Extension of the Generalized Dykstra- Parsons Technique to Polymer Flooding in Stratified Porous Media
- Jalel E. Mahfoudhi (U. of Pittsburgh) | Robert M. Enick (U. of Pittsburgh)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Engineering
- Publication Date
- August 1990
- Document Type
- Journal Paper
- 339 - 345
- 1990. Society of Petroleum Engineers
- 5.1.1 Exploration, Development, Structural Geology, 5.4.7 Chemical Flooding Methods (e.g., Polymer, Solvent, Nitrogen, Immiscible CO2, Surfactant, Vapex), 5.2.1 Phase Behavior and PVT Measurements, 5.7.2 Recovery Factors, 5.3.2 Multiphase Flow, 5.3.4 Reduction of Residual Oil Saturation, 1.8 Formation Damage, 5.4.1 Waterflooding
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Summary. This paper presents an analytical solution for oil recovery from a stratified reservoir during a polymer flood. Although the model used in the derivation does not incorporate several of the mechanisms and characteristics of an actual polymer-flooding displacement process, the analytical solution provides some interesting information concerning the effects of slug sizes, gelling, and permeability reduction. Computational costs are very small for the program.*
The first rational analysis of immiscible piston-like displacement of oil by water in a vertically stratified reservoir was presented by Dykstra and Parsons. Graphical representations of their analytical expressions were generated by use of a multilayered system in which the permeabilities were log-normally distributed. Unfortunately, Johnson coupled these results to a severely restricted recovery correlations that greatly limited the universality of The original Dykstra-Parsons statistical work. Although this fact is implied by Craig, the Johnson representation of the Dykstra-Parsons analysis continues to permeate the literature without qualification. the original Dykstra-Parson analysis, however, remains a viable predictive technique, not only because of its analytical nature, but also because of its ability to generate results that agree favorably with numerical simulation techniques.
Reznik et al. generalized the discrete Dykstra-Parsons analysis by extending it to a continuous, real-time basis. Enick et al. also presented graphical representations of these continuous real-time solutions to reservoirs exhibiting log-normal permeability distribution.
Furthermore, Stevens completed a semianalytical investigation of the effect of a trailing zone on the generalized Dykstra-Parsons technique. El-Khatib presented analytical solutions for the secondary waterflooding of reservoirs consisting of completely com-municating layers.lthough the waterflooding process in stratified reservoirs has been thoroughly studied, no analytical techniques exist that describe the performance of other EOR techniques in the same type of reservoir. Of these EOR techniques, the polymer-flooding process is the first logical choice to analyze with an extended generalized Dykstra-Parsons technique because it does not reduce the waterflood residual oil saturation (ROS); hence, no oil bank will form, and the aqueous polymer slug is incompressible.
Polymer solutions are injected into a reservoir to improve vertical and areal (and hence volumetric) sweep efficiency relative to a conventional waterflood. Two primary mechanisms account for the EOR obtained by polymer flooding in stratified reservoirs. 10 First, a decrease in the mobility of the displacing fluid results in a more piston-like displacement mechanism. Areal sweep is also often found to be improved because finger formation is inhibited as the mobility of the displacing fluid decreases. The second mechanism is a reduction in reservoir heterogeneity. In a polymer flood, the polymer slug preferentially flows into the high-permeability zones. Polymer retention, caused by adsorption and entrapment, reduces the absolute permeability of the layer. Because reduction is proportional to polymer-slug size, the high-permeability zones exhibit the greatest decreases in absolute permeability behind the polymer slug. As a result, the variation of the reservoir is reduced, and subsequently injected drive water is distributed more evenly between layers. Flow through watered-out zones decreases, while the injection rate into previously underswept beds increases.
Currently, no analytical technique is available that provides an exact, continuous prediction of the performance of a linear polymer flood in a stratified reservoir on a real-time basis, even for simplistic models. An exact, continuous, analytical, real-time solution can be obtained if a very simple model of the process is used.
The model used to describe the polymer flood is subject to the following constraints and assumptions. Note that the assumptions implemented in this model enable the derivation of an analytical solution that can predict polymer-slug distribution and oil recovery. It does not provide an accurate description of microscopic flow through a porous medium, but rather a very rough estimate of overall polymer-flood performance and trends that would occur if a parameter such as polymer-slug size was changed.
1. The reservoir is horizontal and composed of a finite number of distinct, parallel layers or beds.
2. Both the spatial and dynamic bed/fluid properties are homogeneous in a given bed.
3. The values of these spatial and dynamic bed/fluid properties may vary from layer to layer.
4. No crossflow exists between layers.
5. Communication between beds exists only at the injection and production surfaces.
6. The total pressure drop is identical for each bed at any moment of time, whether or not the value changes as a function of time.
7. Free-gas saturation is accounted for by the method used by Schauer II and elucidated by Craig. The heterogeneity statistic, the Lorenz coefficient, is used to determine the fraction of the initial gas PV that has to be filled with the invading water before the water will impose a pressure on the oil. This gas-fill-up period simply delays the waterflood or polymer flood and is accounted for by superposition.
8. The sequence of injection fluids is as follows: (1) waterflood this secondary technique typically continues until a specified water cut, coverage, or injected PV has been obtained; (2) polymer slug-a specified total PV fraction usually is injected; and (3) drive fluid-brine usually is injected again after the polymer slug for economic and injectivity purposes.
9. Permeability reduction resulting from polymer adsorption and entrapment is accounted for empirically by reducing the absolute permeability of the bed behind the polymer slug. This reduction is usually proportional to the size of the slug that enters the layer.
10. This model will not account for degradation of a polymer slug, inaccessible PV, viscoelastic effects, and polymer loss from retention.
11. In-situ polymerization or gelling is modeled empirically by changing the polymer-slug viscosity at any time.
12. Fluid flow is unsteady-state but piston-like.
13. Fluid flow is always Darcian. Although most commercial polymers are pseudoplastic fluids that exhibit larger apparent viscosities when flowing at low velocities, they are modeled as Newtonian fluids that can be described by a single viscosity. This viscosity may be determined as an average value over the range of shear rates that may be encountered.
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