Sweep Efficiency in Miscible Displacement in A Five-Spot Pattern

1967 ◽  
Author(s):  
S.M. Farouq Ali ◽  
C.D. Stahl
Keyword(s):  
Miscible Displacement ◽  
Spot Pattern ◽  
Sweep Efficiency

The Effects of Isolated Permeability Interferences on the Sweep Efficiency and Conductivity of a Five-Spot Network

1967 ◽  
Vol 7 (01) ◽  
pp. 20-30 ◽  
Author(s):  
Rafael J. Sandrea ◽  
S.M. Farouq Ali
Keyword(s):  
Porous Medium ◽  
Homogeneous Medium ◽  
Simple Expression ◽  
Computational Scheme ◽  
Critical Parameters ◽  
Quantitative Prediction ◽  
Spot Pattern ◽  
Sweep Efficiency ◽  
Visual Model ◽  
Physical Limitations

Abstract The results of an experimental and theoretical study of the effects of rectilinear impermeable barriers and highly permeable channels on the sweep efficiency and conductivity of a five-spot network are presented. The study was carried out using Hele-Shaw and conductive sheet analogs for both normal and inverted flood patterns. A functional relationship was developed which provides quantitative prediction of the above parameters; i.e., sweep efficiency and conductivity, for the nonhomogeneous system. To evaluate this, it is necessary only to measure the interference modulus of the obstacle using a simple expression. The results indicate that impermeable barriers, with an interference modulus greater than zero, always cause a decrease in the conductivity and the sweep efficiency of the pattern. On the other hand, permeability channels do not have a significant effect on these parameters, unless they are located along the streamlines. The study also discusses a method of formulating the difference equations pertaining to the two-dimensional Laplacian in a system containing rectilinear barriers. In addition, a technique is described for tracing the progress of a free surface, using marked particles, in a stream containing discontinuities such as those occurring at the extremities of barriers. The above computational scheme was used in a digital computer program to simulate results of the Hele-Shaw analog. The computed values of sweep efficiency were in good agreement with the experimental values. INTRODUCTION At the present time waterflooding remains the most widely used technique for the secondary recovery of oil. Among the numerous factors that affect the performance of a waterflood, the areal sweep efficiency constitutes one of the most critical parameters. It is a function only of the geometric distribution of the wells for a homogeneous medium and unit mobility ratio. Geological considerations, however, such as the presence of sealing faults or solution channels in the rock matrix, would generally exert an adverse effect on the areal sweep efficiency of a waterflood network. Surprisingly little information is presently available1-3 on the quantitative implications of such permeability interferences. It was the object of this investigation to consider the presence of rectilinear, impermeable and highly permeable interferences in an otherwise homogeneous five-spot pattern, and to analyze their effects on the resulting sweep efficiency and pattern conductivity. The experimental phase of the study was conducted using two different models: the Hele-Shaw flow cell and the field plotter. For experimental convenience, the geometric boundaries of the five-spot were assumed to constitute streamlines even in the case where the interference was asymmetrically placed with respect to a repeated five-spot pattern. A second object of the study was to develop a computational scheme for numerically calculating the pressure distribution in a five-spot flow pattern containing rectilinear, impermeable barriers, and to use this distribution to compute the sweep efficiency. EXPERIMENTAL PROCEDURE HELE-SHAW ANALOG The Hele-Shaw analog was used both as a visual model and for determining the sweep efficiency for systems involving impermeable barriers. The physical limitations of this model as a means of experimentally studying the motion of a fluid in porous medium have been adequately discussed elsewhere.2,7 Likewise, it can be easily verified that the analogy remain s valid when a portion of the region between the plates contains an obstacle of the same thickness as the distance between the plates.4 HELE-SHAW ANALOG The Hele-Shaw analog was used both as a visual model and for determining the sweep efficiency for systems involving impermeable barriers. The physical limitations of this model as a means of experimentally studying the motion of a fluid in porous medium have been adequately discussed elsewhere.2,7 Likewise, it can be easily verified that the analogy remain s valid when a portion of the region between the plates contains an obstacle of the same thickness as the distance between the plates.4

Areal Sweep Efficiency of Pseudoplastic Fluids in a Five-Spot Hele-Shaw Model

1968 ◽  
Vol 8 (01) ◽  
pp. 52-62 ◽  
Author(s):  
K.S. Lee ◽  
E.L. Claridge
Keyword(s):  
Porous Medium ◽  
Oil Recovery ◽  
Polymer Solutions ◽  
Newtonian Fluids ◽  
Mobility Ratio ◽  
Spot Pattern ◽  
Sweep Efficiency ◽  
Flood Water ◽  
Miscible Displacements ◽  
Connate Water

Abstract Areal sweep efficiency of oil displacement by enhanced-viscosity water exhibiting pseudoplastic behavior was measured in a Hele-Shaw model representing one-quarter of a five-spot pattern. The pseudoplasticity of polymer solutions and the velocity distribution in the five-spot pattern produced a condition under which the mobility ratio between the displacing and the displaced fluid could not be assigned a single value. Instead, the movement of the displacement front is governed by local mobility ratios which are also time dependent. The areal sweep at breakthrough with polymer solutions was poorer than the sweep obtained with Newtonian fluids of comparable viscosity. However, the areal sweep and 1 PV throughput was greatly improved as compared to flood water without polymer. It was also demonstrated that, even after the oil-cut had declined to a low value during a regular waterflood, switching to polymer flood efficiently swept out the oil remaining in the model. Introduction The behavior of fluid displacements in isotropic porous media for various patterns of injection and production wells has been extensively investigated. These investigations all concerned Newtonian fluids, i.e., the viscosity of each fluid was constant regardless of flow rate. The generally unfavorable influence on areal sweep efficiency of higher mobility of the displacing fluid as compared to the mobility of the displaced fluid has been established for both miscible and immiscible fluids. The principle was also established that a close correspondence exists between miscible and immiscible flood front behavior, although oil recovery in a waterflood at unfavorable mobility ratio may be less than that observed in a miscible displacement at the same mobility ratio. This is true even when oil recovery is expressed on the basis of movable oil. The reason is that oil saturation only slowly achieves its final value behind the waterflood front in accordance with the Buckley-Leverett simultaneous flow relations. It is convenient to use miscible displacements for laboratory simulation of waterflood frontal advance since the interfacial tension forces which are negligible in proportion to viscous forces on a reservoir scales are thus made nonoperative in the laboratory model. For miscible displacements, the Hele-Shaw type of model adequately represents a porous medium so long as the appropriate scaling rules are observed in its design and operation. During simulation of waterflood front behavior in the laboratory by using miscible displacements, the behavior of connate water may ordinarily be disregarded since it is usually indistinguishable from flood water in this process. However, when the flood water is deliberately thickened to improve the mobility ratio between water and oil, the effect on the sweep efficiency due to generation of a connate water bank during the process must be considered. In a uniform porous medium, such a bank is generated and efficiently displaced by injection of thickened water. The oil originally in-place at the start of the waterflood is then displaced by connate water followed by thickened water. If the flood water must be thickened to obtain a favorable mobility ratio, the mobility of the oil phase is appreciably less than that of the connate water. Hence, the oil phase is inefficiently displaced by the connate water bank, and a considerable proportion of the oil comes in contact with and is displaced by the thickened waterflood front. SPEJ P. 52ˆ

The Use of Capillary Tube Networks in Reservoir Performance Studies: 1. Equal-Viscosity Miscible Displacements

1971 ◽  
Vol 11 (02) ◽  
pp. 99-112 ◽  
Author(s):  
Ralph Simon ◽  
F.J. Kelsey
Keyword(s):  
Flow Behavior ◽  
Three Dimensional ◽  
Reservoir Rock ◽  
Reservoir Engineering ◽  
Interconnected Network ◽  
Spot Pattern ◽  
Capillary Tubes ◽  
Sweep Efficiency ◽  
Miscible Displacements ◽  
Electrical Resistivities

Abstract This paper concerns the use of network principles to study displacement phenomena in porous media. The information presented is for equal-viscosity, equal-density miscible displacements. The paper explains the reasons for using an interconnected network of capillary tubes to model the interconnected network of pores in a reservoir rock. A method is presented for defining the heterogeneity of a presented for defining the heterogeneity of a network of tubes based on tube-size and tube-location distribution functions. A technique is described for constructing a network whose heterogeneity models the heterogeneity of pores in a reservoir rock. The use of networks to provide information which can be used in the solution of reservoir engineering problems is illustrated with example calculations of the effect of heterogeneity on fingering, breakthrough, and selective plugging in linear systems, and the effect of heterogeneity on areal sweep efficiency in a five-spot pattern. Introduction Oil in a reservoir is contained in an interconnected three-dimensional network of pores. Direct evidence of the nature of this network of pores comes from examination of petrographic thin sections and three dimensional Scanning Electron Microscope (SEM) pictures of the pores. The SEM pictures show that the pores in a reservoir rock are channels through which flow can occur. These channels have highly irregular configurations so irregular that it is not practical at this time to calculate flow behavior through individual channels or through the interconnected network of the channels. It is practical, however, to use a computer to calculate flow behavior in an interconnected network of capillary tubes and several investigators have studied the problem of using a network of tubes to model a network of pores. pores. Fatt pioneered the idea of using a network of cubes model for reservoir engineering studies. He demonstrated that capillary pressures, relative permeabilities, and electrical resistivities permeabilities, and electrical resistivities calculated for a network model have the same characteristics as those measured for real pores in reservoir rocks. From this, Fatt concluded that the network of tubes is a valid model of real porous media. Rose reinforced Fatt's conclusion and showed that computers can be used to study the displacement characteristics of networks and to obtain results "…which can be supposed to have a direct bearing on the mechanics of petroleum recovery…" This paper takes two steps beyond the work of Fatt and Rose. First, it describes a technique for constructing a network whose heterogeneity models the heterogeneity of natural pores. This is done by matching calculated equal-viscosity miscible displacement behavior in the network with measured behavior in a laboratory core. Second, it illustrates the use of the network model for calculating the effects of heterogeneity on fingering, breakthrough, and plugging in linear systems and areal sweep efficiency in a five-spot pattern. The networks used in the studies in this paper consist of several hundred interconnected capillary tubes of different sizes. Four different types of connections or configurations were investigated and are shown below. These configurations are discussed in detail later in the paper. SPEJ P. 99

Effect of Isolated Vertical Fractures Existing in the Reservoir On Fluid Displacement Response

1966 ◽  
Vol 6 (01) ◽  
pp. 81-86 ◽  
Author(s):  
J.W. Givens ◽  
Paul B. Crawford
Keyword(s):  
Gas Injection ◽  
Great Influence ◽  
Dimensionless Time ◽  
Spot Pattern ◽  
Sweep Efficiency ◽  
Copper Strip ◽  
Vertical Fracture ◽  
Fluid Displacement ◽  
The Matrix ◽  
Vertical Fractures

Abstract A potentiometric model study has been made of the effect of vertical fractures existing in the matrix of the reservoir on the flooding or cycling performance. Fractures can have unusual flow characteristics. Fluid entering one side of a fracture can emerge on either the same or opposite side of the fracture, depending on the particular streamline. Fracture orientation has a great influence on the sweep efficiency. However, sustained fluid injection may still permit large areas to be swept. Introduction One can find considerable information available in the literature on the effect of fractures originating at the wellbore on sweep efficiencies of waterflooding or gas cycling programs. However, there are few, if any, quantitative data reported in the literature on the effect of vertical or horizontal fractures existing out in the reservoir matrix on secondary recovery performance. Several papers have been presented on the effect of vertical and horizontal fractures on the productivity or conductivity of waterflood and gas injection patterns, but in all cases the fractures initiated at the well and simulated commercial fractures. It is believed that natural fractures may exist out in the reservoir matrix and would effect the displacement performance. The purpose of this report was to study the effect of a few isolated vertical fractures existing out in the reservoir matrix on the performance of waterflood or gas injection patterns. DESCRIPTION AND EQUIPMENT Since the potentiometric model was described by Lee it has been widely used to study numerous types of fluid displacement problems. The potentiometric model can be used for fluid displacement studies when the following assumptions are valid:(a) steady-state conditions exist;(b) the mobility ratio is one; and(c) the capillary and gravitational effects can be neglected. Five-spot and direct line drive square patterns were studied using a copper strip of the desired length and orientation to simulate a vertical fracture in the reservoir matrix. The 20 x 20-in. model was considered to represent only one element of an infinite array of similar patterns. DISCUSSION AND RESULTS FIVE-SPOT PATTERN ONE FRACTURE BETWEEN INJECTION AND PRODUCING WELLS Fig. 1 shows a quadrant of a five-spot pattern with the vertical fracture existing out in the matrix along a line connecting the injection and producing wells. Length of the fracture was equal to 35.4 per cent of the distance between injection and producing wells. In this particular pattern it is noted that fluid breaks through from the injection well to the producing well when the dimensionless time is equivalent to 26.9. Dimensionless time is defined as volume of fluid injected divided by the volume of displaceable fluid in the pattern expressed as a per cent. SPEJ P. 81ˆ

Investigation of Anisotropic Mixing in Miscible Displacements

2013 ◽  
Vol 16 (01) ◽  
pp. 85-96 ◽  
Author(s):  
Olaoluwa O. Adepoju ◽  
Larry W. Lake ◽  
Russell T. Johns
Keyword(s):  
Oil Recovery ◽  
Dispersion Model ◽  
Flow Direction ◽  
Miscible Displacement ◽  
Scale Model ◽  
Local Concentration ◽  
Fine Scale ◽  
Sweep Efficiency ◽  
Transverse Mixing ◽  
Transverse Dispersivity

Summary Dispersion (or local mixing) degrades miscibility in miscible-flood displacements by interfering with the transfer of intermediate components that develop miscibility. Dispersion, however, also can improve oil recovery by increasing sweep efficiency. Either way, dispersion is an important factor in understanding miscible-flood performance. This paper investigates longitudinal and transverse local mixing in a finite-difference compositional simulator at different scales (both fine and coarse scale) using a 2D convection-dispersion model. All simulations were of constant-mobility and -density, first-contact miscible flow. The model allows for variations of velocity in both directions. We analyzed local (gridblock) concentration profiles for various miscible-displacement models with different scales of heterogeneity and permeability autocorrelation lengths. To infer dispersivity, we fitted an analytical 2D convection-dispersion model to the local concentration profile to determine local longitudinal and transverse dispersivities simultaneously. Streamlines of simulation models were traced using the algorithm proposed by Pollock (1988). To our knowledge, this is the first systematic attempt to numerically study local transverse dispersivity. The results show that transverse mixing, which is usually neglected in the 1D convection-dispersion model of dispersion, is significant when the flow direction changes locally as a result of heterogeneity. The computed streamlines, which highlight the variation in flow directions, agree with the computed transverse-dispersivity trends. We find that both transverse and longitudinal dispersion can grow with travel distance and that there are several instances in which transverse dispersion is the larger of the two. Often, the variations in the streamlines are suppressed (homogenized) during upscaling. This paper gives a quantitative and systematic procedure to estimate the degree of transverse mixing (dispersivity) in any model. We conclude that local mixing, including transverse mixing, should be considered when upscaling a fine-scale model for miscible displacement to ensure proper preservation of fine-scale sweep and displacement efficiency and ultimate oil recovery for miscible-displacement simulations.

Sweep Efficiency by Miscible Displacement in a Five-Spot

1966 ◽  
Vol 6 (01) ◽  
pp. 73-80 ◽  
Author(s):  
J.L. Mahaffey ◽  
W.M. Rutherford ◽  
C.S. Matthews
Keyword(s):  
Oil Recovery ◽  
Parallel Plate ◽  
Molecular Diffusion ◽  
Miscible Displacement ◽  
Sweep Efficiency ◽  
Miscible Displacements ◽  
Model Studies ◽  
Convective Mixing ◽  
Plate Spacing ◽  
Diffusion Effects

Abstract This paper gives results of an experimental study of the sweep efficiency of a miscible displacement in a five-spot. The study was carried out in a parallel-plate glass model in which effects of diffusion were scaled at or near the molecular diffusion level. The experiments show that very early breakthrough (25 to 35 per cent of pore volume (PV) injected) may be expected in miscible floods because of the unfavorable viscosity ratio. However after 1 PV of displacing fluid is injected, the sweep rises to a reasonable value (50 to 60 per cent). Photographs show that small slugs of less than 10 per cent of PV tend to dissipate before breakthrough. A minimum slug size of 15 per cent of PV would appear to be necessary even in a relatively homogeneous formation. Presence of a slug whose viscosity is intermediate between that of oil and gas increases the sweep efficiency of the oil-gas system. In a typical system the sweep at breakthrough rose from 26 to 37 per cent of PV for a 25 per cent slug. The increase in sweep brought about by use of a large slug could well pay for the extra deferment cost of the additional slug material. Introduction Most miscible displacement processes involve the displacement of oil with fluids of much lower viscosity and density. The displacement process at these adverse viscosity and density ratios is dominated by instability phenomena, i.e., viscous fingers and gravity tongues. These phenomena have highly adverse effects on oil recovery. Although a number of laboratory studies have been made to determine the effect of adverse viscosity ratios on five-spot sweep patters,1,2 the scaling of diffusion effects is uncertain. In the series of scaled model studies reported herein, an attempt was made to scale diffusion. Model studies of miscible displacements in which molecular diffusion predominates are permitted by controlling the parallel plate spacing which reduces convective mixing to arbitrarily small levels. To decide how this scaling relates to any particular field displacement necessitates an estimation of diffusion effects for the natural rock being considered and conditions under which displacement will be conducted. The approach normally taken is to extrapolate data obtained from stable miscible displacements performed in the laboratory, such as those presented by Brigham et al.3 The validity with which such an extrapolation can be applied to an unstable flow system has yet to be established. If this approach is accepted, a family of oil recovery curves can be generated for a single viscosity ratio based on Brigham's observation that the magnitude of the dispersion coefficient is dependent, among other things, upon specific rock properties. Objective of our test was to define the lower limit of this range by presenting the case where dispersion effects were reduced to the molecular diffusion level in both the transverse and longitudinal directions. The scaling of diffusion effects can be handled in two-dimensional systems by the usse of narrow-gap, parallel-plate models. In parallel-plate models the Taylor diffusion coefficient for convective mixing in the direction of flow at low flow rates is given by (following Taylor4):Equation 1 where h is the plate spacing and D is the molecular diffusion coefficient. Clearly, convective mixing can be reduced to arbitrarily small levels by manipulating the gap spacing h. This was the method used in these studies.

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