Pressure-driven Growth Research Articles

Lumen expansion is initially driven by apical actin polymerization followed by osmotic pressure in a human epiblast model

Post-implantation, the pluripotent epiblast in a human embryo forms a central lumen, paving the way for gastrulation. Osmotic pressure gradients are considered the drivers of lumen expansion across development, but their role in human epiblasts is unknown. Here, we study lumenogenesis in a pluripotent-stem-cell-based epiblast model using engineered hydrogels. We find that leaky junctions prevent osmotic pressure gradients in early epiblasts and, instead, forces from apical actin polymerization drive lumen expansion. Once the lumen reaches a radius of ∼12μm, tight junctions mature, and osmotic pressure gradients develop to drive further growth. Computational modeling indicates that apical actin polymerization into a stiff network mediates initial lumen expansion and predicts a transition to pressure-driven growth in larger epiblasts to avoid buckling. Human epiblasts show transcriptional signatures consistent with these mechanisms. Thus, actin polymerization drives lumen expansion in the human epiblast and may serve as a general mechanism of early lumenogenesis.

Breakdown of similarity solutions: a perturbation approach for front propagation during foam-improved oil recovery

The pressure-driven growth model has been employed to study a propagating foam front in the foam-improved oil recovery process. A first-order solution of the model proves the existence of a concave corner on the front, which initially migrates downwards at a well defined speed that differs from the speed of front material points. At later times, however, it remains unclear how the concave corner moves and interacts with points on the front either side of it, specifically whether material points are extracted from the corner or consumed by it. To address these questions, a second-order solution is proposed, perturbing the aforementioned first-order solution. However, the perturbation is challenging to develop, owing to the nature of the first-order solution, which is a similarity solution that exhibits strong spatio-temporal non-uniformities. The second-order solution indicates that the corner’s vertical velocity component decreases as the front migrates and that points initially extracted from the front are subsequently consumed by it. Overall, the perturbation approach developed herein demonstrates how early-time similarity solutions exhibiting strong spatio-temporal non-uniformities break down as time proceeds.

Modelling foam improved oil recovery: towards a formulation of pressure-driven growth with flow reversal.

The pressure-driven growth model that describes the two-dimensional (2-D) propagation of a foam through an oil reservoir is considered as a model for surfactant-alternating-gas improved oil recovery. The model assumes a region of low mobility, finely textured foam at the foam front where injected gas meets liquid. The net pressure driving the foam is assumed to reduce suddenly at a specific time. Parts of the foam front, deep down near the bottom of the front, must then backtrack, reversing their flow direction. Equations for one-dimensional fractional flow, underlying 2-D pressure-driven growth, are solved via the method of characteristics. In a diagram of position versus time, the backtracking front has a complex double fan structure, with two distinct characteristic fans interacting. One of these characteristic fans is a reflection of a fan already present in forward flow mode. The second fan however only appears upon flow reversal. Both fans contribute to the flow's Darcy pressure drop, the balance of the pressure drop shifting over time from the first fan to the second. The implications for 2-D pressure-driven growth are that the foam front has even lower mobility in reverse flow mode than it had in the original forward flow case.

Foam-liquid front motion in Eulerian coordinates.

A mathematical model formulated as a system of Hamilton-Jacobi equations describes implicitly the propagation of a foam-liquid front in an oil reservoir, as the zero-level set of the solution variable. The conceptual model is based on the 'pressure-driven growth' model in Lagrangian coordinates. The Eulerian mathematical model is solved numerically, where the marching is done via a finite volume scheme with an upwind flux. Periodic reinitialization ensures a more accurate implicit representation of the front. The numerical level set contour values are initially formed to coincide with an early time asymptotic analytical solution of the pressure-driven growth model. Via the simulation of the Eulerian numerical model, numerical data are obtained from which graphical representations are generated for the location of the propagating front, the angle that the front normal makes with respect to the horizontal and the front curvature, all of which are compared with the Lagrangian model predictions. By making this comparison, it is possible to confirm the existence of a concavity in the front shape at small times, which physically corresponds to an abrupt reorientation of the front over a limited length scale.

Pressure-driven growth in strongly heterogeneous systems

.The pressure-driven growth model for advance of a foam front through an oil reservoir during foam improved oil recovery is considered: specifically the limit of strong heterogeneity in the reservoir permeability is treated, such that permeability variation with depth more than outweighs the tendency of the net pressure driving the front to decay with depth. This means that the fastest moving part of the front is not at the top of the solution domain, but rather somewhere in the interior. Moreover the location of the foam front on the top boundary of the system can no longer be specified as a boundary condition, but instead must be determined as part of the solution of the problem. Numerical solutions obtained from the pressure-driven growth model under these circumstances are compared with approximate analytic solutions. An early-time approximate solution is found to break down remarkably quickly (far more quickly than breakdown would occur in the analogous homogeneous system). Numerical solutions agree much better with local quasi-static solutions centred about local maxima in the front shape, each local maximum corresponding to a depth within the reservoir at which a high permeability stratum is found. These individual local solutions meet together at sharp concave corners to cover the entire depth of the foam front. As time continues to progress however, the system evolves towards a long-time, global quasi-static solution, corresponding to the fastest moving of the aforementioned local maxima. Additional key features of the predicted front shapes are elucidated. The foam front is found to meet the top boundary obliquely despite an established convention in pressure-driven growth that the front and top boundary should meet at right angles. In addition, at each sharp concave corner, discontinuous jumps are predicted in the path length that material points travel to reach either side of the corner. Moreover the long-time, global quasi-static solution is found to admit smooth concavities, as opposed to the aforementioned sharp concave corners, which only tend to be prominent earlier on.Graphical abstract

Foam front advance during improved oil recovery: similarity solutions at early times near the top of the front

The pressure-driven growth model is used to determine the shape of a foam front propagating into an oil reservoir. It is shown that the front, idealised as a curve separating surfactant solution downstream from gas upstream, can be subdivided into two regions: a lower region (approximately parabolic in shape and consisting primarily of material points which have been on the foam front continuously since time zero) and an upper region (consisting of material points which have been newly injected onto the foam front from the top boundary). Various conjectures are presented for the shape of the upper region. A formulation which assumes that the bottom of the upper region is oriented in the same direction as the top of the lower region is shown to fail, as (despite the orientations being aligned) there is a mismatch in location: the upper and lower regions fail to intersect. Alternative formulations are developed which allow the upper region to curve sufficiently so as to intersect the lower region. These formulations imply that the lower and upper regions (whilst individually being of a convex shape as seen from downstream) actually meet in a concave corner, contradicting the conventional hypothesis in the literature that the front is wholly convex. The shape of the upper region as predicted here and the presence of the concave corner are independently verified via numerical simulation data.

Foam front displacement in improved oil recovery in systems with anisotropic permeability

A foam front propagating through an oil reservoir is considered in the context of foam improved oil recovery. Specifically the evolution of the shape of a foam front in a strongly anisotropic reservoir (vertical permeability much smaller than horizontal permeability) is determined via the pressure-driven growth model. The shape of the foam front is demonstrated to be extremely close to that predicted in the limiting case of a reservoir with no vertical permeability whatsoever, in particular any deviations from this shape are found to be second order in the ratio of vertical to horizontal permeabilities. Material points used to represent the foam front shape are shown to exhibit a uniform downward vertical motion, with a vertical velocity component which is proportional to the ratio of vertical to horizontal permeabilities. As the material points in question migrate downwards, they are replaced by new material points arriving from higher up, representing a long-time asymptotic solution for the front shape. This long-time asymptotic shape is sensitive to the ratio of vertical to horizontal permeabilities, with the foam front sweeping the reservoir less effectively as this ratio decreases.

Modelling foam improved oil recovery within a heterogeneous reservoir

The displacement of foam within a heterogeneous reservoir during foam improved oil recovery is described with the pressure-driven growth model. The pressure-driven growth model has previously been used to study foam motion for homogeneous cases. Here the foam model is modified in such a way that it includes terms for variable permeability. This model gives the evolution of the foam motion over time and the shape of the foam front, a wet foam zone between liquid-filled and gas-filled zones. The foam front shape for a heterogeneous or stratified reservoir develops concave and convex regions. For shapes such as these, the numerical solution of pressure-driven growth requires special numerical techniques, particularly in the case where concavities arise. We also present some analysis of the level of heterogeneity and how it affects the displacement, the shape of the front developing a set of concave corners. In addition to this we consider a heterogeneous and isotropic reservoir, in which case the foam front can sustain concavities, without these concavities having the same tendency to develop into corners.

Foam front propagation in anisotropic oil reservoirs.

The pressure-driven growth model is considered, describing the motion of a foam front through an oil reservoir during foam improved oil recovery, foam being formed as gas advances into an initially liquid-filled reservoir. In the model, the foam front is represented by a set of so-called "material points" that track the advance of gas into the liquid-filled region. According to the model, the shape of the foam front is prone to develop concave sharply curved concavities, where the orientation of the front changes rapidly over a small spatial distance: these are referred to as "concave corners". These concave corners need to be propagated differently from the material points on the foam front itself. Typically the corner must move faster than those material points, otherwise spurious numerical artifacts develop in the computed shape of the front. A propagation rule or "speed up" rule is derived for the concave corners, which is shown to be sensitive to the level of anisotropy in the permeability of the reservoir and also sensitive to the orientation of the corners themselves. In particular if a corner in an anisotropic reservoir were to be propagated according to an isotropic speed up rule, this might not be sufficient to suppress spurious numerical artifacts, at least for certain orientations of the corner. On the other hand, systems that are both heterogeneous and anisotropic tend to be well behaved numerically, regardless of whether one uses the isotropic or anisotropic speed up rule for corners. This comes about because, in the heterogeneous and anisotropic case, the orientation of the corner is such that the "correct" anisotropic speed is just very slightly less than the "incorrect" isotropic one. The anisotropic rule does however manage to keep the corner very slightly sharper than the isotropic rule does.

Foam-improved oil recovery: Modelling the effect of an increase in injection pressure.

A model, called pressure-driven growth, is analysed for propagation of a foam front through an oil reservoir during improved oil recovery using foam. Numerical simulations of the model predict, not only the distance over which the foam front propagates, but also the instantaneous front shape. A particular case is studied here in which the pressure used to drive the foam along is suddenly increased at a certain point in time. This transiently produces a concave front shape (seen from the domain ahead of the front): such concavities are known to be delicate to handle numerically. As time proceeds however, the front evolves back towards a convex shape, and this can be predicted by a long-time asymptotic analysis of the model. The increase in driving pressure is shown to be beneficial to the improved oil recovery process, because it gives a more uniform sweep of the oil reservoir by the foam.

Analysis of a model for foam improved oil recovery

AbstractDuring improved oil recovery (IOR), gas may be introduced into a porous reservoir filled with surfactant solution in order to form foam. A model for the evolution of the resulting foam front known as ‘pressure-driven growth’ is analysed. An asymptotic solution of this model for long times is derived that shows that foam can propagate indefinitely into the reservoir without gravity override. Moreover, ‘pressure-driven growth’ is shown to correspond to a special case of the more general ‘viscous froth’ model. In particular, it is a singular limit of the viscous froth, corresponding to the elimination of a surface tension term, permitting sharp corners and kinks in the predicted shape of the front. Sharp corners tend to develop from concave regions of the front. The principal solution of interest has a convex front, however, so that although this solution itself has no sharp corners (except for some kinks that develop spuriously owing to errors in a numerical scheme), it is found nevertheless to exhibit milder singularities in front curvature, as the long-time asymptotic analytical solution makes clear. Numerical schemes for the evolving front shape which perform robustly (avoiding the development of spurious kinks) are also developed. Generalisations of this solution to geologically heterogeneous reservoirs should exhibit concavities and/or sharp corner singularities as an inherent part of their evolution: propagation of fronts containing such ‘inherent’ singularities can be readily incorporated into these numerical schemes.

Evidence for isovolumetric replacement in some Terra Rossa profiles of northern Jordan

We investigated the rock-soil transition zones of three different Terra Rossa profiles near the ancient site of Abila, in northern Jordan, in order to demonstrate the possibility of a metasomatic origin for these soils using a scanning electron microscope (SEM) equipped with an energy-dispersive system (EDS). The field interpretation suggested that the first Terra Rossa might partially have formed by isovolumetric replacement, the second appeared to represent mainly the residue of the underlying limestone, and the third seemed to be derived from colluvial material. However, all investigated rock-soil transition zones showed microfossils that had partially been replaced by clay, which could be geochemically confirmed using EDS. The replacement matrix was free of detrital clay and revealed a jelly-like, amorphous structure. Large phyllosilicates, some rare feldspars, and heavy minerals that occurred throughout the investigated rock-soil transition zones are probably remains of sandy interlayers in the weathered limestone. We conclude that isovolumetric replacement contributes to Terra Rossa formation in northern Jordan although it is not yet possible to quantify the extent of its contribution or the sources that supply the elements triggering the pressure-driven growth of clay minerals.