A new correlation bas been developed for estimating oil recovery in unstable miscible five-spot pattern floods. It combines existing methods of predicting areal coverage and linear displacement efficiency and was used to calculate oil recovery for a series of assumed slug sizes in a live-spot CO2 slug-waterflood pilot test. The economic optimum slug size varies with CO2 cost; at anticipated CO2 costs the pilot would generate an attractive profit if performance is as predicted Introduction Selection of good field prospects for application of oil recovery processes other than waterflooding is often difficult. The principal reason is that other proposed displacing agents are far more costly proposed displacing agents are far more costly than water and usually sweep a lesser fraction of the volume of an oil reservoir (while displacing oil more efficiently from this fraction). Such agents must be used in limited amounts as compared with water; and this amount must achieve an appreciable additional oil recovery above waterflooding recovery. For these reasons, there is in general much less economic margin for engineering error in processes other than waterflooding. The general characteristics of the various types of supplemental recovery processes are well known, and adequate choices can be made of processes to be considered in more detail with respect to a given field. Comparative estimates must then be made of process performance and costs in order to narrow the choice. A much more detailed, definitive process-and-economic evaluation is eventually process-and-economic evaluation is eventually required of the chosen process before an executive decision can be made to commit large amounts of money to such projects. It is in the area between first choice and final engineering evaluation that this work applies. A areal cusping and vertical coning into producing wells. These effects can be seated by existing "desk-drawer" correlation which can confirm or deny the engineer's surmise that he has an appropriate match of recovery process and oil reservoir characteristics is of considerable value in determining when to undertake the costly and often manpower-consuming task of a definitive process-and-economic evaluation. process-and-economic evaluation. An examination of the nature of the developed crude oil resources in the U.S. indicates that the majority of the crude oil being produced is above 35 degrees API gravity and exists in reservoirs deeper than 4,000 ft. The combination of hydrostatic pressure on these oil reservoirs, the natural gas usually present in the crude oil in proportion to this pressure, the reservoir temperatures typically found, and the distribution of molecular sizes and types in the crude oil corresponding to the API gravity results in the fact that, in the majority of cases, the in-place crude oil viscosity was originally no more than twice that of water. A large proportion of these oil reservoirs have undergone pressure decline, gas evolution and consequent increase in crude oil viscosity. However, an appreciable proportion are still at such a pressure and proportion are still at such a pressure and temperature that miscibility can be readily attained with miscible drive agents such as propane or carbon dioxide, and the viscosity of the crude oil is such that the mobility of these miscible drive agents is no more than 50 time s that of the crude oil. Under these circumstances, a possible candidate situation for the miscible-drive type of process may exist. process may exist. Supposing that such a situation is under consideration, the next question is: what specific miscible drive process, and how should it be designed to operate? In some cases, the answer is clear: when the reservoir has a high degree of vertical communication (high permeability and continuity of the permeable, oil-bearing pore space in the vertical direction), then a gravity-stabilized miscible flood is the preferred mode of operation; and the particular drive agent or agents can be chosen on the basis of miscibility requirements, availability and cost. SPEJ P. 143
SPE MembersWWht 19S5, Sodety of Petroleum Engineera rhis paper wee prepared for presentation at the Wfh Annual Technical Conference and Exhibitionof the Sodety of Petroleum Engineers held in Laa Vegas, NV September 22-25, 19S5. mia paper waa eetected for presentation by an SPE Progrem Committee fol!owingreview of information contained in an abstract submitted by the Iuthor(s). Contenta of the peper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the !uthor(s).The material, as presented, dees not necessarily reflect any positionof the S@ety of Petroleum Engineera, its officers, or members. Papera waeentad at SPE meetings are subject to publication review by Editorial Committees of the SmXety of Petrofeum Engineera. Permission to copy is restrictedto an abstract of not more than S00 words. Illustrationsmay notbe copied. The abatract shoutdcontain conepicuouaacknowledgmentof where and by whom the paper is presented. Write Publications Manager, SPE, P.O. Sox S2SS36, Richardson, TX 7S0S24S2S. Telex, 7S0SS9 SPEDAL.
In carbonated waterflooding, carbon dioxide transfers from the injected water to crude oil lagging behind the waterflood front. When the oil viscosity is high and the carbon dioxide saturation pressure is 1,000 psi or more, the oil-phase pressure is 1,000 psi or more, the oil-phase viscosity is reduced by a factor of 5 to 20 by the dissolved carbon dioxide. We present here an extension of Welge's graphical method of calculating immiscible displacements of oil by injected gas or water. This extension takes into account the effect of interphase mass transfer on the phase mobilities. Thus it is able to represent the carbonated water displacement process. Oil displacement efficiencies obtained by this method should be supplemented by corrections for areal and vertical sweep efficiency, if predictions of oil recovery under field conditions are desired. Introduction In considering possible supplemental recovery processes for given oil fields, it is helpful to processes for given oil fields, it is helpful to establish ranges of reservoir characteristics that are required or are particularly favorable for various processes. A good example of such a classification processes. A good example of such a classification was given recently by Geffen. These ranges often have regions of overlap for two or more processes. One of the overlap regions occurs for viscous oil reservoirs, which may be candidates for waterflooding, polymer-thickened waterflooding, carbonated waterflooding, or steam flooding. In particular, for mobility ratio M = 5 or more (M = particular, for mobility ratio M = 5 or more (M = k rw o/k ro w), polymer flooding or carbonated waterflooding may be more attractive than plain waterflooding. When the oil viscosity is very high (M = 100 or more), there is no effective substitute for thermal methods such as steam drive or in-situ combustion. However, steam drive is also attractive at lower mobility ratios, despite its higher cost compared with that of waterflooding, since it produces very low residual oil saturations in the produces very low residual oil saturations in the swept zone. Hence, all of these methods may be applicable between M = 5 and M = 100. When a given reservoir appears to be a candidate for more than one process, rapid methods for estimating the comparative profitability of these processes are useful. Relatively simple methods processes are useful. Relatively simple methods have long been available for estimating process performance of waterflooding. We give below a performance of waterflooding. We give below a simple graphical method of calculating linear displacement efficiency that is applicable to polymer flooding and to carbonated waterflooding, polymer flooding and to carbonated waterflooding, as well as to waterflooding, and thus enables comparison of these three processes. The same method may be used to calculate the course of immiscible displacements of oil by a condensing or a vaporizing gas drive, given be gas/oil relative permeability curves and phase viscosities, and data on the variation of the relative permeabilities and phase viscosities as hydrocarbon intermediates are transferred between phases. While the method is described below in phases. While the method is described below in terms of carbonated waterflooding, we believe that As mode of application to gas drive with mass transfers will become apparent. A typical starting point for a simplified oil recovery estimation method is calculation of the linear oil displacement efficiency inside the swept zone of an oil reservoir. For two-phase immiscible displacements, Leverett, Buckley and Leverett, and Welge gave the essential physical analyses and mathematical methods, for the limited case of one-dimensional flow in a homogeneous porous medium. Capillary pressure forces, gravity forces, and viscous drag forces were included in Leverett's original fractional flow equation, but capillary and gravity forces have usually been neglected in simple numerical or graphical solutions. Our graphical method is a direct extension of this previous work, and is subject to the same limitations. SPEJ P. 609
A method for designing graded banks, to prevent deleterious effects of viscous fingering, was obtained by repeated application of Koval's equations, which define the dimensionless length of a fingering zone. Examples are given for miscible and polymer flooding. Introduction While it has been shown experimentally that a gradual change from a more to a less viscous injected fluid (i.e., a graded bank) can mitigate the deleterious effects of viscous fingering on areal sweep efficiency in reservoir displacement processes, it also is apparent that the rate of processes, it also is apparent that the rate of change is important. Viscous fingering occurs despite the diffusional blending of fluids occurring at the surface of the fingers. The viscous fingering process follows the stretching behavior (linearly process follows the stretching behavior (linearly growing with distance or time) of the characteristic solutions of hyperbolic, partial differential equations, while the diffusion process grows with the square root of distance or time, reflecting the parabolic nature of the partial differential equation parabolic nature of the partial differential equation describing it. Thus, viscous fingers can grow faster than the diffusion band that tends to moderate them. Attempts were made to define this competition using perturbation analysis. Chuoke's analysis for immiscible fingering was accompanied by research on miscible fluids available to me from private communication. Perrine published a private communication. Perrine published a similar linear analysis for miscible fluids that was challenged by Outmans, who published an analysis proceeding from linear (first-order) terms up to fourth-order terms. More terms indicated a more bulbous shape of developing fingers; but a relationship for the minimum wave length of perturbations that would not be eliminated by perturbations that would not be eliminated by transverse dispersion could be derived only from the linear form. Both Chuoke and Perrine obtained an equation relating a concentration gradient or viscosity gradient to this critical wave length, which enables predictions to be made for a graded bank. Chuoke's form of this equation is C = 2 [DT /u(d /dx)] 1/2..................(1) Fingers will be eliminated when C is equal to twice the maximum transverse breadth b of a linear displacement system. Substituting 2b and solving for the viscosity gradient, d 1n /dx = DT 2/ub 2.........................(2) Perrine obtained this equation in the form Perrine obtained this equation in the formdc/dx = DT 2/ub2(dln /dc).....................(3) If we multiply both sides of Perrine's equation by (d ln /dC), we get Eq. 2. Integrating, ln (2/ 1) = ln M = x DT 2/ub2...........(4) As an example, let b = 660 ft (width of a 1:1 line drive with 10 acres/well), D T = 1 x 10(-4) sq cm/sec; u = 3.528 x 10(-4) cm/sec (1 ft/D); and M = 10. We obtain x = 11 million ft (about 16,500 PV through-put) as the length required to make this mobility ratio change to avoid completely any viscous fingering, which seems unattainable in practice. Kyle and Perrine performed experiments in a 9-ft-long sand pack that explains this further. From their work, I conclude thatTo make a mobility change of 4.85:1 a graded bank length of 295 ft (33 PV) is calculated using the above equation. When this change was made in shorter (5-, 10-, or 20-ft) graded banks, viscous fingers were observed, but the fingers were successively weaker as the gradient decreased. When a graded bank 50 ft long was used, fingers did not appeal within the 9-ft length of the pack. They might have become visible had a longer pack been used.When fingers were observed, their wave length in the transverse direction was in accordance with predictions made with computer simulations based predictions made with computer simulations based on first- and second-order effects. The shapes of fingers were reasonably in accord with the simulation, although the simulated fingers were fuzzy. The fingering-zone length was not appreciably affected by displacement rate. SPEJ P. 315
The paper is presented as a discussion of the work of Simon and Kelsey on the use of capillary tube networks in reservoir performance studies. The author believes that calculation of oil recovery by the method outlined by Simon and Kelsey will give predictions that are too optimistic for reservoir-scale predictions that are too optimistic for reservoir-scale flooding processes, particularly when the mobility ratio is unfavorable. The reason for this is that the networks are too small to permit proper scaling of longitudinal and transverse dispersion effects. Hence, as early a breakthrough as will occur with fully developed viscous fingers is not observed. Introduction It appears to us that calculation of oil recovery by the method outlined by Simon and Kelsey will give predictions which are much too optimistic for reservoir-scale flooding processes, particularly when the mobility ratio is unfavorable. We believe that the principal reason for this is that the Simon-Kelsey networks are too small to permit proper scaling of longitudinal and transverse proper scaling of longitudinal and transverse dispersion effects. Hence, the authors do not observe as early a breakthrough as will occur with fully developed viscous fingers. Since the authors oil recovery predictions are too optimistic for any given degree of heterogeneity, but decrease with increasing heterogeneity, Simon and Kelsey have attributed too great a degree of heterogeneity to some of the laboratory models involved in previously reported work in attempting to match the observed recovery data. Data derived from the models themselves indicate a much lesser degree of heterogeneity. MODELLING OF PORE STRUCTURE AND THE H FACTOR The mathematical model of reservoir displacement processes described by Simon and Kelsey is related processes described by Simon and Kelsey is related to the capillary network model of pore structure devised by Fatt. However, Fatt intended his model to describe the capillary pressure and relative permeability properties of small samples of reservoir rock, rather than large-scale oil reservoirs. Fatt emphasized the relationship between the form of the network as expressed by his connectivity number, 8, and the degree of similarity of the capillary pressure and relative permeability curves for his model to those of typical reservoir rocks. Fatt found that similarity required a value of 8 in the interval from 7 to 25. This is the average number of other tubes connected to the two ends of a given tube. It means that from 4 to 13 flow channels meet at each junction, on the average. For this reason, Fatt favored the use of a triple hexagonal network (B = 10) in which six tubes meet at each junction. This judgment of natural rock pore structure is supported by more recent scanning electron microscope studies. Simon and Kelsey used the double hexagonal network (B = 7) in part of the work reported in Ref. 1; but the remainder and the second article are based on a diamond grid (B = 6). Fact also found that a reciprocal relationship between tube radius and tube length was required to simulate actual rock permeability-porosity relationships. Simon and Kelsey permeability-porosity relationships. Simon and Kelsey have instead used tubes of constant length. A wide distribution of cube radii was found by Fatt to be necessary to simulate the capillary pressure curves of consolidated porous media. Pore radius distributions are typically log-normal, and the distributions used by Fatt were of this shape. They are not flat-topped distributions such as that used by Simon and Kelsey to define a heterogeneity factor, H, as the ratio of the maximum to the minimum channel radius. However, it is easy to derive for such a flat-topped distribution that the fractional average deviation for a total number of flow channels, N, is given by the following equations: ............(1a) ............(1b) SPEJ P. 352
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