Analytical Modeling of Oil Recovery by Steam Injection: Part I - Upper Bounds

1981 ◽  
Vol 21 (02) ◽  
pp. 162-178 ◽  
Author(s):  
Y.C. Yortsos ◽  
G.R. Gavalas
Keyword(s):  
Latent Heat ◽  
Oil Recovery ◽  
Three Dimensional ◽  
Steam Injection ◽  
Upper Bounds ◽  
Two Dimensional ◽  
Liquid Zone ◽  
Dimensional Flow ◽  
Steam Drive ◽  
Injection Rates

Abstract This paper deals with the derivation of upper bounds for the growth of the steam zone in steam injection processes for one- or multidimensional reservoirs at constant or variable injection rates. The bounds are derived from the integral balances describing a reservoir of arbitrary geometry by introducing lower bounds for the heat losses to the surrounding area and the hot liquid zone. In this way, the effect of preheating in the hot liquid zone is estimated to determine the recovery efficiency of a steam drive. The growth rate of a one-dimensional steam zone at variable injection rates is subject to two upper bounds resulting from the total thermal energy and the latent heat balances, respectively. Each of the bounds controls the rate of growth of the steam zone in a certain time interval, depending on the dominant mode of heat transfer in the hot liquid zone. At constant injection rates, the steam zone growth at large times is controlled by the bound based on the latent heat balance. This balance depends on a dimensionless parameter, F, defined as the ratio of the latent heat to the total heat injected. Based on the relative magnitude of F with respect to the critical value F= 2/pi, the region of validity of the Marx-Langenheim solution is delineated on a Ts vs. fs diagram. The Marx-Langenheim solution is satisfactory at large times when F greater than 2/pi and becomes less satisfactory as F assumes smaller values. Similar upper bounds are obtained for a two-dimensional steam drive (thin reservoirs). In three-dimensional reservoirs, on the other hand, bounds are derived only for a special form of displacement (separable front). These bounds depend on the models for the steam front shape, K can be determined in terms of the physical variables of the process. Introduction Injection of steam (steamflood or steam drive) is an important thermal recovery method that is applied on a commercial scale in many parts of the world. The main elements of continuous steam injection, as a displacement process, were analyzed thoroughly by experimental studies under both laboratory and field conditions. Along with laboratory and field tests, mathematical models are sought to aid in understanding and designing the process. The engineering evaluation of a steam drive often is based on a simplified mathematical description of reservoir heating by hot fluid injection presented by Marx and Langenheim and subsequently modified by Mandl and Volek. This theory was combined further with simple fluid flow considerations to determine the oil recovery rates in one-dimensional reservoirs. To account for the important effects of gravity override in three-dimensional geometries, Neuman and van Lookeren (following different approaches) derived simple analytical formulas for the calculation of the performance of a steamflood in three-dimensional reservoirs. An increasing number of investigators also have concentrated on the development of reliable numerical models. Three-phase numerical simulators were derived by Shutter for one- and two-dimensional flow; by Abdalla and Coats for two-dimensional flow; and by Coats et al., Coats, and Weinstein et al. for three-dimensional flow. The last two models also account for steam distillation of oil. SPEJ P. 162^

Analytical Modeling of Oil Recovery by Steam Injection: Part 2-Asymptotic and Approximate Solutions (include associated papers 10943 and 10951 )

1981 ◽  
Vol 21 (02) ◽  
pp. 179-190 ◽  
Author(s):  
Y.C. Yortsos ◽  
G.R. Gavalas
Keyword(s):  
Heat Transfer ◽  
Oil Recovery ◽  
Dimensionless Parameter ◽  
Approximate Solutions ◽  
Steam Injection ◽  
Operating Conditions ◽  
Liquid Zone ◽  
Approximate Expressions ◽  
Zone Growth ◽  
Injection Rates

Abstract This article studies the development of asymptotic and approximate solutions for the growth of the steam zone in steam injection processes in one-dimensional reservoirs at constant injection rates. These solutions generally are derived by using integral balances which include heat losses to the surroundings and the hot liquid zone. In this way, the effects of preheating caused by heat transport in the hot liquid zone ahead of the steam front are accounted for completely. At the beginning of injection, the advance of the front is well described by the Marx-Langenheim (ML) model, provided that the injection rates are sufficiently high. At longer times, deviations occur and a criterion is developed in terms of a single heat transfer dimensionless parameter, R, that defines the time interval of applicability of the ML model. The asymptotic behavior at large times depends solely on a dimensionless parameter, F, defined as the ratio of the latent to the total heat injected. It is shown that the final dimensionless expression does not depend on R (i.e., on the injection rates) although the time taken to reach the asymptotic state is influenced significantly by R. An approximate analytical solution that reduces to the respective asymptotic expressions at small and large times is obtained under conditions of high injection rates (R »1). The solution is shown to give a better approximation to the steam-zone growth rate for intermediate and large times than the approximate expressions developed by Marx and Langenheim, Mandl and Volek (MV), and Myhill and Stegemeier (MS). For a wider range of operating conditions, including low injection rates (i.e., for R between 1 and), an approximate numerical solution based on a quasisteady state approximation is presented. The proposed solution requiring very modest computation is expected to give reliable results under a variety of operating conditions. Introduction In a previous paper we dealt with the derivation of upper bounds for the volume of the steam zone in one-, two-, or three-dimensional reservoirs. The resulting expressions incorporate minimal information regarding heat transfer in the hot liquid zone and find applications in setting an upper estimate to oil recovery at constant or variable injection rates. To obtain more precise results concerning the steam zone growth, an alternative approach is initiated involving a detailed description of heat transfer in the hot liquid zone. The subject of heat transfer by convection, conduction, and lateral heat losses in the region ahead of a moving condensation front has been discussed separately in another paper. Here we make use of the results obtained in that paper to derive approximate solutions to the volume of the steam zone as a function of time. The relative importance of including preheating effects in the hot liquid zone and the surroundings when calculating the performance of a steam drive is demonstrated by comparing the solutions obtained against simple approximate expressions developed by Marx and Langenheim, and subsequently revised by Mandl and Volek, and Myhill and Stegemeier. From the comparison with exact results, the range of validity of the previous approximations can be delineated. SPEJ P. 179^

Contracting ducts of finite length

1951 ◽  
Vol 2 (4) ◽  
pp. 254-271 ◽  
Author(s):  
L. G. Whitehead ◽  
L. Y. Wu ◽  
M. H. L. Waters
Keyword(s):  
Stream Function ◽  
Finite Length ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Relaxation Method ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Hodograph Plane ◽  
Two Dimensional Flow ◽  
Working Section

SummmaryA method of design is given for wind tunnel contractions for two-dimensional flow and for flow with axial symmetry. The two-dimensional designs are based on a boundary chosen in the hodograph plane for which the flow is found by the method of images. The three-dimensional method uses the velocity potential and the stream function of the two-dimensional flow as independent variables and the equation for the three-dimensional stream function is solved approximately. The accuracy of the approximate method is checked by comparison with a solution obtained by Southwell's relaxation method.In both the two and the three-dimensional designs the curved wall is of finite length with parallel sections upstream and downstream. The effects of the parallel parts of the channel on the rise of pressure near the wall at the start of the contraction and on the velocity distribution across the working section can therefore be estimated.

Three-dimensional flow in cavities

1963 ◽  
Vol 16 (4) ◽  
pp. 620-632 ◽  
Author(s):  
D. J. Maull ◽  
L. F. East
Keyword(s):  
Static Pressure ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Large Span ◽  
Dimensional Flow ◽  
Pressure Distributions ◽  
Oil Flow ◽  
Two Dimensional Flow

The flow inside rectangular and other cavities in a wall has been investigated at low subsonic velocities using oil flow and surface static-pressure distributions. Evidence has been found of regular three-dimensional flows in cavities with large span-to-chord ratios which would normally be considered to have two-dimensional flow near their centre-lines. The dependence of the steadiness of the flow upon the cavity's span as well as its chord and depth has also been observed.

Cellular flow in a partially filled rotating drum: regular and chaotic advection

2017 ◽  
Vol 825 ◽  
pp. 631-650 ◽  
Author(s):  
Francesco Romanò ◽  
Arash Hajisharifi ◽  
Hendrik C. Kuhlmann
Keyword(s):  
Three Dimensional ◽  
Reynolds Numbers ◽  
Chaotic Advection ◽  
Two Dimensional ◽  
Rotating Drum ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Heteroclinic Connection ◽  
Two Dimensional Flow ◽  
Chaotic Streamlines

The topology of the incompressible steady three-dimensional flow in a partially filled cylindrical rotating drum, infinitely extended along its axis, is investigated numerically for a ratio of pool depth to radius of 0.2. In the limit of vanishing Froude and capillary numbers, the liquid–gas interface remains flat and the two-dimensional flow becomes unstable to steady three-dimensional convection cells. The Lagrangian transport in the cellular flow is organised by periodic spiralling-in and spiralling-out saddle foci, and by saddle limit cycles. Chaotic advection is caused by a breakup of a degenerate heteroclinic connection between the two saddle foci when the flow becomes three-dimensional. On increasing the Reynolds number, chaotic streamlines invade the cells from the cell boundary and from the interior along the broken heteroclinic connection. This trend is made evident by computing the Kolmogorov–Arnold–Moser tori for five supercritical Reynolds numbers.

The Experimental Analysis of the Role of Flue Gas Injection for Horizontal Well Steam Flooding

2018 ◽  
Vol 140 (10) ◽  
Author(s):  
Zhanxi Pang ◽  
Peng Qi ◽  
Fengyi Zhang ◽  
Taotao Ge ◽  
Huiqing Liu
Keyword(s):  
Oil Recovery ◽  
Heavy Oil ◽  
Flue Gas ◽  
Three Dimensional ◽  
Steam Injection ◽  
Displacement Efficiency ◽  
Oil Viscosity ◽  
Sweep Efficiency ◽  
Steam Flooding ◽  
Heavy Oil Reservoirs

Heavy oil is an important hydrocarbon resource that plays a great role in petroleum supply for the world. Co-injection of steam and flue gas can be used to develop deep heavy oil reservoirs. In this paper, a series of gas dissolution experiments were implemented to analyze the properties variation of heavy oil. Then, sand-pack flooding experiments were carried out to optimize injection temperature and injection volume of this mixture. Finally, three-dimensional (3D) flooding experiments were completed to analyze the sweep efficiency and the oil recovery factor of flue gas + steam flooding. The role in enhanced oil recovery (EOR) mechanisms was summarized according to the experimental results. The results show that the dissolution of flue gas in heavy oil can largely reduce oil viscosity and its displacement efficiency is obviously higher than conventional steam injection. Flue gas gradually gathers at the top to displace remaining oil and to decrease heat loss of the reservoir top. The ultimate recovery is 49.49% that is 7.95% higher than steam flooding.

Reconstruction of three-dimensional flow fields from two-dimensional data

2020 ◽  
Vol 407 ◽  
pp. 109239
Author(s):  
José Miguel Pérez ◽  
Soledad Le Clainche ◽  
José Manuel Vega
Keyword(s):  
Three Dimensional ◽  
Flow Fields ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Dimensional Flow

Theoretical Aspects of Thrust Vector Control by Secondary Gas Injection in Rocket Nozzles

1968 ◽  
Vol 72 (686) ◽  
pp. 171-177 ◽  
Author(s):  
John H. Neilson ◽  
Alastair Gilchrist ◽  
Chee K. Lee
Keyword(s):  
Vector Control ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Side Force ◽  
Thrust Vector Control ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Thrust Vector ◽  
Secondary Injection

This work deals with theoretical aspects of thrust vector control in rocket nozzles by the injection of secondary gas into the supersonic region of the nozzle. The work is concerned mainly with two-dimensional flow, though some aspects of three-dimensional flow in axisymmetric nozzles are considered. The subject matter is divided into three parts. In Part I, the side force produced when a physical wedge is placed into the exit of a two-dimensional nozzle is considered. In Parts 2 and 3, the physical wedge is replaced by a wedge-shaped “dead water” region produced by the separation of the boundary layer upstream of a secondary injection port. The modifications which then have to be made to the theoretical relationships, given in Part 1, are enumerated. Theoretical relationships for side force, thrust augmentation and magnification parameter for two- and three-dimensional flow are given for secondary injection normal to the main nozzle axis. In addition, the advantages to be gained by secondary injection in an upstream direction are clearly illustrated. The theoretical results are compared with experimental work and a comparison is made with the theories of other workers.

A New High-Temperature Gel for Profile Control in Heavy Oil Reservoirs

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
Changjiu Wang ◽  
Huiqing Liu ◽  
Qiang Zheng ◽  
Yongge Liu ◽  
Xiaohu Dong ◽  
...  
Keyword(s):  
High Temperature ◽  
Oil Recovery ◽  
Heavy Oil ◽  
Three Dimensional ◽  
Heat Stability ◽  
Steam Injection ◽  
Oil Reservoirs ◽  
Steam Flooding ◽  
Profile Control ◽  
Heavy Oil Reservoirs

Controlling the phenomenon of steam channeling is a major challenge in enhancing oil recovery of heavy oil reservoirs developed by steam injection, and the profile control with gel is an effective method to solve this problem. The use of conventional gel in water flooding reservoirs also has poor heat stability, so this paper proposes a new high-temperature gel (HTG) plugging agent on the basis of a laboratory experimental investigation. The HTG is prepared with nonionic filler and unsaturated amide monomer (AM) by graft polymerization and crosslinking, and the optimal gel formula, which has strong gelling strength and controllable gelation time, is obtained by the optimization of the concentration of main agent, AM/FT ratio, crosslinker, and initiator. To test the adaptability of the new HTG to heavy oil reservoirs and the performance of plugging steam channeling path and enhancing oil recovery, performance evaluation experiments and three-dimensional steam flooding and gel profile control experiments are conducted. The performance evaluation experiments indicate that the HTG has strong salt resistance and heat stability and still maintains strong gelling strength after 72 hrs at 200 °C. The singular sand-pack flooding experiments suggest that the HTG has good injectability, which can ensure the on-site construction safety. Moreover, the HTG has a high plugging pressure and washing out resistance to the high-temperature steam after gel forming and keeps the plugging ratio above 99.8% when the following steam injected volume reaches 10 PV after gel breakthrough. The three-dimensional steam flooding and gel profile control experiments results show that the HTG has good plugging performance in the steam channeling path and effectively controls its expanding. This forces the following steam, which is the steam injected after the gelling of HTG in the model, to flow through the steam unswept area, which improves the steam injection profile. During the gel profile control period, the cumulative oil production increases by 294.4 ml and the oil recovery is enhanced by 8.4%. Thus, this new HTG has a good effect in improving the steam injection profile and enhancing oil recovery and can be used to control the steam channeling in heavy oil reservoirs.

Simulation of Steamflooding With Distillation and Solution Gas

1976 ◽  
Vol 16 (05) ◽  
pp. 235-247 ◽  
Author(s):  
K.H. Coats
Keyword(s):  
Temperature Dependence ◽  
Gas Phase ◽  
Relative Permeability ◽  
Steam Distillation ◽  
Laboratory Data ◽  
Three Dimensional ◽  
Steam Injection ◽  
Injection Rate ◽  
Solution Gas ◽  
Injection Rates

Abstract This paper describes a three-dimensional numerical model for simulating steam-injection processes. The model accounts for solution gas and steam distillation of oil. The relative-permeability treatment presented includes a flexible but simple representation of temperature dependence and a history-dependent hysteresis in gas relative permeability. Since computational stability is a major difficulty in steamflood simulation, an implicit treatment of transmissibilities and capillary pressure is presented in detail. Model applications include comparisons with laboratory data, sensitivity experiments, and a field steam-injection test. Introduction Shutler and Abdalla and Coats described two-dimensional, three-phase flow numerical models for simulating steam-injection processes. Weinstein et al. described a one-dimensional model that accounted for steam distillation of oil. Coats et al. described a three-dimensional steamflood model that neglected steam distillation of oil, release of solution gas at elevated temperatures, and temperature dependence of relative permeability. This paper describes an extended formulation that includes these three phenomena and uses a more implicit treatment of capillary pressures and transmissibilities in the fluid-saturation calculations. The extended formulation represents a step toward a fully compositional thermal model without incurring the computational expense of the latter. The relative-permeability treatment described includes a rather flexible but simple representation of temperature dependence and incorporates a hysteresis in gas-phase relative permeability that varies with the historical maximum grid-block gas saturation. The phase-behavior representation is the weakest element of this work. We have found insufficient data relative to PVT behavior of a heavy-oil/steam system to justify sophisticated schemes of the type used in isothermal hydrocarbon systems. The PVT treatment presented is the simplest we could construct subject to the objectives of "directional correctness," reasonable quantitative accuracy, and ability to obtain required parameters from laboratory data either normally parameters from laboratory data either normally available or readily determinable. Model results presented include a comparison with laboratory data for a steamflood of a distillable oil; sensitivity results indicating effects and relative importance of various types of input data; and a comparison between calculated and observed injection rates for a Cold Lake (Alta.) steam-injection test. The latter is of interest in regard to reservations we have had regarding a model's ability to predict steam-injection rates into virtually immobile oil (100,000 cp). The field-test data showed initial and sustained steam-injection rates of 1,400 STB/D (cold-water equivalent). We discuss several reservoir-fluid parameters that had little effect and one independently measured parameter that had a pronounced effect on the calculated injection rate. pronounced effect on the calculated injection rate. MODEL DESCRIPTION The model consists and sewn equations expressing conservation of energy, conservation of mass, and constraints on sums of liquid and gas phase mol fractions. The mass-conservation equations apply to water and to each of three hydrocarbon components. In finite-difference form these equations are the following. SPEJ P. 235

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