Mathematical modelling of a hydrocyclone for the down-hole oil–water separation (DOWS)

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Abstract

In this study, a mathematical model is developed to predict the efficiency of a down-hole oil–water separation hydrocyclone. In the proposed model, the separation efficiency is determined based on droplet trajectory of a single oil droplet through the continuous-phase. The droplet trajectory model is developed using a Lagrangian approach in which single droplets are traced in the continuous-phase. The droplet trajectory model uses the swirling flow of the continuous-phase to trace the oil droplets. By applying the droplet trajectory, a trial and error approach is used to determine the size of the oil droplet that reaches the reverse flow region, where they can be separated. The required input for the proposed model is hydrocyclone geometry, fluid properties, inlet droplet size distribution and operational conditions at the down hole. The model is capable of predicting the hydrocyclone hydrodynamic flow field, namely, the axial, tangential and radial velocity distributions of the continuous-phase. The model was then applied for some case studies from the field tested DOWS systems which exist in the literature. The results show that the proposed model can predict well the split ratio and separation efficiency of the hydrocyclone. Moreover, the results of the proposed model can be used as a preliminary evaluation for installing a down-hole oil–water separation hydrocyclone system in a producing well.

Highlights

► A mathematical model is developed for a down-hole oil–water separation hydrocyclone. ► The proposed model is based on the prediction of the flow field of the dispersed phase. ► The separation efficiency is determined based on droplet trajectory analysis. ► The results show that the model can predict the efficiency of a down-hole hydrocyclone.

Introduction

The largest volume waste stream associated with oil and gas production is produced water. Treatment and disposal of produced water represent significant costs for operators. A new technology, down-hole oil/water separators (DOWS), has been developed to reduce the cost of handling produced water. DOWS may also be referred to as DHOWS or as dual injection and lifting systems (DIALS). DOWS separates oil and gas from produced water at the bottom of the well and re-inject some of the produced water into another formation or another horizon within the same formation, while the oil and gas are pumped to the surface. Since much of the produced water is not pumped to the surface, treated, and pumped from the surface back into a deep formation, the cost of handling produced water is greatly reduced. Hydrocyclones have no moving parts and separate substances of different density by centrifugal force. They could be used for solid–liquid or liquid–liquid separation. The liquid/liquid type of hydrocyclone is used in DOWS application. Fig. 1 shows a schematic drawing of a hydrocyclone. By application of DOWS, additional oil may be recovered as well. Shpiner et al. (2009) showed that the produced water (PW) can serve as an alternative water resource for restricted halo tolerant agricultural purposes if the main pollutants, hydrocarbons and heavy metals, can be removed to below the irrigation standards. In the present study, a mathematical model is proposed for a liquid–liquid hydrocyclone.

As it is shown in this figure, the produced water is pumped tangentially into the conical portion of the hydrocyclone. Water, the heavier fluid, spins to the outside of the hydrocyclone and moves towards the lower outlet. The lighter fluids, oil and gas, remain in the centre of the hydrocyclone where they are carried towards the upper outlet and produced to the surface. The separation of fluids in a hydrocyclone is not complete – some oil is carried along with the water fraction (<500 parts per million [ppm]; <200 ppm (Mattews, 1998); <100 ppm (Chrusch, 1996)), and a significant portion of water (typically 10% to 15%) is brought to the surface with the oil and gas fraction. Nevertheless, hydrocyclones can rapidly separate most of the oil from the water fraction. Hydrocyclones used in DOWS tend to be narrow and tall. Peachey and Matthews (1994), report that hydrocyclones can be smaller than 50 mm in diameter and 1–2 m in length. If a single hydrocyclone does not provide enough capacity to handle the total fluid volume, several hydrocyclones can be installed in parallel.

Most of the available reports on hydrocyclones within literature are focused on solid–liquid separation. Since the 1980s, liquid–liquid separation has become popular due to the relevant application area in the oil industry. The hydrocyclone employs the centrifugal force to separate the dispersed phase from the continuous fluid. The swirling motion is produced by the tangential injection of pressurized fluid into the hydrocyclone body. The flow pattern consists of a spiral within another spiral moving in the same circular direction (Seyda and Petty, 1991). Colman and Thew (1991), developed some correlations to predict the migration probability curve, which defines the separation efficiency for a particular droplet size in a similar way that the grade efficiency does. Estimation of LLHC efficiency based on a droplet trajectory was the target of Wolbert et al. (1995), work. The importance of the tail pipe section to the LLHC separation efficiency was confirmed by comparing the model with experimental results. This fact was elaborated for liquid–liquid hydrocyclone by Moraes et al. (1996). The modification takes into account the difference in the split ratio for liquid–liquid and liquid–solid hydrocyclones. Jinyu and Zheng (2007) developed a multi-region model for determining the cyclone efficiency. The multi-region model used the flow field data from recent experimental studies and applied a more accurate position for the interface between the downward and the upward flows. The model also considered the conical section in the cyclone separation process by calculating the separation efficiency of any given particle size directly without doing any geometric simplifications. Brennan et al. (2007) proposed a multiphase model for prediction of cut-size of hydrocyclone. The model predicts velocity profiles, flow splits, air core position and efficiency curves in hydrocyclones. Schutz et al. (2009) modelled the fluid behaviour during the liquid–liquid separation process in hydrocyclone considering the droplet interactions. In their study, the droplet breakup and coalescence rates are defined as mass transfer rates between the discrete phases.

Section snippets

Swirl intensity

The swirl intensity, Ω, is defined as the ratio of the rate of tangential to total momentum flux at a specific axial location, as follows:Ω=2πρc0RzuwrdrπρcRz2Uavz2Caldentey et al. (2001) developed a swirl intensity correlation that takes into account the semi-angle, β, of the conical section with respect to the centreline. The correlation, given by Eq. (1), was developed based on experimental data for small semi-angles, namely, 0° < β < 0.75°. However, a good prediction has also been obtained for

Validation of model parameters

The prediction performance of the proposed mathematical model has been compared with the previously reported experimental results. To demonstrate that the model can be used for different sizes of hydrocyclones, flow rates, oil densities, and cone angles, 12 sets of experimental data as shown in Table 1, were chosen to validate the model. These data were reported by Colman et al. (1980). Table 2 lists the configuration sizes for the hydro cyclone shown in Fig. 9 which was experimentally studied

Conclusion

A new mathematical model is developed for the down-hole de-oiling hydrocyclone. The required input for the model is hydrocyclone geometry, fluid properties, inlet droplet size distribution and operational conditions at the down hole. The model is capable of predicting the hydrocyclone hydrodynamic flow field, namely, the axial, tangential and radial velocity distributions of the continuous-phase. Although in developing of this model it is assumed that there is no interaction between oil

Nomenclature

    A

    cross sectional area

    C

    constant or coefficient

    CD

    drag coefficient

    Dc

    characteristic diameter

    Dpiu

    pressure drop between inlet and underflow, psi

    Dpio

    pressure drop between inlet and overflow, psi

    d

    diameter

    Eff

    efficiency

    f

    friction factor

    g

    acceleration due to gravity, h layer height

    I

    inlet factor

    L

    length

    M

    mass flow rate

    Mt

    tangential momentum flux at the inlet slot

    MT

    total axial momentum flux at characteristic diameter position

    n

    exponent

    P

    pressure

    q

    volumetric flow rate

    r

    radial position

    R

    radius

    Re

    Reynolds number

    Tm

    maximum

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