Because of the capacity of in-depth plugging and flowing diversion, the deformable preformed particle gel (PPG) is used as an effective solution to severe fluid channeling and low sweep efficiency in oil development. However, the transport, plugging and deformation of PPG are a complex issue that involves both general characteristics of particle suspension and special deformation process. In addition, the flow of deformable PPG in porous media cannot be simulated by the classical seepage flow theory based on continuum assumptions. Thus, the paper develops an efficient simulation method for suspensions of deformable PPG, which combines the discrete idea of immersed boundary (IB) for particle deformation, lattice Boltzmann method (LBM) for fluid flow, discrete element method (DEM) for particle contact and immersed moving boundary (IMB) method for the solid-fluid interaction. The improved method is first validated by matching of the transport, plugging and deformation of PPG in porous media between numerical simulations and microscopic visualization experiments. Next, the method is used to study the effect of the particle-throat diameter ratio and elastic modulus on the critical pressure gradient, which is the smallest pressure gradient for a given PPG to pass through a throat of the porous media. The results indicate that there is a good exponential relationship between the critical pressure gradient of the PPG and the particle-throat diameter ratio. The critical pressure gradient is also linearly related to the elastic modulus of PPG. Finally, a multivariate mathematical model is proposed to characterize the quantitative relationships among the critical pressure gradient, particle-throat diameter ratio and elastic modulus. The proposed model is validated by comparisons between simulation results and prediction results by the quantitative model. Thus, the model can be used as the most important parameter for macroscopic simulations of PPG flooding in large oilfield-scale projects.
The water–oil relative permeability curve is mainly
obtained from linear displacement experiments. Few radial displacement
experiments have been carried out. In the process of linear displacement
experiments, the flow properties of the water–oil two phase
are linear. Nevertheless, it is radial near the bottom holes of an
actual reservoir. With regard to both kinds of displacement experiments,
the flow characteristics are various, which may result in great deviation
to apply the linear calculation theory of the relative permeability
curve to an actual reservoir. As a result of the above-mentioned problems,
on the basis of radial displacement experiments, using the Levenberg–Marquardt
algorithm for automatic history matching, this paper performs optimization
of production performance and relative permeability representation
models. Finally, a novel numerical inversion method for the radial
water–oil relative permeability curve is established. A test
based on the basic data of a radial laboratory displacement experiment
is performed to verify the effect of the proposed method. The results
show that oil relative permeability is more sensitive to the cumulative
production data, while water relative permeability is more sensitive
to the bottomhole pressure data of the producers. It also indicates
that the cubic B-spline model (CBM) is far more general and flexible
and has the advantage of local fitting compared to the power law model
(PM). In addition, the numerical inversion method proposed for the
radial water–oil relative permeability curve is reliable and
can meet the engineering requirement, which provides a basic calculation
theory for the estimation of the water–oil relative permeability
curve.
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