Control Model of Water Injection Into a Layered Formation
- D.B. Silin (Lawrence Berkeley Natl. Laboratory) | T.W. Patzek (U. of California at Berkeley)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- September 2001
- Document Type
- Journal Paper
- 253 - 261
- 2001. Society of Petroleum Engineers
- 3.2.3 Hydraulic Fracturing Design, Implementation and Optimisation, 5.4.1 Waterflooding, 6.5.2 Water use, produced water discharge and disposal, 4.2 Pipelines, Flowlines and Risers
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Here we develop a new control model of water injection from a growing hydrofracture into a layered soft rock. We demonstrate that in transient flow, the optimal injection pressure depends not only on the instantaneous measurements, but also on the whole history of injection, growth of the hydrofracture, and the rock damage. Based on the new model, we design an optimal injection controller that manages the rate of water injection in accordance with hydrofracture growth and the formation properties. We conclude that maintaining the rate of water injection into a low-permeability rock above a reasonable minimum inevitably leads to hydrofracture growth, to establishment of steady-state flow between injectors and neighboring producers, or to a mixture of both. Analysis of field water injection rates and wellhead pressures leads us to believe that direct links between injectors and producers can be established at early stages of waterflood, especially if the injection policy is aggressive. Such links may develop in thin, highly permeable reservoir layers or may result from failure of the soft rock under stress exerted by injected water. These links may conduct a substantial part of injected water. Based on the field observations, we now consider a vertical hydrofracture in contact with a multilayer reservoir, where some layers have high permeability and quickly establish steady-state flow from an injector to neighboring producers.
The main result of this paper is the development of an optimal injection controller for purely transient flow, and for mixed transient/steady-state flow in a layered formation. The objective of the controller is to maintain the prescribed injection rate in the presence of hydrofracture growth and injector/producer linkage. The history of injection pressure and cumulative injection, along with estimates of the hydrofracture size, are the controller inputs. By analyzing these inputs, the controller outputs an optimal injection pressure for each injector. When designing the controller, we keep in mind that it can be used either offline as a smart adviser, or online in a fully automated regime.
Because our controller is process model-based, the dynamics of actual injection rate and pressure can be used to estimate effective area of the hydrofracture and the extent of the rock damage. The latter can be passed to the controller as one of the inputs. Finally, a comparison of the estimated fracture area with independent measurements leads to an estimate of the fraction of injected water that flows directly to the neighboring producers through links or thief-layers.
Our ultimate goal is to design an integrated system of fieldwide waterflood surveillance and supervisory control. As of now, this system consists of the Waterflood Analyzer1 and a network of individual injector controllers, all implemented in modular software. In the future, our system will incorporate a new generation of microelectronic/mechanical sensors (MEMS) and actuators, subsidence monitoring from satellites,2 and other revolutionary technologies.
It is difficult to conduct a successful waterflood in a soft low-permeability rock.3-5 On one hand, injection is slow and there is a temptation to increase the injection pressure. On the other hand, such an increase may lead to irrecoverable reservoir damage: disintegration of the formation rock and water channeling from the injectors to the producers.
In this paper, we design an optimal controller of water injection into a low-permeability rock from a growing vertical hydrofracture. The objective of control is to inject water at a prescribed rate, which may change with time. The control parameter is injection pressure. The controller is based on the optimization of a quadratic performance criterion subject to the constraints imposed by the interactions between the injection hydrofracture and the formation. The inputs include histories of wellhead injection pressure, cumulative volume of injected fluid, and hydrofracture area (Fig. 1). The output optimal injection pressure is determined not only by the instantaneous measurements, but also by the history of observations. With time, however, the system "forgets," so to speak, the distant past.
The wellhead injection pressures and rates are readily available if the injection water pipelines are equipped with pressure gauges and flow meters, and if the respective measurements are appropriately collected and stored as time series. It is now a common field practice to collect and maintain such data. The measurements of hydrofracture area are not as easily available. There are several techniques described in the literature. For example, Refs. 6 through 8 develop a hydraulic impedance method of characterizing injection hydrofractures. This method is based on the generation of low-frequency pressure pulses at the wellhead or beneath the injection packer, and on the subsequent analysis of the reflected acoustic waves. An extensive overview of hydrofracture diagnostics methods has been presented in Ref. 9. Theoretical background of fracture propagation was developed in Ref. 10.
The direct measurements of the hydrofracture area with currently available technologies can be expensive and difficult to obtain. We define an effective fracture area as the area of injected water-formation contact in the hydrofractured zone. Clearly, a geometric estimate of the fracture size is insufficient to estimate this effective area.
We propose a model-based identification method of the effective fracture area from the system response to the controller action. In order to implement this method, one needs to maintain a database of injection pressures and cumulative injection. As noted earlier, such databases are usually readily available and the proposed method does not impose extra measurement costs.
Earlier we proposed4,5 a model of linear-transient, slightly compressible fluid flow from a growing hydrofracture into low-permeability, compressible rock. A similar analysis can be performed for heterogeneous layered rock. Our analysis of field injection rates and injection pressures leads to a conclusion that injectors and producers may link very early in a waterflood. Consequently, we expand our prior water injection model to include a hydrofracture that intersects multiple reservoir layers. In some layers, steady-state flow develops between the injector and neighboring producers.
As in Ref. 5, here we consider slow growth of the hydrofracture during water injection, rather than a spur fracture extension during an initial fracturing job. Our analysis involves only the volumetric balance of injected and withdrawn fluids. We do not try to calculate the shape or the orientation of hydraulic fracture from rock mechanics because they are not needed here.
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