \le {\text{FF}}_{\text{g}}^{ {\rm max} }$$

(66)

$${\text{FF}}_{\text{c}}^{ {\rm min} } \le {\text{FF}}_{\text{c}} \le {\text{FF}}_{\text{c}}^{ {\rm max} }$$

(67)

$$T_{\text{g}}^{ {\rm min} } \le T_{\text{g}} \le T_{\text{g}}^{ {\rm max} }$$

(68)

$$T_{\text{c}}^{ {\rm min} } \le T_{\text{c}} \le T_{\text{c}}^{ {\rm max} } ,$$

(69)

$${\text{Equality constraints:}}\quad y_{\text{gl}}^{ {\rm min} } \le y_{\text{gl}} .$$

(70)

The entire DAE model equations can be written in a compact form as

$f(x,\dot{z}(x),z(x),u(x),v) = 0$, where x is the independent variable which in this case is the height of riser, $z(x)$ is the set of all state variables, $\dot{z}(x)$ is the derivatives of z(x) with respect to the height of the riser, u(x) is the vector of control variables (mass flow rates of feed and catalyst) and v is a vector of invariant parameters, such as design variables (riser diameter and height). In addition, y_C3 is the objective function which is the yield of propylene, the desired product to be maximized in the riser. T_c is the catalyst phase temperature, $T_{\text{g}}$ is the gas phase temperature, ${\text{FF}}_{\text{g}}$ is the mass flow rate of gas oil, ${\text{FF}}_{\text{c}}$ is the mass flow rate of catalyst, $x$ is the height of the riser, x^max is the maximum riser height (30 m) and y_gl is the yield of gasoline. y ^min_gl is the minimum value of gasoline to be maintained while propylene is maximized. $T_{\text{c}}^{{\rm min} } {\text{ and }}T_{\text{c}}^{ {\rm max} }$ are the minimum and maximum bounds of the catalyst phase temperature $(700 \le T_{\text{c}} \le 1000\,{\text{K)}}$ and $T_{\text{g}}^{ {\rm min} } {\text{ and }}T_{\text{g}}^{ {\rm max} }$ are the minimum and maximum bounds of the gas phase temperature $(520 \le T_{\text{g}} \le 800\,{\text{K}}).$ ${\text{FF}}_{\text{c}}^{ {\rm min} } {\text{ and FF}}_{\text{c}}^{ {\rm max} }$ are the minimum and maximum bounds of the mass flow rate of catalyst ($20 \le {\text{FF}}_{\text{c}} \le 500\,\frac{{\rm kg}}{{\rm s}}$) and ${\text{FF}}_{\text{g}}^{ {\rm min} } {\text{ and FF}}_{\text{g}}^{ {\rm max} }$ are the minimum and maximum bounds of the mass flow rate of gas oil ($10 \le {\text{FF}}_{\text{g}} \le 100\frac{{\rm kg}}{{\rm s}}$). x^max is the fixed height of the riser; 30 m, and y_gl is the minimum allowable limit for gasoline 0.40 < Y_gl.

The boundaries for the mass flow rates of gas oil and catalyst are chosen such that it reflects the typical industrial FCC unit limits for C/O ratios of 4:1–10:1 by weight [48], Sadeghbeigi [49], [9]. C/O ratios for propylene production in high severity units and riser-downer are higher [18] than the C/O ratios used in conventional FCC units, which vary between 1 and 6 [16, 29, 50] and 3–25. Hence, the boundaries for the mass flow rates are open wide enough to accommodate low and high C/O ratios (1–25) on the optimization framework.

Case studies

Case 1: Optimizing catalyst mass flow rate FF_c between 20 and 500 kg/s; gas oil temperature, T_g (520–800 K); catalyst temperature, $T_{\text{c}}$(700–1000 K), while gas oil mass flow rate, FF_g, is kept constant at 58.02 kg/s.

Case 2: Optimizing gas oil mass flow rate FF_g between 20 and 500 kg/s; gas oil temperature, T_g (520–800 K); catalyst temperature, $T_{\text{c}}$(700–1000 K), while the catalyst mass flow rate, FF_c, is kept constant at 134.94 kg/s.

Case 3: Optimizing catalyst mass flow rate FF_c between 20 and 500 kg/s; gas oil temperature, T_g (520–800 K); catalyst temperature, $T_{\text{c}}$(700–1000 K); and gas oil mass flow rate FF_g between 20 and 500 kg/s.

Since FCC’s major goal is the production of gasoline, a minimum of 40 wt% of gasoline is imposed as a constraint on all the optimization cases, else most of the gasoline will deplete due to secondary cracking. The choice of 40 wt% is based on the average gasoline yield presented in the literature; 44.13–45.65 wt% [51], 44 wt% [21, 52] and 40 wt% [53].

Results and discussion

Model validation and parameter estimation results

The reason for presenting the simulation results is to determine the capability of gPROMS in handling complex nonlinear DAEs of the riser using the kinetic model of Ancheyta and Rogelio [15], and to compare the simulated results obtained with those predicted results of the same kinetic model obtained experimentally by Ancheyta and Rogelio [15]. Even though the experimental results were obtained at 773 K, the simulated riser temperature was progressive along the length of the riser.

The mass flow rates for gas oil and catalyst used in this simulation are 51.8 kg/s and 190.9 kg/s, respectively, while the C/O ratio is 3.685. These mass flow rates predicted the yields of the six lumps in the range presented by Ancheyta and Rogelio [15] while the parameter estimation was carried out. The estimated kinetic parameters are presented in Table 3.

Table 3 New kinetic parameters estimated

When gas oil meets the catalyst, it begins to crack to form gasoline, butylene, propylene, dry gas and coke. In this study, the cracking reaction takes place at gas oil inlet temperature of 523.0 K at the vaporization section rising to 719.9 K at the first 6 m height of the riser and levelling out for the remaining height of the riser with 706.2 K as the exit temperature. The inlet temperature of catalyst from the cyclone is 1010 K which mixes with regenerated catalyst in the vaporization section to have the catalyst temperature come to 971.4 K at the entrance of the riser. Cracking reactions begin immediately at the riser entrance and the profiles of these cracking reactions are presented in Fig. 3, while the temperature profiles are presented in Fig. 4.

Fig. 3

Lumps of gas oil cracking

Fig. 4

Temperature profile across the riser

The feed in this study is a 97.00 wt% gas oil and the remaining 3.00 wt% is steam. Figure 3 shows that the fraction of gas oil at the exit of the riser is 26.12 wt% which is 26.93% of gas oil unconverted. It also shows that about 73.07% of gas oil was consumed and about 70% of the fraction is consumed in the first 20 m of the riser. In the literature result [15], the fraction of gas oil at the exit of the riser was presented as a range because it was obtained at varied WHSV, and it is between 23.50 and 32.50 wt% which corresponds to 67.5–76.5% of gas oil consumed. The value of 26.93 wt% of unconverted gas oil obtained in this simulation at C/O ratio of 3.685 falls within the range of results from Ancheyta and Rogelio [15].

Likewise, gasoline started yielding as soon as cracking starts at the entrance of the riser. It rises from 0 to 51.36 wt% at the exit of the riser. This accounts for 52.95% of the total product of the riser with about 80% of the gasoline formed in the first 20 m of the riser. The value of 51.36 wt% of gasoline yield in this simulation is within the range of 50.85–55.19 wt% presented by Ancheyta and Rogelio [15].

The butylene lump (C₄’s) rises from 0 to 9.39 wt% at the exit of the riser. This accounts for 9.68% of the total product of the riser and it is within the range of 7.50–9.49 wt% presented by Ancheyta and Rogelio [15].

Similarly, the propylene lump (C₃’s), which is of more interest in this work, also builds up as cracking commences at the riser entrance from 0 to 4.59 wt% at the exit of the riser, accounting for 4.73 wt% of total riser products. The propylene yield of 4.80 wt% is also within the range of 4.23–5.38 wt% presented by Ancheyta and Rogelio [15] and others in the literature [54].

The dry gas lump also rises from 0 to 1.55 wt% at the exit of the riser. This is 1.60 wt% of the total product of the riser and it is within the range of 0.99–1.81 wt% presented by Ancheyta and Rogelio [15]. The remainder being coke deposited on the catalyst which also rises from 0 to 0.0399 wt% and it represents 4.11 wt% of the total product of the riser. It is also found within the range of 3.82–4.55 wt% presented by Ancheyta and Rogelio [15].

In general, the yields of the six lumps are within the range presented by Ancheyta and Rogelio [15]. This shows that the estimated kinetic parameters are true representation of the cracking reactions. The values also show that the experimental data of Ancheyta and Rogelio [15] can actually be used for the parameter estimation and the estimated kinetic parameters are useful for simulation of industrial riser. The profiles of the reactant and products are qualitatively consistent with those found in the literature [9, 19].

As cracking takes place, the endothermic reaction gives up heat from the catalyst to the gaseous phase. The endothermic heat which is determined in this simulation with the aid of the heat of reaction estimated is represented by the profile of the gas phase temperature and shown along with the profile of the catalyst phase temperature in Fig. 4. The temperature of the catalyst phase is about 971.4 K at the entrance of the riser but decreases for the first 5 m and then essentially levels out. The temperature profile of the gas phase at the entrance of the riser is about 523.0 K but rises to a maximum in the first 5 m of the riser and levels out to the exit of the riser. Both profiles start with a difference of about 448.5 K at the entrance of the riser and came so close to the same value with temperature difference of about 4.4 °C at the exit of the riser.

This temperature difference is required to accomplish the endothermic reaction. The temperature of the cracking reactions in Ancheyta and Rogelio [15] experimental work is 773 K. This temperature was reached at the riser entrance where both catalyst and oil mixed vigorously. However, the temperature of cracking in a typical riser varies at the entrance to the exit because the reaction is progressive at varied temperatures along the riser as seen in Fig. 4. The temperature profiles obtained in this work are similar to those obtained in many literatures [19, 21, 55].

Table 4 shows the comparison of the results obtained in this simulation at C/O ratio 3.685, already presented in Figs. 3 and 4, with the results presented by Ancheyta and Rogelio [15] experimental work. All the results are within the corresponding range for each lump which validates the results obtained. With an increment of 50 kg/s of catalyst mass flow rate, the C/O ratio was varied and the results are also presented for C/O ratios of 4.651, 5.616 and 6.581 in Table 4.

Table 4 Comparing simulated riser output with that of Ancheyta and Rogelio [15]

The unconverted gas oil yields at the varied C/O ratios are outside and lower than the range of the results by Ancheyta and Rogelio [15]. This is expected because increasing the C/O ratio increases gas oil conversion as a result of increase in cracking temperature. The absolute difference between the simulated results (C/O = 3.685) and the varied C/O ratios (C/O = 4.651, 5.616 and 6.581) shows decrease for both gas oil and gasoline. All other lumps increase due to increase in the C/O ratio and eventual rise in cracking temperature which increases the conversion of the cracking reaction. Gasoline undergoes secondary cracking to add to the butylene, propylene and dry gas lumps with additional coke deposit on the catalyst. This trend shows that increasing the C/O ratio may favour the yield of the light products such as butylene, propylene and dry gas. However, the absolute difference for propylene (5.46 wt%) at C/O ratio of 6.581 is more than that of butylene (4.31 wt%), which suggest that it would be necessary to operate the riser at C/O ratio of 6.581 to have more propylene in the light components. To get the best operating condition for propylene yield, optimization of the unit is necessary.

Optimization results

Table 5 presents the riser exit values of this simulation along with those riser exit concentrations from the optimization cases.

Table 5 Propylene optimization results for cases 1, 2 and 3 and simulation results

The results for both optimization cases 1, 2 and 3, and base case simulation (this simulation, Figs. 3, 4) are presented in Table 5, showing the riser exit values of the six lumps; gas oil as feed, while gasoline, butylene, propylene, dry gas and coke as products, and temperatures of the catalyst and gas phases. It compares the base case simulation results with the optimized cases 1, 2 and 3.

In the optimisation case 1, as propylene is maximized, the decision variable (catalyst mass flow rate) was set to be optimized between 20 and 500 kg/s, while gas oil temperature, T_g, was between 520–800 K and catalyst temperature, $T_{\text{c}} ,$ between 700 and 1000 K. The gas oil mass flow rate was fixed at 51.8 kg/s. The maximized value of propylene is 8.93 wt% at C/O ratio of 5.44 (gas oil mass flow rate is 51.8 kg/s and catalyst mass flow rate is 282.0 kg/s). The absolute difference between the maximized value and this simulation is 4.34 wt%, an increase from 4.59 to 8.93 wt%. The optimized catalyst mass flow rate is 282.0 kg/s; it is a 47.72% increase on the 190.9 kg/s base case simulation. This increase produced results consistent with the riser hydrodynamics where increase in mass flow rate of catalyst can result in an increase in the reaction temperature and consequent yield of intermediate products [9, 19, 56]. There is 3.81 and 3.89% increase in the temperatures of the gas phase and catalyst, respectively, which in turn causes the increase in the yield of a difference of 5.26 wt% of dry gas from 1.55 wt% at C/O ratio of 3.69–6.81 wt% at C/O ratio of 5.44. Similarly, the yield of butylene has a difference of 5.10 wt% from 9.39 wt% at C/O ratio of 3.69–14.49 wt% at C/O ratio of 5.44. Due to increase in C/O and temperature of reaction, more gas oil cracks, a further 12.02 wt% was achieved from 26.11 wt% at C/O ratio of 3.69–14.09 wt% at C/O ratio of 5.44. This is also a reason for more yield of propylene and other intermediate products; butylene and dry gas. Gasoline also cracks in a secondary reaction and depletes from 51.36 wt% at C/O ratio of 3.69–43.68 wt% at C/O ratio of 5.44 giving rise to a loss of 7.68 wt%, this secondary reaction was also observed in the literature [57]. In optimization case 1, at C/O ratio of 5.44, 9.00 wt% of coke was deposited on the catalyst, against 4.00 wt% at C/O ratio of 3.69 leading to an addition of 5.00 wt% of coke on catalyst. It is also a consequence of increased C/O ratio and reaction temperature. This increase in coke on catalyst may lead to high deactivation of the catalyst, which is not desirable, however, regeneration of the catalyst can be achieved and any eventual consequence is compensated by the much increase in the yield of propylene achieved.

Optimization cases 2 and 3 present similar outcomes as optimization case 1 because their optimum C/O ratios are quite similar; 5.44, 5.48 and 5.45 for cases 1, 2 and 3, respectively, with an absolute average difference of 0.016. This very slight difference is responsible for the slight average variation of 0.01 wt% in the riser outputs for the six lumps.

The optimisation case 2 has its decision variable changed from the mass flow rate of catalyst in case 1 to mass flow rate of gas oil. The gas oil mass flow rate was set to be optimized between 20 and 500 kg/s, while gas oil temperature, T_g, between 520 and 800 K and catalyst temperature, $T_{\text{c}} ,$ between 700 and 1000 K. The catalyst mass flow rate was fixed at 190.9 kg/s. The optimized gas oil mass flow rate is 34.86 kg/s, which is a 32.7% decrease on the 51.8 kg/s of the base case simulation and corresponds to C/O of 5.48, an increase of C/O ratio of 0.04 compared with the C/O ratio of optimization case 1. This result, as in case 1, is consistent with the riser hydrodynamics where increase in C/O results in increase in the reaction temperature and yield of intermediate products [7, 56]. There is 3.90 and 3.95% increase in the temperatures of the gas phase and catalyst, respectively. The increase in temperature in cases 1 and 2 is very similar because only C/O ratio difference of 0.04 between cases 1 and 2 exists, which even though the optimized conditions in case 2 increased the maximum value of propylene by 94.55% the same as case 1 compared with the simulation value of 4.59 wt%; there is no difference between the values of maximized propylene (8.93 wt%) between cases 1 and 2. Similarly, the yield of butylene and dry gas increased, respectively, by 5.11 and 5.26 wt% due to an increase in C/O ratio of 1.79 (C/O of 3.69–5.48). The amount of coke deposited in case 2 is as in case 1, which is 9.00 wt%. Since maximizing propylene is the main aim of this work, and cases 1 and 2 could achieve the same value of 8.93 wt%, any of the operating conditions of cases 1 or 2 can be used for optimal operation of the riser to produce optimum value of propylene, however, case 2 is preferable because of the difference of C/O ratio of 0.05.

The optimisation case 3 used two decision variables, unlike cases 1 and 2. These were gas oil and catalyst mass flow rates. The gas oil mass flow rate was set to be optimized between 20 and 500 kg/s as in case 1, and the catalyst mass flow rate was also set to be optimized between 20 and 500 kg/s as in case 2. The gas oil temperature, $T_{\text{g}} ,$ was set between 520 and 800 K and catalyst temperature, $T_{\text{c}} ,$ between 700 and 1000 K.

The optimized gas oil and catalyst mass flow rates are 53.4 and 290.8 kg/s, respectively, showing a 3.09% increase on the 51.8 kg/s base case condition for gas oil mass flow rate and 52.33% increase on the 190.9 kg/s base case condition for catalyst mass flow rate. These optimized flow rates correspond to a C/O of 5.45, an increased C/O of 1.74 on the base case simulation bringing about a 94.99% increase in propylene yield from 4.59 to 8.95 wt%. There is a slight increase of 0.05 wt% of propylene in case 3 over cases 1 and 2, which represents a 0.44% increase. This increase makes optimization case 3 most preferable because any small improvement to the yield of products in FCC unit amounts to great profitability. In general, the maximized value of propylene is 8.95 wt% achieved at C/O ratio of 5.45, even though, an average of 7.70 wt% of gasoline is lost due to secondary reaction with much coke deposited on the catalyst.

It is observed that the improved yield of propylene is accompanied with increase in some undesirable products such as dry gas and butylene as well as its isomer. It also increased catalyst deactivation. However, FCC units can be modified or operated in a mode shift to produce propylene with less of the aforementioned consequences. This could be achieved by the harmonious combination of the catalyst, temperature, C/O ratio, time, coke make, and hydrocarbon partial pressure [7].

An industrial size conventional FCC riser is simulated in this work to maximize the yield of propylene as a separate lump. The common view is where experimental works were carried out at specific temperature in fixed bed reactors, and propylene mostly considered as part of a general lump of olefins. Instead of using catalyst additives to improve the yield, only the operational conditions of the riser were used in this work. However, it is recommended that the use of both improved catalyst and optimum operating conditions will greatly increase the yield of propylene.

Conclusions

In this work, optimization of the FCC riser has been carried out using a detailed riser process model of a six-lumped kinetic model to maximize the conversion of gas oil to propylene, which is a major building block for the polypropylene production. Parameter estimation was also done to estimate the kinetic variables useful in the model used in this simulation. It is a steady state optimization carried out on a FCC riser and the following were found:

• In the case 1 optimization, the maximum value of propylene obtained is 8.93 wt% at optimal value of 282.0 kg/s catalyst mass flow rate. Compared with the base case simulation value of 4.59 wt% propylene yield, the maximized value shows an increase by 95%.

• Likewise, in the case 2 optimization, the maximum value of propylene obtained is the same 8.93 wt% at optimal value of 34.86 kg/s gas oil mass flow rate. When it is compared with the base case simulation value of 4.59 wt% propylene yield, the maximized value shows an increase by 95%, as in case 1.

• When the two optimal values of 290.8 kg/s mass flow rate of catalyst and 53.4 kg/s mass flow rate of gas oil were obtained in case 3, the maximized propylene yield is 8.95 wt%, slightly higher than cases 1 and 2. When it is compared with the base case simulation value of 4.59 wt% propylene yield, the maximized value shows an increase by 95%.

• New kinetic parameters (frequency factor, activation energies and heat of reactions) were estimated for and used with a six-lumped kinetic model with a separate propylene lump. The yields of the six lumps fall within the range of yields presented in the literature.

• The optimization in all three cases (cases 1, 2 and 3) was achieved at C/O ratios of 5.44, 5.48 and 5.45, respectively. C/O ratio 5.45 gave the higher maximum value of propylene, hence the riser is required to operate at a minimum C/O ratio of 5.44 if optimal operation of the riser is required to maximize propylene yield.

Appendix

Table 6 and Eqs. (71)–(92) are correlations of physical and transport parameters adopted from the literature [2, 19].

Table 6 Distillation coefficients

The distillation coefficient used in this simulation is based on the 10, 50 and 90 vol% as used in Ancheyta and Rogelio [15].

Heat capacity of gas, C_pg, is

$$C_{\text{pg}} = \beta_{1} + \beta_{2} T_{\text{g}} + \beta_{3} T_{\text{g}}^{2} ,$$

(71)

where $\beta_{1}$, $\beta_{2}$, β₃ and β₄, the catalyst decay constants, given as

$$\beta_{1} = - 1.492343 + 0.124432K_{\text{f}} + \beta_{4} \left( {1.23519 - \frac{1.04025}{{S_{\text{g}} }}} \right),$$

(72)

$$\beta_{2} = ( - 7.53624 \times 10^{ - 4} )\left[ {2.9247 - (1.5524 - 0.05543K_{\text{f}} )K_{\text{f}} + \beta_{4} \left( {6.0283 - \frac{5.0694}{{S_{\text{g}} }}} \right)} \right],$$

(73)

$$\beta_{3} = (1.356523 \times 10^{ - 6} )(1.6946 + 0.0884\beta_{4} ),$$

(74)

$$\beta_{4} = \left[ {\left( {\frac{12.8}{\text{Kf}} - 1} \right)\left( {1 - \frac{10}{\text{Kf}}} \right)\left( {S_{\text{g}} - 0.885} \right)\left( {S_{\text{g}} - 0.7} \right)\left( {10^{4} } \right)} \right]^{2} \quad {\text{for }}10 < {\text{Kf}} < 12.8.$$

(75)

Else $\beta_{4} = 0$ for all other cases

Kf is the Watson characterization factor written as

$${\text{Kf}} = \frac{{\left( {1.8T_{\text{MeABP}} } \right)^{{\frac{1}{3}}} }}{{S_{\text{g}} }},$$

(76)

where M_wg is the molecular weight of the gas and can be calculated using

$$M_{\text{wg}} = 42.965\left[ {\exp \left( {2.097 \times 10^{ - 4} T_{\text{MeABP}} - 7.787S_{\text{g}} + 2.085 \times 10^{ - 3} T_{\text{MeABP}} S_{\text{g}} } \right)} \right] (T_{\text{MeABP}}^{1.26007} S_{\text{g}}^{4.98308} ),$$

(77)

$$T_{\text{MeABP}} = T_{\text{VABP}} - 0.5556\exp [ - 0.9440 - 0.0087\left( {1.8T_{\text{VABP}} - 491.67} \right)^{0.6667} + 2.9972\left( {\text{Sl}} \right)^{0.3333} ,$$

(78)

where T_VABP is the volume average boiling temperature and (Sl) is the slope given as

$$\left( {\text{Sl}} \right) = 0.0125(T_{{90{\text{ASTM}}}} - T_{{10{\text{ASTM}}}} ),$$

(79)

$$T_{\text{VABP}} = 0.333(T_{{10{\text{ASTM}}}} + T_{{50{\text{ASTM}}}} + T_{{90{\text{ASTM}}}} ).$$

(80)

The ASTM D86 distillation temperatures are calculated using

$$T_{{10{\text{ASTM}}}} = a_{10}^{{ - \frac{1}{{b_{10} }}}} \left( {T_{{10{\text{TBP}}}} } \right)^{{\frac{1}{{b_{10} }}}} ,$$

(81)

$$T_{{50{\text{ASTM}}}} = a_{50}^{{ - \frac{1}{{b_{50} }}}} \left( {T_{{50{\text{TBP}}}} } \right)^{{\frac{1}{{b_{50} }}}} ,$$

(82)

$$T_{{90{\text{ASTM}}}} = a_{90}^{{ - \frac{1}{{b_{90} }}}} \left( {T_{{90{\text{TBP}}}} } \right)^{{\frac{1}{{b_{90} }}}} ,$$

(83)

where a _i and b _i are the distillation coefficients (Table 6) and T_iTBP is the TBP distillation temperature.

Interface heat transfer coefficient between the catalyst and gas phases, h_p,

$$h_{\text{p}} = 0.03\frac{{K_{\text{g}} }}{{d_{\text{c}}^{{\frac{2}{3}}} }}\left[ {\frac{{|(v_{\text{g}} - v_{\text{c}} )|\rho_{\text{g}} \varepsilon_{\text{g}} }}{{\mu_{\text{g}} }}} \right]^{{\frac{1}{3}}} .$$

(84)

Thermal conductivity of hydrocarbons

$$K_{\text{g}} = 1 \times 10^{ - 6} (1.9469 - 0.374M_{\text{wm}} + 1.4815 \times 10^{ - 3} M_{\text{wm}}^{2} + 0.1028T_{\text{g}} ),$$

(85)

where M_WM is the mean molecular weight of the combined catalyst and gas

$$M_{\text{WM}} = \frac{1}{{\left( {\frac{{y_{\text{go}} }}{{M_{\text{wgo}} }} + \frac{{y_{\text{gl}} }}{{M_{\text{wgl}} }} + \frac{{y_{{{\text{C}}4}} }}{{M_{{{\text{wC}}4}} }} + \frac{{y_{{{\text{C}}3}} }}{{M_{{{\text{wC}}3}} }} + \frac{{y_{\text{dg}} }}{{M_{\text{wdg}} }} + \frac{{y_{\text{ck}} }}{{M_{\text{ck}} }}} \right)}}$$

(86)

$$M_{\text{wgo}} = M_{\text{wg}}$$

(87)

$$M_{\text{dg}} = 0.0146M_{{{\text{wH}}_{2} }} + 0.4161M_{{{\text{wC}}_{1} }} + 0.5693M_{{{\text{wC}}_{2} }} .$$

(88)

The viscosity of the gas (Table 7)

$$\mu_{\text{g}} = 3.515 \times 10^{ - 8} \mu_{\text{pr}} \frac{{\sqrt {M_{\text{WM}} P_{\text{pc}}^{{\frac{2}{3}}} } }}{{T_{\text{pc}}^{{\frac{1}{6}}} }},$$

(89)

$$\mu_{\text{pr}} = 0.435\exp \left[ {\left( {1.3316 - T_{\text{pr}}^{0.6921} } \right)P_{\text{pr}} } \right]T_{\text{pr}} + 0.0155,$$

(90)

$$\begin{aligned} T_{\text{pc}} & = 17.1419\left[ {\exp \left( { - 9.3145 \times 10^{ - 4} T_{\text{MeABP}} - 0.5444S_{\text{g}} + 6.4791 \times 10^{ - 4} T_{\text{MeABP}} S_{\text{g}} } \right)} \right] \\ & \quad \times T_{\text{MeAB}}^{ - 0.4844} S_{\text{g}}^{4.0846} , \\ \end{aligned}$$

(91)

$$\begin{aligned} P_{\text{pc}} & = 4.6352 \times 10^{6} \left[ {\exp \left( { - 8.505 \times 10^{ - 3} T_{\text{MeABP}} - 4.8014S_{\text{g}} + 5.749 \times 10^{ - 3} T_{\text{MeABP}} S_{\text{g}} } \right)} \right] \\ & \quad \times T_{\text{MeAB}}^{ - 0.4844} S_{\text{g}}^{4.0846} . \\ \end{aligned}$$

(92)

Table 7 Tuned coefficients for $0.2 \le P_{\text{pr}} \le 3$ [22]

Table 8 summarizes the variables, feed and catalyst characteristic and other parameters used in this simulation. Most of the parameters were obtained from the industry and literature [19, 20, 58] (Table 9).

Table 8 Specifications of constant parameters and differential variables at x = 0

Table 9 Catalyst and feed properties