Development of a synthesis tool for Gas-To-Liquid complexes

Computers and Chemical Engineering 42 (2012) 2–14

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Development of a synthesis tool for Gas-To-Liquid complexes Jerome Ellepola a , Nort Thijssen a , Johan Grievink b , Govert Baak a , Abhijeet Avhale a , Jan van Schijndel a,∗ a b

Shell Global Solutions International BV, P.O. Box 38000, Amsterdam,1030 BN, The Netherlands Department of DelftChemTech, Delft University of Technology, 2628 BL Delft, The Netherlands

a r t i c l e

i n f o

Article history: Received 30 September 2011 Received in revised form 28 November 2011 Accepted 1 December 2011 Available online 13 December 2011 Keywords: Syngas manufacturing Fischer–Tropsch Process synthesis Non-linear optimisation

a b s t r a c t Optimal synthesis of a Gas-To-Liquid complex is complicated due to many degrees of freedom in a highly constrained design space. One can choose between alternative, competing syngas manufacturing technologies, different types of Fischer–Tropsch catalysts and reactors, with numerous connectivity options and a range of operational conditions. On the other hand, the design space is confined by equipment, operational and knowledge constraints. Furthermore, economic performance needs to be aligned with carbon and energy efficiencies. To support GTL process design a computational synthesis tool is under development. Its purpose is to find and analyse the optimum structure and operational conditions for a given market scenario. The process model covers alternative syngas generation units and Fischer–Tropsch reactors with an extensive syngas recycle structure. The process units interact with the utility system, where power can be generated from off-gas and/or excess steam. The units are modelled in a reduced, input–output way by algebraic equations, reflecting mass and energy balances and pressure effects. A superstructure arises when considering multiple stages for Fischer–Tropsch synthesis with parallel reactors. The synthesis tool, implemented in AIMMS® , is applied to a realistic sample problem, showing profit optimisation by varying the distribution of NG to syngas generation units with different efficiencies. A sensitivity analysis is carried out by means of Singular Value Decomposition of sensitivity matrices to find dominant patterns of parametric influence on the optimum. © 2011 Elsevier Ltd. All rights reserved.

1. Introduction Liquid hydrocarbon energy carriers, such as gasoline and diesel, are very convenient transportation fuels because of high energy content per unit mass, the presence of a worldwide logistic system and combustion engines designed to the use of these fuels. It is to be expected that liquid hydrocarbons will continue to play a major role in fuelling transportation in the 21st century for combustion engines and possibly also fuel cells. As crude oil is the current feedstock to produce transportation fuels, it is necessary to anticipate a future decline in its availability and to search for alternative sources. Among other companies, Shell Global Solutions International develops the commercial use of alternative feeds, such as natural gas (G), coal (C) and biomass (B), to manufacture liquid hydrocarbons (L). The vision is that in future manufacturing complexes, gas, coal and biomass will be used as feedstock for syngas manufacturing. Long chain hydrocarbons (‘heavy paraffins’) can be produced from syngas by means of Fischer–Tropsch synthesis. These long chains must be hydro cracked to proper length for the selected target products. Any imbalance in carbon to hydrogen

∗ Corresponding author. Tel.: +31 20 6303558. E-mail address: [email protected] (J. van Schijndel). 0098-1354/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.compchemeng.2011.12.005

ratios between feed and liquid products can be utilised to generate additional power and thermal utilities for use within the complex and for export. Manufacturing complexes for cogeneration of liquid hydrocarbons, hydrogen and power are called XTL complexes {X = G, C, B}. A recent overview of XTL Fischer–Tropsch processes in general is given by DeKlerk (2011), while Davis (2005) reviews associated reactor developments. In spite of the long history of the Fischer–Tropsch conversion process (patented in 1926), only a handful of GTL process plants have been erected today. The main reason is that economically viable GTL plants must be large scale in order to compete cost-wise with crude oil derived products and only then if the price of crude oil is high enough. With expected declining availability of crude oil the prospects for XTL implementations become brighter. Shell’s initial focus in development will be on generalising and improving Gas-To-Liquid (GTL) designs. Shell have been operating a GTL plant in Malaysia since 1993 (14,700 barrels liquid product per day), where middle distillates are the main product (Schrauwen, 2004; Senden, Punt, & Hoek, 1998; Sie, 1998). In 2011, Shell has started ramping up their large PEARL GTL complex in Qatar (140,000 barrels liquid product per day) (Shell, 2011). GTL plants with a capacity of 70,000 barrels of liquid product per day are referred to as world-class complexes. Another GTL project in Qatar is the Oryx GTL plant (32,400 barrels liquid product per day) being in operation since 2007. This process uses technology

J. Ellepola et al. / Computers and Chemical Engineering 42 (2012) 2–14

Nomenclature Abbreviations ATR auto thermal reforming of NG to SG FT(S) Fischer–Tropsch (synthesis) (natural) Gas-To-Liquid route GTL G/S gas/solid catalytic system GT/HRSG gas turbine/heat recovery steam generator hydrocarbon product HC HER heat exchanging reforming high pressure steam HP HMU hydrogen manufacturing unit liquefied natural gas LNG LP low pressure steam (MI)NLP (Mixed Integer) Non-Linear Programming MP medium pressure steam NG natural gas NPV net present value POx Partial Oxidation of NG, implemented in SGP SG syngas SGP shell gasification process SGMU syngas manufacturing unit SMR steam methane reforming TLP total liquid hydrocarbon product Roman letters cP specific heat at constant pressure (J kmol−1 K−1 ) Throughput capacity of an equipment item (ton h−1 ) C Cref base case capacity of an equipment item (ton h−1 ) F molar flow rate (kmol s−1 ) specific enthalpy (J kmol−1 ) H I0 base level capital investment (Euro) Iref base case capital investment at capacity (Euro) Cref Mw,i molecular weight (kg kmol−1 ) P pressure (Pa) P0 vapour pressure of pure component (Pa) heat effect of reactions in a unit (W) QR s stoichiometric coefficient (>0 for formation of product) T temperature (K) molar fraction xi XFTS cross-sectional area of FTS reactor (m2 ) y standard yield rate on FT catalyst (kmol s−1 vol−1 cat ) Greek letters (k) split factor to stream k in unit m ˛m compr energy efficiency factor of compressor  extent of reaction (kmol s−1 ) ϕASU ASU energy consumption factor per unit flow of O2 (W kmol−1 ) (k) i,m separation factor for component i to stream k pressure drop over a FTS reactor (Pa) ˘ FTS  empirical parameters in FT pressure drop correlation  set of kinetic parameters in FT yield correlations Subscripts i index of chemical component j index of chemical reaction l index of quality level (HP, MP, LP, CND) of steam in utility system m index of a process unit

3

Superscripts index of a stream k * saturated conditions

developed by Sasol where the FTS process is based on a slurry phase distillate process (Bao, El-Halwagi, & Elbasi, 2010). The supply chain structure in which a GTL process will function is shown in Fig. 1. Natural gas (NG) with condensates is produced, purified and NG is separated from the condensates. One part of the NG can be liquefied by cryogenic cooling in a LNG (liquefied natural gas) process. GTL technology can be deployed to convert the other part into liquid hydrocarbons. The financial stakes in a GTL complex are very high: depending on scale and complexity investments in a world-class complex can reach ten billion US$ or more. E.g., the PEARL project in Qatar, comprising Offshore Gas Production facilities, the onshore Field Gas Processing plant and a GTL plant was announced to require an investment of 18–19 bln$. Improving future designs by reducing capital investment while keeping operations energy and carbon efficient offers potentially great rewards. When designing a GTL complex, opposing demands for a sustainable performance of such a plant must be balanced: i.e., a high capital productivity must be matched with excellent energy and carbon efficiencies. Such design task gets intricate as many combinatorial options arise with respect to available design decision variables. Such variables involve, e.g., the selection of feeds and products, different syngas manufacturing technologies, alternative Fischer–Tropsch synthesis reactor technologies, superstructures for connectivity of units, energy integration and interactions with the utility system. When the architecture of a complex would be a given, process simulation tools as PRO/IITM (PRO/II, 2011) can be used to model the complex and simulate steady state mass and energy balances and to assess the technical performance. However, it is believed that key opportunities for designing more (capital-)efficient complexes arise from exploring different flow sheet structures with alternative combinations of processing technologies. This article reports on the development of a (proprietary) computational synthesis tool for GTL plants. This tool should enable synthesizing alternative flow sheet structures, while optimising under various operational scenarios the use of monetary and physical resources, like carbon, hydrogen, energy and up-time, while respecting equipment, operational and knowledge constraints. In view of the many degrees of freedom and strong interactions in the process network a model-based optimisation approach (Mixed Integer Non Linear Programming or MINLP in short) is chosen, using AIMMS® (AIMMS manual, 2011) as a model implementation environment and computational vehicle. Similar synthesis endeavours for processing networks have been reported in the area of water treatment and polygeneration energy systems. Karrupiah and Grossmann (2006) present an improved global optimisation algorithm for water treatment networks. Polygeneration energy systems are closer to the nature of a GTL complex and, in fact, conceptually embed it. Polygeneration energy systems address the co-generation of fuels, power and chemicals from a range of feeds. From that perspective GTL complexes fall within this range. Liu, Georgiadis, and Pistikopoulos (2011) present a methodological framework for energy systems engineering. Recent results on synthesis of polygeneration energy systems are reported, among others, by Liu, Pistikopoulos, and Li (2010) and Chen, Adams, and Barton (2011), based on application of MINLP approaches with Pareto trade-offs between economic and environmental objectives. Liu et al. (2010) use coal as a feed to

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Fig. 1. Supply chain structure of NG to liquid products.

co-generate methanol and power, while Chen et al. (2011) use a mixture of coal and biomass to produce liquid hydrocarbons (naphtha, diesel), methanol and power, dealing also with carbon capture aspects. Studies dedicated to simulation and economic analysis of GTL processes are presented by Hao et al. (2008), Kim, Jun, Joo, Han, and Song (2009) and Bao et al. (2010). Hao et al. (2008) investigate optimal flow sheet structures for different catalysts, aiming for a high syngas conversion in FT and considering CO2 removal. Kim et al. (2009) base their modelling on a small scale laboratory set-up and take a single pass approach with respect to syngas and optimise the slurry phase FT reactor conditions with respect to maximum hydrocarbon yield. The study by Bao et al. (2010) addresses an economic analysis and optimisation of processing and heat integration conditions, accounting for the effects of potential recycling of unconverted syngas to the Fischer–Tropsch and syngas generation sections. The impact of applying alternative syngas generation technologies as a combination is not considered in either study; all use ATR (auto thermal reforming). Setting up a new GTL synthesis tool is challenging in the following ways:

2. Structure of a Gas-To-Liquid complex with design decision options

• • • •

2.1. Structure diagrams of a GTL complex

creating a flexible enough (super) structure, doing systemic modelling with model reduction, proper model scaling and initialisation, analysing the robustness and significance of optimisation results in view of underlying model uncertainty.

The remainder of this article presents the generic structure of a Gas-To-Liquid complex and associated design decisions, the setup of models of the process units and their connectivity, leading to an optimisation problem in MINLP format. The implementation of the optimisation problem in AIMMS and some associated computational considerations are discussed followed by an application of the synthesis tool to a realistic sample problem.

The purpose of a GTL complex is to convert natural gas into liquid hydrocarbon products in the naphtha to gasoil range. The performance of a world-class complex, which requires a tremendous capital investment, must certainly be expressed in economic terms – such as NPV (net present value) – but also in ecological terms, related to emissions of chemical waste (e.g., CO2 ) and irreversible energy losses. One option is to include these losses as a penalty in the economic performance function. However, that requires the presence of clear policy on how to assign economic value to such losses. We would like to see these losses in a more explicit quantitative manner as a function of process synthesis decisions which has the merit of greater transparency in effects of decision making. Having multiple performance indicators necessitates making trade-offs when optimising a design of a GTL complex. This section introduces at a conceptual level the structure of a GTL complex; it outlines the choices for design decision variables and specifies the nature of the inequality constraints and the performance metrics. The inequality constraints delineate the feasible domain for design and operation. The associated mathematical model is highlighted in Section 3.

The structure of a GTL complex derives from the chemical route that is chosen and the associated energy effects. Fig. 2 shows the main reactions to generate syngas and convert syngas into hydrocarbons. Syngas manufacturing is a gas phase operation. Two manufacturing technologies are shown here: Partial Oxidation (POx) and steam reforming of methane (SMR). They use different oxygen carriers (O2 and H2 O), resulting in different hydrogen to carbon monoxide ratios: POx: 2:1 and SMR: 3:1. Having such a composition difference is attractive because mixing becomes possible to obtain an optimal feed to the Fischer–Tropsch (FT) synthesis reactions. The oxygen feed also contains minor amounts of inerts (nitrogen, argon). These inerts will become significant when recycling syngas

J. Ellepola et al. / Computers and Chemical Engineering 42 (2012) 2–14

Natural gas

~ NPV

(a) Partial oxidation: CH4 + ½ O2 => CO + 2 H2 => CO2 + 2 H2O CH4 + 2 O2 CO + H2O <=> CO2 + H2

ΔH0R= - 71.8 kJ/mol ΔH0R= - 803 kJ/mol ΔH0R= - 41.0 kJ/mol

Ecological: carbon - efficiency

(b) Steam methane reforming: Water

Economic :

Performance indicators

Syngas manufacturing main reactions: Oxygen

5

CH4 + CO +

H2O => CO + 3 H2 H2O <=> CO2 + H2

Natural gas

ΔH0R= +206 kJ/mol ΔH0R= - 41.0 kJ/mol

(CH4) Oxygen source 1:

Synthesis gas

Fischer-Tropsch synthesis reactions: CnH2n + CO + 2H2 => Cn+1H2n+2 + H2O CO + H2O => CO2 + H2

ΔH0R= ΔH0R=

- 170 kJ/mol - 41 kJ/mol

CO + 2HHeavy –(CH2)n– 2HeavyParaf fins Paraff ins Synthes is Synthesis

Water

Off-gas

GTL products

H O complex Gas-to-Liquids

H2O

Reaction

(NG=> SG => HC) Liquid product

Water

Oxygen Source 2:

O2

Off gas

(CnHn+2)

2

Power

Power

Off-gas combustion for energy generation: CO + 2 H2 + 3/2 O2 => CO2 + 2 H2O

ΔH0R= - 732 kJ/mol

Capital Hot utilities

investments Fig. 2. Main conversion steps in a GTL process. Fig. 3. Input–output diagram of a GTL complex.

in the GTL system. The energy effects in these syngas manufacturing techniques differ. Partial Oxidation is exothermic and takes place at a very high temperature (∼1250–1400 ◦ C). The heat of (partial) combustion can be used to generate steam for the utility system. The steam methane reforming reaction is quite endothermic, running at ∼900 ◦ C and requires heating by combusting an externally supplied fuel. The excess heat can be used for the generation of utilities. Thus, the syngas generation units are coupled to the utility system as heat sources and sinks. The FT synthesis reactions are catalysed in a G/S system with solid catalytic particles. In addition to the formation of hydrocarbons a side reaction to CO2 takes place. The FT reactions are exothermic and take place a relatively low temperature (T ∼ 200–280 ◦ C). The heat of reaction is taken away by cooling and steam generation for the utility system. The reactants, water and the lighter fractions of the hydrocarbon products are in the gas phase. The main reaction product from FT is a mix of predominantly alkanes with some alkenes and alcohols. In this study it assumed that the product is 100% straight paraffinic, ignoring the finer details of internal product distributions. To retain proper catalytic activity all reaction water should stay in the gas phase, avoiding partial condensation as liquid on the catalyst particles. The partial pressure of water in the syngas should remain below the saturation pressure of pure water at the reaction temperature. The formation of reaction water thus limits the extent to which syngas can be converted without a water removal step. The above FT reaction stoichiometry shows that for each additional CH2 – moiety (Mw = 14) one water molecule (Mw = 18) is produced. Thus, on mass basis the FT reactions produce even more water than hydrocarbons. The reaction water is largely removed from the gas phase by condensation after the reaction section. Achieving the optimum composition of the syngas for best use of the reactants is an important design aspect. The FT reaction suggests a stoichiometric H2 :CO ratio of 2:1. Ideally, this ratio is to be attained at the catalytic sites in the particles, supplying both reactants at the right proportion for the propagation reaction. Hydrogen has a relatively high diffusivity compared to CO in the transfer from the bulk of the gas phase to the catalytic sites. Therefore, the H2 :CO ratio in the bulk of the gas phase must be lower than the target value of two at these sites. Lowering this can be achieved by mixing fresh syngas with a fraction of the syngas leaving the reactor. Due to the afore mentioned water constraint on FT catalyst activity syngas can only be partially converted. Syngas at the exit of the FT reactors has a low H2 :CO ratio as hydrogen is consumed at twice the rate of carbon monoxide. The exit syngas can be partially recycled over the FT reactors and mixed with fresh syngas from the syngas

manufacturing section. The mixing ratio of fresh and recycle syngas is a degree of freedom in tuning the H2 :CO ratio in the combined syngas feed for optimal syngas conversion. At the reactor exit, only part of the syngas is converted. While one fraction of the exit gas can be recycled, another fraction can be returned to the syngas manufacturing units. The third fraction must be forwarded downstream in order to avoid a high accumulation of inerts and reaction water in the syngas. These splitting fractions are degrees of freedom in the design and operation of a GTL plant. In view of the limited conversion staging of the FT reaction steps is another degree of freedom (to be discussed further on). The long paraffin molecules must be hydro cracked to suitable product molecules. The hydrocracking and product separations are downstream operations which do not interact by some recycle with syngas manufacturing and FT synthesis (see Fig. 4). Therefore, these hydrocracking reactions are not considered in Fig. 2. Having outlined the key features of syngas generation and FT synthesis the resulting input–output diagram of a GTL complex can be composed, see Fig. 3. This diagram shows the physical feeds and outlets. The latter represent valuable products, liquid HC, water and power, as well as the residual unconverted syngas (off-gas). The dotted lines indicate the economic and ecological performance aspects for the various stakeholders, associated with the design and operation of the complex. The internal structure of the complex is depicted as a block diagram in Fig. 4. Syngas recycling is introduced in order to achieve high carbon efficiency, though it causes strong interactions between the syngas manufacturing and FT synthesis sections. Unconverted syngas leaving the FT synthesis has in principle four destinations: (a) long recycle to syngas manufacturing units; (b) short recycle over the FT section; (c) off-gas to utility system; (d) off-gas to export. The off-gas from the FT section has a low H2 :CO ratio but still a significant caloric value due to remaining CO. Thus it can be used for additional power generation in the utility system. When not operating in island mode, both off-gas and/or power can be exported. The hydrocarbons and the water produced by the FT reaction must be removed as liquids by applying condensation and phase separation steps after the reactions in the FT section. An expanded process block diagram of a GTL process is shown in Fig. 5. The synthesis tool will primarily focus on the conversion units for syngas manufacturing and heavy paraffins synthesis and their coupling with the utility system. The downstream units, hydro cracking of heavy paraffins and product separations, are kept outside the scope for the time being. Some additional explanatory remarks are in order with respect to the main function blocks:

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Natural gas

Synthesis gas

Wax

GTL products

Off-gas NG

Hydro-cracking Hydro-cracking Syn-gas Syn-gas her-Tr opsch and FischerTro psch –(CH2)n– and manufact uringg CO + 2H Fisc manufacturin 2 synthes is liquid product t synthesis liquidproduc technologies technologies upgrading upgrading

H2O

Oxygen

Air

CnHn+2 • naphtha • n-paraffins • kerosene • gas oil • base oil

Air Air separation separation

H2O Steam & Power

NG

Utilities Utilities&&General GeneralFac Facilities ilities Export Power Fig. 4. Block diagram of a GTL complex.

syngas manufacturing, FT synthesis and the utility system including the air separation units. (a) The syngas manufacturing options include ATR, SMR, POx (Partial Oxidation) and HER (heat exchanging reforming); see Wilhelm, Simbeck, Karp, and Dickenson (2001) for background information. For the purpose of heat integration, endothermic (SMR) and exothermic operations can be combined (block “Others” in Fig. 5). The temperatures in the units are treated as degrees of freedom in the optimisation, affecting syngas composition by shifting the reaction equilibria. The pressure levels are kept fixed. The intake of oxygen relative to carbon intake is another degree of freedom. (b) The FT synthesis section has an internal structure of multiple sequential stages (≥1 stage). Staging is introduced to overcome a natural limitation in syngas conversion to avoid the formation of liquid reaction water in the FT reactors. Therefore, in

each stage water vapour is condensed and removed after the reaction section. The generic structure of a FT synthesis stage is presented in Fig. 6. The function blocks in this stage diagram will be further explained: (b.1) There is a reaction section of parallel reactors filled with a certain mass of active catalyst material. Within this FT reaction block we aim for modularity regarding the use of different catalysts and types of reactor equipment. (b.2) All reactors in the same stage are identical in the sense of having the same operating conditions (pressure and temperature) as well as amount of catalyst. The amount of catalyst per reactor and the reactor temperature can be used as a degree of freedom to achieve the target yield of hydrocarbons per stage. (b.3) Cooling of the exit gas and condensing and removing hydrocarbons and water as a liquid mixture from the gas phase.

Scope of GTL Process Synthesis Tool H2O

(SMR)

(HMU)

steam methane reforming

hydrogen manufacturing

Natural Gas

Hydrogen

H2

Naphtha N-paraffins

Other

syn-gas production H2O

ATR POx

SMR HER

Fischer-Tropsch Synthesis

Hydrocracking

Liquid Product Upgrading

GasOil BaseOil

O2 Air

Kerosene

Water Treatment

Air separation

Water

Natural Gas

Hot utilities

Raw Water

Steam & Power off-take

Boiler Feed Water, Cooling Water, Chilled Water & General Facilities Fig. 5. Scope of synthesis tool in an expanded GTL block diagram.

Export

J. Ellepola et al. / Computers and Chemical Engineering 42 (2012) 2–14 Syngas

short recycle S

to next stage

(unconverted syngas) Additions of fresh syngas (source B)

compressor Dry syngas FT Reactors

Syngas mix from a preceding stage

Additions of fresh syngas (source A)

in

mix

heavy product separation

light product separation

parallel

Combined syngas

Mainly gas & traces of liquid

7

The diagram shows two parallel syngas manufacturing operations (e.g., Partial Oxidation, POx with pressures up to 80 bar and SMR operating at pressures ranging between 20 and 25 bar). NG entering the POx must be increased in pressure by compression. There are three FT synthesis stages, running at a pressure up to 80 bar. The long recycle to the POx syngas unit requires a compressor to boost the pressure, while the long recycle to the SMR unit can do without a compressor because of the lower SMR pressure. In the latter case the generated syngas from SMR must be boosted by means of a compressor to the inlet pressure level of the first stage of the FT synthesis. The number of FT stages (≥1) is a design degree of freedom. In order to have the complete picture of the entire GTL system this process flow sheet must be connected with the utility grid (not shown here).

Liquid HC + water

2.2. Design decisions, constraints and performance metrics in a GTL complex

Fig. 6. Structure of a Fischer–Tropsch synthesis stage.

(b.4) The “dried” syngas is partially recycled and partially forwarded to the next stage. After the final stage a fraction of the exit gas may be recycled to the syngas manufacturing section while the remaining fraction is off-gas to the utility system and/or export. (b.5) Each short recycle has a compressor to overcome the pressure drop over the reactors. (b.6) The two-phase liquid mixture of the heavier hydrocarbons and water is collected from all stages and allowed to settle such that water and hydrocarbons can be separated. The hydrocarbons form the main product stream to the hydrocracking section, while water is a side product. (c) The number of FT stages and the number of reactors per stage can vary, though the total number of reactors in the FT synthesis section may be kept constant as an investment constraint. E.g., if the allowable total number of reactors would be set at twelve (12) and there are three stages, a typical allocation of reactors to stages could be: six (6) in the first stage, four (4) in the second stage and two (2) in the third stage. Note that the allocation of reactors to stages is an additional degree of freedom in the optimisation space. Increasing the number of stages enhances the overall conversion of syngas, and thus product yield, though the extra cost of investment in these additional stages runs up quickly. Here, an economic trade-off emerges. (d) The utility and power generation system is built-up as a grid with several discrete levels of energy quality (fuel, power, HP, MP, LP steam, condensate). The transfers between these levels occur by means of utility units (e.g., boilers, steam turbines, super heaters, gas turbines combined with heat recovery steam generation systems (GT/HRSG) as well as heat sources and sinks in the process units. A utility system functions for the entire GTL complex and so the use of utilities by other parts of the complex is accounted for by considering estimated fixed duties. Further background reading on the structure of utility systems is offered in Smith (2005), Section 23.5. (e) The air separation unit is accounted for in terms of capital investment and consumption and cost of energy. The envelop of the synthesis tool is chosen to cover the syngas manufacturing and the FT synthesis units and the utility system. This envelop accounts for some 60–65% of the GTL capital and ∼100% of the carbon efficiency. Given this internal structure for the FT synthesis section in Fig. 6, the extended process block diagram (Fig. 5) can be expanded into a process flow diagram. One particular realisation is shown in Fig. 7.

The mode of operation of the GTL complex is steady state. The following decision variables are considered in the flowsheet synthesis: • Type of syngas manufacturing units: SGMU = {POx, SMR, ATR, HER}. • Operating temperature and oxygen to carbon ratio in feed to each SGMU. • Type of FT reactors (e.g., fixed bed, slurry, structured reactors) with corresponding catalyst generations. • Amount of catalyst in a standardised FT reactor type. • Number of stages for FT reactors and number of reactors in parallel per stage. • Distribution of fresh syngas from the SGMU’s over the FT stages • H2 :CO ratio in the combined syngas feed to a FT reactor stage (thus determining the short recycle fraction of unconverted syngas over that stage). • FT reactor temperature per stage. • Long recycle fraction of unconverted syngas with distribution factors to each of the SGMUs. • Fraction of unconverted syngas to the utility system for power generation. • Some transfer rates of high level energy to lower levels in the utility system. • The energy quality levels are fixed at pre-assigned temperature and pressures. The operational scenarios can be split in product driven and feed driven. • Hourly production rate of total liquid product in a production driven scenario, or • Hourly NG intakes to each of the SGMU’s in a feed-driven scenario. • In both cases a target output of hydrogen for the hydrocracking and any additional sales must be set. The feasible design space is limited by constraints on equipment capacity, safety and dependability. Performance metrics involve profit (NPV), carbon and energy efficiencies. 3. Formulation of models and optimisation problem 3.1. Scope of the models and modelling approach The physical resources to be considered in this synthesis study involve mass flows of chemical species, sources and sinks for thermal energy, power generation and mechanical work for

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Fig. 7. A GTL flowsheet example (connectivity with utility system not shown).

compression. Up-time (availability) of the units and the complex is also a physical resource, but it is not included yet in the modelling. Only a lumped average value for up-time is used as input to the economic model. The process and utility models are set up as a network with processing units as nodes and connecting streams as (directed) arcs. The leading principles in our process modelling are that: • Understanding of patterns of interactions in the network and of its overall performance is more relevant than being extremely accurate in the predictive power of individual unit models. • Reduced, input–output models with lumped kinetics have been used for the process units such that computational efficiency in achieved in this optimisation context. • Reduced models of process units will be applied only within experimentally validated domains by imposing domain boundaries as ‘knowledge’ inequality constraints. When an optimum design would be co-determined by one or more knowledge constraints, there could be an incentive to widen the domain of model applicability by additional experimentation. The overall process synthesis model is made up of three parts: structure, behavioural & performance models. The behavioural models are set up per process unit. 3.2. Notes on the structure model The flow sheet structure model is conceptually characterised by means of a connectivity matrix showing how streams are connecting units in terms of in- and outflows. The merging and splitting of streams is controlled by “mixing” and “splitter” units. A “mixer” unit connects incoming streams to one outlet stream and adds the associated incoming flows to one outflow. A “splitter” connects one incoming stream to multiple outlet streams. The associated incoming flow is distributed over the outgoing flows by means of normalised continuous split factors ∈ [0, 1] without changing the intensive variables (x, T, P). The routing of the flows through the stream connections is manipulated by means of these split factors. Discrete variables come into play for the number of FT synthesis stages, the number of reactors per stage, the type of catalyst, the type of FT reactor equipment and the alternative syngas generation techniques to be used. Switching between equipment types and catalyst will require switching between the corresponding behavioural models. So far, models of specific FT reactor equipment and catalyst and a small set of syngas generation techniques are hard-coded in the

Table 1 Selected syngas generation reactions in POx. 1 2 3 4 5 6 7 8

CH4 C2 H6 C3 H8 C4 H10 C5–10 C11+ CO2 CH4

CH4 + (1/2)O2 → 1CO + 2H2 C2 H6 + 1O2 → 2CO + 3H2 C3 H8 + (3/2)O2 → 3CO + 4H2 C4 H10 + 2O2 → 4CO + 5H2 C5–10 + (n5–10 /2)O2 → n5–10 CO + (n5–10 + 1)H2 C11 + (n11+ /2)O2 → n11+ CO + (n11+ 1)H2 CO + H2 O ↔ CO2 CH4 + H2 O ↔ CO +3H2

overall process model. Further comments on the ability to exploit the discrete part of the process model will be given in the computational section of the article. In addition to the flowsheet structure there is the underlying discrete physicochemical structure, involving the number and nature of chemical species, reactions and thermodynamic phases. Thirteen chemical species are considered: oxygen, nitrogen, argon, hydrogen, water, carbon monoxide, carbon dioxide, methane, ethane, propane, butane and two lumped hydrocarbon fractions, one for the C5–10 fraction and the other for the C11+ fraction. The syngas formation reactions for Partial Oxidation, steam methane reforming and FT synthesis reactions are shown in Tables 1–3, respectively in the section on the behavioural model. All reaction rates are related to gas phase conditions in the respective reactors. This discrete physicochemical structure for species, reactions and phases is kept fixed in the modelling and optimisation.

Table 2 Selected syngas generation reactions in SMR. 1 2 3 4 5 6 7

CH4 C2 H6 C3 H8 C4 H10 C5–10 C11+ CO2

CH4 + 1H2 O ↔ 1CO + 3H2 C2 H6 + 2H2 O → 2CO + 5H2 C3 H8 + 3H2 O → 3CO + 7H2 C4 H10 + 4H2 O → 4CO + 9H2 C5–10 + n5–10 H2 O → n5–10 CO + (2n5–10 + 1)H2 C11+ + n11+ H2 O → n11+ CO + (2n11+ + 1)H2 CO + H2 O ↔ CO2 + H2

Table 3 Selected FT synthesis reactions. 1 2 3 4 5 6 7

CH4 C2 H6 C3 H8 C4 H10 C5–10 C11+ CO2

CO + 3H2 + CH4 + H2 O 2CO + 5H2 → C2 H6 + 2H2 O 3CO + 7H2 → C3 H8 + 3H2 O 4CO + 9H2 → C4 H10 + 4H2 O n5–10 CO + (2n5–10 + 1)H2 → C5–10 + n5–10 H2 O n11+ CO + (2n11+ + 1)H2 → C11+ +n11+ H2 O CO + H2 O → CO2 + H2

J. Ellepola et al. / Computers and Chemical Engineering 42 (2012) 2–14

3.3. Features of the behavioural models of units with inequality constraints

(out)

xCO

The behavioural model comprises the joint physical behaviour of all units. The units are modelled in a grey box fashion. I.e., linear molar species balances are formulated, while source and sink terms are related to operating conditions and design parameters either by equilibrium conditions upon exit or by non-linear statistical correlations for kinetics. These latter correlations are obtained either by reduction of a rigorous model or from experimental data. The correlations have a limited accuracy and thus introduce some uncertainty margins in the calculated model outputs. This uncertainty in reaction kinetics propagates into uncertainty in the heat effects of the reactions. The magnitudes of these chemical energy sources and sinks in the process units overwhelm any difference in thermal content of energy in- and outflows. Thus, given the uncertainty effects in sources and sinks, we refrain from formulating and solving complete enthalpy balances. Only the significant sources and sinks are represented for exchanges with the utility system. Thus, a generic process unit model consists of: • Linear mass balances for all relevant species • Non-linear (reduced) equations for source and sinks terms in mass and energy • Pressure drop correlations • Inequality constraints on equipment related operating conditions, on physical feasibility and model validity domains. A stream is characterised by the flows of the associated physical resources (species, energy) and some intensive variables (T, P). 3.3.1. Modelling of the conversion units The molar component balances for a conversion unit m (covering syngas generation units and FT synthesis) are written as: (in)

Fi,m +



(out)

si,j × j,m − Fi,m

=0

(1)

(k)



(k)

Fi

= 0∀ k

(k)

(k)

− xi

=0

The reaction equilibrium constants are evaluated at an empirical off-set (T) from the nominal temperature TPOx of the POx unit. In order to apply these conditions confidently, empirically validated inequality constraints are imposed on the oxygen to carbon ratio in the feed to POx. This is to make sure that there is enough oxygen flow to convert all hydrocarbons to CO (minimum bound on oxygen flow), but not so much that full combustion to CO2 occurs. Since the POx reactions take place at a very high temperature (TPOx ∼ 1250–1400 ◦ C) the NG feed is preheated in a furnace and the syngas made in the POx step must be cooled down to a more moderate temperature to remove water before entering the FT synthesis unit (Tcond,POx ). The required heat input for pre-heating is given by:



Qheat,POx = −

(in)

Fi,POx × [Hi (Tin,POx ) − Hi (Tfeed,NG )]

(8)

i

The heat released by the hot syngas is transferred to the utility system to raise high pressure steam.



Qcool,POx = −

(out)

Fi,POx × [Hi (Tcond,POx ) − Hi (TPOx )]

(9)

i

Eqs. (1)–(9) cover the core of the POx unit model. The temperature of the POx unit is a local degree of freedom for the optimiser to manipulate within a range, while the pressure is kept fixed. (B) Syngas generation by SMR: See Table 2 for the relevant reactions. There are seven extents of reactions for which conditions must be specified.The SMR reactions (2)–(6) are assumed to run to depletion of the hydrocarbon species, leading to five conditions: j = C2 H6 , C3 H8 , C4 H10 , C5–10 , C11+

(10)

The reactions (1) and (7) are at equilibrium at the outlet, again with a small empirical off-set from the nominal temperature of the SMR unit.

(3)

xCO

(out)

(k)

× Ftotal = 0 ∀ k

(out) 2O

× xH

(2)

i

Fi

4

(7)

Fj,SMR = 0

The molar fractions are given by:

(out)

) − K8 (TPOx − T8,POx , PPOx ) × xCH

2

(out)

j

Ftotal −

(out) 3

× (xH

9

(out) 3

× (xH

2

(out)

) − K1 (TSMR − T1,SMR , PSMR ) × xCH

4

(out) 2O

× xH

=0 (11)

The joint heat effect of all reactions in unit m is given by:



Qm = −

j,m × HR,j

(4)

2

The extent of a reaction  can be determined from either a reaction equilibrium condition, or by a depletion condition or by a kinetic correlation. How these extents are determined will be elaborated per conversion unit. (A) Syngas generation by POx: See Table 1 for the relevant reactions. Conditions must be imposed for eight extents of reaction. The POx reactions (1)–(6) are assumed run to depletion of oxygen and all hydrocarbon species, except methane. This leads to the following six conditions: (out)

Fj,POx = 0 j = O2 , C2 H6 , C3 H8 , C4 H10 , C5–10 , C11+

(5)

The remaining two conditions are given by imposing equilibrium for the reactions (7) and (8) at the outlet of the unit: (out)

xCO

2

(out)

xCO

j

(out)

× xH

2

(out)

− K7 (TPOx − T7,POx , PPOx ) × xCO

(out) 2O

× xH

=0

(6)

(out)

× xH

2

(out)

− K7 (TSMR − T7,SMR , PSMR ) × xCO

(out) 2O

× xH

=0 (12)

Empirically validated inequality constraints are imposed on the water (oxygen) to carbon ratio in the feed to SMR, leading to a lower and upper bound. Within this range there is always enough water flow to convert all hydrocarbons beyond methane to CO. There is no thermal coupling between the SMR and the utility system in terms of heat transfer with steam. The SMR needs heat input by combustion of fuel to compensate for the strongly endothermic reactions. Otherwise, it operates energy-wise neutral. The required heat input is given by (4) and can be expressed in fuel equivalents. Eqs. (1)–(4) and (10)–(12) form the core of the SMR unit model. The temperature of the SMR unit is a local degree of freedom for the optimiser to manipulate within a range, while the pressure is kept fixed. (C) FT synthesis reactor:

10

J. Ellepola et al. / Computers and Chemical Engineering 42 (2012) 2–14

See Table 3 for the relevant reactions. There are seven extents of reactions for which conditions must be specified. An FT reactor is operating in the kinetic regime, away from equilibrium conditions or exhaustion of any of the reactants. Extents of reactions are the product of catalyst volume in the reactor and the standard yield rate for components (per unit of catalyst volume): j,FTS − Vcat,FTS × yj,FTS = 0

(13)

A yield rate is the integral effect of a reaction rate over the length of a reactor. Rather than formulating and solving detailed kinetic models along an internal reactor coordinate a lumped description is used. The standard yield rates for the generated hydrocarbon components and CO2 are given by empirically validated statistical correlations at outlet conditions: (out)

(out)

(out)

(out) , 2 ,FTS

yj,FTS − Yj (TFTS , PFTS , xCO,FTS , xH

(out) ; 2 O,FTS

xH

(out)

xCO

2

(in)

(out)

(in)

(in)

(in)

(out)

Fi

The yield rate functions (Y) and the pressure drop function (˘) are non-linear, continuous and (at least once) differentiable with respect to their arguments and always attain positive values. The heat of the exothermic reactions is completely removed by cooling, generating saturated medium pressure steam. The heat removal capacity in the FT reactor is good enough to maintain a fairly constant temperature over the length of a reactor. These FT yield correlations (14) are applicable in a hypercube of operating conditions. Simple lower and upper bounds are imposed on: • • • •

inlet pressure reactor temperature hydrogen-to-carbon ratios at inlet and outlet yield rates

RHFTS =

(out) (out) × PFTS 2 O,FTS 0 PH (TFTS ) 2O

xH

=0



(in,k)

Fi

=0

(18)

k

There is no degree of freedom. Splitter model equations for a split into K streams: (out,k)

(k)

(in)

− ˛m × Fi,m = 0 with (k)

˛m = 1 and

k = 1, . . . , K ≥ 2

(19)

k (k)

The split factors ˛m are independent of the components. There are K − 1 degrees of freedom in a splitter. Separator model equation for separation an incoming stream into two streams k1 and k2 : (out,k1 ) (k1 ) (k1 ) (k2 ) Fi,m − i,m × Fi,m = 0 with i,m + i,m =1

(20)

(k1 ) vary per component. Formally, there The separation factors i,m are Ncomponent − 1 degrees of freedom in a separator. However, a separation factor cannot be chosen at will. It must comply with the thermodynamic possibilities for the phase distribution of a component. This generic separator model is repeatedly applied (see Fig. 7) for the:

• removal of water from syngas after the syngas manufacturing units; • removal of water from syngas after the HMU; • removal of liquids (HC and water) from gas after the FT synthesis reactors in a stage; • separation of water from the liquid hydrocarbons. Fair estimates for the corresponding separation factors are derived from detailed simulation of these individual units.

These bounds are made to coincide with those used in the experimental set-up for deriving the correlations. Last but not least lower and upper bounds are specified for the partial pressure of water in the syngas mixture expressed in terms of relative humidity at the exit of a FT reactor:



−

(in)

(15)

(out) 2O

× xH

3.3.2. Modelling of mixers, splitters and block separation units Mixer model equation:



The standard yield rates depend on the temperature, pressure of the FTS reactor and the molar fractions of CO, H2 and H2 O in the gas phase at the outlet. The outlet pressure is related to the inlet pressure by means of an empirical pressure drop equation:

(out)

− K1 (THMU − T1,HMU , PHMU ) × xCO

The heat of reaction is used to generate HP steam. The HMU temperature is a local degree of freedom in the HMU model within a range.

(14)

PFTS − PFTS − ˘FTS (Ftotal,FTS , PFTS , TFTS , XFTS ; ) = 0

2

(17)

Fi,m

- j ) = 0

(out)

× xH



3.3.3. Energy use by compressors and by air separation units (ASUs) The power consumption of a compressor (single stage) is expressed in the model by: Powercompr =

(16)

The core of the FT synthesis fixed bed reactor model is given by (1)–(4) and (13)–(16). The FT reactor inlet pressure, bed temperature and catalyst volume are local degrees of freedom within their ranges when optimising a design. (D) Hydrogen manufacturing unit (HMU): In this unit only one reaction takes place: CO + H2 O ↔ CO2 + H2 The associated extent of reaction is determined by reaction equilibrium:

1 com

×



Fi,compr × Cp,i

i

 ×T

(in)

×

 1 −

P (out) P (in)

R/Cp,i  (21)

The molar flows, inlet pressure and temperature and the target outlet pressure must be given. Multi-stage compressors with interstage cooling are modelled. The inlet pressure of the first stage is taken a few bars below the outlet pressure of the process unit from which the gas stream is coming. Similarly, the outlet pressure of last stage must be a few bars above the inlet pressure of the process unit of destination. The efficiency factor com makes up for all deviations from the assumptions underlying this equation, e.g., not fully ideal gas conditions. The compressor model is repeatedly applied for the compression of NG to the POx unit, of the syngas from SMR to FT section and of the short and long recycles (see Fig. 7).

J. Ellepola et al. / Computers and Chemical Engineering 42 (2012) 2–14

The power use of the ASU is taken proportional to the oxygen consumption by the POx syngas manufacturing unit: PowerASU = ϕASU × FO2 ,POx

(22)

The oxygen consumption rate is determined by the oxygen-tocarbon ratio of the POx unit which is a degree of freedom in the model. 3.3.4. Utility grid The utility grid is made up of a hierarchy of several levels of utilities {energy carriers: fuel, power, HP, MP, LP steam, condensate and boiler feed water} with generation and transfer units between these levels. At each utility level an energy balance is formulated adding all incoming and outgoing energy flows. There is no storage of energy at any utility level. For those levels dealing with steam and water, the corresponding mass balance over all influent and effluent streams is added. The energy quality per level is not a degree of freedom in the optimisation at this stage; it is fixed, e.g., by setting the corresponding steam pressure level (For examples and more details, see Section 23.6 in Smith (2005).). The utility system will serve more processes than just GTL. The duties exchanged with the other processes are given and kept constant. The connections between the GTL process and the utility system are: • • • •

Fuel – IN: off-gas from FT section; OUT: POx pre-heating and SMR HP steam – IN: cooling of syngas in e.g., POx MP steam – IN: cooling of FT reactors Power – OUT: compressors and ASU

The utility grid offers some degrees of freedom in the optimisation by allowing for manipulation of the transfers from: • • • • • •

Add NG to fuel pool Fuel to power: duty of GT/HRSG Fuel to HP steam: duty of boiler HP steam to power and condensate: duty of steam turbine MP steam to power and LP steam: duty of steam turbine MP steam to power and condensate: duty of steam turbine

• A profit model, reflecting income from product sales minus costs of buy streams and annualised investments. The investment (I) of an equipment item with throughput capacity (C) is obtained from a scaled cost correlation: (23)

• Carbon and energy efficiency expressions The carbon efficiency is defined as: C-eff. =

C-content of TLP C-content in all NG intakes

(24)

The energy efficiency is defined as: E-eff. =

E-content of TLP + power output E-content in all NG intakes

For a flowsheet with a fixed structure and fixed choices of processing technologies the synthesis problem can be cast in a Non Linear Programming (NLP) format. When flow sheet structure is partially set free – e.g., allowing a varying number of stages and parallel reactors per stage – a Mixed Integer Non Linear Programming (MINLP) problem arises, see Eq. (26). max f ( x- , y; p) - x ∈ n , y ∈ {0, 1}q subject to : (26) hi ( x- , y; p) = 0, i = 1, . . . , < n - gi (x- , y; p) ≤ 0, i = + 1, . . . , m - x- L ≤ x- ≤ x- U p ∈ P ⊂ p The degrees of freedom in the continuous variables is (n − ). The solution to this MINLP problem will be numerically determined, see next section. In addition to getting a (global) solution with an overview of active inequality constraints in the optimum, one would like to see also the sensitivity of the optimum to uncertainties in key parameters. Such parameters can be prices of feeds and products as well as some physical parameters in the models of the process units. Suppose that the relevant set of parameters is contained in the vector w. Let z be a sub-set of relevant output variables from the state vector x in (26). Having obtained an optimum solution x* , one could genˆ in the optimum. This erate the local scaled sensitivity matrix, ˙, matrix consists of the scaled partial derivatives of output variables (z) with respect to the parameters (w): ∂ ln zr (w -) ∂ ln ws

in x- = x- ∗ ; z- ⊆ x- ; w ; - ⊆p -

ˆ = matrix{ˆ r,s } ˙

To determine patterns of dominant interactions between paramˆ can be subjected to a eters and outputs this sensitivity matrix, ˙, Singular Value Decomposition:

The performance model is made up of a few objective functions:

Cref

3.5. Remarks on the optimisation problem

(27)

3.4. Performance model

I(C) = I0 + Iref ×

One of these three performance metrics can be used as an objective function in an optimisation, while demanding a threshold performance for the other two.

ˆ r,s =

The transfer units in the utility system are modelled as linear transformations of one energy quality into another one.

 C 0.65

11

(25)

ˆ = U ·  · VT ˙

U, V orthonormal;  diagonal

(28)

i.e., when considering the larger singular values in the left upper corner on the main diagonal of  and the associated singular vectors left (in U) and right (in V) one can analyse which combinations of parameters in w affect the outputs (or combination of outputs z) in the strongest way. 4. Computational and software engineering aspects The process synthesis tool has been implemented in AIMMS because it supports advanced modelling concepts and handling units of measurement which is found very useful in scaling of the problem. Furthermore it includes links to state-of-the-art solvers for major mathematical programming types, e.g., CONOPT and LGO for NLP and BARON for MINLP, it provides user friendly graphical point-and-click user interfaces both for developer and end-user and it allows for the distinction between model and data necessary for generic data-driven systems. CONOPT is a solver for large-scale Non Linear Programming problems (NLP). It is a feasible path solver based on the proven GRG (Generalised Reduced Gradient) method. CONOPT has been designed to be efficient and reliable for a broad class of models. CONOPT ends in an optimum which can be a local or global optimum. The drawback of not knowing whether a local or

12

J. Ellepola et al. / Computers and Chemical Engineering 42 (2012) 2–14

Fig. 8. Process block diagram of key process units and recycle structure.

global optimum is achieved can be removed by applying LGO (the Lipschitz-continuous Global Optimiser) which is a solver arriving at a global solution of general Non Linear Programming (NLP) models. The same holds for BARON (Branch-And-Reduce Optimisation Navigator) which can be applied both to non-linear (NLP) and to Mixed Integer Non Linear Programming (MINLP) methods. The solution of the underlying problem is currently done using CONOPT. The rationale behind starting with CONOPT and not with LGO and/or BARON is that it is considered important to build up experience on possible correlations between optimal solutions and operating variables first. For investigating the presence of local optima provided by the solver the parametric programming and multi-start options are used. This supports the verification and validation process and it also allows for saving cases/data needed for the Singular Value Decomposition approach (refer. Section 3.5). Another advantage of keeping control in the above mentioned approach is that High Performance (Parallel) Computing capabilities can be used possibly in a Virtual Private Cloud environment. For the – currently – limited number of integer choices in the model an automated full enumeration logic has been implemented. As CONOPT is a feasible path and GRG based solver, experience learns that it substantially helps if variables can be initialised such that a feasible starting point is obtained. Non zero starting values also help in ensuring that relevant non zero first order derivatives exist. The strategy implemented to initialise the variables for the complete network is by initialising the variables for a growing sub-network. To do so the units in the network are ordered in sequence based on the incoming streams. This ordering gives the sequence how each unit should be included in the sub-network. Special attention is given to units which will have (weak/short) recycle streams. For these units a coherent group will be defined and added to the network as a group instead of as individual units. In case of long recycle streams the user can specify these to ensure that the coherent groups do not get too large. The rationale behind this procedure is that it mimics the start-up procedure of a plant. Thereafter the utility network and heat integration relations are added to the entire problem in subsequent steps. A typical size of the problem is around 2100 constraints (both equality and inequality constraints), 2100 variables and 6600 nonzeros in the matrix having around 70 degrees of freedom. There are about 650 non-linear constraints. According to other publications (e.g., Chen et al. (2011)) these type of problems can indeed be solved by using LGO and/or BARON. The current NLP model which is smoothly solved by CONOPT however cannot straightaway be solved by LGO or BARON. This indicates that more attention should

be given to scaling and pre-processing, which is part of future R&D work. 5. A sample result Extensive verification and validation tests were performed to build up confidence in unit models, problem formulation and in understanding of the results. Verifications were obtained by comparison with analytical and existing numerical solutions. Validations were done by simulating complex business scenarios in the synthesis tool and in comparison with more rigorous simulation models in process simulators. The benefit of having this synthesis tool is demonstrated by means of a simple, yet realistic example (Fig. 8). Natural gas with a composition (see Table 4) can be allocated to two synthesis gas (SG) manufacturing units with different efficiencies and synthesis gas compositions (characterised by the H2 /CO ratio). The Partial Oxidation (POx) Unit produces a SG that has a slightly lower H2 /CO ratio, requires proportionately more O2 (for the same mass of NG) and is more energy intensive. The Heat Exchange Reforming unit (HER), by contrast, consists of a steam methane reformer and a Partial Oxidation sub-units. Heat from the exothermic reactions in the POx sub-unit is used to drive the endothermic reactions in the steam methane reformer to produce a higher quality (higher H2 /CO ratio) SG more energy efficiently. However, the HER is more expensive to build than the Partial Oxidation Unit. As the HER operates at a lower pressure, SG is compressed before joining SG from the POx unit. The mixed fresh SG is combined with off-gas from the Fischer–Tropsch Reactor (FTR). The off-gas still contains unconverted H2 and CO, albeit at a lower H2 /CO ratio. The combined SG enters the FTR where the Fischer–Tropsch conversion reactions take place converting the H2 and CO into paraffins based on a defined CH2 chain growth probability. Some off-gas is also recycled (long recycle) to the SG manufacturing units to influence the reversible reactions and improve the overall economics and carbon efficiency of SG manufacturing. The FTR’s by-product, water, is treated to meet local environmental legislation. No value is attributed to the produced water in the model. Table 4 Molar composition of treated natural gas entering the gasification units. Natural gas composition CH4

C2+

Inerts

94.21%

0.52%

5.27%

J. Ellepola et al. / Computers and Chemical Engineering 42 (2012) 2–14

13

10%

8.0%

Profit and Carbon Efficiency 9%

7.0%

8%

Annualised Profit change

5.0%

6% 5%

4.0%

4%

3.0%

3%

Carbon Efficiency improvment

6.0% 7%

2.0% 2% 1.0%

1% 0% 50%

55%

60%

65%

70%

75%

80%

85%

90%

95%

0.0% 100%

% of NG routed to Syngas-2 Process Annualised Profit Change (%)

C efficiency improvment

Fig. 9. Profit and carbon efficiency improvement as a function of NG to the Heat Exchange Reforming unit.

In the optimisation the following variables are kept fixed: 1. The mass flow rate of the Total Liquid Product (i.e. C5+) 2. The NG split between the two gasification units is fixed per optimisation case but varies between cases 3. The pressures in the units 4. The number of FT reactors The following variables are allowed to vary within defined upper and lower bounds 1. 2. 3. 4. 5. 6. 7.

Average bed temperature of the FT reactors The inlet mixed feed H2 /CO ratio to FT reactors The outlet H2 /CO ratio in effluent gas of FT reactors The H2 O partial pressure in the FT reactors The flow-rate of off-gas in the short and long recycle The steam to carbon ratio in the SMR The oxygen to carbon ratio in the POx processes

A minimum quantity of NG goes into the fuel header of the utilities system (the rest is made up of off-gasses). When the configuration is optimised on profit, Fig. 9 shows changes in Profit and corresponding Carbon Efficiency when gradually shifting natural gas intake from the POx unit to the more efficient HER unit. With the increasing use of the HER, Carbon Efficiency increases. The resulting profit increases up to a point where the long recycle of unconverted SG with high inert content causes the marginal cost of the more expensive HER to increase more steeply than the increase in carbon efficiency, resulting in a decrease in profit. The total amount of NG intake required to make the fixed quantity of TLP steadily decreases with the increasing use of the HER. The marginal value analysis of the Profit optimised (50/50) case indicated that the binding constraints are: 1. The O2 to Carbon lower bound in POx (i.e. If the O2 /C ratio could be reduced profit could be increased) 2. FT Reactor inlet H2 /CO upper bound

3. FT Reactor outlet H2 /CO lower bound 4. The minimum NG requirement to the integrated utility system’s fuel header. As one moves up to the 90/10 case the binding constraints, 1, vanishes. If the optimisation is carried-out on carbon efficiency for the 50/50 case in addition to the above constraints, the upper bound of the H2 O to the steam methane reformer is also a constraint. The Singular Value Decomposition of the system sensitivity matrix in the 50–50 base case indicates that the objective function Profit is strongly influenced by the H2 /CO ratio of the FTR inlet, the FT reactor temperature and prices of products and natural gas. 6. Conclusions and prospects A modular set-up of a process synthesis tool for GTL plants, implemented as an MINLP problem in AIMMS has been presented. Each of the challenges in setting up a synthesis tool, as mentioned in the Introduction section, will be retrospectively addressed. • Creating a flexible enough (super) structure: Our challenge was to strike a balance between rather obvious extensions of the structure of existing designs (too limited) and a universal scheme covering all conceivable options (too complex). The outcome is having a fair slate of practically proven syngas manufacturing and Fischer–Tropsch reactor technologies, a generic structure for syngas delivery to the Fischer–Tropsch reactor section with recycling of its off-gas, and enough utility units to create flexible energy transfers between utility levels. This scheme is already complicated enough to require interventions in making the MINLP problems converge. • Doing systemic behavioural modelling with model reduction: Grey-box modelling has been applied with rigorous massbalances and an approximate, lumped description of internal rate processes. Achieving matching levels of relative accuracy per unit model within the network and consistency with more mechanistic, detailed reference models was a major modelling effort.

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J. Ellepola et al. / Computers and Chemical Engineering 42 (2012) 2–14

• Proper model scaling and initialisation: The necessary initialisation of the process unit models was done in a sequential manner, unit by unit in downstream direction of the main stream process streams in the flow sheet. Both initialisation and scaling need further attention to enhance convergence of MINLP solvers. • Analysing the robustness and significance of optimisation results in view of underlying model uncertainty: Practical use of the tool demands that a clear interpretation can be given how the degrees of freedom of the optimisation problem have been fixated in the optimum, using a constraint analyser, and which parameters (physical, economic) have the larger influence on the optimum. Meeting future application goals for this tool requires more robust handling of MINLP, an easy introduction of new conversion and separation technologies for quick assessment of potential benefits and, longer term, extension to other feeds (coal, biomass). Regarding the modelling process, a more generic, systematic approach to model reduction (with computational support) is needed to cope with process unit models that are connected within a flow sheet structure. After a reduction effort, the unit models should ideally have consistent, matching levels of predictive accuracy within the flow sheet structure. Acknowledgements The contributions by Bernadette Jona, Sinatra Kho and Cor Hurkens of TU Eindhoven, Applied Mathematics Department, to precursors of the synthesis tool are highly appreciated. References AIMMS manual. (2011). http://www.aimms.com/services/documentation. Bao, B., El-Halwagi, M. M., & Elbasi, N. O. (2010). Simulation, integration, and economic analysis of gas-to-liquid processes. Fuel Processing Technology, 91, 703–713.

Chen, Y., Adams, I. I. T. A., & Barton, P. I. (2011). Optimal design and operation of static energy polygeneration systems. Industrial and Engineering Chemistry Research, 50, 5099–5113. Davis, B. H. (2005). Fischer–Tropsch synthesis: Overview of reactor development and future potentialities. Topics in Catalysis, 32, 143–168. DeKlerk, A. (2011). Fischer–Tropsch refining (1st ed.). Wiley-VCH Verlag GmbH & Co. Hao, X., Djatmiko, M. E., Xu, Y., Wang, Y., Chang, J., & Li, Y. (2008). Simulation analysis of a gas-to-liquid process using aspen plus. Chemical Engineering and Technology, 31, 118–196. Karrupiah, R., & Grossmann, I. E. (2006). Global optimization for the synthesis of integrated water systems in chemical processes. Computers and Chemical Engineering, 30, 650–673. Kim, Y. H., Jun, K. W., Joo, H., Han, C., & Song, I. K. (2009). A simulation study on gasto-liquid (natural gas to Fischer–Tropsch synthetic fuel) process optimization. Chemical Engineering Journal, 155, 427–432. Liu, P., Pistikopoulos, E. N., & Li, Z. (2010). A multi-objective optimization approach to polygeneration energy systems design. AIChE Journal, 56, 1218–1232. Liu, P., Georgiadis, M. C., & Pistikopoulos, E. N. (2011). Advances in energy systems engineering. Industrial and Engineering Chemistry Research, 50, 4915–4926. PRO/II simulator. (2011). http://iom.invensys.com/AP/Pages/SimSci-Esscor ProcessEngSuite PROII.aspx. Reference to the use of BARON. http://cepac.cheme.cmu.edu/pasilectures/sahinidis/ NVSpaperfour.pdf. Reference to use of CONOPT. (2011). http://www.conopt.com/. Reference to the use of LGO. http://www.pinterconsulting.com/PCS Software Summary.pdf. Senden, M. M. G., Punt, A. D., & Hoek, A. (1998). Shell’s Gas-to-liquids processes: current status and future prospects. Studies in Surface Science and Catalysis, 119, 916–961. Schrauwen, F. J. M. (2004). Shell middle distillate synthesis (SMDS) process. In R. A. Meyers (Ed.), Handbook of petroleum refining processes (3rd ed., pp. 15.25–15.40). McGraw-Hill Handbooks (Ch. 15.3) Shell Company. (2011). http://www.shell.com/gtl. Sie, S. T. (1998). Process development and scale up: IV. Case history of the development of a Fischer–Tropsch synthesis process. Reviews in Chemical Engineering, 14(2), 109–157. Smith, R. (2005). Chemical process design and integration. John Wiley & Sons. Wilhelm, D. J., Simbeck, D. R., Karp, A. D., & Dickenson, R. L. (2001). Syngas production for gas-to-liquids applications: Technologies, issues and outlook. Fuel Processing Technology, 71, 139–148.