Computer-implemented method, computer program and computer for generating a digital twin for a chemical process or chemical plant device or system

Abstract

The present invention relates to a computer-implemented method for generating a digital twin (20) for a device or system of a chemical process or chemical plant, in particular for substance synthesis and / or substance separation, the method comprising: a) inputting a plurality of boundary conditions (1) into a calculation model (2), the calculation model (2) including simultaneous equations, each boundary condition (1) including a plurality of parameter values ​​(4); b) entering initial conditions for solving the simultaneous equations; c) in the simulation step, solving the simultaneous equations using each of the boundary conditions (1) and providing corresponding simulation results, respectively; a step in which one of the parameter values ​​(4) of each boundary condition (1) is changed from one simulation step to the next, while the other parameter values ​​(4) belonging to each boundary condition remain unchanged; d) providing a digital twin (20) as a set of data points obtained from the simulation step; Includes. The invention also relates to a computer program and a computer (55) for generating a digital twin for an apparatus or system of a chemical process or chemical plant, in particular for substance synthesis and / or substance separation.

Description

[Technical Field]

[0001] The present invention relates to a computer-implemented method, a computer program and a computer for generating a digital twin for an apparatus or system of a chemical process or chemical plant. [Background technology]

[0002] It is generally known that gas mixtures can be separated by gas separation membranes due to the different permeabilities of the individual gases. To produce such gas separation membranes, polymers are processed into hollow fibers or flat membranes. Membranes feature a very thin separating layer to maximize the membrane permeance.

[0003] In addition to new membrane materials, various methods of connecting membranes have been investigated in the prior art. Several single-stage or multi-stage membrane compounds for gas separation are known in the literature.

[0004] Exemplary references include Baker, IndEngChemRes, Natural Gas Processing with Membranes, 47 (2008); Bhide MemSci, Hybrid processes for the removal of acid gases from natural gas, 1998. Certain methods have the disadvantage that they partially involve multiple recompression steps or can only achieve high permeate or retentate purity.

[0005] WO 2012 / 00727; WO 2013 / 098024; WO 2014 / 075850; KR 10-1327337; KR 10-1327338; U.S. Pat. No. 6,565,626; U.S. Pat. No. 6,168,649; JP 2009-242773; WO 2014 / 183977; and EP 0799634 each disclose a membrane separation process having three membrane separation stages in which the retentate stream from stage 3 and the permeate stream from stage 2 are recycled to the crude gas stream. WO 2012 / 00727; WO 2013 / 098024; and WO 2014 / 075850 represent optimized versions of all of these processes. These patents describe equipment and processes optimized for product purity combined with minimal energy consumption. In other words, these processes provide two high-purity product streams in an energy-optimized manner. [Prior art documents] [Patent documents]

[0006] [Patent Document 1] International Publication No. 2012 / 00727 Brochure [Patent Document 2] International Publication No. 2013 / 098024 Brochure [Patent Document 3] International Publication No. 2014 / 075850 Brochure [Patent Document 4] Korean Patent No. 10-1327337 [Patent Document 5] Korean Patent No. 10-1327338 [Patent Document 6] U.S. Patent No. 6,565,626 [Patent Document 7] U.S. Patent No. 6,168,649 [Patent Document 8] Japanese Patent Application Laid-Open No. 2009-242773 [Patent Document 9] International Publication No. 2014 / 183977 Brochure [Patent Document 10] European Patent No. 0799634 [Non-patent literature]

[0007] [Non-Patent Document 1] Baker,IndEngChemRes,Natural Gas Processing with Membranes,47(2008) [Non-patent document 2] Bhide MemSci,Hybrid processes for the removal of acid gases from natural gas,1998 Summary of the Invention [Problem to be solved by the invention]

[0008] However, new problems have recently emerged that are not adequately solved by prior art devices and processes. The problem is that optimization is generally required when dealing with different natural or artificial gas sources, such as fermenters. For example, changes or variations in the respective feed gas composition or impurities trigger optimization requirements. The specific requirements of the plant's location also trigger optimization needs. For example, in the case of an offshore drilling rig, it is necessary to minimize the space and weight of the equipment without adversely affecting the plant's performance and / or capacity. Therefore, there is a multifaceted need for solutions to more efficiently simulate gas separation devices and processes, for example, to take into account the different requirements, optimization goals, different materials, and / or different architectures, characteristics, or capacities of existing plants and equipment. An adequate solution to this problem has not been found in the state of the art. Furthermore, to make such processes commercially viable, they are typically performed on a large scale. For this reason, it is often impractical to perform test processes to determine optimal conditions. Furthermore, physically testing a wide range of scenarios is impractical and carries the risk of damaging the equipment. [Means for solving the problem]

[0009] This problem is solved by a computer-implemented method for generating a digital twin for an apparatus or system of a chemical process or a chemical plant, a computer program product, and a computer for generating a digital twin for an apparatus or system of a chemical process or a chemical plant according to the independent claims. Advantageous embodiments of the computer-implemented method for generating a digital twin for an apparatus or system of a chemical process or a chemical plant are given in the dependent claims. The embodiments of the invention can be freely combined with each other, if they are not mutually exclusive.

[0010] A first aspect of the present invention relates to a computer-implemented method for generating a digital twin for an apparatus or system of a chemical process or chemical plant, in particular for material synthesis and / or material separation.

[0011] A digital twin may be a digital representation of a system or device. The digital twin may, in some cases, include one or more of at least partially identical and / or scaled geometric properties, material properties, initial conditions, and boundary conditions that are at least partially identical to those of the real system or device. The geometric properties may include geometric dimensions, which may also be at least partially scaled or modified using methods known to those skilled in the art. The material properties may include material density, material conductivity, material porosity, and other material properties known to those skilled in the art. The digital twin may be generated by simulation software, in which physical transport equations or numerical models are solved for a predetermined set of boundary and operating condition values ​​of the corresponding real system or device to provide resulting simulated parameter values. The resulting parameter values ​​can be validated with corresponding actual parameter values ​​obtained from experiments on the corresponding real system or device for the same predetermined set of boundary and operating conditions. The digital twin may include all data values ​​resulting from multiple simulation runs, or a subset thereof, such as a subset of validated parameter values ​​or parameter values ​​that meet other criteria.

[0012] Boundary conditions define the inputs of a simulation model. Some boundary conditions, such as velocity and volumetric flow rate, determine how fluids enter and exit the model. Other constraints, such as heat flow, determine the energy exchange between the model and its environment. Boundary conditions connect a simulation model to its environment. Most boundary conditions can be defined as either steady-state or transient. Steady-state boundary conditions persist throughout the simulation. Transient boundary conditions change over time and are often used to simulate events or periodic phenomena.

[0013] When the geometry of the digital twin is at least partially altered or scaled, the boundary conditions can be adjusted such that the effect of the adjusted boundary conditions, along with the at least partially altered or scaled geometry of the digital twin, is the same as that of the real system or device. Such adaptation of boundary conditions is known to those skilled in the art.

[0014] Unlike boundary conditions, initial conditions are only implemented at the beginning of the analysis. Initial conditions define the initial values ​​of each solution field. Therefore, they can play an important role in the stability and computation time of steady-state simulations. To ensure good convergence rates for steady-state simulations, it can be good practice to initialize the domain close to the expected solution. For example, if you are studying the cooling effect of a heat exchanger, initializing the heat exchanger surface at 350 K or 800 K can make a big difference in the time required to reach convergence. For transient analyses, initial conditions can be important to setup. They define the state of the system at time 0 and play an important role in the simulation.

[0015] One embodiment of the computer-implemented method includes a first step of inputting a plurality of boundary conditions into a computational model, the computational model including a system of equations, each boundary condition including a plurality of parameter values.

[0016] The simultaneous equations may be partial differential simultaneous equations, such as transport equations, and / or algebraic equations, such as thermodynamic equations of state, associated with chemical process or plant equipment or systems, particularly for substance synthesis and / or substance separation. Boundary conditions, including multiple parameter values, may be specified by a set of discrete time / property pairs, such as a table. Furthermore, boundary conditions may be specified as a continuous set of time / property pairs, such as a curve or mathematical function. Parameter values ​​may include pressure, temperature, mass flow rate, molar flow rate, volumetric flow rate, feed composition, species purity in a particular stream, ratio of membrane capacity in one stage compared to another stage, ratio of retentate pressure to permeate pressure in a particular stage, quotient of the pressure ratio of one stage to another, membrane selectivity, permeance, permeance, and / or area, and / or any other characteristic property or parameter. This allows process parameters that are particularly likely to change over the life of a chemical process facility or that are adapted to the design of chemical or other industrial plants, e.g., gas separation facilities, to be considered in a manner that will yield or produce favorable results with respect to optimization objectives despite restrictive and challenging framework conditions, etc.

[0017] The input of multiple boundary conditions can be performed by selecting sets of parameter values ​​corresponding to each boundary condition from a database, another external source such as a cloud service / system, or multiple external sources. Multiple boundary conditions can also be entered manually using a data entry device. Multiple boundary conditions can also be entered by a user-defined function, which may be in the form of computer code or a computer program. Multiple boundary conditions can be selected and then provided to the computational model. Once the boundary conditions are included in a system of equations, they can be solved using software such as Aspen Custom Modeler (ACM), although other software such as Aspen Plus, Aspen Hysis, ProMax, MATLAB, and MathCad can also be used.

[0018] According to some examples, the system of equations is solved by software that may include a numerical solver, i.e., a solver for numerical equations. The numerical solver may use one or more numerical approximations to find an approximate solution to the problem. The incremental optimization and corresponding simulation results obtained in a given simulation step may be maintained, e.g., stored in main memory and / or a database, and may be reused in subsequent simulation runs. This may have the advantage of improving performance because the simulation may converge to a (local or global) optimum more quickly, reducing the number of simulations, also referred to herein as "simulation steps," and the associated time and computational resources required to load input data and / or update the solver.

[0019] The software may include a numerical solver or solvers that can solve simultaneous equations in a coupled manner, where the equations can be solved together, or in a decoupled manner, where the equations can be solved one after the other.

[0020] A second step of the computer-implemented method embodiment includes inputting initial conditions for solving the system of equations.

[0021] The third step of the computer-implemented method embodiment involves, in a simulation step, solving the system of equations using each of the boundary conditions to provide corresponding simulation results. According to the present invention, a system of equations for steady-state process simulation is established for a given chemical process, apparatus, or system, as is known per se. Furthermore, a simulation space is defined that can include multiple predetermined boundary conditions. For each of these predetermined boundary conditions, a simulation result is to be determined. This should be done in as short a computation time as possible.

[0022] A solution to the underlying problem is provided by a computer-implemented method of the present invention, in which one of the parameter values ​​of each boundary condition is changed from one simulation step to the next, while the other parameter values ​​belonging to each boundary condition remain unchanged. This means that only one of the parameter values ​​is changed from one simulation step to the next, while the other parameter values ​​belonging to the boundary condition remain unchanged. For example, the single parameter may not be arbitrarily changed in the data space; specifically, the closest data point or value of the parameter within the set of boundary conditions is selected. This proximity to the boundary condition leads to faster convergence of the simulation, thus improving the overall simulation speed.

[0023] In other words, if a simulation is used to solve an equation involving three parameters, i.e., a first parameter X, a second parameter Y, and a third parameter Z, a first set of parameter values ​​is calculated using a first plurality of data points, e.g., X1 through X2. n and a second set of parameter values ​​is comprised of a second plurality of data points, e.g., Y1 through Y m and a third set of parameter values ​​is comprised of a third plurality of data points, e.g., Z1 to Z2. o Then, according to the computer-implemented method of the present invention, the first parameter X can be changed from one simulation step to the next through its value set 1 to n, while the other parameter values ​​belonging to the respective boundary conditions remain unchanged in Y1 and Z1. That is, for the first 1 to n simulation steps, the values ​​of the first parameter set are changed covering all n data points. However, the values ​​of the second and third parameters remain unchanged, e.g., the second parameter is changed from Y1 to Y m the third parameter may have a constant value for the first data point among the corresponding m data points Z1 to Z2 corresponding to the o data points Z1 to Z3; oThe first of the data points may have an unchanged value.

[0024] After the first n simulation steps by varying the first parameter X, for the second n simulation steps, the value of the first parameter X is changed covering n data points of X. However, the value of the second parameter Y is changed from Y1 to Y2, and the third parameter Z remains unchanged at Z1. For example, if n=4, i.e., the first parameters are X1, X2, X3, and X4, then m=3, i.e., the second parameters are Y1, Y2, and Y3, and o=2, i.e., the third parameters are Z1 and Z2.

[0025] Next, for a first set of n=4 simulation steps, in this case the following points are simulated: (X1, Y1, Z1), (X2, Y1, Z1), (X3, Y1, Z1), and (X4, Y1, Z1).

[0026] Next, for a second set of n=4 simulations, the following points are simulated: (X4,Y2,Z1), (X3,Y2,Z1), (X2,Y2,Z1), and (X1,Y2,Z1).

[0027] Next, for a third set of n=4 simulations, the following points are simulated: (X1, Y3, Z1), (X2, Y3, Z1), (X3, Y3, Z1), and (X4, Y3, Z1).

[0028] Next, for a fourth set of n=4 simulations, the following points are simulated: (X4,Y3,Z2), (X3,Y3,Z2), (X2,Y3,Z2), and (X1,Y3,Z2).

[0029] Next, for a fifth set of n=4 simulations, the following points are simulated: (X,Y2,Z2), (X2,Y2,Z2), (X3,Y2,Z2), and (X4,Y2,Z2).

[0030] Next, for a sixth set of n=4 simulations, the following points are simulated: (X4,Y1,Z2), (X3,Y1,Z2), (X2,Y1,Z2), and (X1,Y1,Z2).

[0031] This process is repeated in this manner until all possible combinations of the three parameters have been simulated.

[0032] Thus, according to an embodiment, the simulation steps are preferably performed such that the parameter values ​​do not "jump" (increase or decrease) from one step to another by a predetermined increment of 2 or more, such as the integer "1" or another value, depending on the parameter. This preferably means that there is no "jump" from the lowest possible value to the highest possible value within a predetermined parameter value set or range. In the above example, there is no "jump" of parameter X from 1 to 4 or from 4 to 1. The increment is sometimes referred to as the "step length."

[0033] The parameter values ​​used in the simulation are increased or decreased by predefined minimum increments, as if selected by a moving slider.

[0034] Furthermore, the selection of parameters as those whose values ​​are changed while other parameters are kept constant can depend on the time required to complete the entire simulation process, i.e., can be selected to achieve a simulation process that is completed in the shortest possible time interval.

[0035] Thus, by this means the solver can converge quickly and therefore calculate new simulation results accordingly quickly.

[0036] The simulation of the computer-implemented method of the present invention can be calculated in parallel and / or sequentially. In the case of parallel calculation, the simulation space of each set of boundary conditions is divided into several subspaces that are simulated in parallel. Depending on the embodiment, the simulation results for each subspace of corresponding boundary conditions among the plurality of boundary conditions are determined at once or with a time offset. However, in the case of serial calculation, one simulation result for one boundary condition is determined at once, i.e., each corresponding simulation result for each corresponding boundary condition among the plurality of boundary conditions is determined sequentially.

[0037] A fourth step of the computer-implemented method embodiment includes providing a digital twin as a set of data points obtained from the simulation step. The digital twin may be a parametric model or a mathematical formula. The parametric model may be in the form of a polynomial function that can be obtained by interpolation or curve-fitting methods that relate simulation results as a function of corresponding boundary conditions from a plurality of boundary conditions. The parametric model may also be in the form of a Gaussian function. This is advantageous because such a parametric model is computationally cheaper and faster than calculating simulation results for a set of boundary conditions using software.

[0038] The method of the present invention allows for efficient and rapid calculation of simulation results for a large set of boundary conditions for equipment or systems in a chemical process or chemical plant, particularly for substance synthesis and / or substance separation. Additionally, the use of changing one of the parameter values ​​of each boundary condition from one simulation step to the next, preferably to the parameter's closest data point or value, while leaving other parameter values ​​belonging to each boundary condition unchanged, allows for configurations that can be performed in a short time on a standard computing machine. Thus, the computer-implemented method steps may be executed on at least one processor of a computer. Furthermore, due to the complexity and the vast amount of data that must be processed and calculated by the processor, it may be advantageous to use an array of parallel processors to perform the calculations required to perform the computer-implemented method steps.

[0039] It is to be understood that additional intermediate steps, which may be known to those skilled in the art, may be performed between any successive steps of the computer-implemented method of the present invention.

[0040] According to some embodiments of the present invention, one of the parameter values ​​of each boundary condition can be varied in a simulation within its entire set of data points from the start data point to the end data point, and then in a subsequent series of simulations, one of the parameter values ​​of each boundary condition is varied backward, i.e., from the end data point to the start data point. This is a "back and forth" mechanism, where in one series of simulations, i.e., the fourth step, one of the parameter values ​​of each boundary condition can be varied within its entire set of data points from the start data point to the end data point, and in a subsequent series of simulations, i.e., the back step, a single one of the parameter values ​​of each boundary condition can be varied backward, i.e., from the end data point to the start data point. This "back and forth" mechanism can be continued for subsequent series of simulations.

[0041] It is preferable to vary the parameters that are varied in the simulation within that entire set of values ​​of the data points from the start parameter forward to the end parameter, and in subsequent series of calculations backward from the end parameter to the start parameter. For example, referring to the example above, if the simulation is used to solve an equation involving three parameters, a first parameter X, a second parameter Y, and a third parameter Z, the first parameter value set may be varied for a first plurality of data points, e.g., X1 through X2. n and a second set of parameter values ​​is comprised of a second plurality of data points, e.g., Y1 through Y m and a third set of parameter values ​​is comprised of a third plurality of data points, e.g., Z1 to Z2. o The parameter X is composed of data points. In the first simulation, X1 to X n In the second simulation, n to X1, and in the third simulation from X1 to X nIt has been found that the "back and forth" mechanism can save a great deal of computation time compared to always starting with starting parameters or randomly selecting parameters for each successive calculation. n If we start with the simulation result of Y1Z1, then X n The solution for Y2Z1 is much closer and can be found much faster than the solution for X1Y2Z1. Details of the method described previously are provided further below when describing Figure 2.

[0042] In a preferred embodiment, the "back-and-forth" mechanism can be combined with a specific scheme that determines the preferred, typically parameter-specific, increment size ("step length") and / or the order in which multiple parameters are selected to change their respective parameter values ​​"back and forth" during a simulation, further reducing overall simulation time. This combination of the mechanism and computational rules can reduce computational time by up to 99% compared to traditional methods, thereby providing the basis for simulating much larger data spaces with far more boundary conditions in an economically acceptable time. For example, in a complex process such as a three-stage biogas process, if the pressure value is changed from an upper limit to a lower limit, the simulation may not converge at all. The next point can then be "approached" by homotopy. In this case, this could take 30-60 seconds, whereas the method may require only 0.5-1.5 seconds. This can reduce computational or simulation time by up to 99%.

[0043] According to some embodiments of the present invention, simulation results from one simulation step can be used as initial conditions for the next simulation step. In other words, the solution found by the solver is used by the solver in a subsequent simulation step for the modified boundary conditions, e.g., as initial conditions or values, to enable a solution for the modified boundary conditions to be found more quickly. This is also known as a gradient-based method.

[0044] This is advantageous because it ensures that the solution converges in a much shorter time, since the initial conditions for the current simulation step, obtained from the simulation results of the previous simulation step, are closer to the final simulation results for the current simulation step. If the solver cannot find a solution for the boundary conditions, homotopy can be used. Two continuous functions from one topological space to another are called homotopic if one can be "continuously transformed" into the other, and such a transformation is called homotopy between the two functions.

[0045] Homotopy can allow for small increments from one steady-state solution to another. In some situations, a simulation may not converge from the current steady-state solution to the target steady-state solution. Homotopy allows for incremental approaches to the target steady-state solution, thereby improving the likelihood of reaching the target steady-state solution.

[0046] Homotopy can provide a way to move from one converged solution to another solution with different values ​​for one or more homotopy variables. This is a useful technique when convergence for a particular specification is difficult to obtain, but a converged solution with different specifications already exists. Homotopy can work by moving along a path to a new solution and solving several interim points along that path. For example, let HOM1 be a vector of values ​​of homotopy variables at points already solved, and HOM2 be a vector of values ​​for points to which you want to move. In a homotopy simulation, the simulation software attempts to solve several points with the following values ​​of the homotopy variables:

[0047] Homotopy = HOM1 + theta × (HOM2-HOM1) Here, theta is the homotopy parameter. It is a number that goes from 0 to 1 in successive solutions. When theta is 1, this corresponds to the specification HOM2. We can control how theta changes between successive solutions.

[0048] If homotopy is used, saved snapshots, i.e., point solutions, are loaded, and then non-converged points are re-approximated by homotopy. Preferably, only one snapshot is loaded before starting the simulation, and it is not important which points do not converge. Furthermore, snapshot saving can be switched off for each single simulation, so that additional time is not lost saving snapshots or the simulation software crashes due to the possibility of saving 10,000 or more snapshots. The modified parameter values ​​of the current boundary conditions are subdivided into multiple corresponding parameter values ​​between the parameter values ​​of the previous simulation step and the final parameter values ​​of the current simulation step. In this case, several simulation steps are interleaved, and the simulation results of each simulation step are used as the initial conditions for the subsequent simulation step. This procedure is repeated until the final simulation results using the final modified parameter values ​​of the boundary conditions are obtained.

[0049] According to some embodiments of the present invention, a plurality of boundary conditions can be obtained from the simulation space, and the boundary conditions for the first simulation step are selected from the central region of the simulation space. In other words, the starting boundary conditions are not selected at the edges of the simulation space, but from the central region of the simulation space, because the boundary regions of the simulation space usually contain extreme values ​​of the range of parameter values ​​of the boundary conditions for which simulation results need to be obtained, and therefore there is a risk that the solver will not be able to find a solution there.

[0050] Some boundary regions of the simulation space can contain maximum values, while other boundary regions of the simulation space can contain minimum values ​​for corresponding parameter values. For example, if the simulation results are for determining the reaction rate of a reaction mechanism, one parameter value of the boundary conditions to be varied corresponds to the temperature of the reaction mixture. In one boundary region, the parameter value includes the maximum possible value of the reaction mixture temperature, resulting in a very high reaction rate because the reaction rate is an exponential function of temperature. Similarly, in another boundary region, the parameter value includes the minimum possible value of the reaction mixture temperature, resulting in a very low or even unrealistically negative reaction rate. Simulations with such boundary conditions may take a long time to converge, fail to converge, or diverge, leading to unrealistic values. This results in a disproportionate loss of time when attempting to numerically find a solution in a physical or chemical boundary region. Therefore, bypassing such boundary regions can avoid or reduce the use of homotopy.

[0051] Alternatively, the boundary conditions for the first simulation step can be selected in part from any random points from the simulation space, or from points near the edges of the simulation space.

[0052] According to some embodiments of the present invention, the path for selecting boundary conditions for a next simulation step can be dynamically adjusted through the simulation space based on the time required to obtain simulation results in the previous simulation step. In other words, it is conceivable to dynamically adjust the path through the simulation space during the execution of a simulation, for example, if the time required by the solver for a simulation result becomes longer and longer. Physical boundaries or infeasible regions can be "bypassed" in this manner. For example, multiple boundary conditions can be obtained from the simulation space, and the boundary conditions for a first simulation step can be selected from a region between the boundary region and the central region of the simulation space. Here, the path for selecting boundary conditions for a next simulation step can be selected based on whether the time required by the solver for a simulation result will be longer than the previous simulation step. If the required time is longer, certain boundary conditions can be bypassed, and the path for selecting boundary conditions within the simulation space can be adjusted accordingly, for example, the path can take the form of a meander. Here, by avoiding boundary conditions that require a long simulation time, the use of homotopy can be avoided or reduced.

[0053] According to some embodiments of the present invention, the system of equations can be a steady-state system of equations for a quasi-steady-state process. This is advantageous because it leads to faster simulations and easier analysis. However, the solver can also perform unsteady or transient simulations.

[0054] According to some embodiments of the present invention, input of boundary conditions and initial conditions for a simulation step may be achieved by an interface to an external source. To access the external source or resource, the external source or resources may be selected to be compatible with the software used to solve the simultaneous equations of the simulation. For compatibility with the external source, the computer-implemented method may include receiving data from and / or transmitting data to the external source, resource, or system. For versatility, the computer-implemented method may further include accessing external software, providing data to the external software, and / or receiving data from the external software. For compatibility, an interface suitable for receiving instructions for actions from additional simulators may also be used.

[0055] According to some embodiments of the present invention, a digital twin is a set of data points including multiple simulation results corresponding to respective boundary conditions. This is advantageous because it allows a user to select or exclude specific groups of points from the digital twin according to requirements, and quickly and efficiently obtain respective simulation results corresponding to respective boundary conditions. Furthermore, it is believed that a parametric model or mathematical formula can be derived from the set of data points of the digital twin. Therefore, the parametric model or mathematical formula can be easily incorporated into other computer programs or software for real-time-like applications.

[0056] According to some embodiments of the present invention, the chemical process can correspond to a gas separation membrane or a gas separation arrangement having a plurality of gas separation membranes, or the chemical plant equipment or system can be a gas separation arrangement having a gas separation membrane or a plurality of gas separation membranes, which is advantageous because it allows for testing and development of a gas separation membrane or a gas separation arrangement having a plurality of gas separation membranes, or the chemical plant equipment or system can be a gas separation arrangement having a gas separation membrane or a plurality of gas separation membranes that can operate over a wide range of operating conditions in an efficient and economical manner.

[0057] According to some embodiments of the present invention, multiple simultaneous equations, each using corresponding boundary conditions to provide a corresponding simulation result, can be solved in parallel in a simulation step. For this purpose, the simulation space can be divided into several parallel "slices," i.e., subspaces of the simulation space that are parallel to each other. A path for the parallel simulation can pass through each of the subspaces. Furthermore, the simulation space can be subdivided into blocks of subspaces that are not in the form of parallel slices, or a combination of blocks of subspaces and parallel slices, each of which can be solved in parallel to each other in a simulation step. Such parallel simulations can be performed on a single computer or on a cluster or cloud computer system.

[0058] According to some embodiments of the present invention, a time offset can be used to start solving each of the systems of equations in parallel with solving one of the systems of equations, the time offset being a predetermined fraction of the average time of a simulation step. Starting the parallelized simulation with a time offset is advantageous because it smooths the total processor power required over time.

[0059] The predetermined percentage of the average time of a simulation step can be 5% to 10% of the average time of a simulation step. For example, a simulation step can take 0.5 to 1.5 seconds, and then the offset can be selected or set to 45 seconds. Generally, starting a simulation takes much longer. The converged solution from a previous simulation can be saved as a "snapshot" file, and this "snapshot" can then be loaded into appropriate software, such as ACM software. This snapshot is then converged for a new set of boundary conditions. If convergence is not achieved, homotopy can be used, and a simulation step can take approximately 30 to 60 seconds.

[0060] According to some embodiments of the present invention, simulation results can be stored in one or more data files. This allows for efficient storage and convenient use of large amounts of simulation results as needed. For clarity and convenience, the computer-implemented method may further include providing a sequence of simulation results and allowing detailed review of each result in the sequence. For convenience, the simulation results may be displayed in the form of charts, plots, lists, tables, and / or graphs. The progress of the simulation can be displayed in the form of cumulative values ​​for the ongoing simulation.

[0061] According to some embodiments, the number of simulation steps performed is at least 100,000, particularly at least 250,000, particularly at least 500,000, particularly at least 1 million. The number of data points comprising each of the simulation steps may also be at least 100,000, particularly at least 250,000, particularly at least 500,000, particularly at least 1 million.

[0062] According to some embodiments, the number of boundary condition parameters whose values ​​change in a simulation step is at least three, in particular at least five, in particular at least seven, in particular at least nine.

[0063] According to some embodiments, the average number of predetermined values ​​assigned to one of the boundary condition parameters changed during a simulation step is at least 2, particularly at least 4, particularly at least 8, particularly at least 64, for example at least, particularly at least 256.

[0064] Thus, the specific method in which a simulation is performed by increasing only one parameter at a time, preferably by only single increments, preferably according to specific parameter prioritization, and the specific method of selecting appropriate parameter-specific step widths, allows for the calculation of a huge number of simulation results and, therefore, the covering of a huge combinatorial space that previously could not be covered by either empirical, observational, or brute-force simulation approaches. According to some embodiments of the present invention, the simulation results (e.g., the plot shown in FIG. 10 ) can be displayed via an augmented reality display system, for example, via augmented reality glasses (AR glasses). The AR glasses can be controlled by AR software configured to create and display one or more digital twins (digital representations) of equipment or systems of a chemical process or chemical plant. This allows a user wearing the AR glasses to immediately recognize problems that may arise under certain process conditions and take immediate action to prevent or remedy critical situations. For example, according to one embodiment, the controller is configured to calculate a digital twin for the user wearing the AR glasses and enable the user to move their virtual twin relative to a digital twin representing, for example, part of a chemical reaction or part of a chemical plant, by moving their head and / or body in the real world.

[0065] According to some embodiments, the computer-implemented method further includes displaying the digital twin. For example, the displaying may include displaying the digital twin via an augmented reality display system, such as via AR glasses.

[0066] Because embodiments provide particularly fast calculation of data points / digital twins, particularly fast ways of displaying digital twins are also provided; graphical representations of the digital twins, for example, multi-dimensional plots of data points or more sophisticated graphical representations of individual hardware components of the plant, can be quickly loaded into a frame buffer without the need to solve numerical equations to determine the predicted state of the chemical process or plant.

[0067] According to some embodiments, displaying the digital twin includes loading a graphical representation of the digital twin or a portion thereof into a frame buffer of a display system and displaying the data contents of the frame buffer on the display system. A frame buffer is a portion of random access memory that contains the bitmaps that drive a video display. It is a memory buffer that contains data representing all the pixels in a complete video frame.

[0068] In some embodiments, a method includes sequentially displaying at least two different states of a chemical process, plant, or machine on a display system, the displaying including selecting a first subset of data points obtained throughout the simulation, generating a first graphical representation of the process, plant, or machine using the selected first subset, loading the first graphical representation into a frame buffer, displaying the contents of the frame buffer containing the first graphical representation on the display system, selecting a second subset of data points, generating a second graphical representation of the process, plant, or machine using the selected second subset, loading the second graphical representation into the frame buffer to replace the first graphical representation, and displaying the contents of the frame buffer containing the second graphical representation on the display system.

[0069] For example, a rules engine can be used to identify subsets of data points corresponding to two or more different states of a chemical process, machine, or plant of interest. In some cases, the subsets may include a single data value. For example, if a user is interested in the state (defined by multiple parameter values) of a gas separation plant where a specific purity is required at a specific pressure, the user may use the rules engine to obtain a first data point containing the required purity and annotated with temperature T1, and a second data point containing the required purity and annotated with a different temperature T2. The different temperatures represent different states of the process, machine, or plant. The user may navigate in real time between graphical representations of different states of the chemical process, machine, or plant, which is particularly useful in the context of industrial control processes, especially when control is performed via an augmented reality display system. Typically, the state selection rules used to traverse the set of data points obtained by a simulation become more complex and may include filter criteria for multiple different parameters, such as gas permeance (e.g., O2 or N2), gas purity, membrane surface area, temperature, pressure, feed gas flux, permeate gas flux, and retentate gas flux.

[0070] According to some embodiments of the present invention, a digital twin can be used to train an artificial intelligence model or a machine learning-based model. The artificial intelligence model, or AI twin, or machine learning-based model, is advantageous for big data visualization of simulation results along with corresponding boundary conditions, enabling fast optimization and also real-time optimization and advanced process control. Furthermore, the artificial intelligence model can be used in gray-box models and surrogate models, such as neural network models, radial basis function models, support vector machine models, or Gaussian process regression models. The machine learning-based model can be a model based on the k-nearest neighbor algorithm, a nonparametric supervised learning method. Supervised learning is a machine learning task that learns a function that maps inputs to outputs based on example input-output pairs. This model can be used for performance prediction and can also be used for other unit operations, such as distillation, absorption, and other operations in the field of chemical processes known to those skilled in the art.

[0071] According to some embodiments of the present invention, a digital twin may be a set of data points comprising multiple simulation results corresponding to respective boundary conditions, and is represented graphically so that a specific set of data points of the digital twin's set of data points can be selected or filtered by a user, for example according to requirements. This is advantageous because good and bad solutions can be directly displayed, making them comparable, understandable, and even allowing the user to move in or through the data space, for example by means of a digital slider in a 2D or 3D plot.

[0072] A second aspect of the present invention is a computer program comprising instructions that, when executed by a computer, cause the computer to perform the steps of the computer-implemented method of the present invention for generating a digital twin for an apparatus or system of a chemical process or chemical plant, in particular for substance synthesis and / or substance separation. For example, substance separation may be performed by permeation, adsorption, absorption, distillation, filtering, or other technical means. Separation may be performed to fractionate or purify a substance mixture, such as a gas mixture or other type of mixture. The computer program may also include a computer program product comprising instructions that, when executed by a computer, cause the computer to perform the steps of the computer-implemented method of the present invention.

[0073] In particular, the set of parameters may be provided to the computer program from a non-transitory computer storage medium, as detailed in the context of the first aspect of the invention.

[0074] A third aspect of the present invention is a computer for generating a digital twin for an apparatus or system of a chemical process or chemical plant for material synthesis and / or material separation, particularly configured to use the steps of the computer-implemented method of the present invention. Furthermore, the computer running the computer program may be connected to a display configured to display any output of the computer program.

[0075] A further aspect of the present invention is a display system comprising an electronic display and a computer configured to generate a digital twin. For example, the computer can be a distributed or monolithic computer system. The electronic display can be an LCD screen, an OLED screen, or any other type of electronic display. The computer is further configured to generate 2D or 3D computer graphics that visualize data in the digital twin (e.g., plots, charts, or near-realistic representations of a chemical process or a plant or machine in which the chemical process is performed). The computer is configured to display the 2D or 3D computer graphics on the electronic display.

[0076] A further aspect of the invention is a data structure configured for use in visualizing a digital twin of a chemical process or chemical plant equipment or system, the data structure including a plurality of data points obtained by a method according to any one of the embodiments and examples described herein. The data structure, when processed by a display system, is configured to cause the display system to generate 2D or 3D computer graphics that visualize the data in the digital twin and display the 2D or 3D computer graphics on an electronic display of the display system.

[0077] This can have the advantage of providing a particularly fast and lightweight display system that can visualize chemical processes or plants or machines that perform chemical processes very quickly. Graphical representations can be derived directly from sets of data points without the need to solve complex simulations, and calculations of sets of data points can also be performed very quickly. In fact, because the density of data points in a multidimensional parameter space reflects the resolution of the 2D or 3D model of the entity represented by the digital twin, the display system can be a particularly fast and high-resolution display system. Given a certain amount of computational time and resources, methods that calculate data points by changing only one parameter value from one simulation to the next can provide better resolution because more simulations can be run and converged per available amount of time / CPU power.

[0078] The terms "computerized device," "computerized system," or similar terms refer to an apparatus that includes one or more processors that are operable or operate according to one or more programs.

[0079] The term "computer" or system thereof may be used herein in its normal context in the art, such as a general-purpose processor or microprocessor, RISC processor, or DSP, possibly including additional elements such as memory or communication ports. Optionally or additionally, the term "computer" or its derivatives may refer to a device that can execute a program provided or embedded therein and / or control and / or access other devices, such as data storage devices and / or input / output ports. The term "computer" may also refer to multiple processors or computers that are connected and / or linked and / or communicate, possibly sharing one or more other resources, such as memory, which may represent a non-transitory storage medium.

[0080] As used herein, the terms "server" or "client" or "backend" refer to a computer or computerized device that provides data and / or operational services to one or more other computerized devices or computers.

[0081] The terms "software," "computer program," "software procedure" or "procedure" or "software code" or "application" or "app" may be used interchangeably depending on the context and generally refer to a product or method that includes one or more instructions or directions or circuitry for performing a sequence of operations that represent an algorithm and / or other process or method. The program may be stored on a medium such as RAM, ROM, or disk, or may be embedded in circuitry that is accessible and executable by a device such as a processor or other circuitry.

[0082] The processor and program may constitute at least part of the same device, such as an array of electronic gates, such as an FPGA or ASIC, optionally including or linked with a processor or other circuitry, designed to perform a programmed sequence of operations.

[0083] As used herein, without limitation, a process represents a collection of actions for achieving a particular purpose or result.

[0084] Similarly, a model may represent a set of actions to achieve a particular goal or result.

[0085] The terms "configured" and / or "adapted" to a purpose or variations thereof means using at least software and / or electronic circuitry and / or auxiliary devices designed and / or implemented and / or operable or operable to accomplish a purpose.

[0086] Devices such as non-transitory storage media that store and / or comprise computer programs and / or data specifically constitute articles of manufacture. Unless otherwise specified, the programs and / or data are stored in or on the non-transitory media.

[0087] In the context of embodiments of the present disclosure, by way of example and not limitation, terms such as "operate" or "perform" also mean the ability, such as "be able to operate" or "be able to execute," respectively.

[0088] In the following, embodiments of the invention will be described in more detail, by way of example only, with reference to the drawings, in which: [Brief explanation of the drawings]

[0089] [Figure 1] FIG. 1 is a block diagram of one embodiment of a system of the present invention for generating a digital twin for a chemical process or chemical plant device or system. [Figure 2] 1 is a parameter table containing a plurality of boundary conditions including sets of parameter values. [Figure 3] FIG. 1 illustrates a digital twin as a set of points resulting from a simulation step. [Figure 4] FIG. 1 illustrates a first path for selecting boundary conditions from a simulation space. [Figure 5] FIG. 10 illustrates a second route for selecting boundary conditions from the simulation space. [Figure 6] 1 is a flowchart of an embodiment of a computer-implemented method in which a digital twin is provided as a set of data points obtained from a simulation step. [Figure 7] FIG. 10 shows a comparison of simulation results obtained by the ACM solver and the artificial neural network model. [Figure 8]FIG. 10 illustrates a flowchart embodiment of a computer-implemented method in which, for parallel simulations, a time offset is used to initiate the solving of each of the systems of equations in parallel with respect to the solving of one of the systems of equations. [Figure 9] FIG. 1 is a schematic diagram of a computer configured to use a computer-implemented method for generating a digital twin for a chemical process or chemical plant apparatus or system for material synthesis and / or material separation. [Figure 10] FIG. 1 illustrates filtering of data obtained from a digital twin. [Figure 11A] FIG. 10 is an illustration of the effect of step selection on simulation performance. [Figure 11B] FIG. 10 is another illustration of the effect of step selection on simulation performance. [Figure 12] 1 is a set of tables illustrating the identification of appropriate step widths. [Figure 13] 1 is a set of tables illustrating the identification of proper parameter ordering. [Figure 14] 10 is a plot showing observed simulation times for three different parameters, assuming different numbers of allowed values ​​for each parameter. [Figure 15] 1 is a flowchart of one embodiment of a computer-implemented method of the present invention for generating a digital twin for a chemical process or chemical plant device or system. DETAILED DESCRIPTION OF THE INVENTION

[0090] FIG. 15 shows a flowchart of one embodiment of a computer-implemented method of the present invention for generating a digital twin for equipment or systems in a chemical process or chemical plant, and FIG. 1 shows a corresponding system configured to execute this method. Accordingly, FIGS. 1 and 15 will be described together. The computer-implemented method includes a first step 150 of inputting a plurality of boundary conditions 1 into a computational model 2. The computational model 2, which includes a system of simultaneous equations, is solved using process simulation software 8, such as Aspen Custom Modeler (ACM). Each boundary condition 1 includes a plurality of parameter values ​​4. The boundary condition 1, which includes a plurality of parameter values ​​4, may be specified by a set of discrete characteristic pairs at a steady state. The parameter values ​​4 of each boundary condition 1 may be stored in a tabular database 6, such as Microsoft Excel. This tabular database 6 may be input into the computational model 2. The parameter values ​​4 of each boundary condition 1 read from the tabular database 6 may be stored in the form of parameter table data 5, as shown in FIG. 2. The parameter values ​​4 can include pressure, temperature, mass flow rate, molar flow rate, volumetric flow rate, feed composition, and / or any other characteristic property or parameter, each shown in a respective column 7 in the parameter table data 5. Input of multiple boundary conditions 1 can be performed by selecting a set of parameter values ​​4 corresponding to each boundary condition 1 from a tabular database 6, in this case Microsoft Excel, or another external source, such as a cloud service / system, or multiple external sources. Note that in Microsoft Excel, variables such as temperature or pressure can be defined by entering their maximum and minimum values ​​as outer limits of the data points at which the simulation is performed, as well as a step size for calculating other data points between them. Alternatively, a sequence or grid of data points can be entered, or a tabular database can be entered, which can be created in software such as Konstanz Information Miner (KNIME).

[0091] A second step 152 of the computer-implemented method of the present invention includes inputting initial conditions for solving the simultaneous equations into the computational model 2 of the process simulation software 8. Input of boundary conditions 1 from the tabular database 6 into the computational model 2 is done automatically via data analysis software such as KNIME. The double arrows indicate that simulation results from one simulation step from the computational model 2 are used as initial conditions 3 for the next simulation step.

[0092] FIG. 1 shows the graphic user interface 9 of the process simulation software 8. Boundary conditions 1 can be included in the system of equations to be solved by the process simulation software 8. Furthermore, for speed, the GUI does not have to be opened by the ACM, but rather is turned on automatically.

[0093] A third step 154 ​​of the computer-implemented method includes, in a simulation step, solving the system of equations using each of the boundary conditions 1 to provide corresponding simulation results.

[0094] A fourth step 156 of the computer-implemented method includes providing the digital twin 20 as a set of data points 21 obtained from the simulation step.

[0095] 2 shows a representative portion of parameter table data 5 to further illustrate the "before and after" described above. A first column 10 represents a simulation step number, starting with 1, representing a first simulation run using boundary condition 1 with corresponding parameter value 4 corresponding to a first row 11 in parameter table data 5.

[0096] A third step of the computer-implemented method includes, in a simulation step, solving the system of equations using each of the boundary conditions 1 to provide a corresponding simulation result, where a first simulation step shown in first column 10 and first row 11 uses a first parameter value, a first value 12 from second column 13, a second parameter value, a first value 14 from third column 15, and a third parameter value, a first value 16 from fourth column 17. Here, parameter values ​​12, 14, and 16 in first row 11 represent a first boundary condition 18.

[0097] According to the computer-implemented method, one of the parameter values ​​4 of each boundary condition 1 is changed from one simulation step to the next, while the other parameter values ​​4 belonging to each boundary condition 1 remain unchanged. Considering the first five simulation steps, as shown in FIG. 2 , it can be seen that the value of the first parameter value 12 is changed from 0.400 to 0.600, while the value of the second parameter value 14 remains unchanged at 7.000, and the value of the third parameter value 16 remains unchanged at 10.000, as indicated by the numbers 1 through 5 in the first column 10. By this means, the process simulation software 8 can converge quickly and calculate new simulation results correspondingly quickly. It may further be noted that the step size of the first parameter value 12 is interpreted as a small value of 0.5, since a smaller step size results in better and faster convergence of the simulation results. Furthermore, the simulation results from one simulation step are used as the initial conditions for the next simulation step. For example, the simulation results of a first simulation step using a first boundary condition 18 are used as initial conditions for a second simulation step using a second boundary condition 19 .

[0098] After the first five simulation steps, as shown by numbers 1 through 5 in the first column 10, in the sixth simulation step, the value of the second parameter value 14 from the third column 15 is changed from 7.000 to 7.500 while maintaining the values ​​of the other two parameters. In the sixth simulation step, the first parameter value 12 from the second column 13 is maintained at the same value of 0.600 as in the fifth simulation step. Similarly, the third parameter value 16 from the fourth column 17 is held constant at the same value of 10.000 as in the fifth simulation step. Once the second parameter value is changed to a value of 7.500 in the sixth simulation step, the value of the third parameter value is changed from 0.600 to 0.400, while the second parameter value 14 and the third parameter value 16 remain unchanged at the values ​​of 7.500 and 10.000 for simulation steps six through ten. The same simulation process is then repeated further until all parameter values ​​4 are considered to obtain respective simulation results.

[0099] 3 shows that the digital twin 20 is a set of data points 21 including multiple simulation results corresponding to respective boundary conditions 1, where each of three axes represents a first parameter value 12, a second parameter value 14, and a third parameter value 16 of the boundary condition 1, respectively. The coloring of each data point 21 represents the corresponding simulation result. The value of the simulation result for each data point in the set of data points 21 can be obtained by a color scale 22.

[0100] For ease of understanding, the digital twin 20 shows a first parameter value 12 as dependent on two other parameter values ​​14 and 16. However, in a simulation, the digital twin may include multiple parameter values, for example, over 200. The values ​​and dependencies of each parameter value may be displayed in a multi-dimensional graph or plot, or other representative format known to those skilled in the art.

[0101] Figure 4 shows a first path 24 for selecting boundary conditions 1 from a simulation space 23, with the x-axis representing rotational speed 27 and the y-axis representing torque 28. Here, multiple boundary conditions 1 are obtained from the simulation space 23, and the first boundary condition 18, i.e., the boundary condition 1 for the first simulation step, is selected from a central region 42 of the simulation space 23. Typically, a boundary region 25 of the simulation space 23 includes extreme values ​​of the parameter values ​​4 of the boundary conditions 1 for which simulation results are required. Simulations in such boundary regions 25 may take a long time to converge, fail to converge, or diverge, leading to unrealistic values. This results in a disproportionate loss of time, which occurs when attempting to numerically find a solution in a physical or chemical boundary region. Such boundary regions 23 are not selected, and therefore, the first path 24 is adjusted, as shown by adjustment path 26. This allows the use of homotopy to be avoided or reduced.

[0102] FIG. 5 shows a second path 29 for selecting boundary conditions 1 from the simulation space 23, where the x-axis represents rotational speed 27 and the y-axis represents torque 28. Here, multiple boundary conditions 1 are obtained from the simulation space 23, and the first boundary condition 18, i.e., the boundary condition 1 for the first simulation step, is selected from the region of very low rotational speed 27 from the simulation space 23. The second path 29 for selecting boundary conditions 1 for the next simulation step is dynamically adjusted through the simulation space 23 based on the time required to obtain simulation results in the previous simulation step. Here, the second path 29 for selecting boundary conditions 1 for the next simulation step is selected based on whether the time required by the solver for the simulation results will be longer than in the previous simulation step. If the required time is longer than the time required to bypass a particular boundary condition 1, for example, in the boundary region 25, as shown by adjustment path 26, the second path 29 for selecting boundary conditions 1 in the simulation space 23 is adjusted accordingly, for example, the second path 29 is in the form of a meander 30. Here, by avoiding boundary condition 1, which requires a long simulation time, particularly in the boundary region 25, the use of homotopy can be avoided or reduced.

[0103] FIG. 6 shows a flowchart of an embodiment of a computer-implemented method in which the digital twin 20 is provided as a set of data points 21 obtained from a simulation step. The set of data points 21 is stored in the form of a data file 32, such as “CSV data” (comma-separated values ​​data). The digital twin 20 is the set of data points 21 including multiple simulation results corresponding to respective boundary conditions 1, as shown in FIG. 1 . This allows a user to select or exclude specific groups of points from the digital twin 20 according to requirements to quickly and efficiently obtain the respective simulation results corresponding to the respective boundary conditions 1. The digital twin 20 can be represented by a visualization plot, such as a 3D plot 33, also shown in FIG. 10 . A user can select or exclude specific groups of points from the digital twin 20 according to requirements, for example, by using a digital slider 35, as shown in FIG. 10 . The digital twin 20 is used to train an artificial intelligence model 34 or a machine learning-based model (not shown). The artificial intelligence model 34 or machine learning-based model is advantageous for big data visualization of simulation results along with corresponding boundary conditions 1, which can enable high-speed optimization and also real-time optimization and advanced process control. Additionally, the artificial intelligence model 34 can be used with surrogate models such as grey-box models 36 and neural network models 37 .

[0104] Figure 7 shows a comparison of the simulation results obtained by the artificial neural network model 34 and the ACM solver 8 for a two-step biogas process. It can be seen that the predictions by the artificial neural network model 34 and the ACM solver 8 agree very well, as all the resulting points lie around a straight line 43 inclined at an angle of 45° to each axis.

[0105] FIG. 8 shows a flowchart embodiment of a computer-implemented method in which, for parallel simulations, a time offset 50 can be used to initiate the solving of each system of equations in parallel with the solving of one of the systems. Such parallel simulations can be run on a single computer 55 or a cluster, as shown in FIG. 9. For example, a simulation may typically take 0.4 to 2 seconds. Due to parallelization, a 45-second offset may be present. To load, open, and start a simulation file or step using the ACM, the starting values ​​are read and the first point is approached by homotopy, which may take approximately 1 to 2 minutes. However, this depends strongly on the complexity of the mathematical model and the duration of the homotopy. For example, approximately 6 to 8 parallel simulations may be started simultaneously on a server computing system.

[0106] As shown in Figure 8, three simulation files or steps are shown, but for the sake of understanding only, the first duration 44 of the first simulation file 45 is shown to be greater than the second duration 46 of the second simulation file 47, which is further greater than the third duration 48 of the third simulation file 49. Here, a time offset 50 is used to initiate the solving of each of the simultaneous equations in one simulation file 45, 47, 49 in parallel with the solving of one of the simultaneous equations in the other simulation file 45, 47, 49. The time offset may be a predefined value, which may be varied for different simulation steps.

[0107] For example, assume that 30,000 simulation points need to be simulated, and each simulation point requires one second on average. It is not necessary to wait 30,000 seconds, or approximately 8.4 hours. Therefore, in this case, the ACM simulation can be parallelized into three simulation files or steps: first simulation file 44, second simulation file 47, and third simulation file 49. In each simulation file, 10,000 simulation points need to be calculated, which means approximately three hours. However, if all three simulation files are started simultaneously, the computer / server may crash. Therefore, first simulation file 45 can be opened first and the 10,000-point simulation can be started. Loading, opening, and starting can require significant computer resources. Therefore, only one simulation file, in this case, first simulation file 45, is opened. Additionally, the first point in first simulation file 45 is always started by homotopy because there are no starting values ​​for the initial run, which takes approximately one to two minutes. The second simulation point may take only 0.5-2 seconds because the old results from the simulation of the first point are available as starting values ​​for the second point. Furthermore, each of the following simulations of the following points may only take about 0.5-2 seconds each.

[0108] At a time offset of 50, which may be 45 seconds, a second simulation file 47 is started. Then, again 45 seconds later, a third simulation file 49 is started. The choice of value for time offset 50 depends on how long it takes to start a simulation file and how long the computer is "busy".

[0109] Note that any of the durations 44, 46, 48 may be greater or less than any of the other durations 44, 46, 48. Furthermore, dividing the simulation points into three simulation files is merely an example. The simulation can be parallelized into a number of simulation files selected by one skilled in the art. The selection of the number of simulation files may depend on the total number of simulation points that need to be simulated, the complexity of the simulation itself, the available computational resources, the number of non-converged points and where the respective homotopies need to be considered, and the time required to complete the simulation. Starting the parallelized simulation with a time offset 50 is advantageous because it smooths the total processor power required over time.

[0110] FIG. 9 shows a schematic diagram of a computer 55 for generating a digital twin for an apparatus or system of a chemical process or chemical plant for material synthesis and / or material separation, particularly configured to use a computer-implemented method. The computer 55 includes an input unit 51 configured to receive boundary conditions 1 and form an external source 54, as shown in FIG. 1. Transmission of the boundary conditions 1 between the external source 54 and the input unit 51 can be performed via a wired or wireless manner. The computer 55 includes a storage unit 52 configured to store the received boundary conditions 1. The computer 55 includes a processor 53 with a computational model 2, as shown in FIG. 1, configured to solve the simultaneous equations having the boundary conditions 1. Simulation results obtained from the processor 53 can be stored in the storage unit 52 as the digital twin 20 shown in FIG. 1, as indicated by the double arrow. The computer 55 includes an output unit 54 configured to output the simulation results from the digital twin 20 from the storage unit 52.

[0111] FIG. 10 illustrates filtering of data obtained from a digital twin 20. The digital twin 20 is a data point set 21 containing multiple simulation results corresponding to respective boundary conditions 1. A specific set of data points from the set of data points of the digital twin 20 can be selected or filtered according to requirements to obtain respective simulation results corresponding to respective boundary conditions 1 in a fast and efficient manner. The digital twin 20 can be represented by a 3D plot 33, and a user can select or exclude specific groups of points from the digital twin 20 according to requirements using digital sliders 35, as shown in FIG. 8, to obtain a filtered 3D plot 38. Here, the ranges of three parameter values ​​4, namely, pressure 39, CO₂ concentration 40, and CH₄ purity 41, vary according to requirements, e.g., a pressure range with a maximum pressure 39 of 14 bar, a maximum CO₂ concentration 40 of 0.35, and a maximum CH₄ purity 41 of 0.9825. The coloring of each data point 21 represents the corresponding simulation result. The value of each simulation result for each data point in the data point set 21 can be obtained using a color scale 22. The visualization and filtering process can be incorporated as a web application. The computer-implemented method thus enables the generation of digital twins for equipment or systems of chemical processes or chemical plants, in particular in the field of gas mixtures that are separated by gas separation membranes due to the different permeabilities of the individual gases.

[0112] FIG. 11 illustrates the effect of step selection (step width and path topology) on simulation performance. Often, each simulation uses values ​​for multiple boundary condition parameters as inputs, potentially considering more than three, more than five, more than seven, or even more than nine boundary condition parameters. The number of values ​​evaluated per parameter may, on average, be, for example, at least two, at least four, at least eight, at least 64, or at least 256. Thousands, hundreds of thousands, or millions of simulations may be run. For simplicity, the simulations are run here on a simplified grid of three different boundary condition parameters and six different values ​​per parameter. Therefore, simulating all possible value combinations requires running 6 × 6 × 6 = 2 simulations.

[0113] 11A shows only two of three different boundary condition parameters, and the x-axis of each of grids 102-108 may represent boundary condition parameter B, e.g., the A1 / A3 membrane surface ratio of a three-stage gas separation plant, with six different parameter values ​​B1, B2, B3, B4, B5, and B6 shown. The y-axis of each of grids 102-108 may represent boundary condition parameter A, e.g., the recycle of a three-stage gas separation plant, with six different parameter values ​​A1, A2, A3, A4, A5, and A6 shown.

[0114] For simplicity, grids with six possible values ​​for three different parameters are used as the basis for the simulations, whereby the increments between different values ​​of the same parameter are assumed to be equidistant; the grid shown in Figure 11 has an equidistant grid size in both dimensions. However, parameters typically differ in terms of the number of different values ​​possible, as well as the step size and units, if any.

[0115] Grid 102 represents a single-step data selection (single-step parameter value change) approach according to an embodiment of the present invention, where for the first five simulation runs, only the first boundary condition parameter A is varied from A1 to A6, while parameter B is held constant at value B1. A is then varied backward from A6 to A1, while B (but not the other parameter C) has its value incremented by a single step from B1 to B2. The overall run time required to run all 216 parameter value combinations based on the parameter value change schema shown in plot 102 is 5 minutes and 9 seconds.

[0116] Grid 104 represents a different approach, where for the first six simulation runs, parameter B (and parameter C, not shown) are held constant while A is varied from A1 to A6. B is then assigned a new value incremented by 1, but A again varies from A1 to A6 (rather than from A6 to A1, as shown at 102). Then, for the next six simulation runs, B is again assigned a new value incremented by 1, and A again varies from A1 to A6. The time required to run all 216 parameter value combinations based on the parameter value variation schema shown in plot 104 was nearly twice as long as for grid 102, or 9 minutes and 15 seconds.

[0117] Grid 106 shows boundary condition parameter value selections that "jump" from A3 to A4, then A4 to A2, then A2 to A5, then A5 to A1, and then A1 to A6. During these six steps, the value of B is held constant (indicated by the illustrated parameter B always having the value B1). As can be inferred from grid 106, the changes to boundary condition A are not based on "single steps," but rather on "jumps," i.e., parameter value changes of two or more increments. For further simulation runs (not shown in 106), parameter B was varied on a single-step basis. Although only a single parameter was changed from one simulation to the next, the "jumps" performed when changing a single parameter over two or more increments resulted in a significantly longer runtime of 28 minutes for the 216 simulations.

[0118] Grid 108 illustrates a random boundary condition parameter value selection strategy. In the illustrated example, both the "step size" and the number and identity of boundary conditions are varied randomly in each simulation. In the illustrated example, a run time of 40 minutes was observed to perform 2 simulations, which is nearly 10 times longer than the simulation strategy according to an embodiment of the present invention shown in grid 102.

[0119] 11B shows the cumulative run times for running 216 parameter value combinations for the four parameter selection strategies described above. As can be inferred from plot 110, the parameter value selection strategy according to an embodiment of the present invention (HTS Run0) is faster and significantly better than the three alternatives (HTS Runs 1-3) corresponding to grids 104-106.

[0120] 12 is a set of tables illustrating the identification of an appropriate step size for increasing simulation speed and minimizing the CPU resources required to run the simulation. According to a preferred embodiment, multiple simulations are run such that only one parameter value is changed from one simulation to the next, whereby the change is performed such that the parameter value immediately following the parameter value previously used in a predefined, parameter-specific sequence of parameter values ​​is used. This approach may also be referred to as a "single-step" parameter value change approach (i.e., changing the parameter value by two or more increments from one simulation to the next, without a jump). The parameter may be, for example, a boundary or initial condition parameter.

[0121] For example, the set of data values ​​specific to and assigned to a particular parameter can be a set of discrete, preferably equidistant, different values ​​spanning the range of values ​​allowed for and assigned to said parameter. The range of values ​​is defined by a minimum and a maximum. Depending on the parameter, the values ​​may have units such as °C or kg or m2. Different parameters can have different numbers of allowed parameter values ​​assigned to them.

[0122] Applicant has observed that both the order in which parameters are varied during multiple simulations and the correspondingly determined "step size" (or "increment") of the number of allowable parameter values ​​assigned to each parameter affect the performance and accuracy of the simulations: if the step size is too small, the number of simulations increases significantly and performance decreases significantly; if the step size is too large, the simulations may not converge or may not provide a digital twin that accurately represents a sufficient number of relevant operating states of the chemical process, equipment, or system.

[0123] According to the illustrated example, there are three boundary condition parameters: A1 / A3 ratio, recirculation and compressor outlet pressure.

[0124] The parameter A1 / A3 ratio indicates the ratio of membrane areas used in the first and third stages of a gas separation facility. For example, the gas separation facility can be a facility for separating a crude gas stream, which is carried out in an apparatus including a feed separation stage (first stage), a retentate separation stage (second stage), and a permeate separation stage (third stage). The facility can include one or more membranes in each of the three separation stages and can include at least one compressor. An example of such a system is described in EP 2588217. For example, the first stage can be a membrane separation stage for separating a feed stream into a first permeate stream and a first retentate stream. The second separation stage can be a membrane separation stage, which can be the same or different in structure as the feed separation stage, for separating the first retentate stream into a second permeate stream and a second retentate stream. The third separation stage may refer to a membrane separation stage that may be of the same or different construction as the feed stream separation stage and / or the retentate separation stage and that may be used to separate the first permeate stream into a third permeate stream and a third retentate stream. In the illustrated example, the A1 / A3 ratio is allowed to be a value between 0.700 and 1.200, with minimum and maximum values ​​set accordingly.

[0125] The parameter recycle indicates the fraction of the retentate of the second stage that is compressed relative to the feed stream of the second separation stage and recycled to the previous stage. In the example shown, recycle is allowed to have values ​​between 0.340 and 0.440, with minimum and maximum values ​​set accordingly.

[0126] The parameter "compressor outlet pressure" indicates the pressure on the feed side of the feed stream separation stage (first separation stage). The pressure can be generated by a compressor located upstream of the feed stream separation stage. In the example shown, the pressure generated by the compressor is allowed to be between 10.0 and 15 bar, with minimum and maximum values ​​set accordingly.

[0127] Typically, the minimum and maximum values ​​are set by a user, taking into account, for example, literature values ​​and / or parameter values ​​known to be tolerated or supported by the gas separation equipment whose operation is being simulated. In some embodiments, the minimum and maximum ranges simply define the range of values ​​to be simulated as being of interest for a particular gas separation equipment design or use project.

[0128] Table 1206 not only shows minimum and maximum values ​​for three exemplary parameters, but also step width "delta" that has been found to be advantageous for providing particularly rapid simulation results. To determine the appropriate step width ("delta" or "increment") for each parameter, a "step length determination method" (SLD method) is performed by the computer. To determine the appropriate order of parameters whose values ​​should be changed first, a "parameter order determination method" (POD method) is performed by the computer.

[0129] The SLD method includes the following steps:

[0130] a) assigning to a first parameter (e.g., the A1 / A3 ratio) a first series of distinct, preferably equidistant, parameter values ​​that lie within the minimum and maximum parameters assigned to this parameter. For example, as shown in Table 1206, four different parameter values ​​ranging from 0.70, 0.825 to 1.200 are assigned to the A1 / A3 ratio. The second and third parameters are assigned the average values ​​of their respective parameter ranges (see Avg.Rec and Avg.Comp in Table 1208).

[0131] b) For each set of parameter values ​​obtained thereby, e.g., for each row of table 1208, performing a simulation of the design and / or dynamic behavior of the gas separation equipment using said set as input, e.g., as parameter values ​​for boundary conditions and / or initial conditions.

[0132] c) The first parameter (here, the A1 / A3 ratio) is assigned a second series of distinct, preferably equidistant, parameter values ​​within the range of the minimum and maximum parameters assigned to this parameter, so that the second series is comprised of more values ​​than the first series. For example, as shown in Table 1210, eight different parameter values ​​ranging from 0.70, 0.7625 to 1.200 are assigned to the A1 / A3 ratio. The second and third parameters are assigned the mean values ​​of their respective parameter ranges.

[0133] d) For each set of parameter values ​​obtained in step c), e.g. for each row of table 1210, performing a simulation of the design and / or dynamic behavior of the gas separation equipment using said set as input, e.g. as parameter values ​​for boundary conditions and / or initial conditions.

[0134] e) Steps c) and d) are repeated a number of times, with each iteration increasing (e.g., doubling) the number of distinct data value sequence values ​​assigned to the first parameter. The iterations may continue until a predetermined termination criterion is reached, such as a predetermined maximum number of iterations, a maximum number of distinct data value sequences, etc.

[0135] f) Steps a) through e) are repeated for a different one of the boundary condition parameters. For example, the number of data values ​​in the data value sequence assigned to the parameter "recirculation" may be increased in each iteration, while constant average values ​​are used for the other parameters "A1 / A3 ratio" and "compressor."

[0136] g) Step f) is repeated until each parameter of the boundary conditions is used once as a parameter to which the "allowable" distinct data values ​​of the assigned series are incremented in each iteration defined in c) and d).

[0137] As described above, each of the multiple series of distinct data values ​​assigned to a given parameter (steps a) and c) and tables 1208, 1210) may be used to run a set of simulations, whereby each distinct data value in the series corresponds to one simulation. The total time to run all the simulations in steps b) (and d)) is measured and stored.

[0138] Applicant has observed that the total simulation time required for each step b) or d) of all simulations typically decreases as the number of data values ​​in the sequence increases, however, after the sequence of data values ​​exceeds a threshold number of distinct data values ​​contained therein, the total simulation time increases.

[0139] The appropriate sequence of data values ​​to be assigned to a given parameter is often the one that provides the shortest total simulation time for running all simulations defined by the parameter value combinations created in step b) for that sequence. The step width of a single step, i.e., the "delta" in table 1206, is defined by the distance between two subsequent data values ​​in the observed sequence of data values ​​to provide the shortest total simulation time for all values ​​in the sequence. Therefore, according to an embodiment of the present invention, the SLD method automatically identifies an appropriate step length (and thus an appropriate number of different predetermined values ​​to be used and changed during the simulation) for one or more of the boundary condition parameters, where the identification includes identifying a distinct sequence of data values ​​that provides the shortest total simulation time for running all simulations defined by the parameter value combinations created in step b) for that sequence. An example of selecting an appropriate step length for a parameter is shown in table 1302 of FIG. 13, where the first column contains the number of discrete values ​​per parameter evaluated and the second column contains the simulation time for a single simulation. The total simulation time for lines 1-4 is shown in the third column of each table.

[0140] Therefore, for the parameter A1 / A3 ratio, an appropriate step length / separate data value sequence should be selected so that the predetermined parameter value range includes the four different parameter values ​​that are changed during the simulation, since four different parameter values ​​corresponds to the shortest total simulation time of 7.2 seconds.

[0141] Different parameters may be assigned different step lengths / different numbers of discrete data values.

[0142] According to some embodiments, the automatically identified best fit list of distinct parameter values ​​may be manually modified, for example, to obtain better resolution. For example, using 8 instead of 4 different values ​​for the A1 / A3 ratio doubles the resolution of the simulation results with only a small increase in simulation time.

[0143] Furthermore, for some parameters, a minimum curve may not be observed when evaluating total simulation time for an increasing number of different data values. For example, the total simulation time for lines 1-4 in Table 1304 for parameter recirculation is minimized when only two different parameter values ​​are used. In these cases, the number of different values ​​assigned to a parameter and changed during the simulation may be manually set as a trade-off between simulation run time and the need to evaluate different values ​​to receive a sufficiently fine-grained set of data points that reflects the impact of this parameter on the entire gas separation process in sufficient detail. Smaller step sizes are typically (somewhat) slower than larger step sizes (from 4), but may not provide sufficient detail for each parameter.

[0144] Therefore, the above automatically performed SLD method may optionally include a manual step for manually modifying the number / step width of different data values ​​identified for each parameter by the SLD method.

[0145] The SLD method is used to identify appropriate parameter-specific schemes for value increments, whereby the increments can be of the same or different sizes. If the parameter's value increments are the same, this means that the parameter value is always incremented or decremented by increments of a constant parameter-specific size ("step length") from one simulation to the next.

[0146] The simulation performed to determine the step length of the parameters, corresponding to the number of different values ​​to be assigned to the parameters, uses the same simultaneous equations that are later used to perform the simulation that results in the digital twin. However, since other boundary condition parameters always use constant average values, the simulation is much faster and is not used to generate the digital twin. Therefore, the simulation performed with the SLD method is also called a "preliminary simulation."

[0147] FIG. 13 shows a set of tables illustrating the identification of an appropriate parameter order (POD method). The POD method is typically performed after the SLD method has been performed, i.e., after identifying parameter-specific "step lengths" (corresponding to distinct parameter values ​​for each series within a value range defined by given minimum and maximum values). This may have the advantage of utilizing existing computation time, as shown in the table in FIG. 12. However, it is also possible to perform the POD method after the user has completely manually selected the appropriate parameter-specific step lengths. In this case, however, preliminary simulations are performed, since the results may be needed as a basis for particularly rapid determination of the order of parameters to be changed.

[0148] The POD method is performed to identify a boundary condition parameter among a plurality of boundary condition parameters to be varied first during a simulation. This is performed by selecting, as the first boundary condition parameter to be varied during the course of the simulation, the parameter that produces the fastest results per simulation, at least for the determined optimal number of data values ​​assigned to this parameter by the SLD method. In some embodiments, this is performed by selecting, as the first boundary condition parameter to be varied during the course of the simulation, the parameter that produces the fastest results per simulation for the majority of the distinct data value sequences assigned to this parameter by the SLD method. The simulation time may be determined using a preliminary simulation, and the values ​​of the other parameters are not varied but rather are set to a constant value, for example, the average of their assigned range of values.

[0149] For example, the parameters to be used for the first parameter to be varied can be determined by analyzing the results of the SLD method, and simulations are run based on boundary parameter values ​​selected such that the value of only one parameter is varied at a time, and all other parameters have only the average of their range of values, assigned in each case by a minimum and maximum.

[0150] The three tables 1302, 1304, and 1306 show the simulation time per preliminary simulation (second column) and all simulations for a given number of different parameter values ​​(third column) obtained for a particular parameter assuming a given number of different values, e.g., 2, 4, 8, 32, and 64.

[0151] Table 1302 shows the time required to perform the various simulations performed when implementing the SLD method, with the average measurement time for calculating an individual simulation being 4.11 seconds when a series with only two different values ​​for the A1 / A3 ratio is assigned (while constant average values ​​are assigned to the recirculation and compressor parameters), the average measurement time for calculating an individual simulation being 1.81 seconds when a series with four different values ​​for the A1 / A3 ratio is assigned (while constant average values ​​are assigned to the recirculation and compressor parameters), and the average measurement time for calculating an individual simulation being 1.18 seconds when a series with eight different values ​​for the A1 / A3 ratio is assigned.

[0152] Table 1304 shows the time required to run various further simulations performed when implementing the SLD method, with the average measurement time to calculate an individual simulation being 1.88 seconds when a series with only two distinct values ​​for recirculation is assigned (when the A1 / A3 ratio and compressor parameters are assigned constant average values), the average measurement time to calculate an individual simulation being 1.24 seconds when a series with four different values ​​for recirculation is assigned (while the A1 / A3 ratio and compressor parameters are assigned constant average values), and the average measurement time to calculate an individual simulation being 1.20 seconds when a series with eight different values ​​for recirculation is assigned.

[0153] Table 1306 shows the time required to run various additional simulations performed when implementing the SLD method, with the average measurement time to calculate an individual simulation being 6.74 seconds when the pressure generated by the compressor ("Compression") is assigned a series of only two different values ​​(while the A1 / A3 ratio and recirculation parameters are assigned constant average values). The average measurement time to calculate an individual simulation when Compression is assigned a series with four different values ​​is 2.32 seconds. The average measurement time to calculate an individual simulation when Compression is assigned a series with eight different values ​​is 1.41 seconds.

[0154] As can be inferred from the measured times in the three tables, the smaller the step size / the higher the number of distinct parameter values ​​assigned to the parameters, the faster the individual simulations. However, the performance gain per individual simulation slows down and reaches a plateau.

[0155] A comparison of the simulation times obtained for different parameters and different numbers of allowed discrete parameter values ​​shown in Tables 1302-1306 reveals that for essentially any number of discrete values ​​(e.g., 2, 4, 6, 8, 16, 32 or 64 discrete values), a single-step variation of the recirculation ratio has faster performance than a single-step variation of A1 / A3, and especially than a single-step variation of the compression parameters.

[0156] For example, assuming each of the three parameters is assigned a set of 16 discrete values, each representing an optimal number of distinct data values, the time per individual simulation step is 1.06 seconds for the A1 / A3 ratio, which is slower than the 0.86 seconds for recirculation, but faster than the 1.22 seconds required for a stepwise variation of the compression parameter assuming 16 distinct values. Thus, under the assumption that each of the three parameters has eight distinct values, the order of parameters varied during the simulation is, from left to right, recirculation, A1 / A3 ratio, and compression.

[0157] However, different parameters typically have different numbers of data values ​​to be changed. For example, as explained above, the optimal number of distinct parameter values ​​for the parameter A1 / A3 ratio is 4, resulting in the shortest total time to run the preliminary simulations: 4 x 1.81 seconds = 7.2 seconds. However, recirculation may be assigned 16 different parameter values ​​to provide sufficient detail during the simulation of this parameter. The compressor may be assigned four different values, since 4 x 2.32 seconds = 9.28 seconds provides the shortest time to run all preliminary simulations shown in table 1306. Thus, the situation for the example shown in FIG. 13 is as follows:

[0158] [Table 1]

[0159] As shown in the table above, the SLD method is used to identify an appropriate number of different values ​​for each parameter. The order in which the parameters are varied is then determined so that the shorter the run time for one preliminary simulation relative to the number of values ​​determined by the SLD method, the sooner the value of each parameter is changed. Thus, in the example shown, recirculation is varied first, followed by the A1 / A3 ratio, and then compression.

[0160] In many cases, the number of distinct "allowed" data values ​​for each parameter may not be the same: for example, in the final simulation, recirculation may be assigned 16 different parameter values ​​that may have to be used as boundary parameter values, the A1 / A3 ratio may be assigned 4 (or, for example, 8) parameter values, and compression may be assigned 4 different parameter values.

[0161] Assuming that the parameters have only two allowed values, called V1 and V2, the results of selecting recirculation as the first parameter, the A1 / A2 ratio as the second parameter, and compression as the third parameter and varying them stepwise in a sequence of single-step parameter variations during subsequent simulation runs can be shown as follows:

[0162] [Table 2]

[0163] Thus, the order of the parameters may ensure that the "fastest" parameter, recirculation, is changed most frequently during a simulation run, and the "slowest" parameter, compression, is changed least frequently.

[0164] More generally, the simulation steps for calculating the digital twin may be performed such that the first three boundary condition parameters whose values ​​are changed increase or decrease from one step to another according to the following schema, where "BCP" is the "boundary condition parameter" and V1, V2 are the respective values ​​assuming two different assigned series of values ​​for each parameter:

[0165] [Table 3]

[0166] For simplicity, the value changes during the eight consecutive simulation runs shown in the table above are based on only three parameters, each assigned a set of only two distinct values. In practice, the number of parameters and parameter-specific data values ​​may be much higher.

[0167] Figure 14 shows a plot 1400 illustrating the observed average simulation times for individual simulation runs when running the SLD method assuming 2, 4, 8, 16, 32, and 64 different values ​​per parameter. The x-axis is a logarithmic scale. As can be inferred from this plot, the recirculation parameter runs the fastest, with the exception of eight parameter values ​​per parameter, and stepwise changes in the compression parameter take the longest time.

[0168] 15 shows a flowchart of a computer-implemented method for computing a digital twin of a chemical process or a digital twin of a chemical plant's equipment or systems. The method steps have already been described with reference to FIG.

[0169] Examples of the present invention may have the advantage that the CPU and memory consumption required to run multiple simulations is minimized. For example, by changing only a single parameter value from one simulation to the next and keeping other boundary condition parameters constant, the number of parameter values ​​that must be read from a storage device into main memory is reduced. Preferably, the single parameter value is changed so that the value increases or decreases by a single increment from one simulation to the next, so that no jumps are performed.

[0170] Preferably, the specific manner in which a single boundary parameter value is changed (with respect to the order of the parameter that first changes its value and / or with respect to the increment by which this parameter is changed) is selected to reduce processing time. The selection of the parameter order and increment size ("step length") may be based on empirical measurements of the time required to perform preliminary simulations, thereby taking into account the particularities of the computer system used to perform the simulations (preferably, the preliminary and final simulations may be performed on the same or similar computer systems). Furthermore, because only a single boundary parameter value is changed at a time in a highly specific manner, the simultaneous equations can be solved faster as the equations converge more quickly.

[0171] Thanks to significant performance improvements, it is now possible to create digital twins containing vast amounts of data points, thereby providing a highly detailed and therefore highly accurate digital representation of a chemical process or facility. There may be multiple technical devices for the digital twin, each consisting of hundreds of thousands or even millions of data points, each with multiple boundary condition parameter values ​​assigned.

[0172] For example, the set of data points generated and provided as a digital twin can be used, fully or at least partially, to simulate, control, or design equipment or systems of a chemical process or chemical plant. For example, a simulation can be performed during the design phase of a facility to create or optimize the design of a plant or chemical facility, such as a facility for separating gases or other types of materials. The data points may be used directly, for example, by executing an algorithm (e.g., a rules engine or another type of predetermined algorithm) that uses the set of data points, or a subset thereof, as input. Alternatively, at least some of the data points obtained from the simulation step are used as a training data set for training a predictive model using a machine learning approach. In subsequent steps, the trained predictive model is used to simulate, control, or design equipment or systems of a chemical process or chemical plant. [Explanation of symbols]

[0173] 1 Boundary conditions 2. Computational model 3 Initial conditions 4 Parameter Values 5 Parameter Table Data 6 Tabular Database 7 columns 8. Process Simulation Software 9 Graphic User Interface 10 First Column 11 First Line 12 First parameter value 13 Second Column 14 Second parameter value 15 Third Column 16 Third parameter value 17 Fourth Column 18 First boundary condition 19 Second boundary condition 20 Digital Twin A set of 21 data points 22 Color Scale 23 Simulation Space 24 First Route 25 Boundary area 26 Adjustment Path 27 Rotational Speed 28 Torque 29 Second Route 30 Meandering 32 data files 33 3D Plots 34 Artificial Intelligence Models 35 Digital Slider 36 Gray Box Model 37 Neural Network Model 38 Filtered 3D Plots 39 Pressure 40 CO2 concentration 41 CH4 purity 42 Central area 43 straight line 44 First Duration 45 First Simulation File 46 Second Duration 47 Second Simulation File 48 Third Duration 49 Third Simulation File 50 hour offset 51 Input Unit 52 Memory Unit 53 processors 54 External Sources 55 Computer 102-108 Parameter Value Grid 110 Plot 1202 minimum 1204 Maximum 1206 Parameter Table 1208-1210 Table with parameter value combinations 1302-1306 Simulation time observation table 1400 plots

Claims

1. 1. A computer-implemented method for generating a digital twin (20) for a device or system of a chemical process or chemical plant, in particular for substance synthesis and / or substance separation, said method comprising: a) inputting a plurality of boundary conditions (1) into a calculation model (2), the calculation model (2) including a system of equations, each boundary condition (1) including a plurality of parameter values ​​(4); b) inputting initial conditions for solving the simultaneous equations; c) in a simulation step, solving the simultaneous equations using each of the boundary conditions (1) and providing corresponding simulation results, respectively; one of the parameter values ​​(4) of each boundary condition (1) is changed from one simulation step to the next, while the other parameter values ​​(4) belonging to each boundary condition remain unchanged; d) providing said digital twin (20) as a set of data points (21) obtained from said simulation step; 11. A computer-implemented method comprising:

2. 2. The computer-implemented method of claim 1, wherein the one of the parameter values ​​(4) of the respective boundary conditions (1) is varied in a simulation within its entire set of values ​​of data points from a start data point to an end data point, and in a subsequent series of simulations, the one of the parameter values ​​(4) of the respective boundary conditions is varied backward, i.e., from the end data point to the start data point.

3. 3. The computer-implemented method of claim 1, wherein simulation results from one simulation step are used as initial conditions (3) for a next simulation step.

4. The computer-implemented method of claim 1 , further comprising displaying the digital twin.

5. 5. The computer-implemented method of claim 4, wherein the step of displaying the digital twin comprises displaying the digital twin via an augmented reality display system.

6. 6. The computer-implemented method of claim 4 or 5, wherein the step of displaying the digital twin comprises generating 2D or 3D computer graphics that visualize data in the digital twin, loading the 2D or 3D graphics into a frame buffer of a display system, and displaying the contents of the frame buffer on the display system.

7. 7. The computer-implemented method of claim 1, wherein the plurality of boundary conditions (1) are obtained from a simulation space (23), and the boundary condition (1) of a first simulation step is selected from a central region of the simulation space (23).

8. 8. The computer-implemented method of claim 1, wherein a path (24, 29) for selecting boundary conditions (1) for a next simulation step is dynamically adjusted through the simulation space (23) based on the time taken to obtain simulation results in a previous simulation step.

9. The computer-implemented method of claim 1 , wherein the system of equations is a steady-state system of equations for a quasi-steady-state process.

10. 10. The computer-implemented method of claim 1, wherein the digital twin (20) is a database containing a matrix of multiple simulation results corresponding to the respective boundary conditions.

11. the chemical process corresponds to a chemical process of a gas separation arrangement comprising a gas separation membrane or a plurality of gas separation membranes, or the apparatus or system of the chemical plant is a gas separation membrane or a gas separation arrangement having a plurality of gas separation membranes; A computer-implemented method according to any one of claims 1 to 10.

12. 12. The computer-implemented method of claim 1, wherein a plurality of simultaneous equations, each using a corresponding boundary condition (1) to provide a corresponding simulation result, are solved in parallel in a simulation step.

13. 13. The computer-implemented method of claim 12, wherein a time offset (50) is used to start solving each of the systems of equations in parallel with respect to solving one of the systems of equations, the time offset (50) being a predetermined percentage of an average time of a simulation step.

14. The computer-implemented method of claim 13 , wherein the predetermined percentage is between 5% and 10% of the average time of a simulation step.

15. 15. The computer-implemented method of claim 1, wherein the digital twin (20) is used to train an artificial intelligence model (34) or a machine learning-based model.

16. 16. The computer-implemented method of claim 1, wherein the digital twin (20) is a set of data points (21) including a plurality of simulation results corresponding to the respective boundary conditions.

17. 17. A computer-implemented method according to any one of claims 1 to 16, wherein the simulation steps are performed such that parameter values ​​do not increase or decrease from one step to another by two or more predetermined parameter-dependent increments.

18. 18. The computer-implemented method of claim 1, further comprising determining, for each of the boundary condition parameters, a sequence of parameter values ​​to be assigned to the respective boundary condition parameter and to be changed continuously during the simulation steps, whereby changing the value of the boundary condition from one simulation step to the next uses one of the data values ​​of the series immediately preceding or succeeding a previously used value of the boundary condition parameter, whereby in particular the sequence of parameter values ​​is determined for each of the boundary condition parameters such that the processing time for performing simulations for all parameter values ​​included in the series is minimized.

19. The step of determining the set of parameter values ​​for each of the boundary condition parameters comprises performing a Simulation Step Length Determination method (SLD method), wherein the SLD method determines, for each of the boundary condition parameters: a) assigning to one of said boundary condition parameters a first series of distinct parameter values ​​that lie within a given minimum and maximum range assigned to said parameter, and assigning to the other boundary condition parameters an average value of the parameter range defined by the respective assigned minimum and maximum values; b) for each parameter value of the first series, performing a preliminary simulation of the design and / or dynamic behavior of the chemical process or equipment or system of the chemical plant using the simultaneous equations, whereby for the other boundary condition parameters, the preliminary simulation uses the respectively assigned mean values ​​as inputs, whereby the time required to perform the preliminary simulation for the parameter values ​​of the first series is measured while the simulation is being performed; c) assigning to said one of said boundary condition parameters a second series of distinct parameter values ​​that are within a given minimum and maximum range assigned to said parameter, said second series of distinct parameter values ​​having parameter values ​​that are greater or less than any series of data values ​​previously assigned to said parameter; d) for each parameter value of the second series, performing a preliminary simulation of the design and / or dynamic behavior of the chemical process or equipment or system of the chemical plant using the simultaneous equations, wherein for the other boundary condition parameters, the preliminary simulation uses the respectively assigned mean values ​​as inputs; e) repeating steps c) and d) until a termination criterion is reached, e.g., a maximum number of parameter values ​​included in the series; f) analyzing the total time required to run all preliminary simulations for each parameter value sequence to identify one of the data value sequences that corresponds to the shortest total execution time; g) using the identified sequence of parameter values ​​as parameter values ​​successively assigned to the respective boundary condition parameters during the simulation steps performed to generate the digital twin, wherein the difference between two successive parameter values ​​in the identified sequence defines a simulation step length when changing one of the parameter values ​​of the boundary condition parameters from one simulation step to the next; 20. The computer-implemented method of claim 18, comprising:

20. - the step of changing one of the parameter values ​​of each boundary condition from one simulation step to the next is performed according to the order of the boundary condition parameters, - said simulation is carried out in such a way that all values ​​of the series of parameter values ​​assigned to said first parameter in said order must be traversed backwards, from minimum to maximum, according to this order, before any value of the value of a subsequent parameter is changed; the method includes a step of identifying a change in the order of boundary condition parameters such that the simulation time is minimized, 20. A computer-implemented method according to any one of claims 1 to 19.

21. Each of the boundary parameters is assigned a sequence of parameter values, and the determination of the order comprises: - running a number of preliminary simulations using said system of equations, in each preliminary simulation the value of only one of said boundary condition parameters is changed, the other parameters being assigned constant values, said constant values ​​preferably representing the average of the range of values ​​specific to the assigned parameters, by which the time required to run said preliminary simulations is measured; - determining, for each of said boundary parameters, the total time required to perform all of said preliminary simulations necessary to pass through all of the values ​​included in said series of data values ​​assigned to said parameter; - identifying said order such that the shorter the total time required, the higher the priority of said respective parameter within said order; 21. The computer-implemented method of claim 20, comprising:

22. - using at least some of said data points (21) obtained from said simulation step to simulate, control or design said equipment or systems of said chemical process or said chemical plant, or - using at least some of the data points (21) obtained from the simulation step to train a predictive model using a machine learning approach, and using the trained predictive model to simulate, control or design the equipment or systems of the chemical process or the chemical plant, 22. The computer-implemented method of claim 1, further comprising:

23. the number of simulation steps performed and the number of data points comprising the result of each one of said simulation steps is at least 100,000, in particular at least 250,000, in particular at least 500,000, in particular at least 1 million, and / or the number of boundary condition parameters whose values ​​change in the simulation step is at least 3, in particular at least 5, in particular at least 7, in particular at least 9, and / or the average number of predetermined values ​​assigned to one of the boundary condition parameters varied during the simulation step is at least 2, in particular at least 4, in particular at least 8, in particular at least 64, for example at least, in particular at least 256, 23. A computer-implemented method according to any one of claims 1 to 22.

24. A computer program comprising instructions that, when said program is executed by a computer (55), cause said computer (55) to carry out the steps of the computer-implemented method of any one of claims 1 to 23.

25. A computer (55) for generating a digital twin (20) for an apparatus or system of a chemical process or chemical plant for substance synthesis and / or substance separation, configured in particular to use the steps of the computer-implemented method according to any one of claims 1 to 23.

26. - an electronic display; - a computer (55) according to claim 25 configured to generate the digital twin, the computer being further configured to generate 2D or 3D computer graphics visualizing data in the digital twin and display the 2D or 3D computer graphics on the electronic display; and A display system comprising:

27. 24. A data structure configured for use in visualizing a digital twin (20) of a chemical process or chemical plant equipment or system, the data structure comprising a plurality of data points obtained by the method of any one of claims 1 to 23, the data structure being configured, when processed by a display system, to cause the display system to generate 2D or 3D computer graphics that visualize data in the digital twin and to display the 2D or 3D computer graphics on an electronic display of the display system.

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