Journal of Petroleum Engineering

Volume 2015, Article ID 804267, 11 pages

http://dx.doi.org/10.1155/2015/804267

## Asphaltene Formation Damage Stimulation by Ultrasound: An Analytical Approach Using Bundle of Tubes Modeling

^{1}Petroleum University of Technology, Tehran 1453953153, Iran^{2}Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran 1136511155, Iran^{3}Texas A&M University, P.O. Box 23874, Education City, Doha, Qatar

Received 31 July 2014; Revised 15 February 2015; Accepted 15 February 2015

Academic Editor: Guillaume Galliero

Copyright © 2015 Arash Rabbani et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This study presents a novel approach for bundle of tubes modeling of permeability impairment due to asphaltene-induced formation damage attenuated by ultrasound which has been rarely attended in the available literature. Model uses the changes of asphaltene particle size distribution (APSD) as a function of time due to ultrasound radiation, while considering surface deposition and pore throat plugging mechanisms. The proposed model predicts the experimental data of permeability reduction during coinjection of solvent and asphaltenic oil into core with reasonable agreement. Viscosity variation due to sonication of crude oil is used to determine the fluid mobility applied in the model. The results of modeling indicate that the fluid samples exposed to ultrasound may cause much less asphaltene-induced damage inside the porous medium. Sensitivity analysis of the model parameters showed that there is an optimum time period during which the best stimulation efficiency is observed. The results of this work can be helpful to better understand the role of ultrasound prohibition in dynamic behavior of asphaltene deposition in porous media. Furthermore, the present model could be potentially utilized for modeling of other time-dependent particle induced damages.

#### 1. Introduction

Ultrasonic waves have a wide variety of applications in the oil field industries. Special characteristics of these waves such as high frequency and performing cavitation have brought them forward as a unique gadget in many stimulation operations [1]. Ultrasound radiation can change the molecular weight of asphaltenes. Lin et al. [2] applied ultrasonic waves to crack refinery oil residue which contains high amount of asphaltenic components in the presence of abundant hydrogen. Because of the local microscale high pressure and high temperature created by ultrasonic cavitation, asphaltene cracking can be even done in the atmospheric pressure. Dunn and Yen [3] successfully converted about 35% of asphaltene into gas oil and resin fractions under very mild condition using the ultrasound power and its cavitation feature. Kang et al. [4] published experimental results discussing the effects of ultrasound frequency on changing the average molecular weight of asphaltene content and showed that there is no direct relationship between frequency and capability of breaking down the asphaltene molecules.

The viscosity of asphaltenic oil can be changed by radiating ultrasonic waves. Islam et al. [5] ran experiments to ascertain the relationship between asphaltene content molecular weight and bitumen viscosity. They showed that oil viscosity significantly increases if containing more asphaltenic heavy components. Consequently, by accepting that ultrasound can crack the asphaltene molecular chains, it can also reduce the viscosity of oil. Chakma and Berruti [6] reported 15% viscosity reduction of heavy asphaltenic oil samples after radiating the ultrasonic waves.

The viscosity of colloids is related to the size distribution and stability of their dispersed particles [7]. Zhang et al. [8] studied the effect of ultrasonic waves on the stability of asphaltene emulsion and, by comparing the data before and after ultrasonic treatment, they found that the colloidal stability of asphaltene improves and it is mainly a physical process.

Mousavi et al. [9, 10] discussed the applicability of ultrasonic waves on the reduction of asphaltene flocculation. Najafi et al. [11] observed the results of ultrasonic irradiation on asphaltene particle size distribution (APSD) and found that the average sizes of asphaltene particles can be mitigated if they were exposed to the ultrasonic waves for specific time. Rad et al. [12] developed a model describing the behavior of asphaltene flocculation kinetics to show that ultrasonic exposure can reduce the asphaltene flock size after passing an optimum time of sonication.

Although it has been shown that ultrasonic waves positively affect the size of asphaltene particles, fundamental understanding of how formation damage induced by asphaltene deposition can be inhibited under the influence of ultrasonic waves is not well understood. Here, a bundle of tubes-based model is developed and used for predicting of formation damage inhibition under the influence of ultrasound. Most of previous dynamic models of permeability impairment cannot take into account the role of ultrasound prohibition on asphaltene precipitation; especially they suffer from the weakness in considering the role of APSD in the model behavior [13–15]. Here, the experimental data of APSD available in the literature measured by confocal microscopy at different ultrasonic exposure times is used for the modeling of permeability impairment in asphaltene-induced damage formations.

#### 2. Methodology

##### 2.1. Damage Prediction

In order to predict the formation damage, an appropriate permeability modeling should be done as well as considering the particle migration and deposition mechanisms. Stein [17] is almost the pioneer in combination of bundle of tube model and filtration theories to describe particle entrapment mechanisms inside the porous media. Modeling of the asphaltene-induced damage is mainly based on the theories of fine particle straining and clogging inside the porous medium. Here, to predict formation damage, bundle of tubes model is used.

###### 2.1.1. Bundle of Tubes Modeling

One of the prevailing methods in order to model the fluid flow through porous media is bundle of tubes. Considering this model, the permeability of porous media in 1D flow can be expressed as [18] where is permeability, is the total number of tubes, is average radius of pores, is cross-sectional area, and is the tortuosity of the medium. Lanfrey et al. [19] have presented a tortuosity model for randomly packed fixed beds as follows: where is the mean sphericity of grain particles and is the porosity. Sphericity is a measure of how spherical (round) an object is. It depends on porosity and specific surface of porous media which could be experimentally obtained [20]. Considering the bundle of tubes model, medium porosity with length is obtained as follows:

In order to find the number and radius of tubes, combining (1) and (3) results, we get

###### 2.1.2. Asphaltene Particle Size Distribution

It seems that the most of previous dynamic models of permeability impairment cannot take into account the role of ultrasound prohibition in asphaltene precipitation; meanwhile they rarely consider the effect of APSD in the model behavior [13–15, 21–25]. It has been expected that APSD majorly affects permeability impairment. It has been shown that the relatively large particles have a noticeable chance to plug the pore throats of the rock [24]. Plugging the throats will decrease the permeability, so considering an appropriate size distribution for asphaltene particles seems indispensable. The size distribution can be estimated by image processing methods applied on the microscopic images of the precipitated samples of asphaltenic oil [11]. Also, there are computational models which can estimate the APSD such as the thermodynamic colloidal model which is a phase behavior model capable of simulating the APSD as a function of the thermodynamics of the system [26–28]. Although many distribution functions can be fitted on asphaltene particle size data, we have chosen Gamma distribution because it is common in the literature [29, 30]. This is partly due to the fact that the gamma distribution provides high flexibility in representing such data [29]. The gamma distribution function is given as where and are parameters related to the mean and standard deviation, always greater than 0. When is the standard deviation of data and is the arithmetic mean, and can be expressed. is the gamma function given by the formula

###### 2.1.3. Filtration Theories

Fine migration in porous media occurs in three main patterns. For the particles larger than the average size of the pores, migration cannot be observed. As a result severe particle deposition occurs and permeability reduces significantly (Figure 1, Case I) [31].