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E-mail address:(H.Jin).

Bubble column reactor has simple structure,large capacity,easy operation,adequate heat and mass transfer,and small bed pressure drop[1–3].Therefore,bubble columns are widely used in industry including chemical engineering,petrochemical,bio-engineering,environmental energy etc.[4].Many scholars have applied the population balance model in studying atmospheric bubble columns[5–7].But bubble columns in chemical production are generally operated under high pressures and examples are hydrocracking of petroleum(P=5.0–21 MPa),Fischer-Tropsch synthesis(P=2.0–5.0 MPa)and benzene hydrogenation(P=5.0 MPa)[8–11].Although high-pressure bubble columns are widely used in chemical and biochemical processes,their fundamental hydrodynamic behaviors,which are essential for reactor scale-up and design,are still not fully understood.

The effect of pressure on the hydrodynamic behaviors of bubble columns has been experimentally investigated by many gas holdup in high-pressure columns significantly increases due to the decreased bubble size[12–14].The gas–liquid mass transfer and reaction performance are enhanced as the pressure rises[10,15].With the development of computer technology,numerical simulation of gas–liquid two-phase flow has been greatly them,Krishna et al.[16]used a CFD model to simulate the high-pressure bubble column with the drag force between gas and liquid was considered only,and a density correction term ρ/ρ0due to pressure change was introduced into the drag force et al.[17]modified the gas density correction term in the drag model based on[16].Although the radial and axial velocity components were better predicted,the bubble diameter distribution was assumed the population balance model(PBM)can resolve the influence of bubble coalescence and breakup on bubble size distribution,the simulation of high-pressure bubble columns has been intensively conducted using the CFD-PBM coupled model in recent et al.[18]imposed the energy and capillary constraints in the bubble breakup model,and got a modified PBM to express the effect of bubble size distribution was then reasonably predicted by the modified PBM.Xing et al.[19]proposed a unified breakup model for both bubbles and droplets with the effect of pressure this unified breakup model gave good predictions of both the effect of pressure(or gas density)on the bubble breakup rate and the different daughter size distributions of bubbles and works have been reported on the effect of pressure in bubble columns,but the mechanism of pressure effect was little addressed.

Although the influence of pressure on the hydrodynamics in bubble columns is pronounced and very important for the design and scale-up of reactors at high pressures,further studies need to be conducted on the effects of this paper,based on the Luo bubble coalescence kernel model,a correction coefficient Ceabout density ρ/ρ0is introduced in the bubble coalescence efficiency item.The modified CFDPBM coupled model is used to simulate the flow field in a high-pressure bubble effects of pressure on the gas–liquid two-phase flow in the high-pressure bubble column were investigated at 0.5–2.0 MPa.It is shown that the modified CFD-PBM coupled model can describe the effect of pressure on the hydrodynamic parameters in the high-pressure bubble column.

Model

2.1.Two- fluid model

In the present work,the main approach for simulating gas–liquid flow s in a bubble column is Euler–Euler model.In contrast with the Euler–Lagrange approach,the gas phase and the liquid phase in the bubble column were considered as continuous phases of mutual penetration with the Euler–Euler approach gives a possibility of lower computational cost and particle size control equations of the two- fluid model are generally based on the Reynolds-averaged method[20–22],assuming that the gas is incompressible,ignoring the heat transfer and mass transfer between the two a simplified form of control equations can be obtained:

Continuity equation:

Momentum conservation equation:

equations

The standard k-ε model is selected for turbulence is a classical representation of the Reynolds-averaged method.

The k and ε equations are:

with C1ε=1.44,C2ε=1.92,C3ε=1.2,Cμ=0.99,σk=1.0,σε=1.3.

Turbulent viscosity is calculated by:

forces

The exact expression of the interphase forces is the key to simulating the gas–liquid two-phase flows,and many researches exist on the inter phase forces between gas and liquid[23,24].In this work,the drag force,transverse lift force,turbulent dispersion force and wall lubrication force are considered.

drag force

It is generally believed that the drag is the predominant force in modeling the gas–liquid flow s of bubble columns[25],as did in many simulation[14,26].Air bubbles are formed from the bottom of the tower with a certain gas the control volume formulation,all bubbles in the control volume suffer the total drag force as follow s: