Productivity Enhancement In Unconventional Energy Reservoirs By Well Simulation Using Graded Proppant
Engineering Honours Degree, 2011
University of Adelaide
The use of graded proppant was expected to provide a significantly superior result for the stimulation of wells used in unconventional energy reservoirs. Their potential upside was examined through the use of well and fracture indexes, which were evaluated in order to assess their superiority compared to conventional mono-sized proppant stimulation. Specific consideration was paid to the use of this technique in naturally fractured shale gas reservoirs, as the successful implementation of a new highly efficient technique to improve production in reservoirs reliant on a few high permeability regions has the potential for a significant positive impact.
In order to determine the effectiveness of the graded proppant technique, analytical modelling was performed using equations taken from numerous literature sources which quantify relationships between permeability and pressure within tight formations such as shale. These equations were utilised to develop a well stimulation model, describing the variation in fracture aperture after a period of injection, using data from the Barnett Shale as the basis for this model. Radial Darcy flow in terms of the density of natural fractures present and a linear Poiseuille flow relationship was used to develop functions for the well and fracture indices respectively. These relations have demonstrated the relative benefit of graded proppant over conventional mono-sized treatments.
Further analytical modelling was used to develop a size based relationship for the deposition of a proppant particle in a fracture. This work involved the modelling of a number of forces relating to particle motion in fluids which were taken from literature and combined to derive an ordinary differential equation which when integrated described the motion of a particle in the fluid. This was then combined with the specified fracture and flow properties to determine an injection schedule of particles injected versus time.
The Computational Fluid Dynamics Software package COMSOL was used to derive a relationship for the impedance to flow in a fracture resulting from a varying separation between particles, it was also used to verify the proppant trajectories evaluated by the ordinary differential equations derived on the basis of force equilibrium.
An increase in magnitude of ten times was observed for a graded-size particle injection over a 100 mesh mono-size particle stimulation. The graded stimulation case uses standard mesh sizes between 32 and 200. In the well index calculations it has been shown that for any fracture density a graded stimulation will have a greater producibility than traditional techniques. For a fracture density of one fracture per square meter the graded WI is four times that of the mono WI for the same drainage area.
For the flow characteristics and fracture dimensions examined, a relationship between the particle size and its time of deposition was developed and quantified according to a logarithmic trend for increasing ‘mesh size’. Consideration of an injection schedule showed that for the simple case of stimulating a single fracture, the precision required for times and volumes injected was on the order of less than a second for smaller particles, and when factoring in the time of deposition for particles, it was found that particles will not deposit in the order in which they are injected, necessitating the use of a delay factor being some fraction of the deposition time for a particle.
Graded proppant is shown to offer a significant advantage in terms of productivity, however the practical requirements of the injection schedule (albeit for a single fracture) requires a level of precision that is practically unachievable, and not commensurate with the realised benefit of the technique. It is recommended that further effort be devoted to the examination of the performance of graded proppant in a network of fractures, as it is vital for the justification of this technique that it be practical, as well as achieving a superior productivity index.