Effect of the drilling mud filtrate temperature on the resistivity of the stratum saturated by oil and gas

A mathematical model of the axisymmetric distribution of the phases in the zone of invasion of the water-based drilling mud into the productive stratum whose porous space can simultaneously contain three immiscible fluids (oil, gas, and natural water) is constructed; the model takes into account the high rate of heat transfer between the fluids and the rock matrix. It is shown that the resistivity of the invaded zone depends not only on saturation of the latter by the fluids and the concentration of salts in the water phase, but also on the drilling mud filtrate temperature. It is also shown that there is a jump in the function of stratum saturation by oil on the thermal front.     

Phase distribution and intrapore salt exchange during drilling mud invasion of an oil- and gas-bearing formation

As a result of drilling mud filtrate invasion of a formation saturated with oil, gas and natural water, the distribution of the immiscible phases and the electrophysical characteristics of the near-well zone change as compared with its initial state. Taking this change into account is necessary for successful interpretation of electrical well logging data. In this paper, on the basis of the equations of immiscible fluid flow through a porous medium and the system of transfer equations with account for instantaneous salt exchange between the filtrate and the natural water inside the pores, the regions of initial formation fluid saturations for which in the invasion zone the displacement fronts retain their relative position are determined.     

Effect of the wettability of the reservoir rock on the flow into a well

The effect of the wettability of the reservoir rock on the productivity of a well in a flooded reservoir is analyzed for immiscible fluid systems of the oil-water type by means of a computational experiment. The calculations take into account the presence of a drilling mud filtrate penetration zone in the neighborhood of the well.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 172–175, September–October, 1990.     

Two-dimensional problems of displacement in the case of nonlinear filtration laws

A method is proposed for calculating the multidimensional displacement of oil possessing anomalous properties from productive strata by water. Numerical solutions are obtained on the basis of the most generally accepted models of non-Newtonian oil within the framework of the theory of two-phase filtration of immiscible liquids.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 70–75, September–October, 1976.     

Stability of the displacement front and development of “fingering” in a porous medium

The effect of random disturbances at the fluid interface on the formation and development of fingering in the immiscible displacement of liquid hydrocarbons by water is experimentally investigated in a modified Hele-Shaw cell.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 101–106, September–October, 1989.     

Influence of contact-perimeter slip and heat transfer processes on oscillating hydrodynamic flows of immiscible liquids in capillary tubes

The hydrodynamic flows which arise in the presence of mechanical vibrations of a capillary tube filled with immiscible liquids are investigated. At the hermetically sealed ends of the tube there are air bubbles. It is assumed that the interfacial contact perimeters of the immiscible liquids can slip relative to the walls of the tube. The results of numerical calculations are given for a mercury electrocapillary transducer [1–4], which is a capillary tube filled with water and mercury. The calculated and experimental amplitude—frequency characteristics (the dependences of the amplitude of the electric potential difference on the vibration frequency) are compared.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 36–45, May–June, 1993.     

Nonstationary Gas Filtration Caused by an Intense Thermal Action on a Damp Porous Medium

A mathematical model and an algorithm are proposed for evaluating nonstationary heat and mass transfer in a porous medium that contains a mechanically absorbed liquid and a two–component gas (vapor—inert gas mixture). The case of an intense thermal action on a damp porous mixture caused by an external heat flux and convective heat transfer is considered. Typical flow regions and typical regions of the interaction between the phases are described.     

Prediction of amount of entrained droplets in vertical annular two-phase flow

Prediction of amount of entrained droplets or entrainment fraction in annular two-phase flow is essential for the estimation of dryout condition and analysis of post dryout heat transfer in light water nuclear reactors and steam boilers. In this study, air–water and organic fluid (Freon-113) annular flow entrainment experiments have been carried out in 9.4 and 10.2 mm diameter test sections, respectively. Both the experiments covered three distinct pressure conditions and wide range of liquid and gas flow conditions. The organic fluid experiments simulated high pressure steam–water annular flow conditions. In each experiment, measurements of entrainment fraction, droplet entrainment rate and droplet deposition rate have been performed by using the liquid film extraction method. A simple, explicit and non-dimensional correlation developed by Sawant [Sawant, P.H., Ishii, M., Mori, M., 2008. Droplet entrainment correlation in vertical upward co-current annular two-phase flow. Nucl. Eng. Des. 238 (6), 1342–1352] for the prediction of entrainment fraction is further improved in this study in order to account for the existence of critical gas and liquid flow rates below which no entrainment is possible.Additionally, a new correlation is proposed for the estimation of minimum liquid film flow rate at the maximum entrainment fraction condition. The improved correlation successfully predicted the newly collected air–water and Freon-113 entrainment fraction data. Furthermore, the correlations satisfactorily compared with the air–water, helium–water and air–genklene experimental data measured by Willetts [Willetts, I.P., 1987. Non-aqueous annular two-phase flow. D.Phil. Thesis, University of Oxford]. However, comparison of the correlations with the steam–water data available in literature showed significant discrepancies. It is proposed that these discrepancies might have been caused due to the inadequacy of the liquid film extraction method used to measure the entrainment fraction or due to the change in mechanism of entrainment under high liquid flow conditions.     

Relative Permeability Analysis of Tube Bundle Models

The analytical solution for calculating two-phase immiscible flow through a bundle of parallel capillary tubes of uniform diametral probability distribution is developed and employed to calculate the relative permeabilities of both phases. Also, expressions for calculating two-phase flow through bundles of serial tubes (tubes in which the diameter varies along the direction of flow) are obtained and utilized to study relative permeability characteristics using a lognormal tube diameter distribution. The effect of viscosity ratio on conventional relative permeability was investigated and it was found to have a significant effect for both the parallel and serial tube models. General agreement was observed between trends of relative permeability ratios found in this work and those from experimental results of Singhal et al. (1976) using porous media consisting of mixtures of Teflon powder and glass beads. It was concluded that neglecting the difference between the average pressure of the non-wetting phase and the average pressure of the wetting phase (the macro-scale capillary pressure) – a necessary assumption underlying the popular analysis methods of Johnson et al. (1959) and Jones and Roszelle (1978) – was responsible for the disparity in the relative permeability curves for various viscosity ratios. The methods therefore do not account for non-local viscous effects when applied to tube bundle models. It was contended that average pressure differences between two immiscible phases can arise from either capillary interfaces (micro-scale capillary pressures) or due to disparate pressure gradients that are maintained for a flow of two fluids of viscosity ratio that is different from unity.     

Equations of the mechanics of porous media saturated with liquid and gas

The approach proposed by Podil'chuk [1] is used to derive a system of equations of motion for saturated porous media, allowance being made for the mutual influence of the solid, liquid, and gas phases. The permeabilities of the anisotropic porous medium are assumed to depend on the direction. It is shown that when there are no gas phases and the liquid is incompressible the system of equations reduces to the general equations of the theory of elasticity of an anisotropic body with fictitious stress components. For a porous medium saturated with liquid, the relationships between the permeabilities and the anisotropy constants are obtained. The motion of liquid in an elastic porous medium in the form of an orthotropic cylindrical region with a cavity in the form of a circular cylinder is considered as an example.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 82–87, July–August, 1981.     

Numerical simulation and experimental validation of gas–solid flow in the riser of a dense fluidized bed reactor

Gas–solid flow in the riser of a dense fluidized bed using Geldart B particles (sand), at high gas velocity (7.6–15.5 m/s) and with comparatively high solid flux (140–333.8 kg/m² s), was investigated experimentally and simulated by computational fluid dynamics (CFD), both two- and three-dimensional and using the Gidaspow, O’Brien-Syamlal, Koch-Hill-Ladd and EMMS drag models. The results predicted by EMMS drag model showed the best agreement with experimental results. Calculated axial solids hold-up profiles, in particular, are well consistent with experimental data. The flow structure in the riser was well represented by the CFD results, which also indicated the cause of cluster formation. Complex hydrodynamical behaviors of particle cluster were observed. The relative motion between gas and solid phases and axial heterogeneity in the three subzones of the riser were also investigated, and were found to be consistent with predicted flow structure. The model could well depict the difference between the two exit configurations used, viz., semi-bend smooth exit and T-shaped abrupt exit. The numerical results indicate that the proposed EMMS method gives better agreement with the experimental results as compared with the Gidaspow, O’Brien-Syamlal, Koch-Hill-Ladd models. As a result, the proposed drag force model can be used as an efficient approach for the dense gas–solid two-phase flow.     

Percolation through clay crusts

During drilling of oil and gas wells, drilling muds (a suspension of clay particles in water) are pumped into them. During drilling, the muds perform various functions: They free the borehole from fragments of drilled rock, carry them to the surface, and create pressure on the borehole walls to prevent the entry of oil and gas into the borehole. The solid particles of the mud are deposited on the borehole walls, forming a clay crust, and the liquid phase percolates into the permeable bed. The clay crust represents an inhomogeneous deformable porous medium that is denser near the borehole wall. Knowledge of the properties of clay crusts is very important in practice, since it permits determining certain parameters of the bed; furthermore, the very properties of the clay crust depend on the properties of the drilling muds. In this article we will consider percolation of the drilling mud through the crust. Experimental data are used which show that the permeability and compressibility of the clay crust depend on the stresses acting in the particles of the clay crust. The problem is reduced to a self-similar problem. An ordinary differential equation of the second order is derived for the function in terms of which the stress and other characteristics of the crust are expressed. The distributions of permeability and porosity over the thickness of the crust are found and the quantity of fluid that penetrated into the bed at each instant is also determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 70–75, November–December, 1976.     

Mathematical model of water-steam phase transitions in hydrothermal reservoirs

The problem of steam production from a water-saturated hydrothermal reservoir is considered. It is shown that the introduction of a evaporation surface separating the gas and liquid phases leads to superheating of the water in a zone ahead of the front. This contradiction is removed by introducing of an extended phase transitions zone between the single-phase zones. In this case the problem contains two unknown moving boundaries considered as surfaces of discontinuity of the moisture content.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 98–105, November–December, 1994.     

Asymptotic method for solving problems with radial laminar jets of immiscible liquids

Two problems involving radial laminar jets of immiscible liquids are considered: a free radial slit jet and a jet on a rotating disk. An asymptotic method of solution is proposed that makes it possible to determine the flow parameters far from the source. The difference between these flows and those of homogeneous liquids is demonstrated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 192–28, May–June, 1980.     

Percolation model of two-phase flow through porous media

A physical model of the process of two-phase flow of immiscible fluids through a porous medium is developed and used to make an analytical calculation of the dependence of the relative phase permeabilities on the saturation of the medium by one of the phases. The theory is compared qualitatively with experiment for a model capillary radius frequency function and quantitatively with numerical calculations made on a computer. In both cases good agreement is obtained. The pressure dependences of the phase permeabilities are analyzed. The question of residual saturation with the wetting fluid after completion of the displacement process is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 88–95, January–February, 1987.     

On the length of annular jets interacting with an ambient medium

Annular jets of immiscible fluids are the subject of intense study. Particularly topical in applications are jets in the shape of a right circular cylinder. The space within annular jets may be reduced or increased by the influence of transverse forces and also by hydrodynamic instability of the jet flow. Twisting of the jet tends to make it close up. In the present paper, a study is made of ways of obtaining annular jets with nearly cylindrical shape and the greatest cavity length possible, allowance being made for gravity, capillary pressure surface forces, a pressure difference between the two sides of the phase interface, and the interaction with the ambient medium. A study is made of the influence of the velocity of the fluid and the medium in the initial section on the shape of the joint steady axisymmetric flow of immiscible viscous phases, including the shape of the middle surface of the annular jet.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 3–11, November–December, 1983.     

Filtration of a three-phase liquid (Buckley-Leverett model)

Buckley and Leverett [1] formulated the problem of the displacement of immiscible liquids in a porous medium and obtained a very simple one-dimensional solution for a two-phase flow. Different generalizations of it are known [2]. In [3, 4], a method of characteristics is proposed for numerical solution of the problem of three-phase flow. Articles [5, 6] consider the problem of the injection (at a given pressure) of two incompressible liquids into a porous stratum previously saturated with a third, elastic liquid. The authors started from the assumption of the existence, for this problem, of zones of three-, two-, and single-phase flow, separated by unknown mobility gradients. The present work investigates the solution for a three-phase flow, analogous to the Buckley-Leverett solution for two phases. It is shown that the character of the degrees of saturation depends essentially on the initial saturation of the porous stratum and on the phase composition of the mixture being injected.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 39–44, January–February, 1972.     

Self-similar solution of the thawing soil problem

A mathematical model of phase transitions in frozen soils containing unfrozen water is proposed. It is shown that phase transitions in frozen soils always occupy an extended zone. The problem of the interaction of frozen rock with a salt solution is solved on the assumption that the interface between the solution and the frozen rock is permeable both for the liquid and for the dissolved impurity. This problem arises, for example, in drilling wells in frozen ground, when the circulating drilling solution is an aqueous salt solution [7]. A series of natural processes is based on the interaction between groundwaters having different, possibly negative, temperatures and different degrees of mineralization and the surrounding frozen rock [8] and on the thawing of the frozen bed of northern seas in contact with saline seawater [9].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 136–142, November–December, 1988.     

Shock waves in soils and in water near the point of explosion

This paper gives a solution to the problem of the propagation of a plane shock wave in soils and in water; the solution was obtained by the method of characteristics using an electronic computer. Here, the soils were regarded as multicomponent media, in accordance with a previously proposed model [1, 2]. A comparison is made between the parameters of the waves and the dimensions of the gas cavity in soils with a different content of their components and in water.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 151–159, May–June, 1972.The authors thank S. S. Grigoryan and N. I. Polyakov for their evaluation of the work.     

An investigation of hydraulic fracturing. Part II: two-phase flow model

In the previous work presented in Part I (Theoret. Appl. Fracture Mech. 18, 89–102 (1993)), hydraulic fracture in an infinitely large saturated porous medium is analyzed under an assumption of one-phase flow in the medium. The investigation is extended in this paper to the case of a two phase saturated immiscible flow of oil and water in the porous medium. The medium is initially saturated with oil. Flow in the medium is induced by diffusion of water injected into the fracture. The quasi-static growth of the fracture for a prescribed injection rate is analyzed based on the assumptions that the pressure in the fracture is uniform and that the permeating flow in the medium is unidirectional. The constant fracture toughness criterion for plane strain deformation is employed and the effect of capillary pressure is neglected. Empirical formulas are used for the permeabilities of the oil and water phases. It is seen that the distributions of water saturation and pore pressure in the medium are governed by two nonlinear partial differential equations. Numerical solutions are obtained by a finite difference scheme with iterations. It is found that the injected water is restricted within a layer near the surface of the fracture whose thickness is small compared with the length of the fracture. Thus the flow in the medium is governed essentially by the oil phase. To compare our problem with the corresponding problem of one-phase flow, we find that the difference in crack growth in these two problems is small for the ration of kinematic viscosities of the oil and water phases within the practical range. Hence our study confirms the validity of the one phase flow assumption used in the previous work for prediction of hydraulic fracture growth.