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Developing a novel mechanistic model for four-phase oil-water-gas-sand stratified flow in a horizontal pipe.

Moradi, Behshad


Behshad Moradi



Presence of sand and solid particles in untreated petroleum sometime is inevitable. Although many techniques have been developed to prevent sand particles from entering the pipeline, such as downhole gravel packs, these downhole sand control devices can cause significant production loss due to the risk of blockage. Transporting sand along with other flowing phases is the best way of managing produced sand. Pipelines should be designed in such a way that flowing phases keep the sand particles moving and formation of the stationary sand bed should be mitigated by understanding flow physics under realistic multiphase conditions. To better understand the behaviour of multiphase flow, this research aimed to develop and verify a mechanistic model for the stratified four-phase (gas-oil-water-sand) flow in a horizontal pipe. This model takes into account some aspects of the existing multi-layer liquid-liquid and liquid-solid models. The entire stratified flow structure comprising of the stationary sand bed, moving sand bed, water, oil and gas layers are modelled by a system of twelve non-linear equations. An iterative numerical method has been developed to solve this system of non-linear equations. This solving method is using pressure balance in the moving phases as a criterion to converge to a solution that is physically possible. This model can also predict the flow structure by differentiating between fully suspended flow, stratified flow with moving and stationary beds, and stratified flow with moving bed only, and then adjusting and solving the governing equations accordingly. In the case of three-phase water-oil-gas flow, the developed code was run for two oil viscosity values of 1 (cP) and 100 (cP), where variation in the height of each layer versus total flow rate was studied. Comparison with three layer solid-liquid model was done by running the code while sand volumetric concentration was increased from 4% to 20% with 2% increments. Results of simulations compare well with the published data. The developed code was then employed to model the four-phase horizontal stratified sand-water-oil-gas flow. A parametric study was performed to evaluate the impact of particle size, solid concentration, solid density, slurry velocity and oil velocity on holdup and pressure gradient. At constant solid concentration, increase in solid size up to a certain threshold resulted in a reduction in stationary sand bed height and an increase in moving sand bed height, due to an increase in particle surface and torque applied on each particle. A further increase in particle size resulted in accumulation of stagnated particles. To further study the effect of particle size, slurry and oil flow rates were increased whilst gas flow rate remained unchanged. This resulted in an increase in both oil and water layer heights. An increase in particle size resulted in an increase in pressure gradient. The effect of solid concentration was studied by gradually increasing the concentration, whilst slurry, oil and gas flow rates remained unchanged. It was demonstrated that an increase in solid concentration results in sand build-up. Oil layer height showed a downward trend while sand concentration increases and pressure gradient showed a linear increasing trend as solid concentration increases. The effect of particle density was studied by increasing the density whilst other parameters - including particle size - remained unchanged. Density increase resulted in an increase in total sand height and a reduction in water layer height. An increase in slurry flow rate showed a linear relationship with water layer height and also resulted in an increase in moving sand bed height, while at the same time stationary sand bed height was reduced. An increase in oil flow rate showed no noticeable impact on sand bed height. In conclusion, this research developed a technique to solve non-linear equations governing four-phase stratified flow, which proved to be reliable and resulted in satisfactory results. The mechanistic model, which is developed in this research along with the solution algorithm, can be used as a starting point to develop numerical models for flow regimes other than stratified. The code was developed in MATLAB software version "R2017b".


MORADI, B. 2020. Developing a novel mechanistic model for four-phase oil-water-gas-sand stratified flow in a horizontal pipe. Robert Gordon University, PhD thesis. Hosted on OpenAIR [online]. Available from:

Thesis Type Thesis
Deposit Date Mar 2, 2021
Publicly Available Date Mar 2, 2021
Keywords Multiphase flow; Numerical modelling; Mechanistic modelling; Sand particles; Oil and gas engineering; Fluid dynamics
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