EP1230006A1

EP1230006A1 - Autothermic reactor circuit for direct coupling of endothermic and exothermic reactions

Info

Publication number: EP1230006A1
Application number: EP00971427A
Authority: EP
Inventors: Jörg FRAUHAMMER; Grigorios Kolios; Gerhart Eigenberger
Original assignee: Universitaet Stuttgart
Current assignee: Universitaet Stuttgart
Priority date: 1999-11-04
Filing date: 2000-11-06
Publication date: 2002-08-14
Also published as: WO2001032302A1; DE19953233A1; AU1029001A

Abstract

A reactor circuit for autothermic coupling of exothermic and endothermic reactions with separate conduction of both reaction flows, comprising heat exchanging sections (2, 9, 19) between all supplied educt gases (1, 4, 8) and all hot product gases (3, 10), in addition to a reaction area (7, 11, 12) wherein exothermic and endothermic reactions occur in a direct exchange of heat, said exchange occurring in the heat exchanging sections (2, 9, 19) between the supplied educt gases (1, 4, 8) and the hot product gases (3, 10, 15) either in a recuperative manner in a counter flow or in a cross-counter flow or in a regenerative manner, the heat capacity of one partial flow in each heat exchanger section corresponding approximately to the heat capacity of the other partial flow, the exothermic and endothermic reaction in one reaction area (7) respectively occurring in a chronologically or spatially separate manner, whereby the two partial areas (11, 12) in the case of a spatial separation are locally coupled to each other in such a way as to result in an excellent exchange of heat therebetween and whereby the exothermic reaction in the case of a spatial and chronological separation is influenced in such a way that it only begins upon arrival in the reaction area thereof (11) and the reaction heat is released in a substantially evenly distributed manner over a relatively large local area which overlaps with the reaction area of the endothermic reaction (12) and is transferred to the endothermic reaction.

Description

Title: Autothermal reactor circuit for the direct coupling of endothermic and exothermic reactions

description

The invention relates to reactor circuits for the autothermal coupling of exothermic and endothermic reactions with separate guidance of the two reaction streams, comprising

Heat exchanger sections between all feed gases and all hot product gases as well as a reaction area in which the exothermic and the endothermic reactions take place in direct heat exchange with one another.

Such a method or circuit serves for the direct coupling of an endothermic synthesis reaction with an exothermic accompanying reaction. Endothermic synthesis reactions play an important role in the production of basic chemicals and intermediates in the chemical industry. These reactions are usually carried out in the gas phase at elevated temperature and often on solid catalysts, in so-called fixed bed reactors. Typical examples are reforming reactions of hydrocarbons to generate synthesis gas and dehydrogenation.

The required heat of reaction is generated by an exothermic accompanying reaction, typically a combustion reaction, and is usually transferred to the reaction gas by indirect heat exchange. The heat transfer takes place in upstream or intermediate heat exchangers, in tube bundle reactors, which are surrounded by a hot heat transfer fluid, or by the reaction tubes filled with catalyst directly in one Combustion chamber are arranged. In these arrangements, the heat input takes place relatively untargeted, so that locally high excess temperatures occur and the product gas remains at high temperatures for a relatively long time, which favors undesirable secondary and subsequent reactions. In addition, the heat contained in the hot exhaust gases can only be recovered with great effort (expensive, high-temperature-resistant heat exchangers) and at a moderate temperature level and can only be used in a suitable energy network.

For this reason, there have been numerous considerations and attempts in the past to generate the required heat of reaction directly in the reaction system and to use it in the sense of an integrated reaction control to such an extent that the inflows and outflows are largely "cold" and no excess heat has to be dissipated. Such a reaction is referred to below as "autothermal", where "cold" corresponds to the temperature at which the starting materials, for. B. after an evaporator or compressor and the heat contained in the drain streams can no longer be used economically.

The basis for a suitable autothermal reaction is therefore the best possible energetic coupling of an exothermic accompanying reaction with the desired endothermic synthesis reaction. A direct regenerative or an indirect recuperative heat exchange between the hot reactor outlet and the cold reactor inlet is expediently proposed.

The prior art includes processes in which primary and secondary reformers for the steam reforming of hydrocarbons are integrated in a common apparatus in such a way that the heat of reaction of the exothermic (ie operated with the use of oxygen) secondary reforming is used to carry out the endothermic primary reforming. Such methods are, for example, in US Pat. No. 4,678,600, US Pat. No. 4,909,808, EP 0 922 666, EP 0 600 621 AI, DE 197 27 841 AI, DE 39 22 446 AI, DE 39 12 003 AI, GB 22 17 728 A. and DE 15 67 709 described. It is known and in part also documented in the exemplary embodiments of the above publications that very high temperature peaks consistently arise in the secondary reformer, which require special reactor materials and precautions to protect the subsequent steam reforming catalysts.

Methods are also known in which strongly endothermic reactions are carried out by coupling with exothermic reactions in direct regenerative or recuperative heat exchange. These are described for example in DE 692 18 518 T2, DE 198 32 386 AI and DE 34 02 713 AI.

With all of these processes, there is either the disadvantage that the heat of the hot product gases is not used sufficiently in the reactor itself, so that an unnecessarily high energy requirement arises, the waste heat having to be coupled out in additional downstream heat exchangers, or that the exothermic partial reaction is very high Temperature peaks occur because it has so far not been possible to allow the heat released in the exothermic reaction to be absorbed directly by the endothermic reaction.

In RF Blanks, TS Wittrig and DA Peterson. Bidirectional Adiabatic Synthesis Gas Generator. Chem.Eng.Sci. , 45: 2407-2413, 1990 a method for steam reforming methane in a reactor with periodic flow reversal is presented. Sufficient oxygen is added to the reaction mixture to make the overall reaction exothermic. Due to the regenerative heat exchange in the reactor, an autothermal reaction is achieved. The experiments show very narrow and high temperature peaks with the risk of catalyst damage, a very high parametric Sensitivity and problems of back reaction and coke formation in the falling part of the temperature profile.

In M. S. Kulkarni and M. P. Dudukovic. Bidirectional Fixed Bed Reactors for Coupling of Exothermic and Endothermic Reactions. AlChE J., 42 (10): 2897-2910, 1996 and M. S. Kulkarni and M. P. Dudukovic. Periodic Operation of Asymmetry Bidirectional Fixed Bed Reactors with Temperature Limitations. Ind. Eng. Chem. Res., 37: 770-781, 1998 the behavior of a reactor with periodic flow reversal for methane steam reforming is also investigated. In contrast to the method described above, the heat of reaction for the endothermic reforming reaction is not provided simultaneously with this. Rather, the reforming gas mixture is fed from one side of the reactor during a half period, and a fuel gas mixture is fed from the other side during the second half period. It turns out that stable operation is only possible in a very narrow operating range and with unsatisfactory behavior. Again, very steep, high temperature peaks are characteristic during the fuel gas phase. Not enough heat can be stored in the narrow high-temperature zones for the subsequent endothermic period.

In G. Kolios. For the autothermal control of styrene synthesis with periodic change of flow direction. No. 501 VDI - Progress Reports, Series 3. VDI-Verlag, Düsseldorf, 1997 it is shown that an inert border zone in this mode of operation improves but not satisfactory behavior overall.

In J. Frauhammer, G. Eigenberger, L. v. Hippel and D. Arntz. A New Reactor Concept for Endothermic High Temperature Reactions. Chem. Eng. Be. 54 (15/16): 3661-3670, 1999 the methane steam reforming instead of using regenerative with recuperative heat exchange in a so-called "Countercurrent fixed bed reactor" examined. A suitable choice of the catalytically active and the inert areas can be used to improve the originally unsatisfactory reactor behavior. However, the disadvantages are a very narrow, steep reaction zone and an overall unsatisfactory heat integration, since the combustion reaction starts and ends purely thermally shortly after the feed before the heat of reaction can be transferred to the endothermic reaction.

In J. Snyder and B. Subramania. A Novel Reverse Flow Stategy for Ethylbenzene Dehydrogenation in a Packed Bed Reactor. Chem. Eng. Sci., 49 (24B): 5585-5601, 1994 and G. Kolios and G. Eigenberger. Styrene Synthesis in a Reverse-Flow Reactor. Chem. Eng. Be. , 54 (15/17): 2637-2646, 1999 an autothermal reaction control with periodic change of flow direction is proposed for the styrene synthesis, in which the heat of reaction is achieved via a hot gas stream fed into the middle of the reaction. Here, too, the heat integration proves to be not entirely satisfactory because the bed area through which the reaction gas and hot gas flow has a higher throughput than the part through which only the reaction gas flows.

All of the above-mentioned methods for autothermal coupling of exothermic and endothermic reactions have serious disadvantages, which can be summarized in the following points:

very high, narrow temperature peaks, caused by spatial or temporal separation of the exothermic and the endothermic reaction zone, uncontrolled (homogeneous) starting of the

Combustion reaction, poor heat integration, ie partial flows leave the reaction system too hot. 0, D- 3 D.

PJ PJ PJ Φ

D- w Ω P

C co tr

P Φ

Ω φ Φ a tr P- P- O a a 0

<Φ rt

Tr 3 dr

P Φ Φ tr X Φ p

P- o P 3 a rt 0) Φ tr r a

Φ φ Φ

P P a 50 rr 3 Φ

Φ> P ⁾ s: c.

P- <01 rt

P o P- o. P c = 0

- P a ^j a φ P

D. PJ C J

P> a c rart IQ Mi w P- CQ IQ

0 tr Φ

Φ a Φ a

P- P- 0 a P- ra 3

Φ 3 i 3

P p- φ s: Φ a

P> = (- ^■

Φ P $.

P 3 p ^→ H- φ P ⁾ P rt a o.

C = PJ a

P C ra <.

D. Ω 0

P- a ^j P

Φ Φ IQ

P Φ

Φ PJ ra

X er Φ

0 CQ tr rt Ω Φ a ^j ta

Φ a

P P- ra

3 rt φ φ rt P- a

Reaction required reactants is carried out separately and is only admixed after entering the partial reaction zone of the exothermic reaction, the uniform local distribution of the heat release being brought about by the fact that the admixture takes place locally continuously or distributed over several discrete feed points.

It can further be provided that the partial flows for the exothermic and endothermic reaction in the reaction space are carried out in co-current or cross-flow with one another and in close thermal contact with one another, with regenerative or regenerative heat exchange taking place.

The invention further relates to a reactor circuit for the autothermal coupling of exothermic and endothermic reactions, in which the heat exchange in the heat exchanger sections between the feed gases supplied and the hot product gases is either recuperative in countercurrent or cross-countercurrent or regenerative and in each heat exchanger section the heat capacity of the one partial stream corresponds approximately to the heat capacity of the other partial flow and the exothermic and endothermic reactions in the reaction area take place simultaneously and together, the total heat release of the exothermic reaction only exceeding the total heat requirement of the endothermic reaction to the extent necessary to maintain the heat exchange in the heat exchanger and a rapid, locally limited course of the exothermic reactions is prevented by one of the reactants required for the exothermic reaction in the reaction region, namely continuously or distributed in several locally distributed discrete feed points.

Furthermore, the invention relates to a reactor circuit for the autothermal coupling of exothermic and endothermic reactions, the heat required for the endothermic reaction thereby is generated that the hot product fluid of the exothermic reaction is mixed with the reaction mixture of the endothermic reaction, the cold feed for each of the two reaction fluids being preheated in a heat exchanger by a hot feed of approximately the same heat capacity, the components being prevented being prevented from being used for the exothermic reaction already reacts in the heat exchanger and the preheated fluid for the exothermic reaction reacts in a combustion chamber, while the preheated reaction mixture of the endothermic reaction enters a reaction space and is mixed there with the hot product from the combustion chamber, the reaction space being designed in this way that an intensive heat transfer parallel to the main flow direction and a quick and complete mixing takes place and part of the hot discharge from the reaction space is used for heat exchange with the cold feed of the reactants for the exothermic reaction.

It can be provided that the reactor circuit converts the heat demand and production rates in the reaction chamber by influencing the catalyst activity by inert admixture or by a sequence of catalytically active and inert areas and / or by setting the inlet temperature into the reaction space either separately or only for the exothermic or only endothermic reactions or for both takes place together.

Finally, it can be provided in the reactor circuit that the adjustment of the heat demand and production rates is achieved by admixing a separately supplied reactant to the exothermic reaction and / or a separately supplied reactant to the endothermic reaction at discrete or continuously distributed feed points over the length of the reaction space becomes.

The invention further relates to a reactor circuit, 3 tr to <D. tr s 50 to D. <Ό S! $ 3. 50 t S • τ) 50 50 φ Φ P ^→ 50 Φ ^► 0 - - tr ϊ-

P- Φ ra Φ p- Φ Φ o Φ ra 0 = P- 0 PJ PJ = PJ: PJ: Φ ra PJ P Φ Φ P P- PJ Φ P- φ y → Q Φ 0 rt P- P φ ra ra tr PJ P Φ PPPJP PJ Ω 0 PJ J a rt PJ on PJ Φ P- tr

D. P ^→ rt rt P- Φ P ^→ P ^→ tQ rt 3 a 3 P ^{→ →} tr D. P ^→ Pϊ- 0 IQ J pr Φ rt rt tQ to ⁾ Φ ι_ι. Φ J Φ s; Φ rt P- rt PJ D. Φ Φ P- Φ D- Φ rt o- P 0 rt rt P Φ y → rt φ rt Φ Φ P-

Φ a a P- P- a tst P- a P- X CQ X PJ φ y → P- a Φ pr P- P- D. tr ^ P- <a Φ a a

£ a y → P rt O a φ O Φ Φ 0 P φ O a J et 0 0 Φ PJ rt 0 o a ra φ 50 0 tr to PJ a rt tr y → CQ H-

Φ <: a Φ P- 0 ra CQ a Φ P? φ aa P 0 P- a cn y → rt a P 0 TJ rt p- p- φ tr Φ rt 0 = rt ra a et r ra PJP tr φ y → PJ 0 tQ y → aa P? φ a Φ a 0 = PJ P Φ P? P- P ^• V Ω P- φ φ ^→ 0 ra P ^→ P CQ tr s: PJ P- D- PP 0 3 a PJ 0 3 PJ PJ Ω CQ tr 3 PJ P Φ 3 p ⁾ ≤ rt tQ D. Ω J P- 3 rt 0 3 CQ 3 CQ P- D. 3 0 = a 0 P tr P- P ^→ P ^→ s- 0 PJ = φ P- Φ Φ tr 0 D. P 3 Φ rt φ Φ P- Ω iQ Φ 3 HP! 3 rt φ a JS! rt P rt PJ = P rt 0 ra P P- rt Φ tr Φ P tr P- tQ tr φ P Φ J PJ: aa ^→ PJ = P- 0 tr P 3 ζ a Φ Ω Φ P Φ P Φ 50 a Φ P a P Φ rt P 0 rt PJ 3 Φ φ

PJ ra tr N tr ay → a <P Φ - a 0 0 to Φ ⁽ Q 3 0 = P 50 0 P- 3 a P- 0 Φ P- rt

R 0 rt 5 *! IX) 0 3 J> D- P- • Ö a Φ Φ P a φ D. <Φ Φ z rt a PJ

IX. a Φ PJ 0 PJ P φ ^→ cn Φ Φ a PJ 0 rt PJ Φ Φ rt P Φ J Φ 0 y → 0 PJ: 3 P- rt rt \ → IQ rt 0 PP tr P iQ P PJ D. iQ P ^→ P a PJ Φ Φ P- 0 ω ra φ P- ra 0 0 = a PJ CQ Φ 50 P- y → P ⁾ PJ Φ D. 0 P- Φ rt 0 P a CQ cn Ω

P- Φ a iQ y → 5 cn φ 0 0 = Φ cn 0 y → a ra φ P- D. 2 ra D. Φ Ω 50 tr

Ω Φ P- Φ Φ ^ ⁾ 2! Φ J a PJ ra P- rt y → o Φ Ω 0 = 0 PJ PJ Ω N φ tr Φ Φ tr a Φ o CQ rt P- tr P ^→ CQ ra a P- φ φ P rt tr φ tr an rt tr 0 a O φ PJ P φ P- 0 = a P PJ PJ P φ rt 0 cn P- Φ P a Φ a P ra ra Φ Φ CQ D. PP?

P a tr D- rt y → tr a P- a iQ PJ - Φ cn P D- rt T P P rt cr_ Φ rt N

D. Φ a 0 ^• Φ 0 Φ ^ y → NP Φ 0 PJ φ P- P TS P P- P- £ s; 3 PJ P Φ P rt y → ra a 0 a P s: 0 rt P- 5 *! rt P- P P- PJ o = φ: a 0 P-

P) PJ = CQ J rt P- ra φ y → P ^→ Φ 0 = PJ: P Φ a PJ tr cn rt ay → PJ 3 P- PJ a cn

P p ra D. ra PJ ra Ω P- t, 0 PJ 0 p- P P a rt Φ rt a φ p- Φ Ω y → 50 CQ Ω

3 3 p- ra P- 0 Ω tr a Φ y- ¹ cn 3 3 t ^{→ →} JP Φ P φ 0 a tr ra o P tr φ Φ Φ cn Ω tr P- P- PJ Φ Φ y → P- Φ PJ P- 0 = y → 3 0 P a P Φ tr PJ φ

P? rt P- φ rt tr Φ Ω rt y → P PJ iQ P 0 aa ^ φ a D. Ω Φ P 50 P 0 a J PJ φ tQ p- tr tQ Φ α = 0 Φ 0 • 0 rt a ra α iQ Φ P- 'a tr φ tr 3

Ό 0 Φ a 0 PJ 0 rt PJ Φ tr tQ t rt Φ Φ PJ 50 Φ P a Φ tQ 0 = cn Φ

PJ ra P ^→ ra Φ a 0 PJ cn tr Φ PJ n P ra aa rt Φ rt <50 rt Φ a P-

N Ω J PJ D. φ ^ ra Φ a P ra 0 = rt Φ rt cn • 0 PJ 0 = P φ Φ rr a D. PJ a

P- tr y → 3 n P Ό a rt tr tr PP P- PP ^→ P Φ 0 = P- P PJ Φ φ Φ → Φ rt Φ rt rt Ω D_, J t φ p- o = P 0 =, - - 0 = <. φ rt a P φ 3 Ps a P ra 3

PJ: P Φ Φ tr P- Φ P- P Φ P rt P 0 3 tr 3 φ a P- D. a ra P- rt J rt aaa φ aa PJ P- <: P? N 3 a 0 Φ 0 a 0 P- rt Φ φ PJ PJ rt Ω P ^→

3 Φ Φ rt Φ 0 = 0 P- IQ a PJ a a φ p- 3 D. a 0 P- 0 φ J s: tS) P- y → to s; P D. P tr a tQ tQ rt IQ 0 = <Φ Φ <D. tQ y →

P- 0 0 P y → P- PJ = rt PJ Φ 3 tQ Φ φ m ra P): P PJ PJ o s; a Φ IQ ≤ Φ φ rt φ P tr φ a a Φ 0 3 P- 0 φ a P- TJ P P 0 0 a Φ PJ: a Φ PJ: P a Φ

Ω PJ: Φ - ra m Φ aaa 0 = P- P- 3 φ cn cn XP £ tr P CQ a '0 Ό Φ M iQ 50 D. tQ s: Φ tr • τ Ω Φ P- rt D. o 3 P- J 3 rt

Φ cn IQ φ a P- Φ Φ Φ φ D PJ: ra P Φ tr rt a P D. Φ rt Φ P Φ 0 φ P N

P tr Φ Ω y → P- tQ PJ a a Φ P 0 cn rt P Φ Φ Φ a tr rt P rt rt 0 0

Φ tr φ ra 0 Φ 0 = 5Y ra 3 a ^• - "0 J rt 3 Φ PJ ~ J 3 y →

N P- ι_ι. P- P- 0 D. a tr rt £. D- Φ tQ a a IQ Φ 0 = P 0 Φ cn 0 1 J

0 ra Φ Ω Ω a Φ CQ P 0 Φ Φ rt 0 tQ ra φ a tr 3 cn X P- ra 0 ra tr tr tQ P Ω rt PP cn → P 3 D.. φ DP φ Ω PJ oa Ω 0 ⁾ φ Φ rt 3 Φ tr D. 0 P): P- Φ cn 0 p- φ P- tr cn rt D t

0 ra PJ: a PJ PJ ra Φ • O P- tQ rt P rt P IQ a iQ 50 φ cn tr - Φ Φ 0 s Φ CÖ 0 P- P- rt ay → D. Φ PJ rt a Φ Φ P φ PP a

P P- CQ a Φ • 0 cn P iQ Φ P Φ a PJ O ^→ P 0

Φ tQ o φ P- cn 0 P- P? P- rt Φ 3

PJ: rt a 3 ^

P 0 Φ a a Φ rt J P- φ D P- P Φ

0 - → P- ra 0 = Φ Φ P- a a rt Φ P- tQ a P 3 D. 0 Φ 0 a

Φ rt Φ a N Φ P 1 3

50 ⁾ 0

Φ t? a a

PJ Φ IQ D. x P Φ ^, rt y → tQ 0

P- J y → D.

0 T P- Φ a. Ω P cn 0 tr

N a φ D.

0 ⁽ Q a 0 a cn P

Φ tr s Ω

Φ Φ tr

Φ P P

P Φ Di 3 Q P- Φ PJ

P- Ω a Ω tr tr tr rt Di

• N D. 0

SS J ra

P- CQ P- ra CQ Φ

Ω P tr CQ 0

Φ P- aa Ω ⁽ Q tr

Φ <a Φ o

Di P- a

0 a rt to tr 3 D- φ 0 = 0

P tQ x

3 y → rt φ φ

P Ω a tr

0 CQ CQ a rt O

The tQ J

Φ P a

X O Φ

0 CQ P- rt CQ a tr Φ PJ

Φ P a

P Tue

3 Φ

Φ P

P

Finally, it can be provided that the avoidance or reduction of strong temperature fluctuations in the reaction space is brought about by the fact that the reaction mixture for the exothermic reaction and the reaction mixture for the endothermic reaction flow through the reaction space in cocurrent.

The problem solution according to the invention is based on the one hand on ensuring an optimal heat exchange between the hot outlet and the cold inlet. As is well known, such an optimal heat exchange can only take place via an indirect countercurrent heat exchange or a sufficiently rapid direct regenerative heat exchange if the material flows fed in and out in both directions per unit of time have the same heat capacities.

A first characteristic of the problem solution according to the invention is that the material flows in the heat exchange each have the same heat capacities. Since the heat capacity changes due to temperature changes and chemical reactions, this requirement can only be met in practice with a certain range.

The second requirement is that steep, high temperature peaks must be avoided. As the examples known from the prior art show, these temperature peaks always arise because the accompanying exothermic reaction proceeds very quickly, quasi spontaneously and spatially separately from the endothermic reaction. Particularly when the exothermic and endothermic reactions are conducted countercurrently, there is a pronounced tendency of the two reaction zones to separate from one another locally. The higher the reaction rates of the two partial streams, the greater the tendency.

The second characteristic according to the invention thus says D. 3 X 3

Φ Φ 0 φ a μ- a tr rt rt P

0 = φ μ- Φ tr P a P

P Φ 0 Φ μ- μ- Q S Φ 0 =

Φ φ P tr a P y → Φ

X μ- P s 3 Ω

PJ tr D-

3 y → P-

Φ Φ <φ y → Φ

D- 0 P tQ

0 a rt Φ a Di Φ sS Q P- 0 = D <y → a

0 o rt CD a P Φ Ω rt rt tr

Φ φ t rt

P P- μ- Φ y → \ → a

PJ φ cn 50 Q TJ Φ

Φ Di Φ PJ a Φ μ- X

• P cn rt φ P- t 0 O

P P

Hi rt a ra μ- Φ cn a rt

Tue PJ P

0 0 Φ a Hl Ω

CQ N X

0 Φ φ cn

P ts α tQ P ⁾ μ- φ y → ra tr et X

Φ φ P a a Φ rt

CD μ- 0

Ω Di tr Φ

P

PJ

0

CD

Exemplary embodiments of the invention are to be illustrated below with the aid of a drawing. Show:

FIG. 1 a shows a reactor circuit according to the invention, FIG. 1 b shows the temperature profiles to be expected in the individual sections according to FIG. 1 a, FIG. 2 a shows an embodiment of the invention in the event that the exothermic and the endothermic reaction takes place in the same reaction mixture, FIG. 2 b shows the temperature profiles according to FIG. 2 a, Figure 3a shows a special case of separate reaction control with replenishment of a reactant for the exothermic

3b, the temperature profiles for FIG. 3a, FIG. 4a an embodiment with recuperative heat exchange in which the heat is supplied for the endothermic reaction by admixing hot burner gas, FIG. 4b the temperature profiles for FIG. 4a, FIG. 5 a structure with regenerative heat exchange and

Hot gas feed and Figure 6a to 6c configurations of the reaction chamber.

FIG. 1 a shows a basic form of the embodiment according to the invention in the event that the flows of the endothermic synthesis reaction and the exothermic accompanying reaction have to be carried out separately, ie they must not be mixed (“separate reaction control”). The reaction medium of the exothermic reaction 1 is fed into the reaction space 7 via a heat exchanger 2. The exhaust gas from the exothermic reaction 3 leaves the reaction space 7 and releases its heat in the heat exchanger 2 to the inlet. For reasons of energy efficiency, the heat exchanger 2 will expediently be a countercurrent or cross-countercurrent heat exchanger. Alternatively, regenerative heat exchangers in a clocked single or multiple bed or rotor arrangement are also suitable. In N t

B cn S P- 50 3 D. ra 0 50 Ü <φ o rt Φ D. O α 50 to tr D. φ Φ Ό 2: N 50 <sS P- rt J 3 Φ 0 = 0 rt a Φ Φ O 0 = a P- tr μ- Φ D. 3 φ PN P- P- X PJ PJ = 0 Φ φ

Φ a P) PJ IQ P φ rt J P P P rt φ D. φ 3 P Φ rt PJ N sS φ 3 0 y → P IQ PJ P

Ω rt PJ o 3 50 X Ω tr Φ X P ra P- P Φ P Φ X P- CD rt y → 3 φ X IQ

X P a 3 PJ Φ et P- tr φ P rt 50 φ D. • Ö μ- P 3 3 50 P rt Φ Φ 50 tr φ rt y →

3 μ- tQ tr PJ μ- Ω a rt μ- Φ PJ μ- P 3 Φ μ- Φ 0 = CQ P- y → P- P Φ φ rt 0 = μ- φ

PJ = rt ra oo 3 X 0 tr. Φ 0 PJ X Φ Φ X CD iQ PJ P Ω O 0 3 PJ PJ tr O μ- i ö rt P φ rt a ra μ- μ- a X et Ω Ό et Ω Φ X rt tr 3 3 50 X 3 μ - 0 P 3 Ω μ- φ s P- rt φ N y → et P- cn tr μ- tr P rt y → 0 ra tQ 50 Φ rt Φ φ CD rt tr

IQ μ- PJ p- D- O N μ- et 0 P- 0 φ φ iQ N φ μ- PJ ra P Φ J PJ Ω 00 tr

Φ a X φ PJ a 0 <φ Φ ~ a 0 a μ- a 0 0 3 3 Ω cn PJ Φ PJ X 3 50 Q tr 0 J

P et POX y → a rt P IQ 5 ^ IQ rt tr X 0 P- X rt Φ Φ Φ 3 0 = P sS y- p- 0 = PJ 0 = y → O sS ω μ- φ φ Φ 0 Φ 0 3 3 rt μ- PJ PD tr Φ φ Φ 0 a P 0 tr y → rt 0 Φ P 3 y → Ό 3 ^ <3 Φ P- 0 X PJ φ P

P- a a 3 Φ ra tr Φ tr μ- PJ> PJ 0 = • Φ T 0 P 0 3 rt tr SS) D- P ra CD Ό μ- P rt Φ P Φ a 0 2! Tr 0 tr y → 21 P- P 0 3. -. μ- P J 2:

Φ 50 tQ μ- rt PJ = P μ- Φ 3 PJ = P PJ P 0 PJ = 3 rt a X iQ ra CQ t i O PJ CD φ Φ

Φ φ ^| Q rt P a 3 Ω a P rt 3 rt 3 P Φ Φ PJ y → P Φ sS 3 tr tr μ- μ- cn PJ CD 0 <! PJ D. Φ Φ tr o 3 Φ Φ iQ iQ 3 <P- 3 3 φ ⁾ rt φ Φ IQ tQ

Φ a ra

O X Ω P IQ P- cn Φ ω Φ P- φ s

50 rt μ- a Φ Φ y → rt 3 0 P Ω y → cn Φ Φ φ rt tr μ- P Φ ⁽ Q Φ μ- rt D. y → Φ 3 XP rt Φ Ω 3 Φ 5V rt tr 3 iQ μ - sS y → φ 3 a Φ PJ D- P ra J o 0 Φ P μ- PJ iQ Φ tr a 3 ra Φ 0 = μ- sS φ O P- PJ P- • 0 PJ y → φ Φ rt 0 rt a 0 D. rt TJ y → P- N CD 0 a PJ = Ω tr tr y → 2; μ- sS aa Ω φ a X et P- CD tr tQ rt Φ PJ Φ 3 0 PJ = rt tr rt P D PJ = P

PJ: cn y → CD rt 0 ω Ω μ- Ω Φ Φ 3 tsi P- cn ISI Λ N P- 0 _^ rt Φ P D. tr P μ- J Φ Φ 0 μ- a Φ tr a tr PC rt φ μ- Ω D. PJ = sS μ- 0 N CQ 3 • rt 3 y → J tQ P μ- a (Q 0 IQ P Φ 3 Φ 3 rt tr Φ rt Φ iQ IQ 0 φ Φ Φ D. rt 0 X tQ Ω y → a φ y → Φ P φ P P- PJ: 3 N Ω Φ Φ tQ P PJ rt J

3 Φ φ tr sS PJ Φ P- _o μ- a 3 21 rt N y → X a 3 Φ sS 3 ω TJ J CD sS μ- ra ra φ CD μ- Φ Ω a oo N PJ: CD 0 50 P- 3 P- Φ cn P 0

Φ rt rt rt P cn Ω P ra tr φ 50 0 2! Φ P D Φ Ω PJ = 2; ra 0 = P- 21 0 CD 50

P t Φ P D- tr φ φ 0 = a PJ φ CQ P): P 3 rt PJ 3- L »P ⁾ : Ω tr ra PJ: D. Ω Φ

D. y → 0 Φ cn 3 μ- 50 P 0 J Φ P 3 Φ P φ X μ- H tr P φ P PJ 0 tr PJ

Φ ra Φ y → 3 a rt P> = iQ Φ μ- to CD X 3 rt 0 3 rt J ^| Q 3 rt rt 3 ra X Φ X ao P et PJ I) φ J a Φ iQ rt 0 = Φ PJ PJ 3 P- 3 φ Φ rt P et

- • 0 = P μ- cn X μ- P φ μ- tr rt y → 0 0 = O ra 0: sS 0 μ- rt 50 IQ y → Φ tr t X CQ φ et μ- φ Φ ra o P ⁾ y → CD tr 3 3 φ tr Φ 3 φ P ⁾ Φ Φ SO 0 rt a ü P μ- φ rt μ- a μ- Ω a rt 0 ra Ω JP CD Φ μ- Φ P 0, 0 PJ 3 3 J Φ D. P- 0 a PJ N 0 rt φ Ω tr Φ cn tr P P- P £ T 3 P D. CD X μ- cn

CD o φ a Φ Hl 0 rt a Φ a tr y → Φ a Ω ra φ CD CQ J P - rt Φ Φ 3 Ω rt cn Φ iQ

CD rt CQ φ Φ cn a D- 0 P tr o P rt φ 0 Φ P 3 P rt tr μ- Ω 3 φ

PJ tr Φ 3 P ra 0 y → cn 50 φ y → Φ 3 3 P D. PJ cn Φ Φ 0 tr 3 α tr φ <PO s: PJ μ- rt y → cn 0 φ P y → ty → φ μ - IQ, - rt PP 3 50 μ-

Φ P o φ μ- PJ = 0 <! tr φ PJ et y → 50 Φ 3 φ 0 t CD CD y → Φ ra φ P- 3 a P φ P 3 φ Φ a iQ X to φ D. rt φ P- a P- 0 Ω to ⁽ Q PJ Ω

Φ a PJ 3 cn 3 P 0 = φ t Φ - ⁾ 3 CΛ CQ 3 3 tr Φ X tr s: a CD rt φ Φ 3 P sS a J φ ra 3 XN rt cn 3 0 P 3 rt

PJ: rt 0 0 ao ≤ Φ Φ a P φ X et 0 Φ P- ^h rj μ- ra φ μ- 0 μ-

P 50 P a P D- y → PJ = P μ- 50 J J CD y → 3 Φ rt ra PJ ra P 0 φ

3 Φ 0 IQ CD 0 0 P- P 50 μ- φ 0 3 Φ 3 3 ^• ny → P- rt X i Ω Ω 3 P φ J 3 D Ω rt X cn 3 Φ φ Φ PJ ay → φ J 3 rt Φ φ ra Φ 0 P- tr tr CD tr X tQ tr tr PJ rt φ PJ ay → IQ X Φ P- 3 y → 3 Φ P Φ

Φ rt y → Φ sS φ y → PJ X Φ y → X Φ et Φ 3 ra 3 tr * Ό P D. P ⁾ 3

D. 3 JP φ 0 et X cn ω PJ 3 0 P- P φ c IQ PJ 0 rt 0 = Φ 0 D. J 0 0 PJ = a 3 D ra y → - O 0 a 0 H 3 P 3 - P 3 3 0

P a a tΛ X φ - rt 0 rt y → Φ a tr 3 0 • y → in Φ rt

Φ 0 PJ a tr y → p- M φ CD tr 3 0 ^ ~ - <J 3 3 -J 3 ^*

CD PJ a 0 Φ • a PJ P- μ- P 3 0> X 0 rt 0 μ- Φ

P 3 IQ μ- cn P φ 0 3 N J Φ P PJ PJ P Φ cn φ P

PJ Φ φ Ω 3 Ω Φ 0 0 y → y → N CQ 3 rt a tr Φ tr 3 3 y → 0 Φ φ tQ ra P 3

D. μ-

P

Φ

X et

PJ

0

Wed.

3 φ tr

3

Φ

3

•

tr PJ IQ \. PJ V sS 2! 2! 3 cn Φ Ω D. Ω D. 3 Pl <3 5 50 N 0 50 N Pl o N CD PJ 50 Φ H

Φ ry → Φ Ω 3 P P- PJ: PJ = PJ μ- P y → Φ Φ Φ J Φ φ 0 = PJ Φ 0 D. Φ s ^> Φ P 0 0 y → Φ P- a ra CD y → rt Φ CQ P- PPP Ω φ Q φ 3 CQ P Ω 3 P CQ rt PJ 3 Φ Hi φ 3 Φ IQ 3 ra PJ 3 rt rt φ PJ CQ rt 3 D. 3 3 tr Φ P- Φ tr T3 tr y → PJ XP 0 Ω TJ 3 Φ CD X Φ φ

0 = P 3 X Φ Φ N Φ Φ X tr Ω 2! 3 3 Φ P P- y → et tr P X Φ 3 3 rt 50 et P-

Ω o = rt 3 y → P- rt * o Q o-- Φ tr PJ = CD PJ = Ό P Φ Ω ^ Φ 1 3 3 P CQ μ- p- φ P- O a

X 3 D. Φ ω y → OPP y → 3 3 cn P rt tr μ- PJ 3 tr ra 0 μ- D. μ- PJ = PJ PJ cn ^| Q PJ 0 PJ φ φ rt μ- rt rt φ μ- PJ 0 φ 3 rt 3 P φ CQ rt 3 CD PJ 3 CΛ PJ φ Λ rt cn Ω φ X 3 3 P

3 Φ cn φ P φ 3 Di μ- φ ra P Φ O P 0 0 0 rt rt ra Φ 3 P P- 0 ra tr CD et ra TJ

- μ- XP 0 Di y → ra 0 Ω 3 μ- O rt 3 0 PP 3 o P 3 ^< n iQ iQ P Φ rt PJ tQ Hi t ^→ y → 0 3 φ y → • ö X tr Ω 3 J sS 3 Ό CQ 3 P PJ Hl PJ Φ μ-. tr 3 φ P 0

Hi rt 0 1 P O et Φ sS tr sS 0 PJ: iQ \ → P CD J 0 ra P PJ rt p Di 3 φ 3

PJ y → μ- D. * ~~ PJ = P P- 3 Φ PJ: CD P cn PJ 0 P tr D. 3 έr 0 ra SS 3 Φ ü Φ μ- Hi X y → o Φ Φ tr tr rt 0 μ- μ- P Ω 3 sS Hi Φ Φ P- ra y → 3 φ Φ μ- 3 ιl ra 0 P y → PPX μ- 3 3 rt 3 3 tr Φ Φ ra P- PJ φ PJ D. P- P - Φ y → Φ 3 Ω P φ ra Di rt PJ: φ y → Φ Φ Φ rt P- μ- y → X tr o 0 rt cn μ- y → cn Φ tr 3 rt φ Φ PPP μ- 0 tr Mi P 50 rr P PJ ra 3 φ rt N ü Hl 2. Φ Φ 3 <rt μ- P- μ- φ ra 3 0 3 Ω P Φ PJ φ PJ 3 0 φ Di P- sS PJ NP ⁾ φ Di φ 0 3 y → φ ω μ- rt Φ P ⁾ tr Ω ra 3 IQ PJ 0 ω μ- 0 3 0 PJ CD J 3 Φ P Mi P μ-

3 S! Ό μ- rt 3 Φ tr ra Q φ X cn sS Ω iQ CD 3 3 TJ IQ 0 CD P- 3 cn tr Mi pl N 0 φ

PJ = PJ: Φ PJ CQ φ cn Q rt Ω Φ tr y → Ω D. Hi Φ Hl Φ P O P P φ 0 3 P sS P y → P 0 Φ μ. D- P P y → tr P- φ φ tr Di PJ P Mi CQ P Di Φ X 5 Φ Φ μ- 3 CQ 0

PJ 3 y → Φ CQ 3 Φ p- PJ PJ = 0 rt P μ- φ φ 3 P φ 0 = Φ D- μ- μ- Φ 3 μ- y → 3 ra φ Φ 3 Ω o 3 Φ φ et rt 3 0 IQ 3 Ω 3 3 IQ φ Hi tr tr PJ Φ 3 D. J 3 Ω to <! CQ ω rt 3 D- tr 3 TJ P Φ rt ra 3 Φ tr PJ Φ X o P Φ 3 P- Φ PJ X 0 tr D. φ o

Φ J Φ Φ 3 φ PJ Mi a φ P D. tr to Φ rt φ O et P rt μ- TJ 3 P rt et 3 Φ φ μ- 3 Di

P 0 XPP Φ P 3 0 = rt PJ Φ 3 μ- μ- P 3 • N Mi Φ μ- μ- CQ cn P ra Φ ra cn PJ 3 PJ IQ y → Mi 0 D- 3 cn 3 D. PJ P - rt T_. o 0 CD Ό: P rt Ω 3 50 Φ rt Φ y → 0 = s * 3 μ- D. SO 2! Ω N 3 0 φ σ P- S 0 3 3 P _^ -> to μ- 0

O tr 3 Φ φ 3 0 Hi rt P Φ φ PJ: tr φ Φ Hi P 0 0 3 μ- P CD ω Φ μ- φ tr <

Mi φ ra CQ P 0 = P -o IQ cn P rt 0 P 3 ra 0 = X P PJ & 3 y → y → 0

Mi P Φ rt Φ Ω <tr sS 2! D. cn Φ P- 3 μ- 3 Di 3 rt Di 2! Ω CD PJ PJ X 1 cn Φ P c

P ω CD tr 3 Φ Φ P P- PJ = Φ μ- φ P 3 Φ 3 Φ CD Φ IQ PJ: tr Φ rt 0 et - PJ PJ 3 ra φ Φ Φ IQ P rt PP 3 3 μ- J D. X 3 Φ 3 Hi D. P 0 3 PJ 3 μ- Ω rt 0 sS rt

P- N rt P Φ y → Φ Di 3 "- rt Di PJ ^► 0 P- CD μ- Φ 3 3 y → ra 0 PJ N ra PJ φ

Ω sS rt PJ 3 PJ = 3 Φ Φ Φ Φ D- TJ μ- 3 2! rt 3 P φ CQ Pl * <3 cn X CD tr tr 3 Φ Φ rt CD 0 0 <sS rt 3 μ- PJ CQ tr PJ = P ⁾ D. rt P cn o 0 t- ⁱ cn Φ

Φ p- Ω 3 μ- rt Hl S 3 Φ Φ sS Φ 0 φ N 0 ra ra P et Φ 50 PJ <PJ: PJ y → PJ tr 0 φ 3 cn rt X <! P Φ PJ D. P 3 PJ μ- 3 P- P Ω 0 3 rt rt Φ 0 0 tQ rt <_ι. PJ: 3 y → Hi P Di

3 Φ sS 0 tΛ \, tr 3 3 D. Pl rt tr y → φ - Hl CD 3 Φ O Φ 0 φ rt cn Φ cn PJ = μ- PJ: 3 Φ 3 OP D- ra Φ PJ = y → 3 y → rt J 0 Ω PP Hi Di 3 rt 3 o tr i> 3 P 1 P PJ Di PJ D- μ- Ό * Ü 3 rt tr μ- • PJ sS 3 P tr 5 *! CD 3 rt Φ sS tr 0 o μ- μ- Q 3 IQ tr Φ 0 P- φ φ J TJ CD rt 0 0 3 Φ 0 rt 0 P ⁾ 3 J Φ Hi>

1 Hi IQ Φ Φ Φ 3 P Ω Φ μ- P φ CD PJ rt O D tr Φ P- P tr Di Ω J cn cn Mi 0

PJ rt ra rt 0 tr Φ tr IQ ra PJ P rt 3 Φ P- Ω Φ μ- φ y → 0 Φ tr 0 t cn rt φ cn

P X CD φ PJ Di Φ 3 D. 0 Φ 0 y → PJ P IQ 3 φ tr P- 3 P SΩ φ X P Hi μ- φ φ a CQ

3 PJ Φ rt 0 Φ 3 Φ 0 • N 3 y → rt 0 = Φ Hi Φ Q 3 et Φ 3 P tr φ φ rt μ- N CD P <P 3 Φ IQ φ 0 3 CQ Di N y → D- 3 PJ μ- sS 0 tr P D. ra n Φ sS cn cn J 3 rt Ω CD Φ D- CQ μ- y → P Φ Φ Φ 0 PJ = Φ CD 3 JP o Mi φ • n rt 3 P- rt

- y → tr 5: P- P PJ Q <! • O tr cn Ω P CQ cn ra 3 o P Φ 0 • P PJ

^ sS Φ P Ω tr X rr OP μ- Φ Φ tr Φ Φ Ω ra J o P μ- Mi D- y → t) ra Φ p Φ tr Φ μ- • 0 Φ 3 O 0 3 3 <P Φ « Φ P- Φ φ tr CQ Di ra Hi H et

P J Φ P 0 CD PJ 0 3 0 Hi • φ sS 3 J μ- rt CQ P • Φ Φ 0 Φ tr D. 0

0 rt 3 Di μ- IS) cn y → P to P P- P J rt IQ φ φ ra 3 P 3 3 PJ 3

D- O Φ 3 1 sS Φ φ Di T) P Ω y → Φ Hi P IS) PJ 3 a rt> y → iQ 0 cn iQ

0 P 3 Φ p Φ P Φ tr φ 3 3 PJ rt 0 y → Φ y → CD O 0 0 P- φ Di sS

X Φ Ό a rt P 0 3 Hi tr Φ P ^> rt t rt Hi Hi 3 Ω 3 Φ p- M rt 3 0 a 0 Mi 3 Di μ- o P 3 CD Φ P Hi D. tr PP 0 =

CQ y →, p 3 P- CQ Φ 3 y → Φ J 3 0 Q Di φ cn D. PJN 3 3 Q y → J 3 CQ 3 Φ rt Φ 3 PJ φ P - Φ n 0 Φ CD φ ra 3 0 D ra P P- P σ. 3

50 Φ

Φ a

PJ rt

X cn et V y → - P

0 Φ

3 Ω cn tr

P Φ

PJ 3

0 D-

3 dr

H 0 cn tr

Φ

PJ a

0

Ω H tr Φ

3Q TJ

PJ φ a P

N PJ rt

Φ 0

3 P rt φ

3

PJ y → X y → PJ φ 3

3 3 sS Φ

Φ P

3

3 5 ^

PJ

D- rt

P- PJ

Φ y →

* <tr ra o PJ

3 rt

0 O Q P

Φ

3 P- φ 3

3

Reactions are sufficiently quick. Then it makes sense to provide 14 catalysts for post-reforming or the water gas shift reaction in the outflow part of the heat exchanger.

The temperature profiles to be expected according to the configuration in FIG. 2a are indicated schematically in FIG. 2b. For a countercurrent heat exchange in the heat exchanger 14 there are again approximately straight and parallel profiles. In the reaction chamber 16, the overshoot of the temperature caused by the preferential starting of the exothermic combustion reaction is less, the better the additional heat transport was realized parallel to the main flow direction.

Figure 3a shows a special case of the separate

Reaction control when the heat capacity of the fluid stream 1, 3 for the exothermic reaction and that of the fluid stream 8, 10 for the endothermic reaction is approximately the same. Then, instead of the arrangement according to FIG. 1 a with separate heat exchangers 2, 9, an arrangement with a common countercurrent heat exchanger can also be selected, in which the reaction space 7 is also integrated.

In contrast to known counter-current arrangements of similar design, for example according to J. Frauhammer, G. Eigenberger, L. v. Hippel and D. Arntz. A New Reactor Concept for Endothermic High Temperature Reactions. Chem. Eng. Be. 54 (15/16): 3661-3670, 1999 an embodiment according to the invention according to FIG. 3a must meet the conditions that the heat capacity flows 1, 3, 8 and 10 are similar, that is to say they do not differ by more than a factor of 2 and one The reactant 4 is fed in or multiple feeds into the sub-space 11 of the reaction zone 7. With regard to the appropriate choice of the catalyst activity of the endothermic reaction, what was said in the discussion of FIG. 1 applies. It is also expedient that the axial heat transfer in the area of the reaction zone 7 by heat-conducting internals or 50 Φ dr

Φ P- φ

PJ 3 μ-

X CQ CΛ et Φ φ

P- 3

0 P- tö

3 CQ P ra Ω φ

P tr 3

PJ rt 3

0 Q

3 sS P> cn P-CD

P μ> Di PJ t • y → ra sS t μ- P- 2:

P 3 PJ =

D- P pl 3

0 = Φ φ tr P- rt φ y → P

P D PJ = et IQ

D. P Φ φ 0 P a 3

PJ to ω 3

P

Φ D. Di

3 Φ Φ

3 CD 3 Q

PJ? cn

CD rr

SS y → Φ

PJ = J y →

P 0 y →

3 Mi Φ φ CD 3 rt J Di in

0 Φ

CD cn 0

Ω 3 tr Di

Φ

P cn t

to ≤ <; X 3 p- sS 50 Hl Φ 2: PJ 50 iQ φ Pl 2! tQ

P- Φ Φ 0 PJ 3 P- Φ 0 = P- φ 0 e Di i Φ 2! σ sS D. σ to PJ P- <N

Φ Φ 3 PJ Φ P- 0 0 P- 3 3 0 0 φ Φ P- Φ PJ = Φ

3 μ- P 3 Ω P CQ P a Ω Ω m P a rt tr tr PPP 3 D- 3 CD P ⁾ 3 3 P- P Hi rt tt rt tr * Di φ Φ tr tr rt CQ ra ^• Di Ω Ω φ y ^→ PJ = X PJ: Φ y → 3 0 =

> CQ Φ μ- Φ 3 Di CD Φ <50 Φ Φ Di tr tr D- sS P- cn rt rt tr) CQ Φ tr

0 Φ P- 3 y → P 3 Φ P- Φ φ N y → O Φ CQ P P o Hi 0 O CQ rt N P- Φ rt X P

Hl tr y → 0 P- P- 0 P φ ay → ≤ y → y → PJ Φ Di P- sS t 0 =% P tr 0 P y → 0 ^► a P PJ rt tr φ et μ- 3 o 3 PJ rt Φ φ 0 X 3 PJ Φ Φ rt tr 0 Ω Φ P 0 P- 3 P- Φ 0 = • d.

PJ 3 • φ X D. rt to CD P- 3 rt s≤ 3 P Ω tr P P tr P- 3 Ω cn tQ P 3 J

0 D. P ra P- CQ μ- P • d φ Φ J μ-. PJ X ^< 0 Di to tr P 0 Q φ N ö ö y → ra Φ <d Φ PPP φ 3 3 P Hi r 3 y → 3 3 ra D- PJ co φ PJ P Φ P- μ-

3 D. P- P- D. Ω 3 ς a φ φ ra <Di X CQ PJ = tr Q 0 P- P- 0 rt y → rt φ

PJ Φ Φ Ω 0 tr Φ PJ = a Ω cn CQ Φ Φ rt PJ ca Φ 3 Φ Φ Ml Φ 2; 3 ιP »P- PJ = ra

Ω 3 tr P Φ μ- P X tr rt Φ P P 3 Di ra P- 3 <IQ 0 = P PJ = tr CQ 0 rt φ tr l_J. Pl Ω 3 3 3 PJ φ P 3 φ 3 • d 0 Φ Φ CQ to 0 <cn PNPM • Ω 3 P φ φ P- tr CD Φ 3 a 0 = Φ X Φ PJ 3 P ra 0 3 3 Φ rt Φ 3 t tr Di P-

3 3 3 ra 2; PJ rt 3 D. 3 P 0 tr P D- Di y → PJ P P D. 0 φ u 3 pl

P- μ- ^• τt rt φ 3 PJ Φ Φ 0 J • d P rt Φ Φ 0 1 α Ω rt o = Φ CQ ra y → P- 0 | t Φ Q CQ Φ D. P Ω 0 P 3 rt Φ Φ t μ- PP α Φ tr Φ 3 3 rt rt PJ φ O Φ p-

0 Φ P Φ 0 = tr 3 ra CQ p- P 3 PJ 3 3 N Ω Φ tr μ- Φ P cn rt φ rt y →

P 3 PJ 3 3 ra μ- Ω y → 0 CD <PJ D- y → Φ Φ Φ tr tr ^ Ό y → 50 sS 0 = cn 0 = P- 3 sS ra rt rt φ rt tr 00 CD P Φ rt Φ Di PP 0 * <i P- rt 00 Φ Φ 3 φ P 3 rt PJ rt in <! 0 50 • y → Φ CQ P- μ- 3 P rt CQ ra D. P CQ PJ P Φ 3 rt PJ CQ P

0 P Φ i P sS Φ Ω 2! <0 CQ <rt rt P P- 0 s X D. y → y → • d Di 0

X 3 <! PJ σ <φ Φ ra tr PJ = Φ 50 Ω PJ Φ • 0 = μ- Φ P φ σi rt Φ O ra P- Φ P Φ 3

PJ Φ X J 0 3 y → P rt et P 3 Φ X cn P Ω φ P P - P- 3 PJ P- Ω p- P

3 • P et D 3 SO Ω. PJ 0 3 PJ - X t tr P P> f> D. 0 P Ω tr 50 Ω ra

3 μ- y → P- tr Φ y → 3 Φ 2; X PJ 0 ra y → - 0 Φ PJ Φ cn 3 PJ tr Φ 0 = tr 21 0

CQ PJ = o to y → Φ y → - 3 et CQ rt PJ = rt tr Di X 0 3 J 3 ra> y → 3 Ω rt PJ = M

PJ 0 0 3 P μ- μ- 3 0 JP P- CD PJ 0 Φ 3 iQ X φ • P- P 0 y → sS X • PP ¹

0 P Hl CD Φ 3 Di rt N 3 Φ 0 3 O φ CD 3 3 φ • rt μ- 3 PJ Ω φ P- Pl tQ 3

Ω Φ P 3 X φ Φ sS iQ μ- cn Φ 3 3 CQ rt rt μ- CQ 0 tr y → φ Φ Φ α φ CD tr Φ> PJ 3 CD 3 IQ Φ • 3 Ω rt X CQ tr P ö O 3 Di 3 Di 3 sS JXO tr Φ 0 Φ P Ω iQ tr J CQ rt Φ D. PJ: P- PJ 3 Φ P- tr N Φ ^→ J P- 3 PJ

Hi 3 3 P 3 50 P- X σ Φ Φ 0 0 = 3 Φ y → ra CQ Φ rt Φ μ> P- 0 P Φ 3 3 • d IQ

0 = rt PJ PJ Φ Φ 3 P- ra P CD 3 0 Φ CD rt Ω 3 cn φ P P 3 PJ P

P CD y → tr Ω tQ P PJ = Φ φ Ω CD 3 μ- tr tr CD J P Di PJ 0 Hi to 0

^• x) to CQ tr Φ rt EΛ rt H tr rt Di 3 Di Φ Φ sS μ- P- φ K PJ rt 3 0 P- C>

D- P PJ 3 P- N to SO Φ P- CD PJ PJ P- μ- Ω P μ- tr PJ D. 0 CQ y- ^y rt

P- φ φ ra P Φ CQ 0 rt P CQ D. J rt 3 <ta φ tr tr 3 P- 0 0 P iQ PJ = cn φ Ω P- Φ P α Φ Mi 3 cn J 3 J 3 Φ Φ Φ φ w P CQ 3 rt rt φ tr 3 Ω PJ Φ P 0 = sS P- tr 3 y → P D. μ- y → 2; rt rt Ω Ω P- μ- ra Φ iQ P- tr rt P sS tr Φ rt CD Φ μ- 3 ^ <tr to μ- 3 CD μ- Φ ra tr tr rt μ- Di 3 μ- 3 Φ P et P- Φ PP Φ rt μ- cn 0 PP φ n Ω P rt rt sS 3 φ

3 tr D. ra <50 P- 0 D. • d μ- P- rt PJ P Φ Φ tr tr tr P 3 PJ Pl P

0 D- y → sS Φ ra 3 Φ Φ 3 3 α rt N 3 3 cn Φ P- Φ cn 0 = P- 3 Φ 2! D. y → PJ J D. 0 fjj: PJ Φ Q 3 P Mi Φ Di 0 0 3 3 rt ra Ω y → P- 3 3 X 3 PJ = tr PJ et 3 ra PJ 3 PX CD • P- y → cn Φ P tQ 0 Φ ^ 0 tr ra Ω 0 P- 0 OP Φ CD J 3 φ tr D. 3 rt P- y → 0 μ- 0 3 n ra 3 PP 3 rt Ω tr 3 3 3 Φ 3 μ- ra

3 3 Φ Φ μ- 3 φ Ό. Di CQ CD Ω sS CQ PJ O Di tr Q p- CQ P Φ Di φ μ- P- <rt 0 μ- μ- P- 0 CD y → 2: φ tr y → Φ φ μ- PJ = CD φ Φ PJ rt Φ cn

3 0 0 J 3 D. rt CQ ra P rt φ PJ P- Di Q ra P P- Ω tr P P 3 rt PJ 3 φ

3 3 0 CD P- 0 0 Ω • μ- ra cn Φ PJ ^• Φ 3 tr 3 P- φ 0 0 μ-

S Di cn P Φ 3 P tr> Ω ra φ CD ra 3 tQ rt y → Ω 3 P- P CQ 3 μ- P Ω PJ IQ Φ J tr φ rt Mi Φ P P- tr ~ 3 Ή Ω φ rt Φ tr 0 in 3 CQ P σi tr 0 = ra Φ Ω rt P tr rt Ω Φ 3 y → X Φ D. - Φ P Ό J tr 0 D- 0 Φ

Φ tr P - N 0 = sS PJ ra φ X a J Hi P y- ¹ rt 3 H Φ 3 μ- cn Φ Di P- rt sS CQ cn P- cn to | P> P- 3 Ω P- cn O P- cn y → to y → CQ Φ tr Hl φ rt P φ φ so rt 3 rt 3

50 <2! , - ~. 2! 50 50 JM Φ Φ O ^► 0 Ω iQ 3 D. ö φ 0 O α iQ 2: cn N α cn 50 50 H Φ D- 50

Φ O PJ = t ^→ φ Φ O y → 3 XP P- P- y → y → φ P- P- X D. PJ P- y → PJ-- rt 0 PJ rt Φ Φ 00 μ- Φ Φ

PJ P P l_l. Ω Q tr cn ra o Mi Φ IQ φ φ tr Φ φ Φ Φ P φ Φ P P Hi tr φ CQ Hi 3 P PJ

X P 3 0 tr Φ P tr rt P- 0 μ- μ- P 3 P J P- 3 0 = 0 = Φ y → Φ 0 s≤ Q X rt φ Φ 3 CD 3 tr P Φ tr 3! P Ω Ω Hi P-> Ό y → P- Ω Φ 3 tr P- y → 3 P φ Φ Di rt

PJ PJ rt IQ φ Φ 0 = Φ ra Φ Di 0 tr tr PJ 3 0 y → CD y → 3 tr X 0 P φ Φ 3 CQ ra 0 P-

3 X PJ n P 3 X 0 P 0 P to Φ 3 Ω CD PJ xi φ PJ 3 0 P- 3 P P- φ P 0

Di rt 0 rt PJ Di 0 3 3 3 ra PJ cn PJ = tr Ό IQ P P- P "N ra T5 IQ a ra PJ φ rt rt 3

Φ P- ra P Di rt Φ TS Di Φ IQ rt tr J P- Φ P- P 0 P- PJ ra Q rt cn rt P ö N ra

3 0 Ω o = Φ μ- y → Φ Φ 3 ra Φ IQ tQ μ- CQ CQ CD ra J N ra 3 N P cn 0 0 Φ rt iQ Ml

3 tr 3 P <1 P P IQ tr Φ μ- CQ φ 0 rt Ω y → 0 PJ D. P- P- P Φ p- P 3 P Φ 0 =

H - Φ 1 sS PJ φ 50 Φ Φ 3 Φ s≤ P PJ tr Mi P 3 rt Ω P- ra 3 Φ CQ s≤ N tr

P s! cn PJ = 0 rt Φ 3 3 PJ = rt P 0 y → 0 = 3 j: tr Ω 3 50 Φ φ P

NX PJ: rt P D. P- y → PJ PJ = Di Ϊ> φ 3 H rt 0 P t φ rt rt tr PJ D. t ^→ Φ P P- 0

Kt »0 0 P P 3 Φ <PJ X ca Hi 3 Di PJ 0 3 3 PJ 3 cn et 0 Φ H 0 PJ Di CQ 3

3 3 3 0 = Φ P Φ rrt Φ DD 0 = Φ 3 Di P- 0 tr CD 3 0 ra 3 so Hi X Φ rt <Q ra Ml φ 3 rt cn P- 3 P- Φ P l 3 CQ iQ IQ • d PJ rt tQ 3 rt et 3 Φ μ- to p- rt 0 PJ ^ 0 Ω Φ 0 ra 3 Φ Φ Φ CD Φ rt 3 P CQ φ 50 y → J 3 3

Ω Φ ^| Q PJ 3 0 y → Φ 3 3 PJ X D. 3 3 N 3 rt ra iQ 0 = 0 a φ PJ 0 3 PJ tr P- 0 0 CQ CD J CQ Φ 0 0 ra μ- X) Φ PJ J rt 3 3 D- φ J 0 DD t 50 Ω

Φ cn P CD CD Ω rt Φ cn 3 rt rt Ω Φ φ Cn P- Ω P 0 P 3 φ N Φ P X Hl Φ 3 Φ tr

P • d PJ Ω P tr rt 3 P- O P- tr P rt ^| Q tr X ra o = P- 0 ω iQ et Φ P y → X

P- rt tr μ- Φ Φ 1 Ω Φ rt φ Φ PJ P rt CQ 3 rt Hl CD φ P- 3 <- 0

<φ P- Φ Ω P 3 tr μ- tr P 3 0 rt 0 = Φ O CD φ 0 0 = Ω 50 rt 0 Di cn tr P- "d μ- φ y → 0 P tr ra 0 3 Φ rt PJ cn 0 3 P- Ω CD 3 D- P tr φ P- 3 Φ PJ t CQ φ iQ

P 3 rt P- rt Di D- P Φ rt CQ P 0 50 CQ tr rr Q Φ PJ PJ ra cn 3 0 s≤ 0 P 0 tr D. Φ • 0 3 PJ Φ μ- iQ 3 3 p- φ < 3 Φ 0 Φ PJ m P tr y → X Ω P φ PJP

P- 0 3 3 • d P φ P Φ ra cn Φ CQ PJ P 3 y → P Φ et et tr PJ N P rt

3 P 5 IQ φ 0 3 t Ω rt P CD X PJ rt P- <P- φ PJ φ 0 0 ra in P- to

D. Ω p- Φ o y → 5 CQ C) Φ tr PJ et s≤ rt cn rt 0 Ω Φ Di 3 3 3 3 y → rt <PJ

Φ tr ra 3 tr P tr P Φ Φ 5 *! p- Φ y → Φ φ P- tr P- 3 tr P Φ • »Di φ 0 _^ - _^ Hi s≤ t

P rt 3 to 3 PJ Φ to P 0 ra 3 et p- IQ 0 cn ⁽ Q rt tr Φ Ω y → P- Hi tr P ⁾ = PJ = φ y rt CQ - N sS 0 0 Φ Xi 5 0 y → 3 0 P- 0 Φ cn CD 3 P to rt Hi Φ y → P P-

Φ φ <≤ to μ- Ω X) P- 3 0 X CD Di Φ Di 3 CD rt 0 0 = 0 • - - μ- y → 3 3 sS r Di P- 0 φ CQ Q Φ y → φ 0 IQ 3 0 X Φ P Φ tQ CD P y → 3 φ 3 et Φ iQ

Φ P J Ω PJ 3 P- Φ rt CD 0 y → Mi CQ 3 J P rt P φ O D- Di P- iQ s≤ φ rt Φ

P Φ ra tr y → ra Q Φ rt 3 φ tr Di 3 3 IQ P 3 PJ tr Φ 3 Φ P- μ- Q, PJ cn

D. 3 ra Φ CD to φ Φ 3 PJ CQ PJ Φ 0 rt 3 σ. P- 50 Φ 0 0 CD to 3 CQ 3 P 3 PJ 0 φ

Φ 3 3 Φ 3 y → t 0 P 3 Φ Ω 3 Φ 3 3 3 CD s≤ Φ D. Φ 3 CD rt

3 rt φ 50 rt P ra 2! et <φ D <Φ P PJ PJ iQ IQ CD Hi <P 3 Ω to

Φ p- PJ O rt φ rt PJ = 0 O P- <tϋ cn X O X 3 CD μ- 0: O 0 = tr rt

3 3 y → rt Φ JPP 3 3 ^| Q 0 Φ 2! o P): P- et 3 Di P P- ιP> 3 tr P tr 0 ^j Φ

0 Ό Φ y → O 3 y → 0 3 iQ φ 3 J PJ: N 3 CQ P- rt Φ P- φ 3 P tQ φ X Φ P s≤ cn 0 = φ P 3 Φ ra Φ 3 XP 0 P- φ 0 0 Φ ra Ω 3 <rt Φ P μ- D. Φ cn tr Φ PP 3 cn s≤ rt ra 3 y ^→ et 3 3 P 3 3 tr P- 0 tr & P- 50 P

• P X Φ P- μ- PJ = PJ S D. μ- φ Φ to CD 21 et rt y → 0 Φ Di PJ CQ Φ Di

0 0 CQ rt φ P 0 P- 0 Di CQ 0 0 = P- Ό 0 cn X 3 PJ: 0 y → 3 P- P- rt y → IQ Φ ö 3 rt Φ P 3 ra φ rt PJ 0 3 tr 3 P 3 P ⁾ PJ P): P 3 D. - α N φ μ- P- Φ 3

PJ IQ tr 3 O Φ Φ Ω y → tr ra P cn φ Φ PJ 3 PJ 3 IQ Φ rt <Ω 3 ~ Q Φ Φ Φ 3 rt tr P Φ ra XPP CQ to φ 3 3 φ Φ 3 Di <P- Φ tr Φ

Φ Di P P P PJ Φ J P cn PJ rt Φ φ P Φ D. rt 3 μ- φ 0 3 3 P sS Q Φ 3 PJ μ- 0 0 P 0 3 tr J 3 P • P- P Φ P 2; φ P a D. J Φ

Φ P φ rt 0 D- CD 3 Φ Φ 3 P ra PJ: P PJ Φ φ rt Di Di Φ rt 3

3 0 Di Φ Ω s≤ 3 P- φ iQ ö xi 0 P- Mi 3 rt Ω Φ Φ P 0 3

P μ- P tr PJ tr P 0 0 P- rt ra 0 = CD s≤ tr P- PJ 3 P

X Φ ra Φ tr Φ 0 3 P φ Φ rt P X) PJ ra y → 3 to Φ CD

PJ 3 Ω PJ P y- ^y ra 3 φ μ »CQ Ω y → P 3 O Φ rt P 3 rt

3 tr y → s≤ rt P cn • tr rt P- P y → • Di φ PJ

3 φ cn P- φ φ Hi * CQ rt Φ 3 rt 3 3 P- tr PJ 0 = Φ ra Di 3 3 rt

Φ CD et 0 Φ P Φ Φ

CD ra • ra 3 PP

be expedient to integrate catalysts for a post-reaction of the endothermic reaction in the reaction space 7, 12 or 16 in the outflow part of the heat exchanger 9, 14 or 19. The reaction space 7 is characterized according to the invention in that the heat of reaction of the exothermic reaction is distributed as uniformly as possible over the length of the reaction space. This can be supported according to the invention in that a reaction component 4 for the exothermic reaction or a hot partial flow is metered in locally, in that direct current or a meandering (or spiral) flow is provided between the fluid of the exothermic or the fluid of the endothermic reaction Internals with strong heat transport are provided parallel to the main flow direction or a circulating auxiliary medium (for example in the form of a fluidized bed) ensures such heat transport. Furthermore, care should be taken to ensure that the heat demand rates of the endothermic reaction and the heat production rates of the exothermic reaction approximately correspond when entering the reaction space 7. This can be achieved by adjusting the inlet temperatures (i.e. designing the respective heat exchanger 2, 9) and / or selecting or influencing the catalyst activity.

Claims

claims

Reactor circuit for the autothermal coupling of exothermic and endothermic reactions with separate guidance of the two reaction streams, comprising heat exchanger sections (2, 9, 19) between all feed gases (1, 4, 8) and all hot product gases (3, 10) and a reaction area ( 7, 11, 12) in which the exothermic and the endothermic reactions take place in direct heat exchange with one another, characterized in that the heat exchange in the heat exchanger sections (2, 9, 19) between the feed gas (1, 4, 8) supplied and the hot ones Product gases (3, 10, 15) either run recuperatively in countercurrent or crosscurrent or regenerative and in each heat exchanger section the heat capacity of one partial flow approximately corresponds to the thermal capacity of the other partial flow and the exothermic and endothermic reaction in a reaction area (7) each individually takes place separately in time or space, whereby in the case of a spatial separation the the two sub-areas (11, 12) are locally coupled with one another in such a way that there is a very good heat exchange between them and, with spatial or temporal separation, the exothermic reaction is influenced in such a way that it only starts at the entrance to its reaction area (11) and the Heat of reaction is released over a larger local area overlapping with the reaction area of the endothermic reaction (12) in a largely uniform distribution and is transferred to the endothermic reaction.

Reactor circuit for the autothermal coupling of exothermic and endothermic reactions according to claim 1, characterized in that an exothermic pre-reaction in the heat exchanger section (2) is prevented in that >P>

φ CQ 50 pl l 2! t ^→ TJ to μ- P ⁾ Φ Φ to 2: Φ 50 CD P 2! Ω Φ CQ φ 50 Φ 3 Di <50 to 50 Φ

3 φ Φ Φ Φ Φ PJ = P P 0 3 tr X μ- Di PJ: 3 φ rt Φ PJ: y → X Φ 3 Φ p Φ PJ Φ Φ μ- Φ P-

D <P 3 PJ μ- μ- P Φ 0 iQ y → 0 3 0 P Di PJ PJ X P φ O X D. PJ HI tr ra P J 3 PJ 3

O Φ X y → y → 3 0 Di Φ D. PJ rt φ X 3 0 X rt 0 3 μ- rt Φ 0 X 0 P cn rt X rt X Φ rt φ μ- et D cn Φ N 0 Hl φ 0 tr 3 et Φ rt et rt Xi Φ Ω tr 3 et rt y → Φ Φ et P et P tr X 3 P- rt rt rt iQ X 0 = 3 Hi Φ iQ rt tr 0 Hi φ X tr Φ 3 tr O CQ P Di μ- P- μ- y → -

Φ o ra O P P J φ et tr Φ P IQ PJ PJ Φ P μ- P 0 1 P N φ P rt φ P- y → 0 rt 0 Di

P rt PJ 3 0 0 0 CQ IQ P 2! a 3 Φ ra 0 P ra 3 PJ 3 3 Φ P CD • Φ 0 3 rt 3 Φ

3 tr 3 Φ 3 3 CD Φ ⁾ et PJ = ~ φ 3 Φ CD 3 Ω D. rt et 0 φ μ- 3 Ω D. 3 CD P

Φ φ 3 ra n Ω 3 CD Φ P 3 φ 3 Ω Φ tr Φ μ- J D. Ω Φ tr μ- N ⁽ QN μ- Xi

3 P PJ tr CD Φ 3 3 Di μ- tr 3 PJ rt <X Φ 0 tr 3 J ra 0 0 3 PJ Ml

3 tr P- Φ P- φ rt 3 Φ J 0 3, - »Φ • φ et P 3 3 y → X 3 Di IQ P 0 =

50 φ y → 3 3 3 P P to PJ 3 ra .P * P 50 rt P D. Φ 50 rt P P- Φ Φ D- rt P

Φ 3 PJ rt PJ 0, -. 0 0 D. PJ - PJ Φ 0 3 rt Φ 0 φ cn P 3 μ- 3

PJ 0 50 cn Φ tr 3 y → 0 ra P 3 tr PJ 3 0 P- P Φ ^ PJ 3 rt Ω μ- Φ Φ D.

X 50 Ml Φ i rt D in X rt Ω D- Φ y → CD X CQ D. rt Φ 3 X IQ Φ tr 2! ra P P- rt Φ Φ PJ P s≤ Ω 0 - et PJ tr P- 3 ⁾ Ω rt φ Φ 0 D. Di et 0 PJ = Ω pl Φ

P- PJ 3 X P- J 3 ^' i IQ 0 Φ -' tr μ- NP P- N 0 PJ μ- to W 3 P 'r φ, -.

0 X et Ω 3 Φ Φ PJ ra Q 50 3 0 0 3 cn rt CD 0 0 μ- CQ 3 et μ-> P- Φ

3 rt μ- tr Di P- P 3 CD Ω Φ Φ Φ 0 P- a PP PJ rt tr CD 3 P 3 φ y → ~ - ^ - X y- s≤ O et Φ rt rt φ tr X 3 PJ 3 rt Φ φ 3 P Φ Φ ra 0 = Hi s≤ PD

3 O o 3 P rt P s≤ 3 Φ Φ D- X Di rt 3 PJ CQ Di 0 P Di 3 PJ i P P μ- φ iQ rt

0 3 tr CD 0 Φ Φ P 3 0 et Φ 0 Φ Φ 3 3 μ- 0 Φ rt φ P PJ Φ tr

P Φ tr 3 21 CQ Di J 3 rt μ- PJ 3 tr rt 3 P Φ φ 3 rt μ- y → P- Di X rt Φ

D. μ- Φ D. PJ: P- Φ Φ ιP> tr £ 0 tr 0 y → Φ 0 Φ N PJ 0 ra P- ra et P P

P- Φ P P Φ 3 P - m Φ Φ 3 y →, —_ CD rt P IQ 0 50 pl Ω rt 0 Ω φ Φ 3 t

3 3 D. Φ Di 3 Φ Ω P- P CD φ H rt tr PJ Φ Φ Φ φ tr tr 3 tr rt s≤ 0 3 Φ μ- P- P- φ 21 PP y → tr Ω 3 tr 3 t » φ Φ rt Hi P- PJ P- Φ CQ N 0 3 3

D. CQ φ Ω φ X PJ = PJ Φ w 3 tr Φ Φ tr P P- 0 = 3 X y → t P CD X 0 tr ra rt 50

Φ Φ tr PJ P rt X ~ - P- 3 3 P _ι Φ 3 <tr PJ et ra 3 CD 0 3 Φ N Φ

3 cn Q Φ i 3 μ- 0 rt Φ Φ P tsi 3 Φ Φ P 3 rt Ul φ rt 3 tQ P- 0 IQ PJ

PJ Φ -—. X PJ φ <• d 0 rt rt 50 p- 0 ≤ D. 3 P rt D. 0 P Xi 3 φ rt 3 Φ X

2 3 cn y → o N X Φ 3 Φ Φ Ω Di P- Φ 3 0 = P y → μ- Di D- Φ Hl et

PJ rt PJ cn rt μ- PJ PJ P Di 3 PJ tr 0 ra PJ 5 *: 2! ≤ P 3 0 5 y → 3 PJ P- 0 = t> Φ 3 - • tr rt • d tr PJ XX Ω 0 0 PJ = Φ μ- Φ Ω 0 Φ 0 Di Φ _^ . tr 0 φ 3 rt Φ PJ = PJ rt D-, -, PJ et et tr ra Xi PP CD 3 tr • d 3 μ- 0 y → P 3

Φ IQ P rt tO PJ-- P- Φ H CD P- μ »Q Φ Xi 3 D. O, -_ i φ P Q H rt

0 = 2! y → 3 P- 0 <3 P> ra 0 cn PJ 3 → Φ Φ s≤ 50 y → H y →, -.

- P Ω y → -— Φ tr PJ = _~ φ φ D. rt Hi - 3 - CD 0 PJ 3 P- Φ 0 cn y → tr φ s≤ P

Φ P PJ: P- 3 Φ PJ = rr P- tr D. Φ - Φ J 3 0 φ ⁾ 0 3 - - P- μ- D- P- Hi

P 3 P Ω rart 3 Φ t φ 3 3 y → tQ CD X 00 D. CQ Ω tr Ω Φ P 0 ra Φ 3 tr 0 0 P- s≤ P μ- y → rt ≤ P- et Φ <tr Φ tr P Di P rt tr φ 3 PJ D. 3 Ω C> P- IQ 3, - _^ φ <PJ 0 3 μ- P <φ ≤ 3 D

Φ Φ Hl φ D. 3 Φ D- Φ Φ CD 2! y → y → 3 0 0 tr 0 Hl 0 P 0 P- PJ: Φ 0 Φ μ- D. P μ- cn Q 3 Ω P). φ Di in 3 CD Φ Φ 3 0 = to 3 rt Di P P Q PJ φ rt Φ εa X 3

Φ μ- Φ tr P P- Φ to Ω P- 3 CD P - Φ Φ X μ- 0 t D. y → r P P- μ- 3 P Φ 3 3 Φ 3 Ω 3 0 Φ tr IQ P Φ μ - P et CQ rt P-

Hl ra CQ D- Φ μ- 1 3 Φ tr ra iQ X Φ J D. D. X y → φ tr Φ Ω φ 0 3 3 1—1. JN D. 0 Φ 0 3 0 P- J 0 rt PJ ≤ φ P tr ≤ D. rt 0 rt Φ φ 0 D. 0 Φ μ- s≤ Hl 1 3 φ D. 1 0 P- 0 = P cn Φ μ- Φ N 3 tr 3 Di Di Φ ra μ- φ P- 0 = 0 Hi PP 3 rt 3 φ P 0 Di φ Φ Φ 3 rt rt φ tr 0 P 0 Di rt φ

3 P 3 P J μ- P 3 0 Ω 3 3 3 φ IQ 3 0 CQ rt D. ^ - ^ tr D. μ- J

P φ ra Φ Ω Ω

3 Ω 3 μ- tr tr tr 3 φ

cn in

tr 21 sr 50 50 3 e <xi .—. to Φ Tue, -. y ^→ tr N <Φ Di Q ^ 0 Φ φ 50 t 0 tϋ 50 <! y → 2; N

Φ PJ = φ Φ P- o PJ y → P P- Φ y → y → Φ 0 0 μ- Φ Φ Φ P 3 3 φ P- Di Φ Φ Φ O PJ: 0

P- P ra PJ PJ rt y → y → P to Φ a P oo 0 P Q P a P X P 0 Di D- PJ 3 Φ PJ PJ P X P P

I> 3 Xi X X PJ y → PJ - 3 rt P- Φ φ IQ φ φ D. 0 0 X CD P X X tr J 3

Φ φ P et et D- 0 l y → 3 P Φ Di P- Mi Φ 3 X a Φ 0 rt rt rt Xi et et μ- y → φ

3 rt 0 = 0 μ- Φ Hl et y → ra X μ- 3 rt 0 = tr PJ 3 3 X tr tr 0 Φ P- P- y → - 3 rt 0

PJ Ω P 0 3 ra PJ: φ 0 PJ rt D- Φ Hl D tr φ tr y → to D. et Φ φ P P- 3 0 0 D. tr PJ Hi

0 tr ra 3 3 y → 3 rt 0 PJ 0 = P P- φ rt Φ 0 Hi PP ra ω 3 3 Φ φ 0 P tr CD Φ Ω XJ Di CQ 3 rt CQ P P- r N μ- Φ P- rt y → 3 3 Ω 0 3 ra P tQ ra φ y → Ω tr tr PJ 0 μ- N φ φ 0 tr P- 3 Φ rt ff> Ω tr 0 Φ Φ tr 3 Φ tr tr rt P Ω Ω

PJ tr P> PJ Φ y → ra CQ 0 ra P 3 φ φ Di 3 φ tsi tr φ P- 3 PJ CQ tr Φ Φ φ tr tr

0 Φ y → 3 et Φ P rt Di P P P- 2! ≤ 3 0 3 P D. 50 y → CD P P 3 s≤ 3 Φ rt

Ml P tr et 0 φ Di PJ, -. 3 rt φ PJ = 5 ^ P- y → φ 3 Φ 50 et ra Φ Φ 0 'P- N P Φ

P- 0 rt 3 Φ to ra <tu y → y → D. Φ - P 0 P PJ rt φ Di PJ Φ 0 rt P P- rt P rt P

Φ 3 to 3 φ P ⁾ rt oo 0 3 φ 3 3 Di tr 0 - 3 Φ X PJ 3 φ Φ Ω μ- D. Φ, - _ tr

P- s≤ CQ rt CO P 0 Φ P ≤ X Φ Xi »y → Mi P et X CQ h → 3 tr CQ P y → J

3 P- Ul 0 50 3 • d rt rt 50 PJ: 0 rt O PJ Di 50 P- et rt *> y → φ ra - to s≤ y → φ P- rt <Φ tr rt ⁾ 3 ≤ 0, - »PJ Φ Φ O y → - to φ o = _^ φ D- • - - et ra Ω 0 P- J PJ ra CD μ- Φ 3 PJ P tr 0 Φ 0 Mi y → CD JX 3 0 0 a P y → 3 PJ tr

3 "D- P P 0 X Ω rt ra P P- X Φ Φ ra 3 tr - cn X O 3 P rt cn ra y → φ 3

5θ Φ J Di Mi et tr P rt 3 rt et 3 P Ω rt Φ <et rt D. φ, -. y → - 50 cn PJ P ⁽ Q φ a J y → - 0 o = P- P- D. 3 tr Φ P- o oo Mi y → - tr PJ 3 PJ cn P- Φ 0 Hi J 0 0 Di O 3 3 ra D- o φ Φ 3 3 - 0 = 0 φ Di - 0 Ω 0 PJ Φ Mi 0 Di

X Φ P rt Φ 3 CQ 0 Di Ω Φ 3 D. P <P 3 P 0 et tr 3 X P- P Φ et P- Ω 0 P ra 3 PJ tr 3 PJ 50 h Φ Φ P- 3 P ≤ 0 N Di et 3 D- Di cn y → - 3 tr rt P Φ CQ CD rt P- cn Φ P 0 = P rt a l_J. N φ Ω 0 rt 0 <y → - Φ Φ Φ

O Φ tr 50 PJ P ra ra tr 3 PJ Φ P tr ≤ φ 0 3 tr tr tr CQ φ to 0 P P P 2:

3 3 CQ Φ Φ 0 Hi P s≤ φ <X PJ P- PJ Φ D. IQ Φ Φ φ P ≤ 3 y → PJ = ra Φ P PJ 3 O P- Φ P- p- Φ 0 et CQ D. 3 P- Φ Φ 50 Φ P- P Mi rt PJ ra Di Φ y → - P

P X X 3 X y → Ω μ- P (Λ> P- P y → - P- μ- D. iQ 3 CD 3 Φ P 3 0 = Φ P Xi Φ X Ω 3

PJ PJ Φ Φ et _^ - _^ CQ tr 3 D. Φ a IQ 0 Φ φ Φ y → φ μ- PJ to D- φ tr μ- PJ P 0 tr Φ

0 a 3 PJ y → rt rt - 3 Φ φ 3 P P φ 3 Di cn X φ P- 3 P y → X P rt PJ

3 rt 3 3 to 0 μ- 3 s≤ Φ φ rt p- Φ Ω rt 0 Φ rt et 0 rt Pi tr y → - 0 ra Φ o 5 ^ D. - - 0 3 3 s≤ TJ j: P- 3 X Ω 21 P tr P- CQ 5 φ 3 3 0 = φ l CD

3 Φ 0 Φ 3 IQ rt 0 P 50 P 3 0 s≤ tr PJ: rt O rt tr 0 s≤ 3 rt Φ P P et rt

PJ P- * da Hl D- Φ tr 0 Φ 3 0 rt P- Φ P tr 3 Φ • d P- p- P 3 J y → INI Ω • d 0 = 0 3 Φ Di PJ rt Φ 3 tr PP 3 Φ s≤ ≤ 3 Xi P D. 3 D. φ 0 0 ra 0 tr y → Hi P Φ 3 ra P- 0 X Φ μ- D. Φ D. φ P- μ- Di P- 0 = Di μ- 0 ~. P- 3 3 cn y → 3 0 0 = μ- D. μ- X et 3 P •> S! rt Di P Φ P rt 0 ra P- φ D. Ω

Ω PJ Φ 3 P i 3 <D. rt y → - 0 φ Di 3 PJ: PJ φ Di 3 D. P- 3 X φ - - 50 tr φ 0 rt Q Φ Φ φ φ 0 Φ P PJ Φ Di P 0 a - IQ IQ PP φ Φ Φ cn Q Mi ~ D. 3 pl P- PP PJ 3 J CD PJ 3 CD 50 rt φ y → Φ X PJ P- φ 3 P- Φ 3 0 ra X to 50 tn φ Ω 50 D. Φ i Φ <rt y → - P 0 X 3 p-

3 0 Di J φ 21 μ- Φ 2! 50 ω ra et P tn Φ ra X tr Φ J PJ PJ 0 Φ Ω ra rt et 3

CD 3 J Ω PJ: y → PJ = Φ P y → - Φ 0 J PJ Φ PJ D. X ra 21 3 3 tr rt tr y → - CD rt Di CD tr φ P ra P PJ Di PJ o 3 X D Xi PX 0 et PJ: Φ 0 Ω

P ra X 3 D. Ω 3 X φ 0 3 3 <J et μ- PJ et P y → - P Φ <μ- P 3 tr

O Φ Φ 0 Φ Φ tr Φ rt P 3 CD X o y → - φ to Di y → - Ω 0 D. 3 X Φ 3 3 3

3 p- P- rt rt cn 3 r μ- CQ PJ P 0 P- 0 0 tr 3 PJ φ 0 P Φ Di Φ

1 3 3 tr ⁾ Φ PO, -. Φ 3 IQ 3 rt P t → cn ra 1 rt PJ y →

Φ Φ Φ 0 tr y → PJ 3 y → 3 3 φ PJ = Ω l CQ Hi Φ D. y →

0 3 3 P m φ y → 3 ra to p- φ s≤ rt tr Mi Φ tr 0 = 0 μ- 0 φ

Di 3 Ω μ- φ CQ P cn P J: y → 3 φ P 3 y → P P

Φ α φ tr C • d PJ Ω P 0 P- P-Di et Ω

P Φ Φ 0 0 0 tr 3 y → - ra ta tr P 3 3 P 3 et D- Ω φ P- D. rt Φ Φ tr φ

o 00

D. D- μ- Φ φ 3 to 2! μ- PJ =

3 3 ra Di xi Φ φ 3 μ- ra 0

0 D.

3 Φ iQ P φ

3 PJ

0

, -. Hl μ »

- Wed

Ra in ra

•> rt φ cn

• «3 to

00 P-

3 tr y → PJ ω

- • 0 rt

Φ cn 3

0

PJ μ- 3

3 CQ

Φ

O μ- P φ

3

Φ rt

Para

0

3

di

y → H y → 0

<X 50 φ 0 Φ

P 3 PJ rt rt X

Φ P- et

P- 3 PJ y → 0 et a

P-Tue

Φ Φ

3 P Di y → Φ t y → - P

P- Ω

3 doors 3

Xi 0 = Di φ tr 0

P- Φ rt ra P tr

Φ φ o Di P

P P- 3 rt φ φ φ 3

3 t ^→

PJ: 50

-. 3 Φ cn CQ PJ - Φ X et tO D- y → -

0 Φ O

IQ ra 3

Φ

3 50 y

P- Φ 3 m PJ

Ω X i tr et P- et y → - ra

0 X ≤ 3 P μ- ra Φ

P P rt

The PJ Φ

• 0 3

3 ra 0

di

_-. Φ

-j P