Producer/Injector Ratio: The Key to Understanding Pattern Flow Performance and Optimizing Waterflood Design
- C.E. Hansen (EOG Resources Inc.) | J.R. Fanchi (Colorado School of Mines)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- October 2003
- Document Type
- Journal Paper
- 317 - 327
- 2003. Society of Petroleum Engineers
- 5.2 Reservoir Fluid Dynamics, 5.4.1 Waterflooding, 4.1.5 Processing Equipment, 5.4.7 Chemical Flooding Methods (e.g., Polymer, Solvent, Nitrogen, Immiscible CO2, Surfactant, Vapex), 4.1.2 Separation and Treating, 5.6.4 Drillstem/Well Testing, 5.5 Reservoir Simulation, 5.5.7 Streamline Simulation, 5.1.1 Exploration, Development, Structural Geology
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When designing a waterflood, the important aspect of processing rate with respect to pattern selection has not been addressed adequately in the literature. It has not been possible, using the existing analytical background, to determine and compare the flow-rate performance of all the patterns for any given rock/fluid (mobility) system. While general two-phase equations exist for the five-spot and line-drive patterns, flow equations for other patterns either have not been presented (e.g., the seven-spot) or are not sufficiently general (e.g., the nine-spot) to apply to all mobility conditions. A general treatment of skin effect also has not been given.
This paper presents a new, comprehensive analytical treatment of pattern flow for isotropic, homogeneous reservoirs that applies to all patterns and mobility conditions. This is made possible by a new equation for the volumetric average reservoir pressure of regularly spaced, repeated patterns. The new formulas demonstrate how the producer/injector ratio (P/I) controls reservoir pressures and flow rates and (for the first time) allow the differences in the flow capacity of patterns to be quantified. The mobility characteristics that control flow rates are described fully by a newly defined total mobility ratio, MT. The form of the new equations allows for modifications for skin effect and reservoir heterogeneity. We show how skin effect can act disproportionately with injectors and producers because of its interaction with P/I and MT.
The economics of a waterflood depend on two primary variables that engineers seek to optimize when designing a flooding scheme: (1) the processing, or throughput rate, and (2) the incremental oil recovery. Depending on the characteristics of the reservoir, one of these objectives can take a more dominant role in the determination of the optimum flooding pattern. For example, if there is significant permeability anisotropy, incremental recovery will take precedence because of its strong dependency on producer/ injector orientation. Conversely, in isotropic reservoirs, considerations of flow rate will drive pattern selection because incremental recovery in these reservoirs is largely independent of pattern type. In both types of reservoirs, an adequate recovery rate is paramount to an economically viable project.
When attempting to optimize the flow rate of waterfloods in isotropic reservoirs, however, one quickly finds that the existing literature does not provide sufficient background to accomplish this. While waterflooding has, for the most part, a well-established technical basis, the analytical development for two-phase pattern flow rates is incomplete, most notably for the seven-spot and nine-spot patterns. Also, the existing theoretical background does not identify the fundamental mechanisms controlling pattern rates. As a result, there has been an overall lack of insight into factors controlling pattern rates and the flow-capacity differences that exist between the patterns for any two-phase system. This has required that the engineer rely largely on trial and error, numerical waterflood design processes, or field-specific experience. Given that differences in flow capacity can be quite significant depending on the mobility conditions of the reservoir, a trial-and-error approach could be unpredictable and in turn have a negative effect on the economics realized from a waterflood project. Therefore, a more complete analytical understanding of pattern flow behavior is necessary to enable the more effective use of all available design tools.
This paper presents new analytical relationships describing the two-phase, steady-state flow-rate performance of repeated patterns in homogeneous, isotropic reservoir systems. These relationships represent a general, comprehensive pattern flow theory that greatly extends the range of applicability to all patterns, mobility conditions, and stages of the flood. The theoretical development is founded on a new equation for the volumetric average reservoir pressure of patterns. We show how pattern average pressures and flow rates are a function of P/I and MT. Depending on MT, substantial differences can exist in the throughput rates achievable with the different patterns. For any MT, there is a P/I that provides the highest flow capacity relative to all others. The relative differences in flow capacity become more pronounced as MT gets increasingly larger or smaller than unity. The form of the new equations also allows a general treatment of skin effect and reservoir heterogeneity. As shown, skin effect acts as an adjustment to the physical P/I; as such, the pattern flow rate can be influenced disproportionately by the skin effect of one type of well (i.e., injectors or producers) over the other.
As also presented, MT can be correlated to the endpoint mobility ratio, M, and the oil relative permeability curve shape for the prewater-breakthrough period. The correlation is based on numerical results and is useful in determining the economically optimum pattern in isotropic reservoirs using the equations presented. The new equations apply equally well to augmented waterfloods, such as polymer floods.
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