METHOD AND DEVICE FOR MEASURING GAS DIFFUSION COEFFICIENTS THROUGH POROUS MATERIALS UNDER Elevated GAS PRESSURE

Abstract

Method for determining a diffusion coefficient of a diffusion of a first gas (79) through a porous material (2) into a second gas (80) at a gas pressure increased by at least 900% compared to atmospheric pressure, - wherein a sample (1) of the porous material (2) is arranged as a partition of defined thickness between a first gas space (58) and a second gas space (59), wherein the first gas space (58) is at least 5 times the size of an open pore volume of the sample (1), - wherein the first gas space (58), the open pore volume of the sample (1) and the second gas space (59) are purged with the first gas (79), - wherein the purging with the first gas (79) is completed and the first gas space (58) adjacent to the sample (1) is sealed off, - wherein the second gas (80), which is distinguishable from the first gas (79), is subsequently introduced into the second gas space (59) with a defined volume flow rate, and a gas mixture (81) comprising the second gas (80) and components of the first gas (79) is discharged from the second gas space (59), - wherein the diverted gas mixture (81) is maintained at the increased gas pressure and - wherein a concentration profile of the proportion of the first gas (79) in the gas mixture (81) derived from the second gas space (59) is recorded and analyzed with respect to the diffusion coefficient.

Description

TECHNICAL AREA OF INVENTION

[0001] The invention relates to a method for determining the diffusion coefficient of a diffusion of a first gas through a porous material into a second gas at a gas pressure increased by at least 900%, i.e., 10 times, compared to atmospheric pressure. The invention further relates to a device for carrying out such a method.

[0002] The determination of diffusion coefficients through porous materials can be carried out, for example, on rocks and other subsurface materials to investigate a site's suitability for an underground gas storage facility for hydrogen or carbon dioxide. The diffusion coefficients are needed to estimate the tightness of the underground gas storage facility with respect to both the leakage of the stored gas into the subsurface and the ingress of natural gas present in the subsurface into the stored gas, and to simulate resulting gas mixing. STATE OF THE ART

[0003] Diffusion is a physical process driven by concentration differences and therefore occurs even without pressure differences. Diffusion can occur under steady-state and transient conditions. The difference between steady-state and transient conditions is that steady-state diffusion proceeds at a constant diffusion rate, whereas the diffusion rate of transient diffusion is a function of time. Under both conditions, diffusion can be described using Fick's laws and used to measure the diffusion coefficient.

[0004] The Wicke-Kallenbach diffusion cell and the Graham diffusion cell are known for measuring the diffusion coefficient of a first gas through a porous material into a second gas; see SOUKUP, K. [et al.]: Comparison of Wicke–Kallenbach and Graham's diffusion cells for obtaining transport characteristics of porous solids. In: Chemical Engineering Science, Vol. 63, 2008, No. 4, pp. 1003–1011. The Wicke-Kallenbach diffusion cell consists of two chambers separated by a sample of the porous material. Two different gases are continuously passed through one chamber and the opposite chamber. The gas pressure in both chambers is kept equal and constant.When a steady state of diffusion is reached, the compositions of the gases in the two chambers, that is to say in particular the concentrations of the gases from the respective opposite chambers, are analyzed, in current embodiments by means of gas chromatography.

[0005] The setup and initial operation of a Graham diffusion cell are the same as those of a Wicke-Kallenbach diffusion cell. Here, too, two different gases are continuously passed through two chambers separated by a sample of the porous material until a steady state of diffusion is reached. Then, however, the flow of one gas into one chamber is stopped. This allows the diffusion-induced volumetric flow rate of the other gas into the other chamber to be determined using a flowmeter. Unlike a Wicke-Kallenbach diffusion cell, this method does not require analysis of the gas compositions in the two chambers.

[0006] Stationary methods, such as those used in a Wicke-Kallenbach diffusion cell, are difficult to implement for measurements under elevated pressures. Both chambers would have to be separately regulated to the same high gas pressure, which is practically impossible. Even small pressure differences of just a few hPa, however, lead to pressure-driven flow from one chamber to the other. Since diffusion is a relatively slow transport process, any such pressure difference distorts the result of the diffusion coefficient determination.

[0007] For measuring very small diffusion coefficients, an unsteady measurement with a flow meter on a Graham measuring cell is too insensitive, since the diffusion rates to be measured are very small.

[0008] Diffusion cells are also known that can be used for measurements according to both Wicke-Kallenbach and Graham.

[0009] From GANZER, L. [et al.]: Investigation of the effect of CO2 with different accompanying substance compositions on injectivity: Final report on the collaborative project CLUSTER: Project duration: 01.07.2015 to 30.06.2018: Reporting period: 01.07.2015 to 30.06.2018. Clausthal-Zellerfeld: Clausthal University of Technology, Institute of Petroleum and Natural Gas Engineering, 2018 (Funding reference: 03ET7031E). On pages 1-21, a device with a flood cell with a three-layer coating around a rock sample is known. In the flood cell, the rock sample is encased with a first layer of PTFE tape and a PTFE heat-shrink tube to prevent direct contact between fluids and the next layer of aluminum foil. The aluminum foil prevents the diffusive escape of CO2. The third layer is a fluororubber tube that provides a hydraulic seal between the rock sample and an enclosing cavity.This cavity is pressurized with a water pressure of, for example, 24 MPa to simulate rock pressure. The entire unit is housed in a steel cell, and the respective CO2-adjuvant mixture is injected or produced into the rock sample via capillaries embedded in the end pieces. A second capillary in the end pieces allows for differential and absolute pressure measurement directly at the end faces of the rock sample. The CO2-adjuvant mixture is injected via a syringe pump, to which the pre-compressed CO2-adjuvant mixture is fed via a sliding piston container.

[0010] From DE 10 2017 128 269 A1, a measuring cell for measuring the diffusion coefficient of a gas in an analyte is known. The measuring cell has a cell body that forms a measuring cavity suitable for receiving the analyte. The measuring cell comprises a first semipermeable separating layer that delimits the measuring cavity from an opening in a first cell section of the cell body. The cell body further comprises a second cell section with a cavity for receiving the gas, wherein the measuring cell has a second semipermeable separating layer that delimits the measuring cavity from the cavity in the second cell section. The first cell section is designed to maintain a vacuum, at least within a region connected to the opening; and the first cell section is connectable via the opening to a detector suitable for measuring a mass flow rate.

[0011] To measure the diffusion coefficient, a desired gas pressure is set in the cavity, and the mass flow rate is measured by the detector. This mass flow rate corresponds to the flow of gas molecules passing from the cavity into the measuring cavity via the semipermeable interface, out of the measuring cavity via another semipermeable interface, and through the opening to the detector. Furthermore, a pressure change is measured by a pressure sensor when the desired gas pressure is generated in the cavity; the time at which this pressure change is detected is recorded as the starting point of the measurement.

[0012] From EP 0 524 214 B1, a method for measuring the diffusion coefficient of a gas through a membrane separating two chambers that can be filled with the gas is known. In each of the two chambers, the pressure and temperature are measured at a first and a second time point, and from these measurements and the gas constant of the gas, the gas concentration in each chamber is determined. By solving a differential equation, the diffusion coefficient of the gas is then determined from the measured gas concentrations.

[0013] From EP 3 021 103 A1, a system and method for measuring the gas diffusion coefficient of three-dimensional hollow bodies with an opening are known. The system comprises a sealable chamber with an inlet line, a first outlet line, and a second outlet line. The inlet line has an inlet valve for regulating the gas inlet into the chamber. The first outlet line has a first pressure sensor and a subsequent first outlet valve for drawing gas from the body when used with a vacuum device and interacting with a vacuum sensor. The second outlet line has a second outlet valve for drawing gas from the chamber when using a vacuum device. The chamber is in material contact with a second pressure sensor. The system further comprises a data recording system for recording the pressures at the first and second pressure sensors.In operation, the chamber houses the body, and the first outlet line is hermetically sealed to the body's opening. During operation, the gas content of the body and the chamber is extracted through the first and second outlet lines, respectively, with the inlet valve closed and the first and second outlet valves open. This step is repeated until the pressure increase within the body due to outgassing reaches a certain threshold. Gas is then introduced into the chamber in a controlled manner through the inlet line, with the first and second valves closed. The pressures at the first and second pressure sensors are measured. The pressure increase within the body is recorded, and the pressure increase due to outgassing is subtracted. The diffusion coefficient is calculated according to Fick's law for radial diffusion in cylindrical coordinates.

[0014] US Patent 2021 / 0025801A1 describes an apparatus for the experimental measurement of the diffusion coefficient of natural gas. The apparatus includes a core holder, a differential pressure sensor, pressure gauges, multiple valves, a pressure pump, a vacuum pump, a hydrocarbon gas source, a nitrogen gas source, a gas chromatograph, an intermediate reservoir, sample chambers, a pressure stabilization device, and pressure-sensitive alarm devices. A rubber sleeve on the core holder prevents the core from becoming stuck in the holder during core placement due to improper handling. The pressure stabilization device is connected to the sample chambers to ensure a stable internal pressure in the chambers after sampling. This eliminates an experimental variable and results in a more accurate and reliable experimental outcome.If a gas leak occurs, a sensor device can detect the gas leak in time and send an alarm to a mobile device of the experimenter. TASK OF INVENTION

[0015] The invention is based on the objective of providing a method for determining a diffusion coefficient of a diffusion of a first gas through a porous material into a second gas under a gas pressure increased by at least 900% compared to atmospheric pressure, and a device suitable for carrying out this method, with which even very small diffusion coefficients can be accurately determined under very high gas pressure. SOLUTION

[0016] The object of the invention is achieved by a method with the features of claim 1 and by a device of claim 12. The further claims relate to preferred embodiments of the method and the device according to the invention. DESCRIPTION OF THE INVENTION

[0017] In a method according to the invention for determining the diffusion coefficient of a diffusion of a first gas through a porous material into a second gas at a gas pressure increased by at least 900% above atmospheric pressure, i.e., at least ten times higher, a sample of the porous material is arranged as a partition of defined thickness between a first gas space and a second gas space, wherein the first gas space is at least five times the volume of the sample's open pore space. The open pore space of the sample is the product of the sample's open porosity, expressed as a percentage, and the sample's total volume. Preferably, the first gas space is not only at least five times the volume of the open pore space, but at least ten times the volume. More preferably, the first gas space is at least twenty times the volume of the sample's open pore space, and even more preferably, at least 100 times the volume.The first gas chamber, the open pore volume of the sample, and the second gas chamber are purged with the first gas. Purging with the first gas is then stopped, and the first gas chamber adjacent to the sample is sealed off. Subsequently, the second gas, which is distinguishable from the first gas, is introduced into the second gas chamber at a defined flow rate, and a gas mixture comprising the second gas and portions of the first gas is drawn off from the second gas chamber. The drawn-off gas mixture is maintained at the elevated gas pressure at which the diffusion coefficient of the first gas is to be determined. This also maintains the second and first gas chambers at this elevated gas pressure. The concentration profile of the first gas in the gas mixture drawn off from the second gas chamber is recorded and analyzed with respect to the desired diffusion coefficient.

[0018] In the method according to the invention, the concentration profile initially shows a steep decrease in the proportion of the first gas until a quasi-steady-state state of gas diffusion through the sample is reached. In this quasi-steady-state state, only a slow decrease in the proportion of the first gas in the gas mixture occurs. From the concentration profile that then appears, the desired diffusion coefficient can be determined with high accuracy by comparison with model calculations and / or comparison with concentration profiles of samples that have a known diffusion coefficient for the first gas into the second gas.

[0019] In the method according to the invention, only the gas pressure of the diverted gas mixture is regulated by maintaining it at the elevated gas pressure for which the diffusion coefficient is to be determined. With the small, defined volumetric flow rate at which the second gas is introduced into and then diverted from the second gas chamber, the gas pressure in the second gas chamber is equal to the gas pressure at which the diverted gas mixture is maintained. In the first gas chamber, the elevated gas pressure for which the diffusion coefficient of the first gas is to be determined is established by pressure equalization resulting from pressure-driven flow.It is understood, however, that the purging of the first gas chamber with the first gas is carried out, or at least terminated, at a gas pressure close to, and perhaps slightly above, the elevated gas pressure, so that an initial pressure-driven flow forces the first gas from the first gas chamber into the second gas chamber until pressure equalization occurs. The quasi-steady state of diffusion through the sample is then subsequently established. The method according to the invention also functions, however, if the gas pressure of the first gas in the first gas chamber is below the elevated gas pressure at the end of the purging process, at which the gas mixture derived from the second gas chamber is then maintained. In this case, however, a pressure-driven flow of the second gas into the first gas chamber occurs before the quasi-steady state of diffusion through the sample is reached.

[0020] Compared to the second gas chamber, the first gas chamber in the process according to the invention is preferably at least twenty times larger, more preferably at least fifty times larger, and most preferably at least 100 times larger. The relative size of the first gas chamber determines the rate of change in the diffusion rate that occurs during the quasi-steady-state diffusion of the first gas from the first gas chamber with decreasing concentration of the first gas in the first gas chamber. The size of the second gas chamber, together with the defined volumetric flow rate with which the second gas is introduced into the second gas chamber, influences the proportion of the first gas in the gas mixture derived from the second gas chamber, which results from the current diffusion rate.The smaller the second gas chamber and the defined volume flow rate, the greater the proportion of the first gas in the gas mixture derived from the second gas chamber, assuming a constant diffusion rate of the first gas. However, as the proportion of the first gas in the second gas chamber increases, the concentration gradient of the first gas above the sample decreases, and thus the driving force of diffusion of the first gas, i.e., the diffusion rate of the first gas, decreases.

[0021] Preferably, in the diffusion process according to the invention, the first gas space, the open pore volume of the sample, and the second gas space are purged with the first gas until they contain at least 99.9% of the first gas and / or until the gas mixture exiting the second gas space during purging consists of at least 99.9% of the first gas. Accordingly, the first gas itself must have a purity of at least 99.9%. If, at the end of the purging process, the gas pressure of the first gas in the first gas space is at least as high as the increased gas pressure, a defined starting point is established for the concentration profile of the proportion of the first gas in the gas mixture discharged from the second gas space. This occurs as soon as, after purging, the second gas is introduced into the gas space at the defined volume flow rate and the gas mixture comprising the second gas and the proportions of the first gas is discharged from the second gas space.

[0022] Specifically, the first gas space, the open pore volume of the sample, and the second gas space can be purged with the first gas via a first gas line leading into the first gas space. To stop the purging with the first gas and to isolate the gas space adjacent to the sample, a first shut-off valve in the first gas line can then be closed. Alternatively, a second gas line leading out of the first gas space can be provided to accelerate the purging of the first gas space with the first gas, thus avoiding the need to displace all foreign gas through the sample and the second gas space.

[0023] Specifically, the second gas can be introduced into the second gas chamber at a constant volumetric flow rate, which, at the constant elevated gas pressure, corresponds to a constant flow rate of the second gas. The constant volumetric flow rate is typically in the range of 1 to 200 ml / s per square meter of the sample's cross-sectional area, and preferably in the range of 5 to 50 ml / s per square meter of the sample's cross-sectional area.

[0024] In practice, the second gas can be introduced into the second gas space by advancing a sliding piston of a sliding piston container at a constant speed with a constant volume flow.

[0025] The second gas, like the first gas, preferably has a high purity of at least 99.9% in order to measure the diffusion coefficient of interest under defined conditions and, in particular, to be able to detect the first gas diffused through the sample of porous material with high accuracy using the gas chromatograph.

[0026] The increased gas pressure under which the diffusion coefficient of the diffusion of the first gas through the sample into the second gas is determined is at least 10 times atmospheric pressure, i.e., at least 1 MPa. Preferably, it is at least 50 times atmospheric pressure, i.e., at least 5 MPa, or even at least 100 times atmospheric pressure, i.e., at least 10 MPa.

[0027] The method according to the invention is not fundamentally limited with regard to the open porosity of the sample. The method according to the invention is particularly well suited for samples with an open porosity between 5% and 35%. Accordingly, the open pore volume of the sample then accounts for between 5% and 35% of the total volume of the sample.

[0028] With regard to the diffusion rate of the sample at the increased gas pressure, which depends not only on the diffusion coefficient of the porous material but also, in particular, on the thickness of the sample between the two gas spaces, the method according to the invention is particularly suitable for diffusion rates between 2×10 -5 and 2x10 -1 mol / s per square meter cross-sectional area of ​​the sample and in particular between 2×10 -3 and 2x10 -2mol / s per square meter of cross-sectional area of ​​the sample is suitable. The method according to the invention is therefore concerned with the determination of diffusion coefficients that result in only small diffusion rates. It should be noted that the specified ranges of diffusion rates refer to one square meter of cross-sectional area of ​​the sample, whereas in practice the sample has a cross-section on the order of 10 cm². 2 = 1×10 -3 m 2 exhibits.

[0029] In carrying out the method according to the invention, a gas inlet element and a hollow cylinder, which together define the first gas space, the sample, and a gas distribution element, which defines the second gas space, can be arranged one after the other between a first end piece and a second end piece in a sealing tube. The sealing tube can then be pressurized with an external pressure that is higher than the increased gas pressure at which the diffusion coefficient is measured. The external pressure seals the sample at its outer circumference, so that the first gas does not pass around the sample but only through the sample from the first gas space into the second gas space. The radial sealing of the sample can be enhanced by coating the outer circumference of the sample, for example, with a tape and / or a heat-shrink tube made of PTFE and aluminum foil.Preferably, the external pressure is at least 50% and / or at least 3 MPa higher than the elevated gas pressure at which the diffusion coefficient is measured. This external pressure not only achieves a radial seal of the sample but also simulates the pressure exerted on the sample by the surrounding rock.

[0030] An apparatus according to the invention for carrying out the inventive method for determining a diffusion coefficient of a diffusion of a first gas through a porous material into a second gas at a gas pressure increased by at least 900% above atmospheric pressure comprises a diffusion cell that accommodates a cylindrical sample of the porous material as a partition of defined thickness between a first gas chamber and a second gas chamber. A first gas line opens into the first gas chamber, in which a first shut-off valve is arranged and which can be connected to a first pressurized gas source. A second gas line opens into the second gas chamber, in which a second shut-off valve is arranged and which is connected to a volumetric flow meter and can be connected to a second pressurized gas source. A third gas line leads out of the second gas chamber, in which a back pressure regulator is arranged and which is connected to a gas chromatograph.In this arrangement, a portion of the first gas space adjacent to the sample is bounded by a hollow cylinder whose length is at least as great as the thickness of the sample between the first and second gas spaces. The diffusion cell, axially bounded by a gas inlet element (which, together with the hollow cylinder, defines the first gas space) and a gas distribution element (which defines the second gas space), is arranged within a sealing tube between a first and a second end piece. A pressure chamber, connectable to an external pressure source, adjoins the outside of the sealing tube. A fluoroelastomer (FPM) tube is particularly suitable as the sealing tube. The hollow cylinder, the gas inlet element, the gas distribution element, and the end pieces are preferably made of steel. The steel alloy should be selected to minimize corrosion upon contact with the first and second gases and the porous material.

[0031] The volumetric flow meter, to which the second gas line is connected, can have a sliding piston reservoir with a controlled, movable sliding piston. The advancement of the sliding piston can be pneumatic, hydraulic, or electric. In pneumatic or hydraulic configurations, a reservoir chamber on the drive side of the sliding piston can be connected to a working pressure source. A reservoir chamber located on the opposite side of the sliding piston can be filled with the second gas directly from the second pressurized gas source or via a gas booster, which increases the gas pressure. The gas pressure of the first gas during purging can also be increased using a gas booster.

[0032] Advantageous further developments of the invention result from the patent claims, the description and the drawings.

[0033] The advantages of features and combinations of features mentioned in the description are merely exemplary and can have an effect alternatively or cumulatively, without the advantages necessarily having to be achieved by embodiments according to the invention.

[0034] Regarding the disclosure content—not the scope of protection—of the original application documents and the patent, the following applies: Further features can be derived from the drawings—in particular, the geometries depicted and the relative dimensions of several components to one another, as well as their relative arrangement and functional connection. The combination of features from different embodiments of the invention or from features of different claims is also possible, deviating from the chosen cross-references of the claims, and is hereby encouraged. This also applies to features that are illustrated in separate drawings or mentioned in their description. These features can also be combined with features from different claims.Likewise, features listed in the patent claims may be omitted for further embodiments of the invention, but this does not apply to the independent patent claims of the granted patent.

[0035] The features mentioned in the claims and the description are to be understood, with regard to their number, as meaning that exactly that number or a greater number than the stated number is present, without the need for the explicit use of the adverb "at least". Thus, for example, if a gas booster is mentioned, this is to be understood as meaning that exactly one gas booster, two gas boosters, or more gas boosters are present. The features listed in the claims may be supplemented by further features or may be the only features that the subject matter of the respective claim possesses.

[0036] The reference numerals contained in the patent claims do not constitute a limitation of the scope of the subject matter protected by the patent claims. They merely serve the purpose of making the patent claims easier to understand. BRIEF DESCRIPTION OF THE FIGURES

[0037] The invention will now be further explained and described with reference to preferred embodiments shown in the figures. Fig. Figure 1 is a circuit diagram of a device according to the invention for carrying out the method according to the invention for determining a diffusion coefficient of a diffusion of a first gas through a porous material into a second gas under a gas pressure increased compared to atmospheric pressure. Fig. Figure 2 is a schematic representation of a diffusion cell of the device according to Fig. 1. Fig. Figure 3 is a longitudinal section through a specific construction of the diffusion cell according to Fig. 2. Fig. Figure 4 is a block diagram illustrating the process according to the invention. Fig. Figure 5 shows a concentration profile of the first gas which is detected in the inventive method and evaluated with respect to the diffusion coefficient of interest. Fig. Figure 6 shows a domain of a one-dimensional simulation model used to evaluate the concentration profile according to Fig. 1 is used. Fig. 7 compares the results of the simulation model with the measured values ​​of the concentration profile according to Fig. 5. FIGURE DESCRIPTION

[0038] In the circuit diagram according to Fig. Figure 1 shows a diffusion cell 3, which receives a sample 1 of a porous material 2, only schematically represented. A first gas line 4 is connected to one side of the diffusion cell 3, in which a first shut-off valve 5 is arranged, and which can be connected to a first pressurized gas source 6. The pressurized gas source 6 provides a first gas 79, for which the diffusion coefficient through the porous material 2 into a second gas 80 at increased gas pressure is determined using the device according to Figure 1. Fig. 1. Furthermore, a first absolute pressure sensor 7 is connected to the first gas line 4, and the first gas line 4 is connected to a differential pressure sensor 8. The differential pressure sensor 8 measures a differential pressure between the first gas line 4 and a second gas line 9, which is connected to an opposite side of the diffusion cell 3. The differential pressure sensor 8 is connected to the first gas line 4 and the second gas line 9 via shut-off valves 50 and 51 and can be vented via vent valves 52 and 53.

[0039] A second shut-off valve 10 is provided in the second gas line 9. A second absolute pressure sensor 11 is connected to the second gas line 9, and the second gas line can be connected to a second pressurized gas source 12 for the second gas 80 and to a sliding piston container 13. The sliding piston container 13 serves as a volumetric flow meter 14 for the second gas 80, which is introduced from the second pressurized gas source 12 into a first reservoir chamber 15 on one side of a sliding piston 16 of the sliding piston container 13. The gas is then introduced into the diffusion cell 3 by pressurizing a second reservoir chamber 17 on the other side of the sliding piston 16 with water 18, which is supplied by a syringe pump 19. The water 18 is drawn from a storage tank 20 via a three-way valve 21. Between the syringe pump 19 and the sliding piston container 13, a shut-off valve 22 and a vent valve 23 are also provided.Further shut-off valves 24 and 25 are located in the branches of the second gas line 9 to the second pressurized gas source 12 and the sliding piston container 13. A venting valve 26 allows the second gas line 9 to be vented. While the first pressurized gas source 6 comprises a pressurized gas cylinder 27 for the first gas 79 with a pressure regulating valve 28, the second pressurized gas source 12 comprises a pressurized gas cylinder 29 for the second gas 80 with a pressure regulating valve 30.

[0040] From the same side of the diffusion cell 3 to which the second gas line 9 leads, a third gas line 31 leads away. A shut-off valve 32 and a backpressure regulator 33 are provided in the third gas line 31. The third gas line 31 then leads to a gas chromatograph 34, to which a pressurized gas cylinder 35 with a pressure regulating valve 36 for the carrier gas (e.g., argon) is connected, and from which an exhaust line 37 leads. The gas chromatograph 34 is used to analyze the composition of a gas mixture 81, which is drawn from the diffusion cell through the third gas line 31. The gas pressure to which the backpressure regulator 33 regulates is set by means of a backpressure regulator 38, which includes a syringe pump 39 to which a pressurized gas cylinder 40 with a pressure regulating valve 41 for nitrogen is connected via a three-way valve 42. The back pressure control 38 is connected to the back pressure regulator 33 via a shut-off valve 43.Another syringe pump 44 is provided for applying external pressure to an annular space of the diffusion cell 3. The syringe pump 44 draws water 45 from a reservoir 46 via a three-way valve 47 and forces the water through a shut-off valve 48 and a pressure line 60 into the annular space of the diffusion cell 3. The diffusion cell 3 can be heated by a heating device 49, for example by raising the temperature of the water in the annular space.

[0041] The internal structure of diffusion cell 3 is shown schematically in Fig. Figure 2 is shown. The sample 1 of porous material 2 is arranged in a sealing tube 57 between a gas distribution element 54 and a hollow cylinder 55, to which a gas inlet element 56 is connected. The hollow cylinder 55, together with the gas inlet element 56, forms a first gas space 58 on one side of the sample 1. The gas distribution element 54 forms a much smaller second gas space 59 on the other side of the sample 1. The first gas 79 is introduced into the gas space 58 via the first gas line 4 connected to the gas inlet element 56. The second gas 80 is introduced into the second gas space 59 via the second gas line 9 connected to the gas distribution element 54, and gas, i.e., the gas mixture 81, is discharged from the second gas space 59 via the third gas line 31. The pressure line 60 opens into the annular space 61 between the sealing hose 57 and a jacket 62 of the diffusion cell 3.The jacket 62 can be a hollow jacket that is heated by the heating device 49. End pieces 63 and 64 extend through the jacket 62 to the gas inlet element 56 and the gas distribution element 54, respectively, and provide access to them.

[0042] Fig. Figure 3 shows a specific embodiment of the diffusion cell 3 in an axial longitudinal section. The casing 62 comprises a pipe section 65 onto which end caps 66 and 67 are screwed. A screw-in element 68 is screwed into the end cap 66, which presses against the end piece 63. The opposite end piece 64 rests directly against the opposite end cap 67. The sealing hose 57 extends over the ends of the end pieces 63 and 64 facing it. The annular space 61, to which the pressure line 60 is connected, has a very small volume. Fig. 3 Two connections of the annular space 61 to the pressure line 60 are provided. Heating of the diffusion cell 3 according to Fig. 3 can be done with the help of heating elements wound onto pipe section 65, which are not shown here.

[0043] Fig. 4 is a flowchart of the method according to the invention, which is carried out using the device according to the invention. Fig. 1 with the diffusion cell according to Fig. 2 respectively Fig. The process is carried out in step 3. In step 69, sample 1 is positioned between the first gas chamber 58 and the second gas chamber 59. In step 70, this arrangement is sealed within the diffusion cell 3. For this purpose, the annular space 61 is pressurized to an external pressure higher than the increased gas pressure at which the diffusion coefficient of interest is measured. In a subsequent step 71, the diffusion cell 3 is purged with the first gas 79. The first gas 79 is introduced into the first gas chamber 58 via gas line 4 through the gas inlet element 56 and discharged from the second gas chamber 59 on the other side of sample 1 via the third gas line 31. Purging 71 continues until the gas discharged from the second gas chamber 59 is pure first gas. This can take several hours to several days. Then, in step 72, the first gas chamber 58 is sealed off.Subsequently, in a first sub-step 73 of step 74, the second gas is introduced into the second gas chamber 59. In a second sub-step 75 of step 74, the gas mixture 81 is discharged from the second gas chamber 59. In a third sub-step 76, the gas pressure of the discharged gas mixture 81 is maintained at the elevated gas pressure at which the diffusion coefficient is to be measured, using the back-pressure regulator 33. Simultaneously, in step 77, the concentration profile of the proportion of the first gas 79 in the gas mixture 81 is measured. In step 78, the concentration profile is then analyzed with respect to the diffusion coefficient of interest. Since the first gas chamber 58 has a very large volume compared to the open pore volume of sample 1, the total volume of sample 1, and especially the volume of the second gas chamber 59, the concentration of the first gas 79 in the first gas chamber 58 decreases only very slowly.At the beginning of the measurement, after the first gas chamber 58 is sealed off in step 72 and the introduction of the second gas into the second gas chamber 59 begins in substep 73, the diffusion behavior is highly unsteady. After a certain time, however, a spatially constant concentration gradient is established in sample 1, which decreases only very slowly due to the slow change in the concentration of the first gas 79 in the first gas chamber 58. The measurement then proceeds under pseudo-steady-state conditions. Falsification of the measurement by pressure differences is prevented because the backpressure regulator 33 effectively regulates not only the gas pressure in the second gas chamber 59, but also the gas pressure in the first gas chamber 58 (sealed off except for the flowable open pore volume of sample 1) to the increased gas pressure for which the diffusion coefficient is to be measured.

[0044] For a specific embodiment, in which the porous material 2 was sandstone, the first gas 79 was hydrogen and the second gas 80 was methane, and the increased gas pressure was 12.5 MPa and the temperature was 40°C, the following is shown. Fig. Five measurements of the fraction of the first gas 79 in the gas mixture 81 derived from the second gas chamber 59 and the resulting concentration profile over time are shown. The fraction of the first gas is plotted as a mole fraction, and time is shown in minutes. The quasi-steady state of diffusion is reached after approximately 30 to 40 minutes. The measurement then continues for several hours under quasi-steady conditions. The diffusion coefficient is determined from the concentration profile by comparison with data on known diffusion coefficients or by comparison with a numerical simulation model.

[0045] For such a simulation model, the following partial differential equation, based on Fick's second law, is solved numerically in a one-dimensional domain. This domain shows Fig. 6. pRTϕ∂c∂t=pRTD∂2c∂x2 p is the increased gas pressure in Pa, R is the universal gas constant in J / (mol*K), T is the temperature in K, ϕ is the open porosity of the sample as a fraction, c is the mole fraction of the first gas, D is the effective diffusion coefficient in m 2 / s and x are the length position in m in sample 1. The boundary conditions are described by the following differential equation. On the side of the second gas space, that is, at position 1 in Fig. 6, the following equation is solved: pVTRT∂cT∂t=−qcT+pRTDA∇c1 V T is the volume of the second gas space in m³ 3 , q the rate at which the second gas is introduced into the second gas chamber 59, in mol / s, A the frontal area of ​​the sample in m² 2, ∇c1 the spatial derivative of the mole fraction c at position 1 and c T the mole fraction of the first gas in the second gas space 59, which enters the first equation at position 1 as a boundary condition.

[0046] On the side of the first gas space 58 at position 2 according to Fig. In step 6, a similar differential equation is solved: pVKRT∂cK∂t=−pRTDA∇c2

[0047] V K is the volume of the first gas space in m³ 3 , ∇c2 is the spatial derivative of the concentration at position 2 and c K the mole fraction of the first gas in the first gas space, which enters the first equation at position 2 as a boundary condition.

[0048] For example, in Fig. 7 a comparison of the concentration profile according to Fig.Figure 5 shows the results using the simulation model. The effective diffusion coefficient determined in this way between the two gases hydrogen and methane at the increased gas pressure of 12.5 MPa and the temperature of 40°C is 1.25*10 -7 m 2 / s. REFERENCE MARK LIST 1 sample 2 porous material 3 Diffusion cell 4 first gas pipeline 5 shut-off valve 6 first pressurized gas source 7 Absolute pressure sensor 8 Differential pressure sensor 9 second gas pipeline 10 Shut-off valve 11 Absolute pressure sensor 12 second pressurized gas source 13 sliding piston containers 14 volume flow dispensers 15 container chamber 16 sliding pistons 17 Container chamber 18 Water 19 syringe pump 20 storage containers 21 Three-way valve 22 Shut-off valve 23 Vent valve 24 shut-off valve 25 shut-off valve 26 Vent valve 27 pressurized gas cylinder 28 Pressure regulating valve 29 pressurized gas cylinder 30 Pressure regulating valve 31 third gas pipeline 32 Shut-off valve 33 Back pressure regulators 34 Gas chromatograph 35 pressurized gas cylinder 36 Pressure regulating valve 37 Exhaust duct 38 Back pressure control 39 Syringe pump 40 pressurized gas cylinders 41 Pressure regulating valve 42 Three-way valve 43 Shut-off valve 44 syringe pump 45 Water 46 storage containers 47 Three-way valve 48 Shut-off valve 49 Heating system 50 shut-off valve 51 Shut-off valve 52 Vent valve 53 Vent valve 54 Gas distribution element 55 hollow cylinders 56 Gas inlet element 57 Sealing hose 58 first gas chamber 59 second gas chamber 60 Pressure line 61 Ring space 62 coat 63 End piece 64 End piece 65 Pipe section 66 End cap 67 End cap 68 Screw-in element Step 69 70 steps Step 71 72 steps 73 Sub-step 74 steps 75 Sub-step 76 Sub-step Step 77 78 steps 79 first gas 80 second gas 81 Gas mixture

Claims

[1] Method for determining a diffusion coefficient of a diffusion of a first gas (79) through a porous material (2) into a second gas (80) at a gas pressure increased by at least 900% above atmospheric pressure, - wherein a sample (1) of the porous material (2) is arranged as a partition of defined thickness between a first gas space (58) and a second gas space (59), wherein the first gas space (58) is at least 5 times the size of an open pore volume of the sample (1), - wherein the first gas space (58), the open pore volume of the sample (1) and the second gas space (59) are purged with the first gas (79), - wherein the purging with the first gas (79) is completed and the first gas space (58) adjacent to the sample (1) is sealed off, - wherein the second gas (80), which is distinguishable from the first gas (79), is subsequently introduced into the second gas space (59) with a defined volume flow rate, and a gas mixture (81) comprising the second gas (80) and components of the first gas (79) is discharged from the second gas space (59), - wherein the diverted gas mixture (81) is maintained at the increased gas pressure and - wherein a concentration profile of the proportion of the first gas (79) in the gas mixture (81) derived from the second gas space (59) is recorded and analyzed with respect to the diffusion coefficient. [2] Method according to claim 1, characterized by , that the first gas space (58) is at least 20 times larger than the second gas space (59). [3] Method according to claim 1 or 2, characterized by , that the gas pressure of the first gas (79) in the first gas space (58) at the end of the purging is at least as large as the increased gas pressure. [4] Method according to any one of the preceding claims, characterized by , that the first gas space (58), the open pore volume of the sample (1) and the second gas space (59) are purged with the first gas (79) until they contain at least 99.9% of the first gas (79) and / or until the gas mixture exiting the second gas space (59) during purging consists of at least 99.9% of the first gas (79). [5] Method according to any one of the preceding claims, characterized by , that the first gas space (58), the open pore volume of the sample (1) and the second gas space (59) are purged with the first gas (79) via a first gas line (4) opening into the first gas space (58) and that a first shut-off valve (5) in the first gas line is closed to stop the purging with the first gas (79) and to shut off the first gas space (58) adjacent to the sample (1). [6] Method according to any one of the preceding claims, characterized by, that the second gas (80) is introduced into the second gas space (59) at a constant volume flow rate in a range of 1 to 250 ml / s per square meter of cross-sectional area of ​​the sample (1). [7] Method according to claim 6, characterized by , that the second gas (80) is introduced into the second gas space (59) by advancing a sliding piston (16) of a sliding piston container (13) at a constant speed. [8] Method according to any one of the preceding claims, characterized by that the increased gas pressure is at least 5 MPa. [9] Method according to any one of the preceding claims, characterized by , that the open pore volume of the sample (1) is between 5% and 35% of the total volume of the sample (1). [10] Method according to any one of the preceding claims, characterized by , that a diffusion rate of the first gas (79) through the sample (1) at the increased gas pressure between 2·10 -5 and 2·10 -1mol / s per square meter of cross-sectional area of ​​the sample (1). [11] Method according to any one of the preceding claims, characterized by , that a gas inlet element (56) and a hollow cylinder (55), which together define the first gas space (58), the sample (1) and a gas distribution element (54), which defines the second gas space (59), are arranged one after the other between a first end piece (63) and a second end piece (64) in a sealing hose (57) and that the sealing hose (57) is subjected to an external pressure which is at least 50% and / or at least 3 MPa higher than the increased gas pressure. [12] Apparatus for carrying out the method for determining a diffusion coefficient of a diffusion of a first gas (79) through a porous material (2) into a second gas (80) under a gas pressure increased by at least 900% above atmospheric pressure according to one of the preceding claims, wherein the apparatus - a diffusion cell (3) which accommodates a cylindrical sample (1) of the porous material (2) as a partition of defined thickness between a first gas space (58) and a second gas space (59), - a first gas line (4) opening into the first gas space (58), in which a first shut-off valve (5) is arranged and which can be connected to a first pressurized gas source (6), - a second gas line (9) opening into the second gas space (59), in which a second shut-off valve (10) is arranged and which is connected to a volume flow meter (14) and can be connected to a second pressurized gas source (12), and - has a third gas line (31) leading out of the second gas space (59), in which a back pressure regulator (33) is arranged and which is connected to a gas chromatograph (34), characterized by , - that a part of the first gas space (58) adjacent to the sample (1) is bounded by a hollow cylinder (55) whose length is at least as large as the thickness of the sample (1), - that the diffusion cell (3), which is axially limited by a gas inlet element (56), which together with the hollow cylinder (55) defines the first gas space (58), and a gas distribution element (54), which defines the second gas space (59), is arranged between a first end piece (63) and a second end piece (64) in a sealing hose (57), and - that a pressure chamber adjoins the outside of the sealing hose (57), which can be connected to an external pressure source. [13] Device according to claim 12, characterized by , that the volume flow meter (14) has a sliding piston container (13) with a controlled sliding piston (16). [14] Device according to claim 13, characterized by, that a container chamber (17) on a drive side of the sliding piston (16) can be connected to a working pressure source.

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