Process for producing a light-water nuclear reactor core, in particular a pressurised-water nuclear reactor (PWR) core, in batch operation at low power density and temperature, comprising weakly 235u-rich, highly poisoned UOX-type fuel assemblies

Abstract

The invention relates to a process for producing a light-water nuclear reactor core, in particular a pressurised-water nuclear reactor (PWR) core, in batch operation at low power density and temperature, comprising weakly 235U-rich, highly poisoned UOX-type fuel assemblies. The invention relates to a process for producing a light-water nuclear reactor core, in particular a pressurised-water nuclear reactor (PWR) core, comprising the following main steps: i / defining a plan for loading the fuel assemblies constituting the core, in accordance with four zones arranged in a three-dimensional pattern that is symmetrical with respect to two orthogonal planes; ii / once the loading plan is defined in accordance with step i / , defining a sequence for controlling the core.

Description

[0001] Description

[0002] Title: Method for producing a light water nuclear reactor core, in particular a pressurized water reactor (PWR) operating in batches at low volumetric power and temperature, comprising fuel assemblies of the UOX type that are low in 235U enriched and highly poisoned.

[0003] technical field

[0004] The present invention relates to the general field of light water nuclear reactors (LWRs), in particular pressurized water reactors (PWRs). More specifically, it relates to the field of so-called small or medium power reactors or SMRs (Small Modular Reactors), designed for heat generation.

[0005] For the purposes of this invention, "SMR reactor" means the usual technological meaning, namely a nuclear fission reactor, smaller in size and power than conventional SLR reactors, of which a block is manufactured in a factory and transported to a nuclear site for installation.

[0006] For the purposes of this invention, "reactor block" means the reactor vessel, as well as all the components and parts of the fluidic circuit, including the reactor core which generates heat through nuclear fission reactions, and which is housed inside the reactor vessel.

[0007] In general, the invention applies to a nuclear reactor core of the family of so-called second, third, fourth generation (GEN IV) reactors.

[0008] The main objective of the invention is to propose a new design for a nuclear reactor core intended for heat generation.

[0009] For the purposes of this invention, "heat-producing reactor" refers to a nuclear installation, nuclear power plant, or nuclear reactor whose core power is primarily dedicated to heat production. A heat-producing reactor may be 100% dedicated to heat production. However, a small portion of its power may also be used to generate electricity. Prior art

[0010] In the context of climate and energy transition, the nuclear industry must meet several challenges for the future. Indeed, to address tomorrow's energy and societal challenges, it will be essential to design nuclear reactors that enable:

[0011] - to limit the need for so-called "environmental" liquid cold sources (rivers, streams, sea) and the associated discharges into the environment;

[0012] - to be more flexible and therefore more complementary to other so-called renewable energies (RE), to meet the fluctuating demand for electricity and the intermittency of RE;

[0013] - to decarbonize processes by supplying heat to consuming industries (desalination, heat networks, hydrogen...) while increasing energy efficiency;

[0014] - to capture atmospheric CO2 to limit the effects of global warming and contribute to closing the carbon cycle as a source of carbon for industrial processes; and this, without degrading the profitability of the installation, either by economically benefiting from the new services provided, or by significantly increasing the amount of electricity produced during the day.

[0015] In the current general context of energy decarbonization, heat production represents a significant market to be decarbonized.

[0016] One of the current development topics for nuclear reactors concerns so-called heat-generating reactors designed to provide a thermal power level of a few tens of MWth, for the purpose of producing decarbonized hot water at the temperature required by industrial processes, mainly for the supply of so-called urban heat, i.e. in urban networks, for cities / agglomerations of several hundred thousand inhabitants.

[0017] Historically, the use of nuclear energy for purely power generation purposes has constrained the design of nuclear facilities.

[0018] Indeed, nuclear reactors, which are generally used to produce electricity, have a reactor core with fuel elements that undergo chain fission reactions to heat the water and steam circuits that supply a thermal energy-to-electricity conversion system, such as a Rankine cycle.

[0019] For a heat-producing reactor, the thermal power produced in the core is used to heat water circuits, including a downstream circuit that goes to the end users, i.e., factories that use superheated water.

[0020] In general, a low thermal output from the core is sufficient for industrial heating needs. Typically, 50 MWth is enough to power several factories operating in the same geographical area. The core of a nuclear reactor will therefore be smaller compared to the cores of power-generating reactors, which have much higher thermal outputs, typically exceeding 2700 MWth in France.

[0021] Nuclear reactors operate on cycles that are generally 2 years long, with part of the fuel being renewed between each cycle.

[0022] More specifically, the cores of power-generating reactors are designed to be fractional, that is to say to operate in short cycles, typically between 1 and 2 years, with a partial refueling of the fuel at each irradiation cycle in order to consume it to the maximum, that is to say to increase the combustion rate ("burn-up" in Anglo-Saxon language) for the unloading of the fuel.

[0023] In a fractionated core, part of its fuel assemblies is new, meaning it has not undergone an irradiation cycle; part has already undergone a first irradiation cycle, with its fuel assemblies therefore being partially worn and their positions in the core changing with each cycle; another part has already undergone two cycles, ...

[0024] This splitting implies an increase in operating costs due to frequent reactor shutdowns for refueling and the construction of a building called a fuel building in which the irradiated assemblies are stored before being transferred to other plants.

[0025] To reduce these costs, batch reactor cores have already been considered, i.e., those designed so that all fuel assemblies loaded new at the beginning of a cycle are unloaded from the reactor vessel and sent to a fuel reprocessing plant at the end of the cycle. Batch cores have already been described in the literature, but their thermal power does not meet the specifications of a heat-producing reactor.

[0026] Thus, a batch reactor core helps to reduce costs, because the cycle time is extended.

[0027] Typically, in France, a target cycle length can be 10 years so that reactor shutdowns coincide with the ten-year inspections by the Nuclear Safety Authority (ASN). In other words, a batch core operates continuously for a 10-year cycle. Furthermore, during the shutdown between cycles, all fuel assemblies are replaced.

[0028] These long cycle times are rarely mentioned in the literature. Nevertheless, reactors operating with cycles of 6.5, 10 or 20 years have been mentioned, but their technology, power or application do not correspond to the specifications of a heat-producing reactor.

[0029] Among the various technological solutions that provide heat from nuclear fission, it is generally accepted that to date, pressurized water reactors (PWRs) are the most suitable for providing heat at relatively low temperatures.

[0030] In a PWR reactor, the fuel assemblies are immersed in water, also called a moderator, which has a dual function: slowing down the neutrons to allow the fission reaction on fuel enriched in 235 U and cool the combustible elements.

[0031] For this type of reactor, the reactivity of the core is generally controlled by the addition of soluble boron in the moderator and by the insertion by vertical translation from the top of absorber clusters in the active zone of the core, i.e. the zone of presence of the nuclear fuel.

[0032] The use of soluble boron complicates the core design and therefore increases costs.

[0033] In the literature, some concepts without soluble boron propose to control the reactivity of the core with absorbing clusters; other concepts exist but whose power or application does not correspond to the configuration targeted by the invention.

[0034] Our aim is therefore to design a core that incorporates the various constraints mentioned above. There is thus a need for a solution for a low-power, low-volume PWR reactor with a batch core that can operate in the absence of soluble boron and for a typical cycle of at least 10 years.

[0035] The aim of the invention is to at least partially meet this need.

[0036] Description of the invention

[0037] To this end, the invention relates, in one of its aspects, to a method for constructing a light water nuclear reactor core, in particular a pressurized water reactor (PWR), comprising the following steps: i / defining a loading plan for the fuel assemblies constituting the core, according to four zones arranged in a three-dimensional pattern symmetrical with respect to two orthogonal planes, comprising the following sub-steps: i1 / choosing a total number of assemblies, i2 / defining, as a function of the total number chosen in sub-step i1 / , the position of the assemblies, which gives a number n of zoning types, i3 / defining for each of the n zoning types and for each of the four zones, the nature of the assemblies defined by a percentage of neutron poison,the number of fuel rods containing this percentage of neutron poison and a percentage of enrichment, considering that: each of the four zones consists of assemblies having the same initial isotopic composition, and that the fuel assemblies each include uranium oxide (UOx) fuel rods enriched to less than 5% in uranium 235 (, 235U), rods containing the defined percentage of neutron poison, as well as guide tubes adapted to accommodate by insertion one of the number of neutron absorber rods grouped in a cluster, i4 / determine the possible combinations between the number of assemblies, the number n of zoning types and the nature of the assemblies, i5 / select from the possible combinations those for which the effective multiplication coefficient (keff) is greater than one, which corresponds to a state where the core reactivity is not subcritical at the beginning of life, then those resulting in a predetermined lifetime T, ii / once the loading plan is defined according to step i / , define a core control scheme which consists of: iil / considering at least three groups of neutron absorber rod clusters (PI, P2, P3) whose number and / or neutron absorption material is different from one group of clusters compared to another,ii2 / First, insert one of the groups into the core areas exhibiting the highest DDV reactivity, then modify the positions of the clusters within each group, the number of clusters in a group, the total number of groups, their insertion order in the core, their overlap in the core, and the nature of their neutron absorber until a value is obtained that respects a power limit (Fxy) to prevent water boiling, throughout the reactor cycle, while maintaining the effective core multiplication coefficient (keff) equal to 1 throughout the cycle.

[0038] Preferably, assemblies according to step i3 / include pencils containing a percentage of neutron poison from gadolinium pencils of composition UOi-GdiCh and / or erbium (EriCh).

[0039] Preferably, step i3 / consists of defining four types of assemblies with different enrichments and a number of pencils containing a different percentage of neutron poison as follows:

[0040] - blends enriched to 1.5% in 235 U and eight gadolinium-coated pencils,

[0041] - blends enriched to 2% in 235 U and eight gadolinium-coated pencils,

[0042] - blends enriched to 3% in 235 U and twenty-four gadolinium-coated pencils,

[0043] - blends enriched to 4% in 235 U and sixteen gadolinium-coated pencils,

[0044] According to an advantageous embodiment, the at least two criteria of step i5 / are at least two criteria of peak power in evolution, and / or combustion rate and / or reactivity at the beginning or end of the cycle.

[0045] According to this mode, the at least two criteria of step i5 / are respectively that the maximum two-dimensional heart power peak reached during evolution (FXY) and the effective multiplication coefficient of the heart (keff) at Early Life (DDV) calculated by considering all the clusters inserted into the heart are minimal.

[0046] According to an advantageous embodiment, the fuel assemblies each comprise an equal number of 17x17 uranium oxide (UOX) fuel rods enriched to less than 5% in uranium 235 (235U) and having a fissile column height less than or equal to 1.60 m.

[0047] The invention also relates to a computer program comprising instructions which, when the program is executed by a computer, cause the computer to implement step i / of the process described above.

[0048] The invention also relates to a light water nuclear reactor core, in particular pressurized water (PWR), of batch type, obtained by implementing the process as defined above.

[0049] The intended operation is preferably at a thermal power, less than or equal to 300MWth, typically equal to 50 MWth.

[0050] The invention also relates to the use of the reactor core described above to provide heat at a temperature below 200°C, typically equal to 150°C.

[0051] Thus, thanks to the process according to the invention, a PWR nuclear reactor core is obtained which can operate with a single cycle for 10 years and in batch, without partial refueling, i.e. with at the beginning of the cycle, all the assemblies new, and at the end of the cycle all the assemblies unloaded to be reprocessed or permanently stored.

[0052] This core operates at low thermal power and low temperature imposed by the target markets, particularly the industrial heat market.

[0053] Despite the long cycle duration, the low thermal power, combined with the number of assemblies, results in a low operating power volume throughout the cycle. This leads to low residual power in the fuel assemblies after reactor shutdown, which is consistent with the objective: eliminating the need for a fuel building since the fuel assemblies no longer require cooling before transport.

[0054] Other advantages and features of the invention will become clearer upon reading the detailed description of illustrative and non-limiting examples of implementation of the invention, with reference to the following figures. Brief description of the drawings

[0055] [Fig 1] Figure 1 illustrates in cross-sectional view a fuel assembly with UOx rods, standard as currently used in a PWR nuclear reactor.

[0056] [Fig 2] Figure 2 illustrates five configurations with a total number of different assemblies implemented in the loading plan definition step of the process according to the invention.

[0057] [Fig 3] Figure 3 illustrates an example of the number of zoning types for a fixed total number of assemblies.

[0058] [Fig 4] Figure 4 illustrates a 3D power peak with a quarter core mesh for calculations performed with a deterministic code according to the method of the invention.

[0059] [Fig 5] Figure 5 illustrates with the same mesh as Figure 4 the 2D power peak in DDV with driver clusters partially inserted in the core.

[0060] [Fig 6] Figure 6 illustrates arrangements of the four types of assemblies retained in an example according to the invention, with UOx and UOi-GdiOa pencils implemented in the process according to the invention.

[0061] [Fig 7] Figure 7 shows a core diagram according to an optimal configuration obtained according to the process of the invention.

[0062] [Fig 8] Figure 8 illustrates in the form of curves the evolution of the 2D and 3D power peaks of the heart during the cycle.

[0063] [Fig 9] Figure 9 illustrates in the form of curves the evolution of the residual power of a core assembly according to an optimal configuration of the invention and in comparison those of different residual powers of PWR reactors according to the state of the art.

[0064] [Fig 10] Figure 10 is an enlargement of Figure 9, at the beginning of the curves.

[0065] Detailed description

[0066] Figure 1 shows the radial dimensions of a standard PWR assembly. The assemblies used are standard PWR UOx assemblies (17x17 rods) but with a lower height: 160 cm active height (i.e., combustible height).

[0067] Step i: According to the invention, a fuel assembly loading plan for the core is defined first, according to four zones arranged in a three-dimensional pattern symmetrical with respect to two orthogonal planes. A total number of fuel assemblies is then chosen. Figure 2 shows five different core sizes depending on the total number. The position of the assemblies is then defined based on the total number chosen in substep 11 / , resulting in a number n of zoning types. Figure 3 illustrates five zoning types corresponding to a total number of assemblies equal to 45.

[0068] Sub-section i3 / for each of the n zoning types and for each of the four zones, the nature of the assemblies is defined by a percentage of neutron poison, the number of neutron poison rods and a percentage of enrichment, considering that: each of the four zones consists of assemblies having the same initial isotopic composition, and that the fuel assemblies each include uranium oxide (UOx) rods enriched to less than 5% in uranium 235 ( 235 U) and guide tubes adapted to house by insertion each one of the number of neutron-absorbing pencils grouped in a cluster.

[0069] In the illustrated example, the core contains 4 types of assemblies with different enrichments and pencils containing a different percentage of neutron poison as follows:

[0070] -blends enriched to 1.5% in 235 U and possessing 8 gadolinium-based pencils,

[0071] - blends enriched to 2% in 235 U and possessing 8 gadolinium-based pencils,

[0072] - blends enriched to 3% in 235 U and possessing 24 gadolinium-based pencils,

[0073] - blends enriched to 4% in 235 U and possessing 16 gadolinium crayons.

[0074] Sub-e i4 / : we then determine the possible combinations between the number of assemblies, the number n of zoning types and the nature of the assemblies.

[0075] A combination is not considered if the heart is subcritical at the beginning of life, that is, for an effective multiplication coefficient keff less than 1.

[0076] Then we retain the combinations giving a heart cycle duration between 9 and 11 years.

[0077] Under -é i5 / we then select from the possible combinations those for which: A / the maximum power peak of the core in two dimensions (X, Y) reached during the evolution (FXY) is minimal, which allows the reactor power sheet to be flattened,

[0078] B / the effective multiplication coefficient of the heart (k e ff) Early Life (DL) calculated by considering all clusters inserted into the core is minimal.

[0079] The two-dimensional power peak F xy is defined according to the following equation [1]:

[0080] [Equation 1]: where H represents the active height, that is, the area of ​​presence of the nuclear fuel or in other words the height of the fissile column, and P(x,y,z) the power at a given point in space in the core.

[0081] Step i / is preferably performed entirely by a deterministic calculation code. This step can advantageously be implemented by the deterministic calculation code implemented by the software called "APOLLO" as described in the publications.

[0082] Figure 4 illustrates a quarter-core mesh for calculations performed with this deterministic code, for a reactor core with 45 assemblies, using a homogeneous radial mesh of 2x2 cells per assembly and a cell height of 10 cm. In Figure 4, the color scale represents the 3D power peak in DDV with driver clusters partially inserted into the core. It should be noted that, due to the symmetries of the core pattern, a calculation performed on a quarter of the core is sufficient.

[0083] Figure 5 illustrates, using the same mesh, the 2D power peak in DDV with driver clusters partially inserted into the core. Thus, the maximum core power peak in two dimensions (X, Y) represents the axial power integral in a channel delimited by the computational mesh.

[0084] For the application of criterion A / , a high value of L xy represents a high power output in the channel, and therefore a high water outlet temperature.

[0085] In the process, a limit was set to prevent the water exiting a channel from boiling; it is calculated using the following equation 1:

[0086] [Equation 1]: with :

[0087] Qt denotes the total power of the core, equal in this example to 50MWth, m' denotes the total throughput in the core which depends on each configuration,

[0088] Cp refers to the specific heat which depends on the pressure / temperature in the core,

[0089] Tin refers to the core inlet temperature.

[0090] Tsat denotes the saturation temperature which depends on the pressure.

[0091] For the application of criterion B / , in order to guarantee a moderate initial core reactivity to facilitate its control, and compliance with the safety criterion, the value of keff in DDV is set less than or equal to 0.95.

[0092] Step ii / : once the loading plan is defined according to step i / , a core control scheme is defined.

[0093] Sub-step ii 1 / : we consider three groups of neutron-absorbing pencil clusters (PI, P2, P3) whose number and / or neutron-absorbing material is different from one group of clusters compared to another.

[0094] Substep ii2 / : firstly, one of the groups is inserted into the areas of the core exhibiting the greatest reactivity in DDV, then the positions of the clusters of each group are modified, the number of clusters in a group, the total number of groups, their order of insertion in the core, their overlap in the core, and the nature of their neutron absorber.

[0095] This is done until a value is obtained that respects a power limit (Fxy) to avoid boiling the water, over the entire duration of the reactor cycle, and this while keeping the effective core multiplication coefficient (keff) equal to 1 throughout the cycle.

[0096] In the example with 45 fuel assemblies, we obtain an optimal configuration with arrangements of the four types of assemblies previously defined shown in figure 6, a core scheme as shown in figure 7.

[0097] In the optimal configuration, as illustrated in Figure 7, the neutron absorber clusters are inserted in the following order: P1, then P2, then P3. The overlap between these three groups of clusters is 12.5% ​​of the active height. This percentage represents the distance traveled by one group of clusters before the next group begins to be inserted. The stop clusters are designated by PA.

[0098] The inventor made calculations of evolution to guarantee compliance with the duration of the cycle, that is to say until exhaustion of the heart.

[0099] Under the assumptions, the core is considered exhausted when the effective multiplication coefficient of the core without any inserted clusters becomes very close to 1, typically keff is equal to 1.001. At each step of the combustion rate, a calculation is performed, assuming that the clusters are inserted in such a way as to ensure that the keff coefficient is equal to 1.

[0100] The resulting cycle duration is equal to 11 years.

[0101] To maintain flexibility at the end of the cycle, it is always possible to stop the cycle before 11 years. This allows sufficient leeway to move the fuel assemblies to vary the power output for load following. Indeed, at the beginning of their life, the assemblies are firmly inserted into the core to compensate for the core's initial reactivity. This reactivity increases at the beginning of the cycle as the gadolinium is consumed. Maximum insertion of the assemblies occurs at the gadolinium peak. Subsequently, fuel degradation reduces reactivity, and the assemblies are gradually removed during the cycle. At the end of their life, the assemblies are almost completely extracted from the core.

[0102] Figure 8 illustrates in the form of a curve the evolution of the 2D and 3D power peaks of the core during the cycle.

[0103] The inventor also performed calculations of the residual power.

[0104] At the end of the cycle, the residual power of each assembly is calculated over a cooling period of 6 months.

[0105] Figure 9 shows that the residual power of the assemblies in the optimal core configuration obtained according to the process of the invention is much lower than that of typical PWR generator assembly configurations according to the state of the art. This can be explained by:

[0106] - the low discharge burnup rate, which is about ~ 22 GWj / tM according to the invention against about 50 to 60 GWj / tM for the state of the art, - the low volumetric power according to the invention despite an irradiation cycle of 10 years against about 2 years for generator PWR reactor configurations according to the state of the art.

[0107] An enlargement of the beginning of the curves in Figure 9, illustrated in Figure 10, shows that the residual power of the optimal configuration according to the invention drops to less than 4 kW after 6 days of cooling. This is compatible with unloading the assemblies directly into the transport towers after a few days of reactor shutdown. A cooling pool is therefore unnecessary, and the reactor building can thus be eliminated.

[0108] The invention is not limited to the examples just described; in particular, features of the illustrated examples can be combined in unillustrated variants.

[0109] Other variants and embodiments may be considered without departing from the scope of the invention.

[0110] Thus, if the criteria chosen at substep i5 / are the 2D power peak and the core reactivity at the beginning of the cycle, other criteria can be considered such as minimizing the 3D power peak, maximizing the combustion rate at the end of the cycle, or others.

[0111] List of cited references

[0112] [1]: P. Mosca et al. ''APOLLO3®: Overview of the New Code Capabilities for Reactor Physics Analysis' published May 20, 2024, Nuclear Science and Engineering.

[0113] [2]: R. Sanchez et al. “APOLLO2 YEAR 2010” NUCLEAR ENGINEERING AND TECHNOLOGY, VOL.42 NO.5 OCTOBER 2010.

Claims

Demands 1. Method for constructing a light water nuclear reactor core, in particular a pressurized water reactor (PWR), comprising the following steps: i / definition of a loading plan for the fuel assemblies constituting the core, according to four zones arranged in a three-dimensional pattern symmetrical with respect to two orthogonal planes, comprising the following sub-steps: i1 / choose a total number of assemblies, i2 / define, as a function of the total number chosen in sub-step i1 / , the position of the assemblies, which gives a number n of zoning types, i3 / define for each of the n zoning types and for each of the four zones, the nature of the assemblies defined by a percentage of neutron poison, the number of fuel rods containing this percentage of neutron poison and an enrichment percentage, considering that: each of the four zones is made up of assemblies having the same initial isotopic composition,and that the fuel assemblies each comprise uranium oxide (UOx) rods enriched to less than 5% in uranium 235 (, 235 U), rods containing the defined percentage of neutron poison, and guide tubes adapted each to accommodate, by insertion, one of the number of neutron absorber rods grouped in a cluster, i4 / determine the possible combinations between the number of assemblies, the number n of zoning types, and the nature of the assemblies, i5 / select from the possible combinations those for which the effective multiplication coefficient (keff) is greater than one, which corresponds to a state where the core reactivity is not subcritical at the beginning of its life, then those resulting in a predetermined lifetime T, ii / once the loading plan is defined according to step i / , define a core control scheme which consists of: i1 / Consider at least three groups of neutron-absorbing pencil clusters (PI, P2, P3) where the number and / or neutron-absorbing material differs from one group of clusters to another; ii2 / First, insert one of the groups into the core areas exhibiting the highest DDV reactivity, then modify the positions of the clusters within each group, the number of clusters in a group, the total number of groups, their insertion order in the core, their overlap within the core, and the nature of their neutron absorber until a value is obtained that respects a power limit (F). xy ) to avoid boiling the water, throughout the reactor cycle, and this while keeping the effective core multiplication coefficient (keff) equal to 1 throughout the cycle.

2. Method according to claim 1, the assemblies according to step i3 / comprising pencils containing a percentage of neutron poison.

3. Method according to claim 2, step i3 / consisting of defining four types of assemblies having different enrichments and pencils containing a percentage of neutron poison as follows: - blends enriched to 1.5% in 235 U and eight gadolinium-coated pencils, - blends enriched to 2% in 235 U and eight gadolinium-coated pencils, - blends enriched to 3% in 235 U and twenty-four gadolinium-coated pencils, - blends enriched to 4% in 235 U and sixteen gadolinium-coated pencils, 4. Method according to claim 1 to 3, the at least two criteria of step i5 / being at least two criteria of peak power in evolution, and / or combustion rate and / or reactivity at the beginning or end of cycle.

5. Method according to claim 4, the at least two criteria of step i5 / being respectively that the maximum two-dimensional core power peak reached during evolution (FXY) and the effective core multiplication coefficient (keff) at Early Life (DDV) calculated considering all clusters inserted in the core are minimal.

6. A method according to any one of the preceding claims, the fuel assemblies each comprising a number equal to 17x17 uranium oxide (UOX) fuel rods enriched to less than 5% in uranium 235 ( 235 U) and whose fissile column height is less than or equal to 1.60 m.

7. Computer program comprising instructions which, when the program is executed by a computer, cause the computer to implement step i / of the method according to claim 1.

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