Phosphonate scale inhibitors (SIs) applied in downhole squeeze applications may be retained in the near-well formation through adsorption and/or precipitation mechanisms. In this paper, we focus on the properties of precipitated calcium phosphonate complexes formed by 9 common phosphonate species. The stoichiometry (Ca/P ratios) in various precipitates is established experimentally and the effect of solution pH on the molar ratio of Ca/P in the precipitate is investigated. All static precipitation tests were carried out in distilled water, with only Ca2+ (as CaCl2) and SI present in the system at test temperatures from 20oC to 95oC. The molar ratio of Ca/P in the solid precipitate was determined by assaying for Ca2+ and P in the supernatant liquid under each test condition by ICP spectroscopy (Cao and Po are known, but are also measured experimentally). We show experimentally that the molar ratio of precipitated Ca2+/P (or Ca2+/SI; or n in the SI_Can complex) depends on the SI itself and is a function of pH, for all phosphonates tested. It is found that, as pH increases, the molar ratio of Ca2+/P (n in the SI_Can) in the precipitate increases up to a theoretical maximum, depending on the chemical structure of the phosphonate. Our findings corroborate proposed SI-metal-complex ion structures which were presented previously (Shaw et al., 2012c), as discussed in detail in the paper. In addition, the precipitation behaviour of the various compounds is modelled theoretically by developing and solving a set of simplified equilibrium equations. We find that the precipitation behaviour can be modelled, but only if a fraction, ???, of "non-SI?? of the initial phosphonate SI is taken into account. The quantity ??? can be as high as 0.2 (i.e. ~20% non-SI), although there is a degree of variability in this factor from product to product. However, good quantitative agreement is shown comparing the predictions of the equilibrium solubility model with experiment. Such models can be used directly in the modelling of field phosphonate precipitation squeeze treatments.
Over the last two decades there has been an increase in activity on the pore-scale modeling of multiphase flow in porous media. Excellent progress has been made in many areas of pore-scale modeling, particularly in (1) the representation of the rock itself and (2) our description of the pore-scale displacement physics (in model pore geome-tries). Three-dimensional voxelized images of actual rocks can be generated either numerically (e.g. from 2D thin sections) or from micro-CT imaging. A simplified network involving more idealized nodes and bonds can then be extracted from this numerical rock model and this can be used in modeling pore-scale displacement processes. Much progress has also been made in understanding these pore-scale processes (i.e. piston-like displacement, snap-off events, layer formation/collapse, pore-body filling draining). These processes can be mathematically modeled accurately for pores of non uniform wettability, if the geometry of the pore is sufficiently simple. In fact, in recent years these various pore-level processes in mixed and fractionally wet systems have been classified as "events" in an entire capillary-dominated "phase space" which can be defined in a thermodynamically consistent manner. Advances in our understanding and ability to compute several two- (and three-) phase properties a priori have been impressive and the entire flooding cycle of primary drainage (PD), aging/wetting change, and imbibition can be simulated.
In this paper, we review the successes of pore-scale network modeling and explain how it can be of great use in understanding and explaining many phenomena in flow through porous media. However, we also critically examine the issue of how predictive network modeling is in practice. Indeed, one of our conclusions on pore-scale modeling in mixed-wet systems is that we cannot predict two-phase functions reliably in "blind" tests. Interestingly, we make this statement not because we do not understand the pore-scale physics of the process, but because we do understand the physics. It is hoped that our comments will stimulate a more critical debate on the role of pore-scale modeling and its use in core analysis.