GB2602313A

GB2602313A - Method and apparatus for controlling a reactor

Info

Publication number: GB2602313A
Application number: GB2020449.1A
Authority: GB
Inventors: Döring Andreas
Original assignee: Individual
Current assignee: Individual
Priority date: 2020-12-22
Filing date: 2020-12-22
Publication date: 2022-06-29
Also published as: GB202020449D0

Abstract

A method and apparatus for the production and storage of energy comprises a reciprocating or rotary piston engine 2, which in a first mode operates as a combustion engine delivering energy and in a second mode operates as a pulsed compression reactor storing electrical energy in the form of chemical compounds. The individual chambers are arranged in series and housed in a common casing. Together they form a reciprocating engine 2. The compression energy is delivered to the reactor 4 via a shaft 5.

Description

Method and apparatus for storing energy

Description

Due to the energy transition, the requirements regarding the stabilization of the grid have increased, as the need to balance short-term differences between energy demand and energy supply has increased. In addition, the storage of energy is essential for the feasibility of the energy transition. If the demand for electrical energy exceeds the current supply, combustion engines and/or turbines connected to generators are usually switched on to compensate for this difference. If, on the other hand, more electrical energy is produced than can currently be purchased, it would make sense to store this energy. However, electrochemical energy storage is too expensive, and pumped storage power plants face resistance from the public, so the energy is often simply dissipated to prevent overloading the grids.

An alternative would be to store excess energy in the form of chemical bonds, such as methane, methanol or ammonia. Methane, ammonia, and methanol are usually produced catalytically in fluidized bed reactors, particularly fixed bed, fluidized bed, or fluidized bed reactors. Thus, methane is produced from CO, 002, and H2 according to the Sabatier process.

H2 + CO2 -> CO + H20 3 H2+ CO -> CH4 + H20 The same is true for methanol or ethanol, but less hydrogen is added per carbon atom.

CO + 2H2 -> CH3OH CO2 + 3H2 -> CH3OH + H20 2C0 + 4H2 -> CH3CH2OH + H20 2002 + 6H2 -> CH3CH2OH + 3H20 Ammonia production by the Haber-Bosch process proceeds according to the following equation.

N2 + 3H2 -42 NH3 All of the above reactions have in common that they take place on a technical scale on solid-state catalysts. While catalysts containing zinc are usually used for methanol production, catalysts containing iron are used in the Haber-Bosch process and catalysts containing nickel are used in the Sabatier process. The use of flow and fixed-bed reactors is common because they are relatively inexpensive and easy to manufacture. However, there are high requirements for the purity of the reactants CO, 002, N2 and H2, otherwise the catalysts used would be poisoned. As a result, these substances have to be purified in a complex process before they are fed into the respective catalytic process. This applies in particular to CO and CO2 if they were formed in a process in which inorganic components such as calcium, sodium, vanadium, sulfur, phosphorus or similar were present. The disadvantage of this type of reactor also lies in its difficult controllability and its long start-up times, i.e. it is not suitable for absorbing short-term load changes in the electrical network by changing the operating parameters at short notice. In addition, intercooling is necessary due to the strong heat tinting of most reactions. If this is not done, only very low selectivities can be represented. In addition, due to the catalysts used, the reactors are only designed for one specific reaction and can therefore only be used for this one reaction. In addition, it is disadvantageous that the reactor would only be activated during the phases of excess energy in order to store it, i.e., most of the time it stands idle without being used.

The invention disclosed in claims 1 and 9 is based on the problem of presenting a method as well as a device which, in phases of a demand for electrical or mechanical energy, makes it available and, in phases of a surplus of electrical energy, converts it into a chemical bond so that it can be stored.

The method according to the invention solves these problems according to the generic concept of claim 1, the apparatus according to the invention solves these problems according to the generic concept of claim 9.

For this purpose, a device which can present at least two operating modes is used. In a first operating mode, the device serves as a supplier of mechanical or electrical energy, and in a second mode it operates as a chemical reactor by which at least one chemical product, such as methane, methanol or ammonia, is produced. This at least one product is collected downstream of the apparatus and can subsequently be further processed. Storage and subsequent use as a fuel or combustible is also feasible. That is, in the first mode, the apparatus supplies energy if the electricity demand exceeds the supply, and in the second mode, the energy is stored in the form of a chemical bond if the supply of electrical energy exceeds the current demand. This is achieved by having a reciprocating engine operate as an internal combustion engine in the first mode and as a pulsed compression reactor in the second mode.

This type of reactor is generally described in, for example, US 8,691,079 B2, US 2,814,551, US 2,814,552 and in -Pulsed Compression Technology: A Breakthrough in the Production of Hydrogen", M. Glouchenkov and A. Kronberg, WHEC 16/Jun. 13-16, 2006". The basic idea is that gaseous reactants are fed into a reaction chamber via at least one inlet valve, and this gas mixture is then compressed via a piston and thus heated. This initiates the desired reaction, after which the pressure and thus the temperature drop again due to the piston movement, and the products thus generated then leave the reaction chamber via at least one outlet valve. This process is repeated periodically, comparable to an internal combustion engine. The difference, however, is that in internal combustion engines the main focus is on the energy delivered and the exhaust gas is released into the atmosphere, whereas in pulsed compression reactors the goal is to obtain usable products. In this way, temperatures of well over a thousand Kelvin and pressures of several hundred bar can be represented for a short time without placing too high a load on the reactor components, since the subsequent expansion of the gas causes the reaction mixture to cool and thus reduces the component load. In order to utilize the energy dissipated during the expansion, at least two reaction chambers are usually mechanically coupled in such a way that the expansion of one reaction chamber leads to a compression in the second reaction chamber. This can be realized, for example, by a freelectricalpiston arrangement (US8691079B2, "Pulsed Compression Technology: A Breakthrough in the Production of Hydrogen," M. Glouchenkov and A. Kronberg, WHEC 16/Jun. 13-16, 2006). A connection of two opposing, counter-rotating pistons, each closing off a reactor chamber, can also be represented (US2814551). In addition, there are prior art reactors based on reciprocating piston engines that operate as reformers and are used to produce syngas (Lim, Emmanuel G. et al. "The Engine Reformer: Syngas Production in an Engine for Compact Gasto-Liquids Synthesis." The Canadian Journal of Chemical Engineering 94.4 (2016): 623-635).

According to the invention, it is envisaged that the reactor chambers are in the form of cylinders, in which pistons move along the cylinder axis, and are arranged in a row. A two-row arrangement in the form of so-called banks is also possible, with the two banks being arranged tilted at an angle of 40° to 120°, preferably at an angle of 42° to 90°, extremely preferably at an angle of 45° to 60° to each other. In both cases, i.e. the in-line or V-shape design, all pistons moving in the cylinders act on a common crankshaft via a connecting rod in each case. In other words, the design is in principle a reciprocating piston engine. A device, e.g. an electric motor, is coupled to this crankshaft, via which the speed of the shaft and thus the residence time in the reaction chambers can be varied, at least in mode two: If the residence time is to be increased, the crankshaft is braked with the aid of the at least one device; if the residence time is to be reduced, the crankshaft is accelerated with the aid of the device, or the braking torque is reduced. Electrical machines used are, for example, commutators, such as DC or singlelectricalphase AC motors, or rotating field machines, such as threelectricalphase asynchronous machines, threelectricalphase synchronous machines, singlelectricalphase asynchronous motors, singlelectricalphase synchronous motors. Electrical machines, which can be used both as a motor and as a generator are preferable, since they can be used in both operating modes of the device according to the invention. When using the electrical machine as a generator, the energy to be dissipated during braking can be converted into electricity and fed into the power grid, used for electrolysis of water, made available to consumers or temporarily stored. When using an electrical machine as a motor, starting the apparatus is very simple, since the crankshaft is towed for this case. In addition, reactions can also be represented here in which the energy released by the reaction is not sufficient to ensure self-sufficient operation of the apparatus in at least the second mode. This is particularly the case for endothermic reactions. In these cases, the device is driven in the second mode by the electrical machine.

In order to reduce the cost of an electrical machine, a combination of a small electrical machine (for start-up and to compensate for short-term peaks) and a powerful eddy current or water brake, which take over most of the braking power, can be used when the power of the compression reactors is high and the associated braking power of the crankshaft is high. In this case, the current yield is naturally much lower, but high heat flows are then generated which can be used as process heat. In addition to the design described above as a reciprocating piston machine, a design as a rotary piston machine can also be implemented according to the invention. This is also coupled to a device, e.g. electric machine, by means of which the speed of the rotary piston machine and thus the residence time in the reaction chambers can be changed at least in mode two. In addition, as already described above, this makes it possible to generate electrical energy in mode one. The products formed in mode two can be discharged from the process and further processed. Another variant according to the invention is to collect at least one of the products produced in mode two and store it temporarily for use as fuel at a later time in mode one.

According to the invention, at least one of the products produced in mode two and greater, i.e. in the modes different from mode one, has a calorific value of at least 12MJ/kg, advantageously of at least 20MJ/kg, extremely advantageously of at least 30MJ/kg. The proportion of the at least one product with a calorific value of at least 12MJ/kg in the product stream leaving the reactor in mode two is at least 5%, advantageously at least 10%, extremely advantageously at least 20%. Advantageously, the process is suitable when the sum of the volumetric calorific values of the products is higher than the sum of the volumetric calorific values of the reactants. The calorific value of all products formed in mode 2 and larger is in sum at least 10 times as high, advantageously at least 20 times as high, extremely advantageously at least 100 times as high, as the calorific value of the waste gas emitted in mode one. Suitable products or chemical energy storage componends include NH3, alkenes, alkanes, alcohols, ethers and esters, such as CH4, CH3CH2OH, CH3OH, C2H4, HCHO, dimethyl ether (DME), diethyl ether (DEE) and polyoxymethylenedimethyl ether (POMDME). For this purpose, at least one, advantageously at least two, of the following compounds or their derivatives are fed to the reactor chambers during the second mode, among others: N2, H2, CO, CO2, HCHO, CH3OH, ethanol.

The reactants for the production of CH4 and C2H4are CO and/or CO2 as well as H2, for NH3, N2 and H2, for HCHO, CO and/or CO2 and H2, for CH3OH and CH3CH2OH, CO and/or CO2 as well as H2, for DME, CH3OH, for POMDME, CH3OH and HCHO, for DEE, ethanol. In order to achieve sufficiently high yields in the second mode, the oxygen concentration at the start of the reaction is a maximum of 1%, advantageously a maximum of 0.5%, extremely advantageously a maximum of 500ppm. This avoids or reduces oxidation of the products and thus a lowering of the calorific value. In the first mode, the air-to-fuel ratio lambda is at least 0.95, advantageously at least 1, extremely advantageously at least 1.3.

For safety reasons, it is convenient to feed the combustible reactants, such as hydrogen or methanol, directly upstream of the inlet to the reactor chamber, i.e. downstream of the noncombustible reactants, or directly into the reactor chamber. The compression ratio of the piston reactors is at least 1:8, advantageously at least 1:15, extremely advantageously at least 1:20. The residence time of the reactants in the reactor chamber is at most 1s, advantageously at most 0.3s, extremely advantageously at most 0.01s.

The crankshaft is surrounded by a so-called crankcase and this is fastened to the reactor walls by screws. The seals used at the joints are static seals, which ensure a significantly better seal to the outside than the dynamic seals on the pistons. However, these dynamic seals of the piston at the cylinder of the reactor chamber are still a critical point, as reactants can enter the crankcase via them. In conjunction with the oxygen present in the environment, this can lead to the formation of explosive mixtures, such as oxyhydrogen gas, and consequently to an explosion or deflagration in the crankcase. If toxic reactants or products are involved, such as formaldehyde, these can escape into the environment, which should also be prevented. According to the invention, this is prevented by flushing the crankcase with non-flammable and non-toxic or low-toxic reactants, such as N2, CO and/or CO2, which are then fed to the reactor chamber. A further improvement can be achieved if the crankcase or the reactants and products contained therein are sucked out so that a lower pressure is established than in the environment and these reactants are subsequently fed to the reactor chamber. The at least one flammable or toxic reactant is then also introduced directly upstream of the reactor chamber or, better, directly into the reactor chamber. When reactants are introduced directly into the reactor chamber, the introduction is advantageously carried out according to the invention with the inlet and outlet valves closed.

In order to additionally raise the pressures in the reactor chamber in mode two, it is useful to feed the reactants to the reactor chamber already at elevated pressure. In the simplest case, this can be done via compressors, but a turbocharger arrangement makes more sense in terms of efficiency, especially for exothermic reactions: Here, enthalpy is extracted from the heated product stream via a turbine located downstream of the reactor chambers and transferred via a shaft to a compressor on the reactant side. The pressures on the reactant side and thus ultimately the pressures in the reactor chamber can be varied by suitable measures, such as discharge valves on the reactant and/or product side, variable turbine and/or compressor geometries.

The apparatus can be designed in the second mode as a two-stroke, four-stroke or four + 2*xstroke apparatus. The following description refers to, but is not limited to, a reactor chamber and an exemplary design as a reciprocating engine with the crankshaft mounted below the pistons.

Two-stroke apparatus: 1. intake and compression (piston moves upward) 2. main reaction and expulsion (piston moves downwards) For this design, valves can, but do not have to, be dispensed with completely, since the piston alternately closes or opens the inlet and outlet.

Four-stroke apparatus: 1. intake (intake open, exhaust closed, piston moves downward) 2. compression (inlet and outlet closed, piston moves downward) 3. main reaction and expansion (piston moves down) 4. expulsion/push-out (outlet open, inlet closed, piston moves up) This setup requires inlet and outlet valves at the reactor chambers. These can be driven by at least one camshaft. Additional devices are known from the engine sector by means of which the opening and closing times of these valves can be varied and are also used here, such as piezo actuators, hydraulic valve trains, adjustable camshafts, etc.. These measures can be used to influence the reaction conditions in the reactor chamber. For example, it is possible to open the exhaust valve after the third cycle even before the piston reaches bottom dead center in order to lower the pressure and thus the temperature in the reactor chamber more quickly than would be possible via piston movement alone. In this way, it is possible to freeze the reactions and avoid undesirable side reactions. In addition, the inlet valve can be opened before the top dead center of the piston is reached in the extension stroke, in particular before the bottom dead center of the piston is reached, so that products flow back to the reactant side. As a result, a mixture of products and reactants is sucked in during the next suction stroke, which increases the yield of products. A similar effect is achieved if the outlet valve remains open during the suction cycle, so that products are drawn back into the reactor chamber.

Four-stroke + 2"x apparatus: This is a further development of the four-stroke apparatus. In order to increase the yield, the outlet valve is not opened in the fourth cycle, but at least one more compression and one more reaction cycle are added.

1. intake (intake open, exhaust closed, piston moves down) 2. compression 1 (inlet and outlet closed, piston moves upwards) 3. main reaction 1 and expansion 1 (piston moves downwards) 4. compression 2 (piston moves upwards) 5. main reaction 2 and expansion 2 (piston moves down) repeat the compression and main reaction cycle x times 6 +2*x: expansion (outlet open, inlet closed, piston moves upwards) x is an element of the natural numbers, so that in sum cycle numbers of 6, 8, 10 etc. result. It is often useful to add at least one reactant for the second main reaction. This can be done, for example, by opening the inlet valve or directly adding at least one more reactant via an additional feeding device into the reactor chamber. On the one hand, it is possible to feed one of the reactants that has already been fed in the first main reaction, which on the one hand can increase the yield and/or the selectivity. However, it is also possible to feed at least one reactant that is different from the reactants in the first main reaction, which may selectively produce a different product than in main reaction one. The addition can be done, for example, by opening the inlet valve and sucking it into the reactor chamber or direct addition of at least one reactant via an additional feeding device into the reactor chamber.

Regardless of the number of cycles, the yield in mode two is further increased according to the invention by removing a partial product stream downstream of the reactor chamber and returning it to the reactor chamber, in particular on the inlet side. The amount of product recirculated in this way can be varied by suitable actuators, such as valves and/or blowers.

Moreover, the reaction in mode two can be influenced by the temperature of the reactants fed to the reactor chamber. For example, the yield of endothermic reactions or reactions with volume increase can be raised if the temperature of the reactants is increased before they enter the reaction chamber. This temperature increase can be accomplished in an energy-efficient manner by thermally coupling the reactant stream to the product stream downstream of the reactor chambers and/or the cooling medium of the compression reactor. The cooling medium is necessary to prevent overheating of the apparatus. In addition, for exothermic reactions, such as methane production from CO or CO2 and H2, or ammonia production from N2 and H2, cooling of the reactants is useful.

Since, as described above, the start of the reaction in mode two often cannot be initiated in a defined manner and/or the temperatures have to be raised to such an extent that this has a negative effect on the selectivity, additional energy is supplied to the reactor chamber in the short term according to the invention in order to exceed the activation energy and thus start the reaction. This can be done via at least one of the following methods or devices: Electrical spark, in particular by means of a spark plug, corona discharge, microwaves, laser pulse. To further increase the input of energy into the reactor chamber, a small, separate ignition reactor chamber can be used, which is connected to the main reactor chamber via openings. In this chamber, a different gas composition is usually selected than in the main reactor chamber. For example, an ignitable gas mixture containing oxygen can be provided in this chamber, while the main reactor chamber contains no oxygen or at least significantly less oxygen. The gas mixture contained in the ignition reactor chamber is now ignited, e.g. via a spark plug, and the resulting pressure wave and flame front travel through the openings into the main reactor chamber, where they start the main reaction. The reaction can also be started by direct introduction of a compound necessary for accelerating the reaction into the reactor chamber, in particular of a reactant necessary for the reaction. The introduction being carried out according to the invention with the intake and exhaust valves closed, in particular at the end of the compression stroke and/or at the beginning of the main reaction stroke, i.e., in the case of two-stroke apparatus, at the end of the first and at the beginning of the second stroke, in the case of four-stroke apparatus, at the end of the second and/or at the beginning of the third, in the case of four + 2*x-stroke apparatus, at the end of the second and/or second+x-th and/or at the beginning of the third and/or third+x-th, i.e., in the region of top dead center of the piston with the inlet and outlet valves closed. Since the reaction can only proceed when the reactant required for the reaction is added, an uncontrolled reaction can be ruled out before it is added. A further improvement can be achieved if the necessary reactant is not only added completely at a defined time, but is distributed over several additions. According to the invention, the partial amounts of the individual reactant additions differ.

In order to increase the yield, it is also provided in accordance with the invention to remove a partial product stream downstream of the reactor chambers and to feed it back to the reactor chambers. The reaction conditions in the reactor chambers are at least 50bar, advantageously at least 60bar, extremely advantageously at least 70bar. The temperatures before the start of the reactions are between 200°C and 500°C, advantageously between 250°C and 450°C, extremely advantageously between 280°C and 400°C.

A further improvement of the process is to measure the gas composition downstream of the reactor chamber in mode two and to adjust corresponding process parameters via an electronic control unit. If, for example, the yield is too low, the following parameters, among others, can be adjusted: Crankshaft speed is lowered, reactant pressure is raised (for reactions with volume reduction), reactant pressure is lowered (for reactions with volume increase), amount of product returned to the reactant side is raised, the inlet valve is opened before the outlet valve opens, causing the products to flow to the reactant side, the energy supplied to the reactor is raised (e.g., raising the ignition voltage), the number of cycles is raised, especially above four.

If the selectivity is too low, among other things the following is possible: speed of the crankshaft is increased, the number of cycles until push-out is lowered, the reactant pressure is lowered, the amount of product returned to the reactant side is lowered, in the intake cycle the inlet valve is closed before reaching bottom dead center, in the expansion cycle the outlet and/or the inlet valve is opened before reaching bottom dead center, the energy supplied to the reactor is cycled and/or the individual energy is lowered (e.g. several laser pulses or ignition sparks).

If H2 is required for the reaction, it can be produced via electrolysis, for example. In order to increase energy efficiency, it is advisable to resort to high-temperature electrolysis, whereby the thermal energy required to operate the electrolyzer is supplied at least in part by thermal coupling to the hot product stream. For this purpose, water is evaporated with the aid of the hot product stream and supplied to the electrolyzer at at least 500°C, preferably at least 550°C, extremely preferably at at least 600°C. If the thermal energy of the product stream is not sufficient, the water vapor can be thermally coupled to the H2 and/or 02 stream leaving the electrolyzer. In addition, auxiliary heating is possible. A reduction of the investment costs on the side of the hydrogen electrolyzer can be achieved, if CO and H20 are fed to the reaction chamber of the compression reactor, so that a water gas shift reaction occurs CO + H20 <----> CO2 + H2 Based on this process according to the invention, the amount of H2 that has to be produced via electrolysis, for example, can be lowered by about 1/3 when methanizing CO or CO2. In this process, the necessary hydrogen can already be added in parallel with the water. In order to increase the yield, however, it is advisable to add the hydrogen subsequently. The 4+2*x cycle operation is particularly advantageous here, i.e. the hydrogen is only added for the second or one of the following reactions, since in this way a separation of the water-gas shift reaction and the methanation can be ensured. Another possibility is to separate the water-gas shift reaction and the methanation spatially, i.e. to let them take place in two different reactor chambers: The water gas shift reaction takes place in a first reactor, and the CO2 and H2 produced there plus the additionally required hydrogen are then fed to the second reactor in which the methanation takes place. Irrespective of the water gas shift reaction, the advantage of this process is that different reaction conditions can be set in the different reactors via reactant temperatures, compression, valve control times (for inlet and/or outlet valves), reactant pressures, additionally supplied activation energies (e.g. ignition spark), timing of the additionally supplied activation energy. This procedure is particularly useful in the case of a V-shaped arrangement of the reactor chambers: the water gas shift reaction can take place on one bank and the methanation on the other. This procedure is not limited to CH4 production, but can be used for all reactions in which the concentration of intermediates is to be influenced.

One way to further increase the yield and selectivity of methane production in mode two is to install a methanation catalyst downstream of the reactor chambers. Nickel, ruthenium, aluminum, cobalt or cerium can be used as active components. Another improvement is to install catalysts for exhaust gas aftertreatment in the reactor housing required for the methanation catalyst in order to reduce exhaust gas emissions from the internal combustion engine in mode one. Suitable catalysts include, for example, SCR, formaldehyde oxidation and/or CH4 oxidation and/or CO oxidation catalysts.

To prevent reactants from escaping to the outside and/or oxygen from entering from the surroundings during mode two, the air supply required for mode one is cut off via a shut-off device on the intake side. In mode one, the product generated and temporarily stored in mode two can be used as a fuel or combustible, in pure form or as an admixture to other fuels or combustibles. In addition, the following fuels and mixtures containing these substances can be used in mode one: methane, ethane, propane, butane, methanol, ethanol, butanol, propanol, gasoline, diesel, natural gas, DME, DEE, RME, NH3, H2, NH3 + Hz, POMDME. When using carbonaceous fuels in mode one, it is convenient to capture the CO2 formed during combustion, store it temporarily, and then use it as a reactant in mode two. In this case, it is possible to produce hydrocarbon-containing compounds such as methane, ethane, ethene, ethyne, ethanol, methanol, DME, DEE in mode two. These are collected to be used as fuel at a later stage in mode one. In the case of methane, this can also be fed into the natural gas grid so that it can be made available to other consumers and/or stored in the natural gas grid. This highlights another advantage of the process and apparatus according to the invention: the compression reactors can also be used as compressors for compressing the at least one product produced: For this purpose, the piston not only pushes out the products in the push-out cycle, but also pumps them into a storage container and/or a downstream process, in particular a process operating under pressure. In other words, the products are both pumped and compressed by the compression reactors in the ejection stroke; in that case the compression reactors operate like reciprocating compressors. In the best case, an additional compressor or blower for pumping and compressing the at least one product can be dispensed with, or at least they can be designed to be significantly smaller. In exothermic reactions, the energy required for this is provided from the chemical reaction, so that no conversion to another form of energy, such as electrical energy, is necessary. Therefore the efficiency is significantly higher than that of separately operating chemical flow or fixed-bed reactors and compressors. If the energy from the reaction is not sufficient, the products can be pumped or compressed using mechanical energy transmitted to the crankshaft via the electric machine.

Beyond mode two, the apparatus according to the invention can also be operated in other modes, with either their products or reactants being respectively different from those of the other modes, in particular from those of mode two. This shows a further advantage of the process or apparatus according to the invention compared to the prior art, since different reactants can be processed, or different products can be produced, with the same reactors In the following, the apparatus according to the invention and the process are explained with reference to figures.

Figure 1 shows the apparatus according to the invention during mode two. The individual reactor chambers (1) are arranged in series and housed in a common casing. Together they form a reciprocating engine (2). Via a shaft (5), the compression energy delivered by the reactors or to be supplied to them is transmitted to or from an electric machine (4). The reactants (6) and (7) are fed to the reactors, and the products (8) are discharged from the reactor chambers (1) and collected in a container (3).

Figure 2 shows a device according to the invention, which can be used both as a combustion engine for the generation of electrical energy and as a pulsed compression reactor for the formation of chemical products. The individual reactor chambers (1) are arranged in series and housed by a common casing. Together they form a reciprocating engine (2). Via a shaft (5), the compression energy delivered by the reactors or to be supplied to them is transmitted to or from an electric machine (4). In the first mode, in which the apparatus operates as an internal combustion engine, air (9) and fuel (19) are supplied to it through the open valves (13) and (14) and discharged through the valve (15). The valves (11), (12), (16), (17) are closed in this mode. Following the terminology commonly used in internal combustion engines, the reactor chambers can also be referred to as combustion chambers (1). In the second mode, valves (13), (14) and (15) are closed and valves (11), (12) and (16) are opened. As a result, the reactants (6) and (7) are fed to the reactors, and the products (8) are discharged from the reactors (1) and collected in a container (3). To avoid overheating of the apparatus, it is cooled by a suitable cooling medium, such as water. If several products are formed, a separation of the individual products is arranged downstream of the apparatus, e.g. via membrane processes, gas scrubbing, extraction, rectification, adsorption, condensation (not shown here).

This becomes relevant, for example, when gases are fed in as reactants that result from an oxidation reaction with air, such as occurs during the combustion of hydrocarbons in mode one. In this case, CO and CO2 are formed on the one hand, but in addition large amounts of N2 are present which do not participate in the combustion. If this mixture is fed to the reaction chamber together with H2, hydrocarbons are formed, such as methane, but also water and NH3. This NH3 can be easily absorbed with the help of water fed in a column in countercurrent or co-current flow at temperatures below 300, preferably below 20°C, extremely preferably below 15°C. The water is then discharged and heated. This water is then discharged and heated to expel the NH3 again, thus "regenerating" the water so that it can absorb NH3 again. It is then cooled and returned to the product stream to absorb more NH3. Since the water produced in the reaction is also separated from the hydrocarbons in this way, it is removed, since otherwise the amount of water carried in the loop would increase. The amount of heat required for the desorption of ammonia can be applied by thermally coupling the desorption unit to the product stream upstream of the scrubber and/or to the cooling medium of the reactor. If the products formed are not to be further processed but "only" reused as fuel in mode 1, it is often possible to dispense with their separation, in particular the separation of hydrocarbon and hydrogen nitrogen-containing compounds, since both groups of substances have sufficiently high calorific values. For energetic reasons, however, separation of H20 is useful.

Fig. 2 shows another possible embodiment according to the invention: In the first mode, at least parts of the exhaust gas, such as 002, are stored in a container (10). The remaining exhaust gas components, such as water, on the other hand, are discharged into the environment. Since the separation of CO2 is state of the art, reference is hereby made thereto. In mode two, the valve (17) is opened and thus the CO2 formed in mode one is fed to the reactor.

The apparatus can be used to produce methane as product (8) in mode two by adding CO2 and/or CO as reactants, as well as H2. For safety reasons, it is useful to purge the crankcase (32) with CO2 as shown in Figure 3. Furthermore, the production of ammonia is possible by using nitrogen and hydrogen as reactants. In this case, purging the housing (32) with nitrogen is useful. Simultaneous production of NH3 and CH4 is also possible by feeding CO2 and/or CO as well as H2 and nitrogen to the apparatus.

Fig. 3 shows a reactor according to the invention based on the four-cycle or the four+2*X-cycle principle: At least two reactants (6, 7) are fed into the reactor chamber (1) via at least one inlet valve (33). The reactants are sucked in and compressed via a piston (34), which is connected to the crankshaft (37) via a connecting rod (35) and moves up and down in a sleeve, and the products (8) are then pushed out. The reactants can be fed to the reactor together through the inlet valve, as shown in Fig. 3. In the case of explosive substances, such as H2, it is advisable for safety reasons to feed them directly into the reactor chamber or at least to add them directly upstream of the inlet valve (not shown here). Compression causes an increase in temperature and pressure, which brings about the desired reaction. The start of the reaction can also be initiated, or precisely controlled or regulated, by supplying additional energy, e.g. in the form of an ignition spark using a spark plug, a laser pulse, a corona discharge or microwave radiation (not shown here). To avoid leakage of reactants and products into the environment, the piston and the crankshaft are surrounded by a housing (32) which is sealed to the environment by means of static seals (36). To prevent large quantities of reactants and products from entering the housing past the piston, the latter is sealed off from the cylinder in which it moves up and down by means of dynamic seals (39). Since it is nevertheless unavoidable that reactants and products penetrate into the housing (32), it is provided in accordance with the invention, in the event that explosive or corrosive substances are involved, that the housing (32) is flushed with a non-corrosive, non-flammable or non-explosive reactant and this is then fed to the reactor chamber (1) (not shown). The at least one inlet and/or outlet valve can be controlled via camshafts, hydraulically or piezoelectrically. Especially the last two variants are to be preferred if a precise control of the reaction conditions and/or four+2*X-cycles are to be represented, since the valve opening times can be freely chosen.

According to the method of the invention, the control and regulation is carried out with the aid of an electronic control unit. At least one of the following variables serves as input variables for the control: Product composition, energy and storage requirements of the power grid, product requirements, speed of the crankshaft, residence time in the reactor chamber, reactant pressure, reactant temperature, product temperature, reactant composition, product composition. Actuators or manipulated variables are at least one of the following: Educt cooler, educt heater, educt pressure controller, energy supplied/discharged by the electrical machine, ealve opening times (inlet valves, outlet valves, educt valves), product quantity recycled, compression ratio variation, variable turbine geometry, variable compressor geometry, activation time of the additional energy supplied via a spark plug, laser, microwaves or corona discharge.

The purging of the housing (32) is illustrated for the case of a two-stroke apparatus in figures 4a, b, c: According to the invention, in the first cycle (Fig. 4a), the non-corrosive, non-flammable or non-explosive reactant (7) is fed into the housing (32) via a valve or flap. This flows past the piston into the reactor chamber (1). The at least second reactant (6) is added to the reactor chamber (1) or directly in front of it (not shown here). The upward movement of the piston compresses the reactants (Fig. 4b) and initiates the reaction. This can be improved, or precisely controlled or regulated, by using a device for supplying additional energy (42), such as a spark plug, a laser pulse, a corona discharge or microwave radiation. In the subsequent ejection stroke (Fig. 4c), the products (8) are ejected from the reactor. This supply of additional energy is not limited to the two-cycle apparatus, but can also be used with four-and four+2*X-cycle apparatuses.

Fig. 5 shows a modification of the arrangement chosen in Figs. 1 and 2 to increase the yield and/or selectivity in mode 2. For reasons of clarity, not all the details shown in Fig. 2 are shown, and in particular only mode two is shown in this and the following figures, i.e. the supply of power or fuel and combustion air for mode one is not shown.

Here, a product stream (52) is taken downstream of the reactors and this partial product stream, together with the reactants (6,7), is added to the reactors (1). It can be conveyed by a suitable conveying device (51), such as a compressor or a blower. A control of this recirculated product flow with suitable control elements, such as valves or dampers, can also be implemented (not shown). In order to further increase the yield or selectivity, it may be useful to selectively eject products (8a) from this stream via a separator device (53). In particular, if the product stream (8) still contains high amounts of reactants or undesired intermediates or end products. For example, in the production of methane using CO and/or CO2 as well as H2, this involves water being discharged from the cycle.

A similar setup is shown in Fig. 6, but here the separator (53) is located in the main product stream, so that the separation of the product (8) is implemented for the entire product stream.

Figure 7 shows an embodiment for raising the reactant pressure in mode two via a compressor (71). The compressed reactant (7) is then fed to the reactors. The at least second reactant (6) can be added to the reactant (7) upstream of the compressor (not shown), or added directly upstream of the reactors or directly into the reactors. The compressor (71) is connected via a shaft (73) to a turbine (72), via which the product stream (8) is expanded from a high to a lower pressure. The energy released in this process is thus largely reused for compressing the reactants, thus increasing the efficiency of the process. The reactant pressure can be varied by suitable devices, such as blowing off the reactant from the high-pressure to the low-pressure side of the compressor via a suitable control element (75) (compressor bypass), blowing off the product from the high-pressure to the low-pressure side of the turbine via a suitable control element (76) (turbine bypass), variable turbine geometry and/or a variable compressor geometry. Moreover, in order to further raise the pressure, the compressor can additionally be driven electrically and/or another compressor can be arranged within the reactant stream. It is also advantageous in this design if the system design is such that the pressure on the reactant side is lower than on the product side, since this allows product that is returned to the reactant side (52) to flow to the reactant side without a conveying device such as compressors, blowers or pumps. The quantity can thereby be varied or controlled via a variable throttle device (74) and an electronic control unit. According to the invention, it is provided that at least the temperature of a reactant or of the product recycled to the reactor is controlled or regulated by means of an electronic control unit and coolers or heaters. The arrangement of turbine and compressor described above for mode two can also be used for mode one by interconnecting it in such a way that it is used as a turbocharger to compress the air (19) or oxygen (9a, see Figure 12) supplied to the combustion chambers. The design as a turbocharger is state of the art, so that a detailed design is omitted. Since both the delivery rates and the temperatures and pressures upstream of the turbine and downstream of the compressor differ from one another in mode one and two, the invention provides for the delivery rates to be adjusted accordingly by means of suitable control elements, such as turbine bypass (76), compressor bypass, variable compressor geometry or variable turbine geometry.

Figures 8 and 9 show a series connection of several reactors (1) and (la). The reactors (1) and (la) can differ in their geometry, such as piston geometry, diameter and/or stroke, or in their operating parameters, such as temperature, pressure and/or additional energy supplied. This makes it possible to further process an intermediate product (8b) leaving the first reactors (1) with modified reaction conditions, resulting in the final product (8). Between the two reactors, another reactant (81) can be fed and/or an intermediate product (8c) can be discharged. The process can be further improved if a product formed in the second reactor (1a) or unused reactants (52) are fed to the second reactor (la) or first reactor (1) (not shown).

For example, according to the invention, methanol is produced from CO2 and H2 in the first reactors (1), CO2 + 3H2 --> CH3OH + H20 while in the second reactors (la) dimethyl ether (DM E) is formed with separation of H20 (Sc). 2 CH3OH --> 0H3-0-CH3 + H20 Between the two reactors, an intermediate (8c), in this case H20, is removed from the first reaction. This serves to shift the equilibrium to the side of DME (8). This can be further improved if the water formed in the second reactor is removed from the product stream (8a) and this anhydrous product stream (52) is returned to the reactor chambers (la) (Fig. 9).

The two reactor rows can be constructed as separate independent units, i.e. separate piston machines, in the event that different residence times are to be realized in the two reactor rows; however, according to the invention, it is also possible to arrange both rows in such a way that their pistons act on a common crankshaft (37) via the connecting rods (35). This is particularly useful if the residence times in the two reactor rows are to be identical. To ensure this, the two rows are arranged in a V-shape relative to each other, the angle of the two legs being marked as "a" in Figure 10.

Figure 11 shows a variant and a method of the device shown in Figure 2. In addition to the components already described in Figure 2, a device (90) for splitting water (96) into hydrogen (93) and oxygen (9a) using electrical energy is also shown. This splitting of water is illustrated using an electrolyzer, a high-temperature electrolyzer may be used to improve yields. To increase the efficiency, this can be thermally coupled to the product stream (8) and/or the cooling of the reciprocating machine (2). The water (96) required for this electrolyzer can be supplied externally. It is also possible to use water formed in modes one or two. The process according to the invention is described below using the example of a CH4-based process. In principle, the valve circuit described for Figure 2 applies; deviating circuits are described below.

In the mode one, CH4 (19) is fed as fuel to the device and the reactor chambers (1). When the methane is burned with the help of oxygen (9a), CO and CO2 are formed, which are collected and temporarily stored in the tank (10). In mode two the hydrogen (93) leaving the electrolyzer is fed to the reactor chambers (1) together with the intermediately stored CO or CO2 (18), forming CH4, which is intermediately stored in the tank (3). For this purpose, the valves (12) and (17) and (16) are opened, and the valves (15, 13, 97, 94, 14) are closed. If the quantity of CO and CO2 stored in the container (10) is not sufficient, CO and/or CO2 (6) can be supplied from outside the circuit by opening the valve (11). It on the other hand, the stored quantity is sufficient, the valve (11) remains closed. The oxygen (9a) formed by electrolysis in mode two is temporarily stored in the tank (91), with the valve (94) closed. In mode one, the valve (94) is opened and thus oxygen (9a) is supplied to the combustion or reactor chambers (1). In addition, the valve (97) is opened, through which the CH4 stored in the container (3), which was formed in mode two, is supplied to the combustion or reactor chambers (1) as fuel. If the amount of CH4 stored in the tank (3) is not sufficient, additional fuel (19) can be supplied to the reactor chambers (1) by opening the valve (13). The advantage of using oxygen (9a) formed during electrolysis instead of air (9) is that no nitrogen is present in the process. On the one hand, this has the advantage that in mode one no nitrogen oxides can form during the combustion of the CH4 due to the absence of nitrogen. As a result, downstream catalysts to reduce nitrogen oxide emissions in mode one are not required. The second advantage is that in mode one, separation of the nitrogen from CO or CO2 downstream of the combustion or reactor chambers and upstream of the storage vessel (10) can be omitted or the vessel 10 can be made smaller, since no inert nitrogen needs to be stored. Another advantage is that, also in mode one, combustion with oxygen can present a higher output with identical combustion chamber pressure and thus mechanical stress on the components. In addition, combustion with oxygen offers the advantage that a higher CH4 conversion rate is achieved in mode one due to the improved combustion. This results in improved efficiency and lower emissions of unburned CH4.

If the amount of oxygen stored in the tank (91) during mode two is not sufficient for mode one, additional oxygen can be supplied via the valve (14). Air can also be supplied, but this introduces nitrogen into the circuit. This must then be removed again. However, with sufficient H2 supply, the parallel formation of CH4 and NH3 is also possible. Since NH3 can also be used as fuel, it is not necessary to separate CH4; instead, the CH4/NH3 mixture can be fed back to the combustion or reactor chambers (1) in mode one. However, this places higher demands on the control of the combustion in mode one. For this reason, as a further process control according to the invention, it is envisaged to operate the electrolyzer (90) also in mode one in order to generate sufficient oxygen (9a) for the combustion. The hydrogen (93) formed in parallel in this process is temporarily stored in the tank (92) for mode two. If the amount of hydrogen formed exceeds the storage capacity or if the admixture of H2 positively influences combustion in mode one, H2 can also be added to the combustion chambers (1) in mode one. This is particularly useful for the combustion of NH3 in mode one. Regardless of the cycle described above, the products formed in the reciprocating machine and/or the electrolyzer can be discharged from the cycle and used elsewhere (not shown here).

In the above example, the apparatus and process are shown from energy generation and energy storage using CH4 as the storage component. However, the process is not limited to methane, but is suitable for all compounds that have a sufficiently high calorific value, especially above 12MJ/kg. In particular, NH3 lends itself to this by using nitrogen and hydrogen, instead of CO and/or CO2 and H2, as reactants in mode two. Firstly, nitrogen does not have to be removed from the cycle for this purpose, since it is an integral part of the process. Secondly, the ammonia formed in mode two can be liquefied very easily by a slight increase in pressure (to approx. 8bar at 20°C), which allows a significantly higher storage density and thus lower storage volumes to be realized compared with CH4. The same applies to longer-chain hydrocarbons, alcohols, ethers or esters as storage components, such as POMDME, DEE, DME, methanol, ethanol, propanol, propane or butane, which can either be liquefied at low pressure or are already liquid at room temperature. Particularly when NH3 is used as a storage medium, it is a good idea in mode one to additionally feed hydrogen (93) to the combustion chambers (1) in order to improve the ignition of the NH3 fed in and thus the stability of combustion. In the case of hydrogen-containing storage media that contain a carbon-oxygen bond, such as methanol, a further process mode is suitable: Here, in the first mode, hydrogen and CO2 are produced and separated from each other using a reformer. The hydrogen is fed to the compression reactors as fuel, while CO2 is stored. In the second mode, this CO2 is fed to the compression reactors together with hydrogen produced via water splitting, and methanol is produced as already described above. The oxygen produced during water splitting, e.g. via electrolysis, can be fed to the reactors for oxidation of the hydrogen in mode one, as already described above.

In Fig. 12, the switching between mode 1 and mode 2 of the apparatus according to the invention is shown with the aid of an electronic control device: After the start of the program, it is checked whether electrical or mechanical energy is required. If this is the case, the electronic control unit activates mode 1 and opens or closes the valves described in the previous figures and periodically activates corresponding ignition or fuel supply devices to operate the device according to the invention as an combustion engine. If, on the other hand, no energy is required, but electrical energy is available or is to be stored, the electronic control unit puts the device according to the invention into mode 2 by opening or closing the corresponding valves. Moreover, the electronic control unit can be used to supply the actively additional activation energy. That is, the device according to the invention then operates as a pulsed compression reactor. For the explanation of which valves are closed or opened in which mode, please refer to the explanations of the preceding figures. In the case that energy is neither required, nor available, nor to be stored, the device is stopped. In the event that other reactants are to be used, or other products are to be produced than in mode two, the electronic control unit can be used to switch to a mode that is different from modes one and two. This can be done by additional valves and/or control devices (not shown here), but in the simplest case only process parameters are changed. For example, in mode two ammonia can be produced from Nz and Hz, in mode three methane can be produced from CO2 and Hz, and in a mode four methanol can be produced also from CO2 but with less Hz. In addition, the product of a mode different from mode one can serve as the reactant of a mode different from one. Such as methanol from one mode that can be used to produce DME in another mode. In contrast to the state of the art in fixed bed reactors, which must first be ramped up at length, often over several minutes or hours, in the process according to the invention it is possible to switch very quickly between the individual modes, in particular from mode 1 to one of the others. I.e., switching from the "energy delivery" mode to one of the "energy storage" modes and back can be performed highly dynamically, in particular within a few working cycles, since the compression reactors are already at operating temperature.

In addition, at least when the device is not in mode one or is at a standstill, the electronic control unit takes over the regulation of the corresponding process parameters described above or the corresponding actuators, such as valve opening times of the at least one inlet valve, valve opening times of the at least one outlet valve, valve closing times of the at least one inlet valve, valve closing times of the at least one outlet valve, timing of a reactant added directly into the reactor chamber, crankshaft speed, reactant pressure of at least one reactant, educt temperature of at least one educt, educt composition, recirculated product quantity, temperature of the recirculated products, variation in the number of cycles, compression ratio, time of an additionally supplied activation energy independent of the compression energy, energy quantity of the additionally supplied activation energy, number of additionally supplied activation energies per cycle. For this purpose, this control unit evaluates corresponding sensors, such as temperature, pressure, rotational speed and flow sensors, in particular for the reactants, in order to represent a closed control loop and to achieve the respective desired product composition for the respective mode. According to the invention, it is further provided to determine the product composition also with corresponding sensors, such as NH3, CO2, CO, CH4-sensors and/or with the aid of analyzers, such as gas chromatographs, IR, UV, FID analyzers, FTIR and/or mass spectrometers and to change the process parameters described above in such a way that a high yield of desired products is achieved.

Claims

Claims 1. Method for the storage and production of energy with the aid of a reciprocating or rotary piston engine (2), wherein the engine can be operated in at least two different modes, wherein in a first mode it is operated as a combustion engine and in at least a second mode it is operated as a pulsed compression reactor and in this at least second mode at least one product is produced and this at least one product has a calorific value of at least 12MJ/kg, advantageously of at least 20MJ/kg, extremely advantageously of at least 30MJ/kg.
2. Method according to claim 1, wherein the at least one product is collected, temporarily stored (3) and it is used as fuel (19a) at a later time in the first mode.
3. Method according to claim 1, wherein the calorific value of all the products formed in mode greater than one, in particular in mode two, is in total at least 10 times as high, advantageously at least 20 times as high, extremely advantageously at least 100 times as high, as the calorific value of the exhaust gas emitted in mode one.
4. Method according to claim 1, wherein at least one, advantageously at least two, of the following compounds or their derivatives is fed to the reactor chambers (1) during the mode greater than one, in particular in mode two: N2, H2, CO, CO2, HCHO, CH3OH, ethanol, methanol.
5. Method according to claim 1, wherein the reactant pressure of the mode greater than one, in particular in mode two, is raised by means of a compressor (71) connected via a shaft (73) to a turbine (72) driven by the product stream (8).
6. Method according to claim 1, wherein in mode greater than one, in particular in mode two, downstream of the reaction chamber (1, la), a reactant and/or a partial product stream and/or or a product is extracted (52) from the total product stream (8) and fed to the reaction chamber (1, la).
7. Method according to claim 1, wherein in mode greater than one, in particular in mode two, hydrogen (93) and oxygen (9a) are produced via the splitting of water (96) with the aid of an electrolyzer (90), the hydrogen formed in mode greater than one, in particular in mode two, being fed to the reactor spaces (1, 1a) and/or the oxygen formed being fed to the reactor chambers (1, la) in mode one
8. Method according to claim 1, wherein at least one, advantageously at least two, extremely advantageously at least three of the following variables can be changed with the aid of at least one electronic control unit: Valve opening times of the at least one inlet valve, valve opening times of the at least one outlet valve, valve closing times of the at least one inlet valve, valve closing times of the at least one outlet valve, time of a reactant added directly into the reactor chamber, shaft speed, educt pressure of at least one reactant, educt temperature of at least one reactant, reactant composition, recycled product quantity, temperature of the recycled products, variation of the number of cycles, compression ratio, time of an, independent of the compression energy, additionally supplied activation energies, energy quantity of the additionally supplied activation energy, number of cycles, number of additionally supplied activation energies per cycle.
9. Method according to claim 1, wherein in mode greater than 1, in particular in mode 2, at least one of the following compounds is formed: NH3, alkenes, alkanes, alcohols, ethers, esters, CH4, CH3CH2OH, CH3OH, C2H4, HCHO, dimethyl ether (DME), diethyl ether (DEE) and polyoxymethylenedimethyl ether (POMDME).
10. Method according to claim 1, wherein the reciprocating or rotary piston engine is operated in mode greater than one, in particular in mode two, as a two-stroke or four-stroke or four+2*X-stroke apparatus, where x is an element of the natural numbers.
11. Method according to claim 1, wherein the switch between the different modes is handled automatically by an electronic control unit, based on the actual energy demand or availability.
12. Method according to claim 6, wherein the pressure on the reactant side is lower than on the product side, and the two sides are fluidically connected so that products flow onto the reactant side.
13. Method according to claiml, wherein at least two reaction chambers (1, la) are arranged one behind the other in terms of flow.
14. Method according to claim 13, wherein downstream of the first reactor chamber (1) and upstream of the second reactor chamber (la) at least one reactant is supplied and/or at least one product is extracted.
15. Method according to claims 13 and 14, wherein the operating parameters of the two reaction chambers (1, la) are different.
16. Method according to claim 1, wherein the crankcase (32) is purged with an inert gas, in particular CO2 or N2.
17. Method according to claim 16, wherein the crankcase purge gas is supplied to the reactor chamber (1, la).
18. Method according to claim 1, wherein at least one device for separating individual substances from the gas stream, in particular according to one of the following processes: membrane, gas scrubber, extraction, rectification, adsorption, absorption, condensation, is arranged downstream of the reaction chambers (1, la).
19. Method according to claim 1, wherein at least one of the products collected downstream of the reaction chambers (1, la) is liquefied.
20. Method according to claim 1, wherein at least one catalyst is arranged downstream of the reaction chambers (1, la).
21. Method according to claim 1, wherein the temperatures prior to the start of the reactions in the reactor chambers (1, la) are between 200°C and 500°C, advantageously between 250°C and 450°C, most advantageously between 280°C and 400°C.
22. Method according to claim 1, wherein the pressure in the reactor chambers (1, la) is at least 50bar, advantageously at least 60bar, most advantageously at least 70bar.
23. Method according to claim 1, wherein the proportion of the at least one product with a calorific value of at least 12MJ/kg in the product stream leaving the reactor in mode two is at least 5%, advantageously at least 10%, extremely advantageously at least 20% of the whole product stream.
24. Apparatus for generating mechanical and/or electrical energy and for storing electrical energy, wherein it is a reciprocating engine or rotary engine which can be operated in at least two different modes, wherein in a first mode it operates as a combustion engine and in at least a second mode it operates as a pulsed compression reactor, wherein in the at least second mode at least one of the products formed is collected and this at least one product has a calorific value of at least 12MJ/kg, advantageously at least 20MJ/kg, most advantageously at least 30MJ/kg.
25. Apparatus according to claim 23, wherein the apparatus is operated at least in mode two as a two-cycle machine or four-cycle machine or four+2"x machine, wherein in four+2*x operation the third cycle of a four-cycle machine is followed by a number x of compression and expansion cycles before the products are pushed out of the reactor space, wherein x is an element of the natural numbers.