Flow of Hydrolysed Polyacrylamide Mother Liquor through Filter Bag : Detecting the Effects of Formulation and Process Properties on Pressure Drop

Hydrolysed polyacrylamide (HPAM) mother liquor is mainly used to extract oil. The HPAM solution is needed to filter the impurity using a bag filter before it is injected into the oil well. Therefore, the pressure drop of HPAM mother liquor must be less than 0.02 MPa in the processing of impurity filtration. The influence factors on pressure drop need to be researched. In this work, the computational fluid dynamics program (CFD) was used to research some key influence factors on pressure drop, such as porosity, outlet pressure of filter, inlet flow rate and viscosity of mother liquor. The simulation results indicated that with increasing porosity, outlet pressure, inlet flow rate and mother liquor viscosity, the pressure drop had increased after flowing through the filter bag.


Introduction
The application of HPAM first started in the water treatment field, such as raw water treatment, wastewater treatment, industrial water treatment and urban wastewater treatment. 15] At a certain degree, with an increase in polymer concentration and liquor viscosity, the oil displacement efficiency was better.However, at the same flow rate, the flow concentration was greater, the probability of blocking the hole with the polymer particle was greater, and the rise in pressure drop was quicker. 6 Many researchers have used the CFD software to simulate and design the bag filter to replace the test for cost and time cutting.H. Gao and L. J. Guo 9 used CFD software (Fluent 5.0) to optimize a bag filter dust collector by application of the k-ε model.They found that the pressure field of optimized bag filter is quite uniform and its total pressure loss through the bag house is reduced by about 60 % in relation to the prototype bag filter.Li et al. 10 used CFD program to simulate the unit flow distribution of bag filter and drew the distribution graph of filtering velocity along the height direction and the distribution characteristics of flow lifting speed between bags at different heights, thus offering theoretical evidence for improvement and design of bag filter.X. L. Zhang et al. 11 used CFD to simulate the main structur-al parameters of intake uniform board for the airflow distribution in bag filter with orthogonal tests.They found that the impact factors on airflow uniformity are board length, angle, number of boards, height, and increasing length.L. X. Ge et al. 12 used CFD software Fluent 6.3 to simulate the flow field in a bag filter and analysed the internal velocity flow field and pressure distribution.The CFD program can be used to simulate the inter flow field of pressure, velocity and temperature and so on, and can optimize the bag filter.Therefore, in this work we also used the CFD program to study the influence factors on pressure drop of bag filter.
CFD has developed very quickly in the past 20 years, because not only did the development of the computer hardware industry provide the massy material basis, but the theoretical analysis or the experimental method also had limitations.Thus, the analytical solution was not achieved due to the complexity of the question, or the test was not conducted because it was expensive.However, CFD was low cost, and capable of treating complex questions.CFD software can save the science researcher a lot of time, which he could put to good use on the study of physical problems.Therefore, in this work we selected the CFD software to simulate the flow field of the bag filter.
Before the HPAM mother liquor is injected into the oil well, the impurity must be leached by filter bag, so the permeability of the filter bag will change with time.Therefore, we used the CFD program to numerically simulate the inner flow field of the filter, and studied the influence of filter bag porosity, outlet pressure, inlet flow rate and mother liquor viscosity on the flow field and pressure drop, in order to provide a reference for the estimation of pressure drop and change period of the filter bag.

Simulation model and numerical method
The filter bag is shown in Fig. 1.The flow media in the filter was HPAM mother liquor.Medium density was 1010 kg m −3 , mass fraction 0.15 %, working temperature 40 °C, outlet pressure 3.5 MPa, maximum flow 150 m 3 h −1 .Fig. 2 is the three-dimensional geometrical model of the filter; inlet and outlet diameters are 160 mm, vessel diameter is 610 mm, vessel height is 1260 mm.The length, diameter and thickness of the filter bag are respectively 820 mm, 160 mm, 2.8 mm.The geometrical model is a single vessel with five filter bags.The green section is the inlet fluid domain, the cyan section is the outlet fluid domain, the five thin-wall constructions are filter bags.The filter bags are assumed to be porous media at the numerical simulation processing.
The grid information of the filter are statistic as follows; inlet grid is 2.236 million, outlet grid is 1.395 million, filter bag grid total number is 1.397 million.The filter mesh was generated by ANSYS-ICEM software, the self-adaption tetrahedral mesh occupied the main section, and the mesh of the filter bag domain was denser than other mesh and all the wall surfaces of the filter have a boundary layer mesh.
Mesh quality is displayed as a histogram where the abscissa (x-axis) displays the element quality on a scale from 0 (worst) to 1 (best), and the ordinate (y-axis) displays the number of elements in each quality range.The default is 20 bars or divisions between 0 and 1.Thus, the first bar would display the number of elements whose quality is between 0 and 0.05, and the next bar between 0.05 and 0.1.Mesh quality of the bag filter is shown in Fig. 3d.The lowest quality coefficient is 0.4 that completely satisfies the demand for mesh quality by CFD software CFX.The total designed computable cases were 20 by changing porosity, inlet flow rate, outlet pressure and medium viscosity.The boundary conditions were as follows: inlet condition was velocity, outlet condition was static pressure, wall condition was thermal isolation and no slip.The inlet part and outlet part of the filter were defined as the fluid domain, the filter bags construction were defined as porous medium.The turbulence model was k-ε model, the disperse method of governing equation was finite volume method, difference scheme was second order upwind scheme, the pressure and velocity coupling was SIMPLE algorithm.
The turbulence energy k and its turbulent dissipation ε in the standard k-ε model could be achieved by the following transport equation. (1) (2) Computational expression of turbulence viscosity μ t was as follows: (3) Model constants are as follows:

Results and discussion
Fig. 4 shows the three-dimensional streamline and Fig. 5 presents the three-dimensional velocity vector in the filter.These figures indicated that the flow was three-dimensional, in the pipe and the outlet pipe the flow rates were faster than in other places.HPAM mother liquor evenly flowed into the five filter bags.At the inlet position of the filter bag, the flow suddenly accelerated where there was more flow loss than in other places.In addition, the flow loss was mainly made up of boundary flow loss, secondary flow loss and other inner fluid friction.The total porosity of the bag filter is the ratio of total pore space volume of the bag filter and the total volume of the filter bag, and is indicated by percentage.Larger total porosity of the bag filter indicates that the bag filter has larger pore space.When the bag filter is used for a certain amount of time, some particles will block the pore space thus resulting in low porosity.Therefore, it is necessary to study the influence of porosity on the pressure drop.As shown in Fig. 6, with increasing porosity from 0.2 to 0.6, the pressure drop decreased from 3.6 • 10 −4 MPa to 3.4 • 10 −4 MPa.
In terms of increasing amplitude, the total pressure drop was not significant and kept at about 3.5 • 10 −4 MPa.It was indicated that the smaller the porosity, the greater the resistance of flow, and the total pressure drop computed by CFD technology could reflect the pressure change rule in the filter in a wide scope of porosity.
Influence of outlet pressure on pressure drop When outlet pressure of the bag filter increased, the flow resistance of the solution increased, the solution needed more energy to overcome resistance.Therefore, the pressure drop of the bag filter will increase with the increase in outlet pressure.The influence rule of filter outlet pressure on pressure drop could be observed in Fig. 7.With the increase in outlet pressure from 0.5 MPa to 1.5 MPa, the pressure drop increased, with outlet pressure from 1.5 MPa to 3.5 MPa, the pressure drop kept stable at near 5.8 • 10 −4 MPa.
Influence of inlet flow rate on pressure drop As shown in Fig. 8, with the inlet flow rate increasing from 0.1 m s −1 to 2.6 m s −1 , the pressure drop rapidly increased, the dependency of the two was non-linear with large increasing amplitude value, the pressure drop ranged from 1.7 • 10 −4 MPa to 1 • 10 −2 MPa that stepped over two orders of magnitude.The flow resistance in the filter was made of frictional drag and local resistance.The frictional drag was generated by internal friction of flow when flowing through the filter, thus it is also named one-way resistance.Local resistance was mainly induced by the bag filter.The two resistances increased with the increase in inlet velocity.

Influence of viscosity on pressure drop
Fig. 9 -Correlation between viscosity and pressure drop Slika 9 -Odnos između viskoznosti i pada tlaka AN913, AN923, AN934 are three different types of HPAM products all produced by SNF, France. 13These three types of HPAM come in the form of powder and granules, and their relative molecular masses are 1.17 Fluid resistance is proportional to the viscosity, because the internal resistance in the main flow and in the boundary layer will increase with the increase in flow viscidity.This is the main cause of the increased pressure drop in the bag filter.

Conclusion
The physical model of a filter bag was simplified as porosity material, and the CFD simulation model of filter was built.Conducted was the numerical computation of influence factors on pressure drop, such as porosity, outlet pressure, inlet flow rate and viscosity.
1) The total pressure loss, calculated by CFD software, can reflect the pressure drop changing rule in the filter.
2) With the porosity increasing, the pressure drop slightly decreased.But overall, the total pressure drop was not significant and kept at about 3.6 • 10 −4 MPa.
3) When the outlet pressure was in the scope of 0.5 MPa to 1.5 MPa, the pressure drop increased quickly from 1 • 10 −2 MPa to 5.5 • 10 −4 MPa.When the outlet pressure ranged from 1.5 MPa to 3.5 MPa, the pressure drop nearly kept stable, at about 5.8 • 10 −4 MPa.
4) With the inlet flow rate increasing from 0.1 m s −1 to 2.6 m s −1 , the pressure drop rapidly increased, the dependency of the two was non-linear with large increase in amplitude value, the pressure drop ranged from 1.7 • 10 −4 MPa to 1 • 10 −2 MPa that stepped over two orders of magnitude.