Miscible WAG Efficiency Assessment on a Large Mature Carbonate Field

This paper is based on the analysis of miscible WAG for an onshore Middle-East field, with strongly undersaturated light oil. Water Alternate Gas operations have been ongoing for around 5 years, which is relatively recent compared to more than 40 years of production history. Goal of this work was to assess the efficiency of this miscible hydrocarbon WAG and to optimize it on the different compartments, with respect to miscibility, voidage replacement, and recycling. As this is a large mature field, with WAG operations dispatched on around 50 injectors and 9 fault blocks (compartments), the method of analysis had to be robust with respect to the different injection strategies followed in the past. It was essentially based on injection and production data, but also used pressure data when available. We computed the following dimensionless variables: oil recovery factor, BSW, voidage replacement ratio (VRR), and also WAG ratio and gas recycling ratio (GRR). Their evolution versus time was analyzed and compared between fault blocks. Using dimensionless variables allowed to compare fault blocks with different initial volumes in place, and to illustrate trends versus time. It was also found beneficial to lump some compartments, when communication was substantiated by pressure data. On the production side, we used the conventional BSW and GOR variables to quantify the water and gas recycling ratio. On the injection side, we observed that in some compartments, the historical WAG ratio was too low in the oil zone, which could be quantified by excluding the peripheral water injection volumes. The analysis allowed also to estimate the gas utilization factor and efficiency, which confirmed the overall high efficiency of miscible gas injection in 3-phase mode. It was also found that the injected fluid efficiency correlated with geology: gas injection tends to be more efficient in zones with high permeabilities at the bottom (coarsening downwards), while water injection is better adapted to zones with high permeabilities at the top (coarsening upwards). Estimating these water and gas efficiencies also allowed to optimize the injection strategy on a field level, by comparing the water efficiency with other units of the field only under waterflood.

Solution of boundary value problems with moving boundaries by using an approximate method for constructing solutions of integro – differential equations

The problem of oscillations of objects with moving boundaries, formulated as a differential equation with boundary and initial conditions, is a non-classical generalization of a problem of hyperbolic type. To facilitate the construction of a solution to this problem and justify the choice of a solution form, equivalent integro-differential equations are constructed with symmetric and time-dependent kernels and integration limits varying in time. The method for constructing solutions of integro-differential equations is based on the direct integration of differential equations in combination with the standard replacement of the desired function with a new variable. The method is extended to a wider class of model boundary value problems that take into account the bending stiffness of an oscillating object, the resistance of the environment, and the rigidity of the substrate. Particular attention is paid to the consideration of the most common in practice case when external disturbances act at the boundaries. The solution is made in dimensionless variables accurate to second-order values of smallness with respect to small parameters characterizing the speed of the border.

Oscillatory Flow of LDL-C and Blood Fluid through a Slanted Channel with Heat within the Sight of Magnetic Field

In this research, we investigated LDL-C and blood movement through a slanted channel with heat within the sight of magnetic field. In the evaluation, mathematical models for the LDL-C and blood stream and energy transfer were developed as partially coupled arrangement of partial differential equation (PDEs), the PDEs were scaled utilizing the dimensionless variables to dimensionless ordinary differential equation, they are further reduced to perturbed differential equations (ODEs) utilizing the perturbation parameters including the oscillatory term, where the non-homogenous equation and conditions are solved straightforwardly utilizing the technique for undetermined coefficient. The velocity and temperature profiles are gotten for certain overseeing boundaries included, and Mathematica codes were created utilizing simulate the impact of entering parameters on the profile. It is seen that the overseeing boundaries impacted that the entering pertinent parameters influences blood flow and it helps it controlling the LDL-C concentration, aiding treatment of atherosclerosis.

Pole-skipping and hydrodynamic analysis in Lifshitz, AdS2 and Rindler geometries

The “pole-skipping” phenomenon reflects that the retarded Green’s function is not unique at a pole-skipping point in momentum space (ω, k). We explore the universality of pole-skipping in different geometries. In holography, near horizon analysis of the bulk equation of motion is a more straightforward way to derive a pole-skipping point. We use this method in Lifshitz, AdS2 and Rindler geometries. We also study the complex hydrodynamic analyses and find that the dispersion relations in terms of dimensionless variables $$ \frac{\omega }{2\pi T} $$ ω 2 πT and $$ \frac{\left|k\right|}{2\pi T} $$ k 2 πT pass through pole-skipping points $$ \left(\frac{\omega_n}{2\pi T},\frac{\left|{k}_n\right|}{2\pi T}\right) $$ ω n 2 πT k n 2 πT at small ω and k in the Lifshitz background. We verify that the position of the pole-skipping points does not depend on the standard quantization or alternative quantization of the boundary theory in AdS2× ℝd−1 geometry. In the Rindler geometry, we cannot find the corresponding Green’s function to calculate pole-skipping points because it is difficult to impose the boundary condition. However, we can still obtain “special points” near the horizon where bulk equations of motion have two incoming solutions. These “special points” correspond to the nonuniqueness of the Green’s function in physical meaning from the perspective of holography.

Dynamics of Marangoni Convection in Hybrid Nanomaterials Flow With Dust Particles Random Motion

Here we are working on the flow of dust particles in hybrid nanofluid. Marangoni convective flow of hybrid nanofluid is accounted by considering silver and copper as nanoparticles and water as base fluid. Dust particles and nanoparticles are used in this flow are spherical type. For thermal conductivity we have considered the Maxwell model. Porous medium is placed over a stretching sheet. Flow is generated via stretching sheet. MHD effects are also considered. Nonlinear equation of fluid phase and dust phase are converted in to ODE's by suitable transformations. These ordinary differential equations are solved numerically. Effect of involved dimensionless variables against velocity and temperature of hybrid nanofluid and dust phase, skin friction and Nusselt number of hybrid nanofluid is studied through graphs and tables. It is observed that temperature and velocity is more in case of hybrid nanofluid as compared to dust phase. Velocity of Ag-Cu water hybrid nanofluid enhances for greater mass concentration of dust particles. Velocity in both phase decay for higher porosity variable. Good match of results are seen by comparing current situation to earlier study in particular case.

Entropy Optimization in Nonlinear Mixed Convective Flow of Nanomaterials Through Porous Space

Our intention in this article is to investigate entropy optimization in nonlinear mixed convective unsteady magnetohydrodynamic flow of nanomaterials in porous space. An exponentially stretched sheet creates the liquid flow. Nanomaterial is considered electrically conducting. The concentration and energy expressions comprise viscous dissipation, Joule heating, thermophoresis and Brownian motion aspects. Arrhenius activation energy is considered. Computation of entropy generation based upon the second law of thermodynamics is made. Nonlinear partial expressions are obtained via suitable dimensionless variables. Resultant expressions are tackled by the OHAM technique. Features of numerous variables on entropy, temperature, velocity and concentration are graphically visualized. Skin friction and the temperature gradient at the surface are also elaborated. Comparative analysis is deliberated in tabulated form to validate the previously published outcomes. Velocity is reduced significantly via the suction parameter. The entropy rate increases for higher values of Brinkman, Biot and Hartmann numbers.

Simulation of Vibration Combustion

We consider a mathematical model of the laminar process of vibration combustion proposed recently. It allows us to simulate detonation and deflagration modes, the occurrence of which occurs depending on the structure of the standard chemical potential. For simplicity of presentation and analysis, we consider a one-dimensional mathematical model formulated for the reduced dimensionless variables for the case of a two-component mixture. The obtained numerical results are presented and discussed.

Onset Criteria for Bulk-Mode Thermoacoustic Instabilities in Supercritical Hydrocarbon Fuels

We have investigated supercritical-p (p > 1192 psi (8.22 MPa)) methanol at pressures up to 1645 psi (11.3 MPa) flowing through a heated tube at flow rates of 4-7 lb/hr (1.8-3.2 kg/hr). Tube heated lengths have been varied from 4 to 6 in (10 to 15 cm), internal diameters from 0.027 to 0.069 in (0.069 to 0.175 cm), and heat inputs between zero and 800 Watts. Fluid temperature at the tube inlet remained subcritical (T < 464°F (513K)); outlet temperatures were transcritical or supercritical. Two phenomena were observed: system-wide bulk-mode oscillations and localized acoustic modes. In the present study, modeling and predictive efforts are undertaken to characterize system-wide bulk-mode oscillations. The parameter space has been nondimensionalized, yielding four dimensionless variables. Stability criteria based on these dimensionless groups have been established for two separate test articles and fluids; both criteria suggest that the heat required for the onset of oscillations is proportional to the mass flow rate times the mean pressure and inversely proportional to the fuel density.

Study of Lotka–Volterra Biological or Chemical Oscillator Problem Using the Normalization Technique: Prediction of Time and Concentrations

The normalization of dimensionless groups that rule the system of nonlinear coupled ordinary differential equations defined by the Lotka–Volterra biological or chemical oscillator has been derived in this work by applying a normalized nondimensionalization protocol. The normalization procedure, which is quite accurate, does not require complex mathematical steps; however, a deep physical understanding of the problem is required to choose the appropriate references to define the dimensionless variables. From the dimensionless groups derived, the functional dependences of some unknowns of interest are established. Due to the coupled nature of the problem that induces temporal concentration rates of each species that are quite different at each point of the phase diagram, this diagram has been divided into four stretches corresponding to the four quadrants. For each stretch, the limit values (maximum or minimum) of the variables, as well as their duration, are expressed in terms of the dimensionless groups derived before. Finally, to check all the mentioned dependences, a numerical simulation has been carried out.

Stokes layers in oscillatory flows of viscoelastic fluids

Oscillatory flows of viscoelastic fluids are studied from the perspective of Stokes viscoelastic layers. We identify the governing dimensionless variables, and study the flows in a general way for fluids with linear rheology. Nonlinearities can be treated perturbatively to account for reported flow instabilities. This article is part of the theme issue ‘Stokes at 200 (Part 1)’.