Figure 2: Effect of asphaltene particle size on deposition velocity
As shown in the figure below, increasing the asphaltene particle diameter causes a rise in deposition velocity. Since experimental data for asphaltene deposition from petroleum fluid flow were scare, the verification of the model was accomplished using some available aerosols deposition data . As it is shown, the model predictions are in good agreement with deposition data.
It is also shown that among the mentioned forces, the gravitational force is more affected by particle size variation. This is due to the cubic relation of this force to the particle diameter. The concerned results are shown in Figure 3.
Figure 3: Effect of asphaltene size on the magnitude of different forces
Temperature gradient between fluid and pipe wall causes heat transfer phenomenon. This phenomenon can influence the thermophoresis force which is one of the forces for asphaltene deposition. Depending on temperature gradient direction, deposition velocity may be increased or decreased. While the wall temperature is higher than the fluid bulk temperature, heat flows from the wall toward the fluid bulk. This leads to a decrease in asphaltene deposition rate; this is due to thermophoresis force which acts in the direction of temperature gradient.
On the other hand, in the case of a cold wall the temperature gradient, thermophoresis force, and deposition velocity has the same direction and therefore the asphaltene deposition is intensified. Figure 4 shows the effect of temperature gradient on asphaltene deposition velocity. As depicted in this figure, the deposi-tion velocity of asphaltene particles rises by increasing temperature gradient.
Fluid Velocity Effect
Fluid velocity is one of the main parameters affecting the asphaltene deposition phenomena. Changes in velocity influence the temperature gradient which is the major cause of thermo-phoresis force. Furthermore, the velocity variations have crucial effects on the lift force which can delay the asphaltene deposition.
Figure 4: The effect of temperature gradient on deposition velocity
Figure 5 shows the effect of fluid velocity on both thermophoresis and lift force. The results of this work show that the fluid velocity affects the thermophoresis force more effectively than the lift force. Therefore, according to Equation 14, the deposition velocity rises as the fluid velocity is increased. The results obtained from velocity effect investigations are shown in Figure 6. The results obtained from our model are compared with some experimental aerosols deposition data . According to Figure 6 there is a good agreement between the calculated and limited experimental data.
Figure 5: The effect of fluid velocity on forces
Figure 6: Effect of fluid velocity on deposition velocity
Asphaltene Concentration Changes
The deposition of asphaltene particles on pipe surface causes a significant variation in its concentration in the fluid bulk. The amount of deposited asphaltene can be estimated using a material balance around the inlet and outlet of pipe. For this reason, it is necessary to calculate the amount of asphaltene concentration at the pipe exit. The relation between particle concentration and its deposition velocity in a pipe flow was suggested elsewhere . This equation is applied for the proposed system:
where, up is the particle deposition velocity; u is the flow velocity; C and C0 are the particle concentration in the x-direction and the particle concentration at the inlet of the pipe respect-tively; R stands for the pipe radius. We assume that the hydrocarbon mixture contains an initial concentration of asphaltene particles equal to 0.05 gr/cc. Setting x=L under different conditions, the asphaltene concentration at the end of the pipe can be calculated using Equation 14. Since the asphaltene deposition velocity is affected by many different parameters such as particle size, fluid velocity, and temperature gradient, the asphaltene concentration is also changed by those parameters. The effects of some mentioned parameters on asphaltene concentration are investigated and the obtained results are depicted in Figures 7, 8 and 9.
Figure 7: Effect of asphaltene particles size on the exit asphaltene concentration
Figure 8: Effect of fluid velocity on asphaltene exit concentration
Figure 9: Effect of temperature gradient on asphaltene exit concentration
A new dynamic model is introduced for asphaltene deposition. The basis of this model is the contribution of different forces which act on the dispersed asphaltene particles in the petroleum fluid flow. The results show that the gravitational force is more affected by the asphaltene particle size in comparison with the other contributed forces; consequently, the deposition velocity rises by increasing asphal-tene particles size. Also, the thermophoresis force, which is resulted from the temperature gradient between fluid bulk and the pipe wall, is exerted on the asphaltene particles. The results of this work show that the deposition velocity increases by a rise in the temperature difference between the fluid bulk and the pipe wall; the major reason is the existence of thermophoresis force, which is intensified by the temperature gradient increment. In addition, the results show that both the thermophoresis and lift forces are affected by the fluid velocity. Furthermore, the results show that the deposition velocity increases with a rise in fluid velocity. On the basis of the limited experimental data on aerosol deposition, the proposed model is able to predict the asphaltene deposition velocity in petroleum fluids flowing in pipes.