Journal of Engineering

Volume 2015, Article ID 457860, 7 pages

http://dx.doi.org/10.1155/2015/457860

## Modeling of Sand and Crude Oil Flow in Horizontal Pipes during Crude Oil Transportation

^{1}Department of Chemical Engineering, Covenant University, Ota, Nigeria^{2}Department of Chemical Engineering, Ahmadu Bello University, Zaria, Nigeria

Received 31 October 2014; Accepted 4 December 2014

Academic Editor: Tingyue Gu

Copyright © 2015 Samuel Eshorame Sanni 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

Some oil and gas reservoirs are often weakly consolidated making them liable to sand intrusion. During upstream petroleum production operations, crude oil and sand eroded from formation zones are often transported as a mixture through horizontal pipes up to the well heads and between well heads and flow stations. The sand transported through the pipes poses serious problems ranging from blockage, corrosion, abrasion, and reduction in pipe efficiency to loss of pipe integrity. A mathematical description of the transport process of crude oil and sand in a horizontal pipe is presented in this paper. The model used to obtain the mathematical description is the modified form of Doan et al. (1996 and 2000) models. Based on the necessity to introduce a sand deposit concentration term in the mass conservation equation, an additional equation for solid phase was derived. Difference formulae were generated having applied Fick’s equation for diffusion to the mass conservation equations since diffusion is one of the transport mechanisms. Mass and volume flow rates of oil were estimated. The new model, when tested with field data, gave 85% accuracy at the pipe inlet and 97% accuracy at the exit of the pipe.

#### 1. Introduction

During upstream petroleum production practices, rock oils from reservoirs are often transported as a mixture with sand up to the well heads and from the well heads to flow stations. At the head of the wells, horizontal transmission lines with or without screens transport the residual sand in the oil from feeder lines to flow stations. The entrained sand may deposit on the walls of the pipe due to pressure drop causing problems such as abrasion, corrosion, pipe blockage, reduction in flow area, loss in pipe integrity, and most importantly low output from the lines [1]. Sand exclusion measures (sand screens, sand filters, and gravel packs) used hitherto are somewhat laborious and expensive [2]; hence, it is necessary to search for an alternative solution to the problem such as using a mathematical model. Popoola et al. [3] discussed corrosion problems and mitigation of corrosion during oil and gas production. In this paper, about eight commonly encountered corrosion types as they relate to oil and gas production were mentioned alongside methods of controlling them. Amongst the methods suggested are materials selection, injection of inhibitors, the application of protective coatings, corrosion monitoring and inspection, and cathodic protection. To date, a model approach to sand corrosion control is yet to be established; however, various fluid-particle flow models were reviewed so as to make an apt choice. The paper of Srdjan et al. [4] established an internal corrosion prediction model for multiphase flow in a pipeline where a comprehensive CO_{2}/H_{2}S flow model was applied in order to predict the effects of H_{2}S, water entrainment, corrosion inhibition, and localized attack on a pipeline. The model was validated using experimental data where effect of trace amount of H_{2}S on corrosion rate in the absence of iron sulfide scales and the effects at the onset of iron sulfide scale formations were evaluated and measured at pH values less than 5 and equal to 6, at temperature of 20–80°C, pressure of 1 to 7.7 bars, and conditions of = 60°C and 7.7 bars, respectively. Van et al. [5] gave a numerical sensitivity analysis of the Wilson two-three-layer models for fully and partially stratified flows. They confirmed the validity of the two-layer model for partially stratified flows but the three-layer model was found suitable for bed load motion where friction is significant. Patankar and Joseph [6] in their work showed the validation of a developed numerical scheme with experiments using a bimodal suspension in a sedimentation column. The model was used to estimate sedimentation rates using two simulations with different grid sizes, parcel number, and time steps. Frederic et al. [7] modeled the settling of solid particles embedded in a viscous fluid flowing under gravity through a narrower section of a pipe. They studied the effect of particle shape on relaxation time for both disk and rectangular shaped particles. Glowinsky et al. [8] model is useful for the direct numerical simulation of three-dimensional fluidization and sedimentation phenomena. The model suits well the Newtonian and non-Newtonian incompressible viscous flows past moving rigid bodies.

Doan et al. [1] model represents a simulation approach of sand deposition inside a horizontal well. Although the model includes channel height, it can also account for the effect of oil viscosity and particle size on the transport process. It is also suitable for calculating fluid and particles concentration and quantifying fluid delivery but cannot simulate the turbulent transport of oil and sand. Huang et al. [9] focused on the motion of a two-dimensional circular cylinder in Couette and Poiseuille flows of a viscoelastic fluid. Both neutrally buoyant particles and nonneutrally buoyant particles were considered.

Joseph [10] developed a general model for particulate flows. The model incorporates only two types of forces in its phase equations: interaction and viscous forces. The model is suitable for quantifying fluid delivery and can handle a wide range of particle loading and types. Doan et al. [11] model is a simulation of the movement of sand and crude oil inside a horizontal well. Two fluids of different viscosities were considered and the relationship between viscosity, Reynolds number, drag coefficient, and interaction coefficient was determined. The model does not consider the effect of eddies which makes it unsuitable for turbulent transport of crude oil and sand. Therefore, this paper seeks to cover the gap in knowledge by modifying the aforementioned Doan et al. models thus describing a new model for laminar and turbulent transport of sand and crude oil in a horizontal pipe between the head of a well and its flow station.

#### 2. Model Modification

The Doan et al. [1, 11] models were developed for the case of sand and oil flow in an oil well and this informed why they were chosen from the reviewed models for application, other reasons being the inclusion of parameters such as sand and crude oil concentration terms, solid and liquid phase pressures, solid and liquid densities, liquid and solid interaction forces, kinematic pressure, liquid and solid concentrations, solid and liquid velocities, and liquid viscosity among others. The model represented by (1)–(4) was subsequently modified by assuming that all other components (asphaltenes, resins, and olefins) were dissolved in the oil at the flow conditions while taking effect of eddies into account.

##### 2.1. The Doan et al. Model

Consider

##### 2.2. Model Development and Modification

Considering Figure 1, where a mixture of incompressible crude oil and sand flows through an element of length within a pipe of length , the conservation equations can be generated as follows: