Method for preparing high-density coal-based jet fuel by taking indene as raw material
By activating indene by acidic catalyst and carrying out the [2+2] ring-enhancing reaction, combined with metal catalyst treatment under hydrogenation conditions, the selectivity and catalyst adaptability of the indene preparation of high-density coal-based jet fuel in the prior art are solved, and efficient preparation and performance optimization of high-density fuels are achieved.
Patent Information
- Application Number
- CN202510249376.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-04
- Publication Date
- 2025-06-20
AI Technical Summary
The prior art is difficult to effectively utilize indene in high-temperature coal tar to prepare high-density coal-based jet fuel, and faces the problems of low reaction selectivity, poor catalyst adaptability and uncontrollable product distribution.
Indene is activated by acid catalysts, a tetracyclic structure compound is constructed through the [2+2] ring-enhancing reaction, and hydrogen transfer is performed using a metal catalyst under hydrogenation conditions to realize the preparation of high-density coal-based jet fuel.
It has achieved high yield preparation of high-density coal-based jet fuel, with a fuel density greater than 0.90g/mL, excellent performance, simple process and low cost, and is suitable for industrial production.
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Figure CN120173645A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of compound organic synthesis, and in particular to a method for preparing high-density coal-based jet fuel using indene as a raw material. Background Art
[0002] High-density hydrocarbon fuels usually refer to artificially synthesized fuels with a density greater than 0.80 g / cm 3 Alkane fuels provide important power guarantees for various aerospace vehicles such as missiles, rockets and fighter jets, and are the research focus in the field of propellants. At present, the main source of jet fuel is petroleum, and petroleum resources are becoming increasingly depleted. Therefore, how to ensure the growing demand for jet fuel has become an important research topic in the post-petroleum era. With the development of aviation technology, the continuous upgrading of engines, and the increasing requirements for environmental protection at home and abroad. In response to the differentiated needs of my country's military and civil aircraft for fuel quality indicators, the system refers to the international general jet fuel standard system, and scientifically adjusts and optimizes the key performance parameters of kerosene fractions (including density, freezing point, lubricity and thermal oxidation stability) to develop qualified products that meet the technical specifications of aviation fuel. From a global perspective, the process used to produce jet fuel mainly depends on the nature of the raw materials. Therefore, in order to further expand this market share and improve profitability, seeking low-sulfur, low-corrosive and high-stability jet fuel is the ultimate goal.
[0003] As an important by-product of coal pyrolysis, high-temperature coal tar has a complex composition and is rich in high-value-added aromatic compounds (such as indene, naphthalene, fluorene, etc.). Among them, indene (C9H8) has significant chemical conversion potential due to its unique bicyclic structure (benzene ring and five-membered ring fused together). According to statistics, the indene content in high-temperature coal tar can reach 2%-5%, but the existing processes mostly use it as an asphalt blending component or directly burn it, failing to fully realize its value as a precursor of fine chemicals and special fuels. With the transformation of my country's coal chemical industry towards high-end and refined production, the development of efficient conversion pathways for indene has become an important direction for the industry's technological upgrading.
[0004] At present, the main technologies for the ring-increasing of aromatics include catalytic polycondensation, Friedel-Crafts alkylation and Diels-Alder cycloaddition. However, the controllable ring-increasing of indene still faces the following challenges: 1. Low reaction selectivity: The bicyclic structure of indene is prone to ring-opening cracking or disordered condensation at high temperature to generate polycyclic aromatic hydrocarbons (PAHs) and coke, and the yield of the target product is less than 40%; 2. Poor catalyst adaptability: Traditional acidic catalysts (such as HZSM-5) are prone to excessive dehydrogenation, destroying the molecular hydrogen content and reducing the fuel combustion efficiency; 3. Uncontrollable product distribution: It is difficult for existing processes to directionally control the growth of the number of rings (such as the evolution from a bicyclic to a tricyclic / tetracyclic structure), resulting in limited improvement in fuel density (usually <0.90g / cm3 )。Therefore, a method for preparing high-density fuel by controllable ring expansion using indene in high-temperature coal tar fraction as raw material is needed. SUMMARY OF THE INVENTION
[0005] The object of the present invention is to provide a method for preparing high-density coal-based jet fuel using indene as raw material. This method has simple steps, high yield, and can produce high-density coal-based jet fuel through hydrogenation and purification.
[0006] To achieve the above object, the technical solution adopted by the present invention is as follows:
[0007] A method for preparing high-density coal-based jet fuel using indene as raw material, comprising the following steps:
[0008] S1. Dissolve indene compound 1 in an organic solvent and react under the catalysis of an acidic catalyst to form compound 2 with a four-ring structure;
[0009]
[0010] S2. Dissolve compound 2 with a four-ring structure in an alkane solvent and carry out hydrogenation in a hydrogenation autoclave or a fixed bed under the condition of a metal catalyst to generate high-density coal-based jet fuel 3.
[0011]
[0012] Preferably, in step S1, the reaction temperature is 80 - 160 °C and the reaction time is 6 - 14 h.
[0013] Preferably, in step S1, the acidic catalyst is one of Nafion, T-62MP, Amberlyst15, CD750, CD250, H-Beta, H3O 40 PW 12 .xH2O, H4[Si(W3O 10 )4]·xH2O.
[0014] Preferably, in step S1, the dosage of the acidic catalyst is 20% of the mass of indene compound 1.
[0015] Preferably, in step S1, the organic solvent is selected from one or more of dichloromethane, dichloroethane, n-hexane, cyclohexane, n-octane, toluene, dimethyl sulfoxide, N,N-dimethylformamide, acetone, N-methylpyrrolidone, propylene carbonate, dimethyl carbonate, petroleum ether, and the concentration range of indene compound 1 is 0.5 - 1 mol / L.
[0016] Preferably, in step S2, the mass ratio of the dosage of the metal catalyst to compound 2 with a four-ring structure is (0.01 - 1):1.
[0017] Preferably, the metal catalyst is selected from one of commercial Raney nickel, commercial Raney cobalt, Pt / C, Pd / C, Ru / C, Rh / C, Ni-W / Al2O3, Ni-Mo / Al2O3, and Ni / Al2O3. The loading of the active metal in Pt / C, Pd / C, Ru / C, and Rh / C is 3-8 wt%; in Ni-W / Al2O3, Ni and W respectively account for 12-20% and 4-12% of the mass of Ni-W / Al2O3; in Ni-Mo / Al2O3, Ni and Mo respectively account for 4-20% and 4-20% of the mass of Ni-Mo / Al2O3; in Ni / Al2O3, Ni accounts for 24-36% of the mass of Ni / Al2O3.
[0018] Preferably, in step S2, the alkane solvent is cyclohexane or n-hexane. The concentration of compound 2 with a four-ring structure in the hydrogenation autoclave is 0.01-10 mol / L, and the concentration of compound 2 with a four-ring structure in the fixed bed is 1 wt%-20 wt%.
[0019] Preferably, in step S2, when the hydrogenation reaction is carried out in a reaction autoclave, the reaction temperature is 120-300 °C, the reaction time is 4-12 h, and the hydrogen pressure is 1-6 MPa; when the hydrogenation reaction is carried out in a fixed bed, the average reaction temperature is 160-350 °C, the reaction pressure is 0.5-4 MPa, the molar ratio of hydrogen to compound 2 with a four-ring structure is (200-1000):1, and the liquid volume hourly space velocity is 0.1-1 h -1 。
[0020] The present invention proposes to use indene in high-temperature coal tar fractions as a raw material, and through the construction of a "catalytic activation - directional ring expansion - structure stabilization" trinity reaction system, realize the controllable ring expansion to prepare high-density coal-based jet fuel. The core technical path of the present invention includes: (1) Molecular activation regulation: using an acid catalyst to activate the α-carbon-hydrogen bond of indene through the Lewis acid center; (2) Topological directional ring expansion: designing a comonomer with a matching electronic effect based on quantum chemical calculations, and precisely constructing a four-ring skeleton through a [2+2] ring expansion reaction; (3) Hydrogen transfer stabilization: introducing a hydrogen-donating solvent and a bimetallic catalyst to regulate the hydrogen balance of the reaction system, avoiding incomplete hydrogenation of the product, and maintaining a moderate naphthene structure of the fuel components.
[0021] Compared with the prior art, the present invention has the following beneficial effects:
[0022] 1. The present invention can completely realize the preparation of high-density coal-based jet fuel with a high yield from indene extracted from high-temperature coal tar components through a two-step method. Its density is greater than 0.90 g / mL, and it is an aviation kerosene alkane compound with relatively excellent performance;
[0023] 2. The entire route uses indene, a coal tar component, as the raw material. It is a method with a wide range of raw material sources, low costs, and is more conducive to industrial production. Description of the Drawings
[0024] Figure 1 . MS spectrum of compound 2 with a four-ring structure prepared in Example 27;
[0025] Figure 2 . GC spectrum of compound 2 with a four-ring structure prepared in Example 27;
[0026] Figure 3 . 1 H NMR spectrum of compound 2 with a four-ring structure prepared in Example 27;
[0027] Figure 4 . 13 C NMR spectrum of compound 2 with a four-ring structure prepared in Example 27;
[0028] Figure 5 . MS spectrum of the hydrogenation product 3 prepared in Example 39;
[0029] Figure 6 . GC spectrum of the hydrogenation product 3 prepared in Example 39;
[0030] Figure 7 . 1 H NMR spectrum of the hydrogenation product 3 prepared in Example 39;
[0031] Figure 8 . 13 C NMR spectrum of the hydrogenation product 3 prepared in Example 39. Detailed Embodiments
[0032] The present invention will be further described in detail below with reference to the drawings and specific embodiments.
[0033] In the following embodiments, unless otherwise specified, the reagents used can be purchased commercially or obtained according to the methods reported in known literature.
[0034] Embodiment
[0035] A method for preparing high-density coal-based jet fuel using indene as the raw material, comprising the following steps:
[0036] S1. Dissolve indene compound 1 (2 mmol, 0.232 g) in 2 mL of an organic solvent, and react under the catalysis of an acidic catalyst to form compound 2 with a four-ring structure; the dosage of the acidic catalyst is 20% of the mass of indene compound 1; the reaction temperature is 80 - 160 °C, and the reaction time is 6 - 14 h;
[0037]
[0038] S2. When the hydrogenation reaction is carried out in a reaction kettle, dissolve the compound 2 with a four-ring structure (2.32 g, 10 mmol) in 20 mL of an alkane solvent, and react it under the catalysis of 464 mg of a metal catalyst (active metal loading 5 wt%) at 120 - 300 °C and a hydrogen pressure of 3 MPa for 4 - 12 h to obtain high-density coal-based jet fuel 3.
[0039] When the hydrogenation reaction is carried out in a fixed bed, the reaction conditions are as follows: use hydrogen as the raw material gas, and use a cyclohexane solution containing 1 - 20 wt% of the compound 2 with a four-ring structure (2.32 g, 10 mmol) as the raw material liquid. The molar ratio of hydrogen to the compound 2 with a four-ring structure in the reaction is (200 - 1000):1, the reaction temperature range is 160 - 350 °C, the reaction pressure is 0.5 - 4 MPa, and the reaction space velocity is 0.1 - 1 h -1 . Use a stainless steel reaction tube as the reactor, with an outer diameter of 20 mm, an inner diameter of 8 mm, and a length of 300 mm. The catalyst loading is 0.5 g. After the reaction tail gas is condensed and separated, use a Fuli GC9790PLUS gas chromatograph to quantitatively analyze the product.
[0040]
[0041] The differences between Examples 1 - 30 lie in the different catalysts, reaction temperatures, solvents, and reaction times in step S1. The specific parameters are shown in Table 1 below:
[0042] Table 1. Influence of catalyst, temperature, solvent, and time on the reaction
[0043]
[0044]
[0045] It can be seen from the results in Table 1 that the acidic catalysts T - 62MP, Amberlyst15, and CD250 show good catalytic performance in catalyzing the reaction of the raw material indene and achieve a medium to upper yield. Among them, T - 62MP has the best catalytic performance, and the product yield reaches 97% under the conditions of 80 °C for 8 h. Through the screening of different solvents, it is found that n - hexane, dimethyl sulfoxide, n - octane, toluene, cyclohexane, N,N - dimethylformamide, and N - methylpyrrolidone, etc. have relatively good effects on this reaction. However, considering the environmental friendliness and the ease of subsequent separation and treatment, cyclohexane is selected as the solvent. Through the screening of different reaction times, it is found that extending the time will not increase the product yield. The dimer product yield at 8 h of reaction is 97%, which is consistent with the results of reactions at 10 h and 12 h.
[0046] Since the service life of the catalyst needs to be investigated in practical applications, cyclohexane was used as the solvent and the reaction was carried out at 80 °C for 8 h to study the recycling of T-62MP. It should be noted that the catalyst was stirred with 5% hydrochloric acid solution for 3 h before use, and then started to be used after complete drying. After every two reactions, it was treated with the above hydrochloric acid and dried. After the first reaction, the product and the catalyst will automatically separate into layers. The upper layer is the product and the lower layer is the catalyst. The product was separated and the next cycle was continued. It can be seen from the results in Table 2 that the yield of T-62MP did not change significantly after being recycled three times, indicating that this reaction system can be reused.
[0047] Table 2. Recycling experiment of T-62MP
[0048]
[0049] The MS spectrum of compound 2 prepared in Example 27 is as Figure 1 shown. It can be seen from the figure that the maximum mass-to-charge ratio of the molecular ion peak of this substance is about m / z = 232. The relative molecular mass of the raw material indene is 116, and the relative molecular mass of the polymerized four-membered ring structure of the raw material is about 232. The relative molecular mass of compound 2 is 232. Therefore, this product may be the target product 2, and subsequent nuclear magnetic resonance is needed for auxiliary verification.
[0050] The GC spectrum of compound 2 prepared in Example 27 is as Figure 2 shown. The inlet temperature of the gas chromatograph was set at 270 °C, the initial temperature of the column oven was set at 40 °C, the heating rate was 15 °C / min, and it was heated to 280 °C and held for 5 min. The substance eluting at 8.9 min in the GC chromatogram is the internal standard n-tridecane, and the substance appearing at 16.0 min is compound 2.
[0051] The 1 H NMR spectrum of compound 2 prepared in Example 27 is as Figure 3 shown. 1 HNMR(600MHz,Chloroform-d)δ7.85–6.25(m,9H),4.49(t,J=7.8Hz,1H),3.48(q,J=22.7Hz,2H),3.33–2.85(m,2H),2.88–2.42(m,1H),2.27(dq,J=12.5,7.8Hz,1H).
[0052] The 13 C NMR spectrum of compound 2 prepared in Example 27 is as Figure 4 shown. 1313C NMR (151 MHz, Chloroform-d) δ 163.47–113.66 (m), 47.51, 38.85, 33.94, 32.93–27.03 (m).
[0053] Examples 34 - 53 involve hydrogenating the compound with a four-ring structure obtained in Example 27 in a reaction kettle, with the differences being the different catalysts, reaction temperatures, solvents, and reaction times in step S2. The specific parameters are shown in Table 3 below:
[0054] Table 3. Influence of Catalyst, Temperature, Solvent, and Time on the Hydrogenation Reaction (Hydrogenation Kettle)
[0055]
[0056]
[0057] It can be seen from the results in Table 3 that the hydrogenation capabilities of different metal catalysts vary. Among them, metals Rh, Pt, Ru, and Pd exhibit relatively good activities. In the screening of solvents, it is found that both n-hexane and cyclohexane have good effects. However, because n-hexane has a better effect in the separation of subsequent products, n-hexane is used as the hydrogenation solvent. It should be noted that when the temperature rises to 300 °C, non-noble metals also have a good product yield. Considering the reaction temperature limit of the hydrogenation kettle and the possibility of subsequent large-scale production, it is decided to use a fixed bed to further evaluate the hydrogenation performance of this catalyst. In summary, using Rh / C as the catalyst, n-hexane as the solvent at 180 °C in the hydrogenation kettle, the reaction for 12 h has a relatively high yield of 92%, and the optimal conditions for the hydrogenation reaction are obtained.
[0058] It is expected to explore the service life of this catalyst in practical applications. Therefore, with n-hexane as the solvent and reacting at 180 °C for 12 h, the recycling use of Rh / C was studied. It can be seen from the results in Table 4 that the yield of Rh / C shows no obvious change after being recycled four times, indicating that this reaction system can be reused.
[0059] Table 4. Hydrogenation Recycling Experiment
[0060]
[0061] Examples 58 - 104 involve hydrogenating the compound with a four-ring structure obtained in Example 27 in a fixed bed, with the differences being the different catalysts, the concentration of the compound with a four-ring structure 2, reaction temperature, liquid volume hourly space velocity, reaction pressure, and the molar ratio between hydrogen and the compound with a four-ring structure 2 (i.e., the hydrogen-oil ratio in Table 5) in step S2. The specific parameters are shown in Table 5 below:
[0062] Table 5. Influence of Different Parameters on the Hydrogenation Reaction (Fixed Bed)
[0063]
[0064]
[0065]
[0066] As can be seen from the results in Table 5, the hydrogenation capabilities of catalysts with different metal loadings are different. Among them, 10% Ni-10% Mo / Al2O3 shows relatively good activity. When screening the feed concentration, it is found that the raw material concentration of 5 wt% has the best effect and a relatively high conversion rate, which is beneficial to the subsequent product separation. Therefore, a raw material concentration of 5 wt% is adopted. Different temperatures are screened. When the temperature rises above 240 °C, the yield of the product decreases. Considering the energy consumption and the comparison of yields, the present invention selects 180 °C as the optimal reaction temperature. Different liquid hourly space velocities are screened, and it is found that changing the space velocity does not affect the yield. Considering the possibility of long-term production in this fixed bed, 0.5 h -1 is selected. Different hydrogen-oil ratios are screened, and it is found that the hydrogen-oil ratio does not affect the yield of this product. Considering the raw material economy, a hydrogen-oil ratio of 200:1 is selected. Different hydrogen pressures are screened, and it is found that the yield of this reaction is the highest when the pressure is 3 Mpa. When the pressure is further increased, the product yield remains unchanged. To sum up, in the fixed bed, the catalyst loading is 0.5 g, the temperature is 180 °C, the feed concentration is 5 wt%, the liquid hourly space velocity is 0.5 h -1 , the hydrogen pressure is 3 Mpa, the hydrogen-oil ratio is 200:1, the yield is relatively high at 94%, and the catalyst life is 200 h, thus obtaining the optimal conditions for the hydrogenation reaction.
[0067] The MS spectrum of the hydrogenation product 3 prepared in Example 39 is as Figure 5 shown. It can be seen from the figure that the maximum mass-to-charge ratio of the molecular ion peak of this substance is m / z = 246. The relative molecular mass of compound 2 is 232, and the relative molecular mass after complete hydrodeoxygenation should be 246. The GC-MS result shows that the maximum molecular weight is 246. Therefore, this product may be the target addition product 3, and subsequent nuclear magnetic resonance is needed for auxiliary verification.
[0068] The GC spectrum of the hydrogenation product 3 prepared in Example 39 is as Figure 6 shown. The injection port temperature is set at 270 °C, the initial column oven temperature is set at 40 °C, the heating rate is 15 °C / min, and it is heated to 280 °C and held for 5 min. The substance eluting at 8.9 min in the GC chromatogram is the internal standard n-tridecane, and the substances eluting at 14.1 - 15.6 min are the addition product 3.
[0069] The 1 1H NMR spectrum of the hydrogenation product 3 prepared in Example 39 is as Figure 7 shown. 11H NMR (400 MHz, Chloroform-d) δ 3.08–0.44 (m, 30H).
[0070] The hydrogenated product 3 prepared in Example 39 13 The 13C NMR spectrum is as follows Figure 8 shown. 13 13C NMR (151 MHz, Chloroform-d) δ 63.15–16.01 (m).
[0071] By comparing the properties of the high-density coal-based jet fuel obtained in Example 39 with traditional petroleum-based fuels (JP-10, RJ-4, RJ-4-I, RJ-5, and RJ-7), it is found that while maintaining key properties such as density, calorific value, and freezing point, the difficulty and cost of synthesis are greatly reduced.
[0072] Table 6. Comparison of the properties of different fuels
[0073]
[0074] As can be seen from the examples in Table 6, through a two-step method, it is possible to prepare a high-density coal-based jet fuel from the indene component of high-temperature coal tar. The density of the prepared high-density coal-based jet fuel 3 is 0.975 g / cm 3 , the calorific value is 45.80 MJ / L, the freezing point is -64 °C, and the viscosity is 431.8 mPa·s. Some of the properties of the fuel prepared from the raw material indene can be comparable to those of JP-10, and it is a kerosene alkane compound with relatively excellent properties. The entire route uses high-temperature coal tar components as raw materials, which is a new type of green and environmentally friendly route and does not produce harmful substances.
[0075] The above is only a specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention shall be covered by the protection scope of the present invention.
Claims
1. A method for preparing high-density coal-based jet fuel using indene as raw material, characterized in that: The following steps are involved: S1, dissolving an indene compound 1 in an organic solvent, and reacting the indene compound 1 under the catalysis of an acidic catalyst to generate a compound 2 having a tetracyclic structure; S2. Dissolving the compound 2 having a four-ring structure in an alkane solvent, and hydrogenating it in a hydrogenation reactor or a fixed bed in the presence of a metal catalyst to generate a high-density coal-based jet fuel 3.
2. The method for preparing high-density coal-based jet fuel using indene as raw material according to claim 1, characterized in that: In step S1, the reaction temperature is 80-160° C. and the reaction time is 6-14 h.
3. The method for preparing high-density coal-based jet fuel using indene as raw material according to claim 1, characterized in that: In step S1, the acidic catalysts Nafion, T-62MP, Amberlyst15, CD750, CD250, H-Beta, H3O 40 PW 12 .xH2O, H4[Si(W3O 10 )4]·One of xH2O.
4. The method for preparing high-density coal-based jet fuel using indene as raw material according to claim 1, characterized in that: In step S1, the amount of the acidic catalyst used is 20% of the mass of the indene compound 1.
5. The method for preparing high-density coal-based jet fuel using indene as raw material according to claim 1, characterized in that: In step S1, the organic solvent is selected from one or more of dichloromethane, dichloroethane, n-hexane, cyclohexane, n-octane, toluene, dimethyl sulfoxide, N,N-dimethylformamide, acetone, N-methylpyrrolidone, propylene carbonate, dimethyl carbonate, and petroleum ether, and the concentration range of the indene compound 1 is 0.5-1 mol / L.
6. The method for preparing high-density coal-based jet fuel using indene as raw material according to claim 1, characterized in that: In step S2, the mass ratio between the amount of the metal catalyst and the compound 2 having a tetracyclic structure is (0.01-1):
1.
7. The method for preparing high-density coal-based jet fuel using indene as raw material according to claim 1, characterized in that: The metal catalyst is selected from one of commercial Raney nickel, commercial Raney cobalt, Pt / C, Pd / C, Ru / C, Rh / C, Ni-W / Al2O3, Ni-Mo / Al2O3, and Ni / Al2O3, wherein the active metal loading of Pt / C, Pd / C, Ru / C, and Rh / C is 3-8wt%; in the Ni-W / Al2O3, Ni and W account for 12-20% and 4-12% of the mass of Ni-W / Al2O3, respectively; in Ni-Mo / Al2O3, Ni and Mo account for 4-20% and 4-20% of the mass of Ni-Mo / Al2O3, respectively; in the Ni / Al2O3, Ni accounts for 24-36% of the mass of Ni / Al2O3.
8. The method for preparing high-density coal-based jet fuel using indene as raw material according to claim 1, characterized in that: In step S2, the alkane solvent is cyclohexane or n-hexane, the concentration of the compound 2 with a tetracyclic structure in the hydrogenation reactor is 0.01-10 mol / L, and the concentration of the compound 2 with a tetracyclic structure in the fixed bed is 1 wt%-20 wt%.
9. The method for preparing high-density coal-based jet fuel using indene as raw material according to claim 1, characterized in that: In step S2, when the hydrogenation reaction is carried out in a reactor, the reaction temperature is 120-300° C., the reaction time is 4-12 h, and the hydrogen pressure is 1-6 MPa; when the hydrogenation reaction is carried out in a fixed bed, the average reaction temperature is 160-350° C., the reaction pressure is 0.5-4 MPa, the molar ratio of hydrogen to the compound 2 having a tetracyclic structure is (200-1000): 1, and the liquid volume space velocity is 0.1-1 h -1 .