Influence of Abandonment Pressure on Recoverable Reserves, Special Application to the Depleted Dnipro-Donetsk Basin Reservoirs

Volumetric gas reservoirs are driven by the compressibility of gas and a formation rock, and the ultimate recovery factor is independent of the production rate but depends on the reservoir pressure. The gas saturation in the volumetric reservoir is constant, and the gas volume is reduced causing pressure drop in the reservoir. Due to this reason, it is crucial to minimize the abandonment pressure to the lowest possible level. Concerning Dnipro-Donetsk Basin (DDB) gas reservoirs, it is widespread to recover sometimes more than 90% of the OGIP. Often, OGIP was estimated not considering lower permeability gas layers due to inaccurate logging equipment used in the past, causing that such layers were not included in the total netpay. This is one of the reasons for OGIP overestimation and higher recovery factors. On many P/Z graphs, we observe that at certain drawdown, lower permeability reservoirs kick in lifting up P/Z plot curve. Abandonment pressure is a major factor in determining recovery efficiency. Permeability and skin are usually the most critical factors in determining the magnitude of the abandonment pressure. Reservoirs with low permeability will have higher abandonment pressures than reservoirs with high permeability. A specific minimum flow rate must be sustained to keep the well unloading process, and a higher permeability will permit this minimum flow rate at lower reservoir pressure. Abandonment pressure will depend on wellhead pressure, friction and hydrostatic pressures in the system, pressure drop in reservoir, and pressure drop due to skin. This last factor is often neglected, which sometimes leads to a significant reduction of the recovery factor. It is common practice that skin factor and pressure drop due to the skin are solved with well stimulation. Also, well stimulation has its limits concerning the level of reservoir pressure. It is very common that the stimulation effect of low reservoir pressure well is negligible or even negative. This is caused by the minimum required drawdown to flow back a stimulating aqueous fluid out of the reservoir. The required minimum drawdown is caused by the Phase Trapping Coefficient (PTC), which drives reservoir stimulation fluid cleaning behavior. For water drive gas reservoirs, Cole (1969) suggests that the recovery is substantially less than recovery from bounded gas reservoirs. As a rule of thumb, recovery from a water-drive reservoir will be approximately 50 to 75% of the initial gas in place. The structural location of producing wells and the degree of water coning are essential considerations in determining ultimate recovery. In the cases studied in this paper, we consider gas and rock expansion reservoir energy, if abandonment pressure needs to be coupled with a water drive, then it is recommended to use a numerical, not analytical approach.

The minimum flow rate of electrosprays in the cone-jet mode

Stable electrospraying in the cone-jet mode is restricted to flow rates above a minimum, and understanding the physics of this constraint is important to improve this atomization technique. We study this problem by measuring the minimum flow rate of electrosprays of tributyl phosphate and propylene carbonate at varying electrical conductivity $K$ (all other physical properties such as the density $\unicode[STIX]{x1D70C}$, surface tension $\unicode[STIX]{x1D6FE}$ and viscosity $\unicode[STIX]{x1D707}$ are kept constant and equal to those of the pure liquids), and through the analysis of numerical solutions. The experiments show that the dimensionless minimum flow rate is a function of both the dielectric constant $\unicode[STIX]{x1D700}$ of the liquid and its Reynolds number, $Re=(\unicode[STIX]{x1D70C}\unicode[STIX]{x1D700}_{o}\unicode[STIX]{x1D6FE}^{2}/\unicode[STIX]{x1D707}^{3}K)^{1/3}$. This result is unexpected in the light of existing theories which, for the conditions investigated, predict a minimum flow rate that depends only on $\unicode[STIX]{x1D700}$ and/or is marginally affected by $Re$. The experimental dependency on the Reynolds number requires the viscous stress to be a factor in the determination of the minimum flow rate. However, the numerical solutions suggest that a balance of opposing forces including the fixing viscous stress, which at decreasing flow rates may lower the acceleration of the flow to the point of making it unstable, is unlikely to be the cause. An alternative mechanism is the significant viscous dissipation taking place in the transition from cone to jet, and which at low flow rates cannot be supplied by the work done by the tangential electric stress in the same area. Instead, mechanical energy injected into the system farther downstream must be transferred upstream where dissipation predominantly takes place. This mechanism is supported by the balance between the energy dissipated and the work done by the electric stress in the transition from cone to jet, which yields a relationship between the minimum flow rate, the Reynolds number and the dielectric constant that compares well with experiments.

The steady cone-jet mode of electrospraying close to the minimum volume stability limit

We study both numerically and experimentally the steady cone-jet mode of electrospraying close to the stability limit of minimum flow rate. The leaky dielectric model is solved for arbitrary values of the relative permittivity and the electrohydrodynamic Reynolds number. The linear stability analysis of the base flows is conducted by calculating their global eigenmodes. The minimum flow rate is determined as that for which the growth factor of the dominant mode becomes positive. We find a good agreement between this theoretical prediction and experimental values. The analysis of the spatial structure of the dominant perturbation may suggest that instability originates in the cone-jet transition region, which shows the local character of the cone-jet mode. The electric relaxation time is considerably smaller than the residence time of a fluid particle in the cone-jet transition region (defined as the region where the surface and bulk intensities are of the same order of magnitude) except for the high-polarity case, where these characteristic times are commensurate with each other. The superficial charge is not relaxed within the cone-jet transition region except for the high-viscosity case, because significant inner electric fields arise in the cone-jet transition region. However, those electric fields are not large enough to invalidate the scaling laws that do not take them into account. Viscosity and polarization forces compete against the driving electric shear stress in the cone-jet transition region for small Reynolds numbers and large relative permittivities, respectively. Capillary forces may also play a significant role in the minimum flow rate stability limit. The experiments show the noticeable stabilizing effect of the feeding capillary for diameters even two orders of magnitude larger than that of the jet. Stable jets with electrification levels higher than the Rayleigh limit are produced. During the jet break-up, two consecutive liquid blobs may coalesce and form a bigger emitted droplet, probably due to the jet acceleration. The size of droplets exceeds Rayleigh’s prediction owing to the stabilizing effect of both the axial electric field and viscosity.

Qualitative analysis of the minimum flow rate of a cone-jet of a very polar liquid

Electrostatic atomization of a liquid of finite electrical conductivity in the so-called cone-jet regime relies on the electric shear stresses that appear in a region of the liquid surface when a meniscus of the liquid is subjected to an intense electric field. An order of magnitude analysis is used to describe the flow induced by these stresses, which drive the liquid of the meniscus into a jet that issues from the tip of the meniscus and breaks into droplets at some distance from it. When the dielectric constant of the liquid is large, the electric shear stresses extend into the jet and cause a depression that sucks liquid from the meniscus. The induced flow rate is estimated and shown to represent approximately the minimum flow rate at which a cone-jet can be established. It is argued that the meniscus can be stabilized by the electric field that the charge of the jet induces on it. This stabilizing mechanism weakens when the flow rate supplied to the meniscus decreases, and its failure may determine an alternative minimum flow rate for the cone-jet regime. The instability of the jet and existing scaling laws for the size of the spray droplets are discussed.