Numerical modelling of waterhammer pressure pulse propagation in sand reservoirs

• 2D modelling of pore pressure wave in saturated porous media is discussed.
• The formulation is validated against experimental data.
• Biot's theory is inaccurate in calculating pore pressure wave amplitude and speed.
• However, Biot's theory is sufficient in predicting the trends of pore pressure.
• Two distinct waves are expected as a result of a 1D pore pressure shock wave.
• The first wave is undrained and the second one is due to opposite motion of phases.
• The presence of these wave depends on the porous media properties.
• In 2D problems, a shear wave is also generated as a result of the shock wave.
• Only near-wellbore areas could see the dynamic effects of water hammer pressure wave.
• In low permeable rock Darcy's flow cannot support pore pressure increase by waves.
• In low permeable rock pressure returns to the original value after wave propagation.

This paper presents a numerical model with a new approach for analyzing the propagation of pressure waves in porous media and investigates the dynamic response of sand in relation to the attributes of pore pressure pulses. There are various instances in which dynamic phenomena can have a significant impact on porous media in a reservoir. One notable example is the possible influence of waterhammer pressure pulsing on sand fluidization around injection wells in oil reservoirs following a hard wellbore shut-in, which can result in massive sand production. In some extreme cases, this phenomenon can even result in the loss of the wellbore. Nevertheless, the pore pressure wave propagation in porous media has often been neglected in modelling likely due to mathematical complexity.The proposed model solves the momentum balance of fluid and solid coupled with the fluid mass balance equation in the prediction of dynamic fluid flow and mechanical deformation in porous media. The model is a two-dimensional, elasto-plastic, axisymmetric, single-phase and sequentially coupled model. The numerical model was validated against experimental data for a step wave in a shock tube and good agreement between model calculations and measured data has been obtained.Two distinct waves have been observed as a result of a shock pore pressure wave. The first one is an undrained wave where fluid and solid travel at the same speed. The other one is a wave which is often damped far from the source due to the friction between fluid and solid as they no longer travel together. It is found that tortuosity plays an important role on the amplitude of the waves. The results were then compared to the predictions by Biot's theory for waves through porous media. Biot's theory is shown to be inaccurate in predicting the transient dynamic behaviour, but it is sufficient in capturing the overall trends. Finally, the model is used to predict waterhammer response in near wellbore reservoir.