Simple Gas Hydrate Research Articles

Correlation of phase equilibria for gas hydrates in organic inhibitor aqueous solutions within wide concentration range

The calculation result of activity of water (aw) is an important factor affecting the description of phase equilibria for gas hydrate in the inhibited system. In this work, the Chen-Guo model was used to calculate the phase equilibria of simple gas hydrates. In addition, a new aw correlation was proposed to realize the description of gas hydrates in the organic inhibitor solutions containing methanol (MeOH), ethanol (EtOH), monoethylene glycol (MEG), diethylene glycol (DEG), triethylene glycol (TEG) and glycerol (GLY). Mole fraction of these inhibitors ranges from 0.003 to 0.761. Moreover, the calculated results were compared with available experimental data in the literature. Results showed that the existing Margules equation has limited accuracy in the description of methane hydrate within a wide concentration range. Meanwhile, the proposed aw correlation performed much better than the Hu-Lee-Sum (HLS) correlation when incorporated with the Chen-Guo model, which increased the calculation accuracy for methane hydrate by ∼54%. Furthermore, this work also presented an accurate description for ethane and carbon dioxide hydrates in the organic inhibitor solutions, which was evidenced by a series of experimental data.

Influence of N₂ on Formation Conditions and Guest Distribution of Mixed CO₂ + CH₄ Gas Hydrates.

In this contribution, a method based on a solid solution theory of clathrate hydrate for multiple cage occupancy, host lattice relaxation, and guest-guest interactions is presented to estimate hydrate formation conditions of binary and ternary gas mixtures. We performed molecular modeling of the structure, guest distribution, and hydrate formation conditions for the CO2 + CH4 and CO2 + CH4 + N2 gas hydrates. In all considered systems with and without N2, at high and medium content of CO2 in the gas phase, we found that CO2 was more favorable in occupying clathrate hydrate cavities than CH4 or N2. The addition of N2 to the gas phase increased the ratio concentration of CO2 in comparison with the concentration of CH4 in clathrate hydrates and made gas replacement more effective. The mole fraction of CO2 in the CO2 + CH4 + N2 gas hydrate rapidly increased with the growth of its content in the gas phase, and the formation pressure of the CO2 + CH4 + N2 gas hydrate rose in comparison to the formation pressure of the CO2 + CH4 gas hydrate. The obtained results agreed with the known experimental data for simple CH4 and CO2 gas hydrates and the mixed CO2 + CH4 gas hydrate.

Performance Improvement of Various Kinetic Hydrate Inhibitors Using 2-Butoxyethanol for Simple Gas Hydrate Formation in a Flow Mini-Loop Apparatus

The effect of 2-butoxyethanol as an additive on simple gas hydrate formation in the presence of kinetic hydrate inhibitors such as modified starch, polyvinylcaprolactam, and Gaffix VC-713 under various conditions in a flow mini-loop apparatus has been studied. A laboratory flow mini-loop apparatus has been designed and manufactured to measure the induction time of simple gas hydrate formation. Hydrate formers (such as C1, C2, C3, i-C4, and CO2) are contacted with water containing dissolved inhibitor in the presence of 2-butoxyethanol as an additive at desired temperature and pressure. The effect of 2-butoxyethanol on the induction time during gas hydrate formation was investigated in the presence and absence of modified starch, polyvinylcaprolactam, and Gaffix VC-713 as kinetic inhibitors. Results show that the induction time is prolonged in the presence of Gaffix VC-713 compared to polyvinylcaprolactam and modified starch as inhibitors. Moreover, the induction time in the presence of 2-butoxyethanol is greater than in the absence of this additive for simple gas hydrate formation. As a result, the performance of kinetic hydrate inhibitors was enhanced in the presence of 2-butoxyethanol for natural gas components during gas hydrate formation.

Improvement of gas hydrate preservation by increasing compression pressure to simple hydrates of methane, ethane, and propane

In this report, we describe the dissociation behavior of gas hydrate grains pressed at 1 and 6 MPa. Certain simple gas hydrates in powder form show anomalous preservation phenomenon under their thermodynamic unstable condition. Investigation of simple hydrates of methane, ethane, and propane reveals that high pressure applied to the gas hydrate particles enhances their preservation effects. Application of high pressure increases the dissociation temperature of methane hydrate and has a restrictive effect against the dissociation of ethane and propane hydrate grains. These improvements of gas hydrate preservation by increasing pressure to the initial gas hydrate particles imply that appropriate pressure applied to gas hydrate particles enhances gas hydrate preservation effects.

Measurement of H–LW–V and Dissociation Enthalpy of Carbon Dioxide Rich Synthetic Natural Gas Mixtures

In this work, hydrate–liquid water–vapor (H–LW–V) equilibrium data for methane (CH4), carbon dioxide (CO2), and four synthetic carbon dioxide (CO2) rich natural gas mixtures are measured. The measured pressure and temperature are in the range of (1.10 to 15.29) MPa and (272.15 to 290.15) K, respectively. In addition, a thermodynamic model based on Peng–Robinson (PR) EoS coupled with van der Waals–Platteeuw and modified Krichevsky and Kasarnovsky (KK) equation has been used for prediction of the equilibrium condition. The comparison between experimental measurements and model prediction shows excellent agreement obtained with an absolute average error of temperature (AAE) as low as 0.09. Additionally, the enthalpy of dissociation for simple and mixed gas hydrates is estimated using the measured equilibrium data by applying the Clausius–Clapeyron equation.

Enhancement of the performance of modified starch as a kinetic hydrate inhibitor in the presence of polyoxides for simple gas hydrate formation in a flow mini-loop apparatus

The main objective of the present work is the enhancement of the performance of modified starch as a kinetic inhibitor in the presence of polyoxides such as ethylene oxide (PEO) and polypropylene oxide (PPO) for simple gas hydrate formation in a flow mini-loop apparatus. Polyoxides such as PEO and PPO are high molecular weight polymers that are not kinetic inhibitors by themselves. For this investigation, a laboratory flow mini-loop apparatus was set up to measure the induction time and rate of gas hydrate formation when a hydrate forming substance (such as C1, C3, CO2 and i-C4) is contacted with water containing dissolved inhibitor in the presence or absence of polyoxides under suitable temperature and pressure conditions. In each experiment, water containing inhibitor blend saturated with pure gas is circulated up to a required pressure. Pressure is maintained at a constant value during experimental runs by means of required gas make-up. The effect of PEO and PPO on induction time and gas consumption during hydrate formation is investigated in the presence or absence of modified starch as a kinetic inhibitor. The results showed that the induction time is prolonged in the presence of PPO compared to the inhibitor alone. The efficiency of PPO is higher than the PEO, because, the induction time for simple gas hydrate formation in presence of PPO is greater than by using the PEO in presence of kinetic hydrate inhibitors.Also, the results show, that the gas consumption in the presence of modified starch is lower that in the absence of this inhibitor for all experiments. Moreover, the inhibition effect is clearly seen as well as the synergism between the inhibitor and PEO or PPO and this effect is higher in the presence of PPO.

Phase Equilibria and Dissociation Enthalpies of Tri-n-butylphosphine Oxide Semiclathrate Hydrates Incorporated with CH4, CO2, and H2

We investigated the phase equilibrium boundary of tri-n-butylphosphine oxide (TBPO) semiclathrate hydrates incorporated with CH4, CO2, and H2. TBPO aqueous solutions with a molality (m) of (1.61 and 1.98) mol·kg–1 were used for hydrate formation, which corresponded to the clathrate structures of TBPO·34.5H2O and 28H2O, respectively. The phase boundary at both concentrations was shifted to the promotion region represented by lower pressures and higher temperatures, compared to each simple gas hydrate. In particular, TBPO + CO2 double hydrate presented mild hydrate stabilization conditions of <1 MPa at (280 to 285) K. Additionally, the dissociation enthalpy (ΔHd) calculated from the phase boundary curves for the TBPO + CO2 double hydrates was almost the same as that for tetra-n-butylammonium bromide (TBAB) + CO2 double hydrate (219.5 kJ·mol–1 for m = 1.61 mol·kg–1 and 211.6 kJ·mol–1 for m = 1.98 mol·kg–1). These results demonstrate that the TBPO + CO2 double hydrate could be used as refrigerants for cold storage and transportation.

Experimental investigation of gas consumption for simple gas hydrate formation in a recirculation flow mini-loop apparatus in the presence of modified starch as a kinetic inhibitor

The main objective of the present work is to investigate experimentally the formation of simple gas hydrate with or without the presence of kinetic inhibitors such as modified starch in a recirculation flow loop. For this purpose, a laboratory recirculation flow mini-loop apparatus was set up to measure the induction time for hydrate formation and gas consumption rate when a hydrate forming substance (such as C1, C3, CO2 and i-C4) is contacted with water in the absence or presence of dissolved inhibitor under suitable temperature and pressure conditions. In each experiment, a water blend saturated with pure gas is circulated up to a required pressure. Pressure is maintained at a constant value during experimental runs by means of the required gas make-up. The effect of pressure on gas consumption during hydrate formation is investigated with or without the presence of polyvinylpyrrolidone (PVP) and modified starch as kinetic inhibitors at various concentrations. Our results show that the modified starch can be applied as an inhibitor in prevention of simple gas hydrate formation.

Evaluation of various types equations of state on prediction of rate of hydrate formation for binary gas mixtures in the presence or absence of kinetic hydrate inhibitors in a flow mini-loop apparatus

This paper compares the effects of using various types of equations of state (PR,11Peng Rabinson. PSRK,22Soave Ridlich Kowng. ER,33Esmaeilzadeh–Roshanfeker. NB44Nasrifar–Boland. and VPT55Valderrama-Patel–Teja.) for gas consumption during gas hydrate formation based on the Kashchiev and Firoozabadi model for binary gaseous mixtures such as 70% C1/30%C3, 30% C1/70% C3, 70% C1/30% i-C4, 30% C1/70% i-C4 with experimental data points obtained in a flow mini-loop apparatus in presence or absence of kinetic hydrate inhibitors at various pressures and specified temperature. A laboratory flow mini-loop apparatus is designed and built up to measure the gas consumption rate during gas hydrate formation.For the prediction of the gas consumption rate for double gas hydrate formation in a flow mini-loop apparatus, the rate equation based on the Kashchiev and Firoozabadi model for simple gas hydrate formation in batch system was developed. The total average absolute deviation was found to be 17.6%, 18.1%, 18.8%, 19.1% and 19.6% for the PR, NB, ER, PSRK and VPT equations of state for calculating gas consumption for binary gaseous mixtures during gas hydrate formation in the presence and absence of kinetic hydrate inhibitors, respectively. Comparison results between the calculated and experimental data points of gas consumption were obtained in flow loop indicate that the PR and NB equations of state have lower errors than the PSRK, ER and VPT equations of state for this model.

Prediction of induction time for natural gas components during gas hydrate formation in the presence of kinetic hydrate inhibitors in a flow mini-loop apparatus

The objective of this work is the prediction of induction time (ti) for simple gas hydrate formation in the presence or absence of kinetic hydrate inhibitors at various conditions based on the Kashchiev and Firoozabadi model in a flow mini-loop apparatus. For this purpose, the ti model is developed for simple gas hydrate formation in batch system for natural gas components during hydrate formation in a flow mini-loop apparatus. A laboratory flow mini-loop apparatus is designed and built up to measure the ti for simple gas hydrate formation when a hydrate former (such as C1, C3, CO2 and i-C4) is contacted with water in the absence or presence of dissolved inhibitor, such as poly vinylpyrrolidone, PVCap and L-tyrosine. In each experiment, a water blend saturated with pure gas is circulated up to a required pressure. Pressure is maintained at a constant value during experimental runs by means of the required gas make-up. The average absolute deviation (AAD) of the predicted ti values from the corresponding experimental data are found to be about 11% and 9.4% for gas hydrate formation ti in the presence or absence of kinetic hydrate inhibitors, respectively. © 2012 Canadian Society for Chemical Engineering

Experimental Investigation of Natural Gas Components During Gas Hydrate Formation in Presence or Absence of the L-Tyrosine as a Kinetic Inhibitor in a Flow Mini-loop Apparatus

Hydrates are crystalline compounds similar to ice, with guest molecules like methane and ethane trapped inside cavities or cages formed by the hydrogen bounded framework of water molecules. These solid compounds give rise to problems in the natural gas oil industry because they can plug pipelines and process equipments. Low dosage hydrate inhibitors are a recently developed hydrate control technology, which can be more cost-effective than traditional practices such as methanol and glycols. The main objective of the present work is to experimentally investigate simple gas hydrate formation with or without the presence of kinetic inhibitors in a flow mini-loop apparatus. For this purpose, a laboratory flow mini-loop apparatus was set up to measure the induction time and gas consumption rate during gas hydrate formation when a hydrate forming substance such as methane, ethane, propane, carbon dioxide and iso- butane is contacted with water in the absence or presence of dissolved inhibitor at various concentration under suitable temperature and pressure conditions. In each experiment, a water blend saturated with pure gas is circulated up to a required pressure. Pressure is maintained at a constant value during experimental runs by means of the required gas make-up. The effect of pressure on gas consumption during hydrate formation is investigated with or without the presence of PVP (polyvinylpyrrolidone) and L-tyrosine as kinetic inhibitors at various concentrations. The experimental results show that increasing the pressure of the system, causes to increase the experimental gas consumption and decrease the induction time. Also, the extent of gas hydrate formation at a given time is clearly less in the presence of the inhibitors. Moreover, when comparing the gas consumption during the hydrate formation for simple gas hydrate formation in presence of PVP and L-tyrosine inhibitors, it is seen that the gas consumption in presence of L-tyrosine is lower than that of PVP for all experiments.

New Approaches for the Production of Hydrocarbons from Hydrate Bearing Sediments

The presence of natural gas hydrates at all active and passive continental margins has been proven. Their global occurrence as well as the fact that huge amounts of methane and other lighter hydrocarbons are stored in natural gas hydrates has led to the idea of using hydrate bearing sediments as an energy resource. However, natural gas hydrates remain stable as long as they are in mechanical, thermal and chemical equilibrium with their environment. Thus, for the production of gas from hydrate bearing sediments, at least one of these equilibrium states must be disturbed by depressurization, heating or addition of chemicals such as CO2. Depressurization, thermal or chemical stimulation may be used alone or in combination, but the idea of producing hydrocarbons from hydrate bearing sediments by CO2 injection suggests the potential of an almost emission free use of this unconventional natural gas resource. However, up to now there are still open questions regarding all three production principles. Within the framework of the German national research project SUGAR the thermal stimulation method by use of in situ combustion was developed and tested on a pilot plant scale and the CH4-CO2 swapping process in gas hydrates studied on a molecular level. Microscopy, confocal Raman spectroscopy and X-ray diffraction were used for in situ investigations of the CO2-hydrocarbon exchange process in gas hydrates and its driving forces. For the thermal stimulation a heat exchange reactor was designed and tested for the exothermal catalytic oxidation of methane. Furthermore, a large scale reservoir simulator was realized to synthesize hydrates in sediments under conditions similar to nature and to test the efficiency of the reactor. Thermocouples placed in the reservoir simulator with a total volume of 425 L collect data regarding the propagation of the heat front. In addition, CH4 sensors are placed in the water saturated sediment to detect the distribution of CH4 in the sample. These data are used for numerical simulations for up-scaling from laboratory to field conditions. This study presents the experimental set up of the large scale reservoir simulator and the reactor design. Preliminary results indicate that the catalytic oxidation of CH4 operated as a temperature controlled, autothermal reaction in a countercurrent heat exchange reactor is a safe and promising tool for the thermal stimulation of hydrates. In addition, preliminary results from the laboratory studies on the CO2-hydrocarbon swapping process in simple and mixed gas hydrates are presented.

The system E8, a special class of simple polyhedra and gas hydrate structures

The system E₈, a special class of simple polyhedra and gas hydrate structures

Determination of Reference Chemical Potential Using Molecular Dynamics Simulations

A new method implementing molecular dynamics (MD) simulations for calculating the reference properties of simple gas hydrates has been proposed. The guest molecules affect interaction between adjacent water molecules distorting the hydrate lattice, which requires diverse values of reference properties for different gas hydrates. We performed simulations to validate the experimental data for determining , the chemical potential difference between water and theoretical empty cavity at the reference state, for structure II type gas hydrates. Simulations have also been used to observe the variation of the hydrate unit cell volume with temperature. All simulations were performed using TIP4P water molecules at the reference temperature and pressure conditions. The values were close to the experimental values obtained by the Lee-Holder model, considering lattice distortion.

THE EFFECT OF VARIOUS TYPES OF EQUATIONS OF STATE ON DRIVING FORCE CALCULATION AND GAS CONSUMPTION PREDICTION IN SIMPLE AND DOUBLE HYDRATE FORMATION WITH OR WITHOUT THE PRESENCE OF KINETIC INHIBITORS IN BATCH SYSTEMS

This article compares the effects of using various types of equations of state (Peng-Robinson, PR; Soave-Redlich-Kwong, SRK; Esmaeilzadeh-Roshanfekr, ER; Patel-Teja, PT; and Valderrama-Patel-Teja, VPT) on the calculated driving force and rate of gas consumption based on the Kashchiev model in simple and double-gas hydrate formation for methane, ethane, and their mixtures with 1130 experimental published data points with or without the presence of kinetic inhibitors at various pressures and temperatures. For the prediction of gas consumption rate in double-gas hydrate formation, the rate equation based on the Kashchiev model for simple gas hydrate formation was developed using the calculation of gas mole fraction in hydrate phase and then prediction of gas hydrate formation rate for each component in gaseous mixture. The total average absolute deviation was found to be 8.72%, 10.34%, 8.84%, 11.04%, and 14.16% for the PR, ER, SRK, VPT, and PT equations of state for calculating gas consumption in simple and double hydrate formation, respectively.

Intensification of the performance of kinetic inhibitors in the presence of polyethylene oxide and polypropylene oxide for simple gas hydrate formation in a flow mini-loop apparatus

The main objective of the present work is enhancement of the performance of gas hydrate kinetic inhibitors in the presence of polyethylene oxide (PEO) and polypropylene oxide (PPO) for simple gas hydrate formation in a flow mini-loop apparatus. PEO and PPO are high molecular weight polymers that are not kinetic inhibitors by their self. For this investigation, a laboratory flow mini-loop apparatus was set up to measure the induction time and rate of gas hydrate formation when a hydrate-forming substance (such as C1, C3, CO 2 and i-C4) is contacted with water containing dissolved inhibitor in presence or absence of PEO or PPO under suitable temperature and pressure conditions. In each experiment, water containing inhibitors blend saturated with pure gas is circulated up to a required pressure. Pressure is maintained at a constant value during experimental runs by means of required gas make-up. The effect of PEO and PPO on induction time and gas consumption during hydrate formation is investigated in the presence or absence of PVP (polyvinylpyrrolidone) and l-tyrosine as kinetic inhibitors. Results were shown that the induction time is prolonged in the presence of PEO or PPO compared to the inhibitor only. Inclusion of PPO into a kinetic hydrate inhibitor solution shows a higher enhancement in its inhibiting performance compare to PEO. Thus, the induction time for simple gas hydrate formation in presence of kinetic hydrate inhibitor with PPO is higher, compare to kinetic hydrate inhibitor with PEO.

Effect of various types of equations of state for prediction of simple gas hydrate formation with or without the presence of kinetic inhibitors in a flow mini-loop apparatus

This paper compares the effects of using various types of equations of state (PR, 1 1 Peng–Robinson. SRK, 2 2 Soave–Redlich–Kwong. ER, 3 3 Esmaeilzadeh–Roshanfekr. PT 4 4 Patel–Teja. and VPT 5 5 Valderrama–Patel–Teja. ) on the calculated driving force and rate of gas consumption based on the Kashchiev and Firoozabadi model for simple gas hydrate formation for methane, carbon dioxide, propane and iso-butane with experimental data points obtained in a flow mini-loop apparatus with or without the presence of kinetic inhibitors at various pressures and specified temperatures. For this purpose, a laboratory flow mini-loop apparatus was set up to measure gas consumption rate when a hydrate forming substance (such as C 1, C 3, CO 2 and i-C 4) is contacted with water in the presence or absence of dissolved inhibitor under suitable temperature and pressure conditions. In each experiment, a water blend saturated with pure gas is circulated up to a required pressure. Pressure is maintained at a constant value during experimental runs by means of the required gas make-up. The total average absolute deviation was found to be 15.4%, 16.3%, 15.8%, 17.8% and 17.4% for the PR, ER, SRK, PT and VPT equations of state for calculating gas consumption in simple gas hydrate formation with or without the presence of kinetic hydrate inhibitors, respectively. Comparison results between the calculated and experimental data points of gas consumption were obtained in flow loop indicate that the PR and ER equations of state have lower errors than the SRK, VPT and PT equations of state for this model.

Isothermal phase equilibria and structural phase transition in the carbon dioxide + cyclopropane mixed-gas hydrate system

The isothermal phase equilibria of the carbon dioxide + cyclopropane mixed-gas hydrate system were investigated by means of static temperature measurement and Raman spectroscopic analysis. Raman spectra indicated that the crystal structure of the carbon dioxide + cyclopropane mixed-gas hydrate changes from structure-I to structure-II and back to structure-I with an increase of the equilibrium carbon dioxide composition at 279.15 K, while each simple gas hydrate belongs to structure-I at the temperature. Whereas, unlike 279.15 K, no structural phase transition occurs along the isothermal stability boundary at 284.15 K.

Experimental and Theoretical Investigation of Double Gas Hydrate Formation in the Presence or Absence of Kinetic Inhibitors in a Flow Mini‐Loop Apparatus

AbstractDouble gas hydrate formation in the presence or absence of kinetic inhibitors in a flow mini‐loop apparatus was investigated. For the prediction of the gas consumption rate during hydrate formation in this system, the rate equation based on the Kashchiev and Firoozabadi model for simple gas hydrate formation in a batch system was developed for double gas hydrate formation in a flow mini‐loop apparatus. To complete the theoretical evaluation of gas hydrate formation through the mini‐loop apparatus in the presence or absence of kinetic hydrate inhibitors (KHI), a laboratory flow mini‐loop apparatus was set up to measure the induction time for hydrate formation and the uptake rate when a gaseous mixture (such as 75 % C1/25 % C3, 25 % C1/75 % C3, 75 % C1/25 % i‐C4, and 25 % C1/75 % i‐C4) is contacted with water containing or not containing dissolved inhibitor under suitable temperature and pressure conditions. In each experiment, a water blend saturated with gas mixture was circulated up to the required pressure. The pressure was maintained at a constant value during the experimental runs by means of a required gas mixture make‐up. The effect of pressure on gas consumption during hydrate formation was investigated in the presence or absence of polyvinylpyrrolidone (PVP) and L‐tyrosine as kinetic inhibitors at various concentrations. A good agreement was found between the predicted and experimental data in the presence or absence of KHI. The total average absolute deviation percents between the experimental and predicted values of gas consumption were found to be 16.4 and 17.5 % for the double gas hydrate formation in the presence or absence of the kinetic inhibitors, respectively.

Experimental and theoretical investigation of simple gas hydrate formation with or without presence of kinetic inhibitors in a flow mini-loop apparatus

Gas hydrates are ice-like crystalline compounds, which form through a combination of water and suitably sized guest molecules under low temperature and elevated pressure conditions. These solid compounds give rise to problems in the natural gas oil industry because they can plug pipelines and process equipment. Low dosage hydrate inhibitors are a recently developed hydrate control technology, which can be more cost-effective than traditional practices such as methanol and glycols. The kinetics of hydrate growth has been modeled by numerous authors who have measured the gas consumption rate during hydrate formation in batch agitator reactors. The main objective of the present work is to investigate experimentally of simple gas hydrate formation with or without the presence of kinetic inhibitors in a flow mini-loop apparatus. To predict the gas consumption rate during hydrate formation in this system, the rate equation based on the Kashchiev and Firoozabadi model for simple gas hydrate formation in a batch system was developed for this objective. To complete the theoretical evaluation of gas hydrate formation through the pipeline with or without the presence of kinetic hydrate inhibitors (KHIs), a laboratory flow mini-loop apparatus was set up to measure the induction time for hydrate formation and the uptake rate when a hydrate forming substance (such as C1, C3, CO 2 and i-C4) is contacted with water in the absence or presence of dissolved inhibitor under suitable temperature and pressure conditions. In each experiment, a water blend saturated with pure gas is circulated up to a required pressure. Pressure is maintained at a constant value during experimental runs by means of the required gas make-up. The effect of pressure on gas consumption during hydrate formation is investigated with or without the presence of polyvinylpyrrolidone (PVP) and l-tyrosine as kinetic inhibitors at various concentrations. A good agreement is found between the predicted and experimental data with or without the presence of KHIs. The total average absolute deviation percent between the experimental and predicted gas consumption is found to be 15.8% and 14.9% for simple gas hydrate formation with or without presence of kinetic inhibitors, respectively.