Co-optimization of enhanced oil recovery and carbon sequestration
Introduction
There is a growing consensus in both policy circles and in the energy industry that within the next few years, the US Federal government will adopt some form of regulation of CO2 emissions. At the same time, it is widely believed that much of the nation's energy supply over the coming decades will continue to come from fossil fuels, coal in particular (MIT, 2007). Many analysts believe the only way to reconcile the anticipated growth in the use of coal with anticipated limits on CO2 emissions is through the development and deployment of carbon capture and geological sequestration (CCS). There also seems to be agreement that deployment of geological sequestration is likely to start with projects that apply CO2-enhanced oil recovery (EOR).1 This technique, which has been used successfully in a number of oil plays (notably in West Texas, Wyoming, and Saskatchewan), entails injection of CO2 into mature oil fields at pressures high enough to cause the CO2 to mix with some fraction of the oil that still remains underground. Doing so reduces the oil's viscosity, thereby improving its ability to flow through the reservoir rock, and enhancing the rate of extraction.2 Although some of the CO2 resurfaces with the oil, it can be separated from the output stream, recompressed, and reinjected. Eventually, when the EOR project is terminated, much of the injected CO2 remains sequestered.3 EOR has the potential of greatly increasing oil output from depleted reserves. Estimates suggest that recovery rates for existing reserves could be approximately doubled, while the application of EOR on a broad scale could raise domestic recoverable oil reserves in the United States by over 80 billion barrels (ARI, 2006). Similarly, Shaw and Bachu (2003) claim that 4470 fields, just over half of the known oil reservoirs in Alberta, Canada, are amenable to CO2 injection for enhanced oil recovery. Babadagli (2006) states that enhanced oil recovery applied in these reservoirs could translate into an additional 165 billion barrels of oil recovered and over 1 Gt of CO2 sequestration. Snyder et al. (2008) estimate that at current oil and carbon prices and with current technology, approximately half of this capacity is economically viable.
In this paper, we analyze a price-taking producer's problem of optimally extracting oil from a given field when extraction is subject to a realistic, physical constraint on the rate at which oil can be produced. In this sense, the setup of our model is similar to that in Cairns and Davis (2001) as well as to the manner in which oil-industry practitioners tend to model the producer's decision problem.4 Cairns and Davis focus, however, on physical constraints that arise during the so-called primary or secondary stages of oil recovery from a field. The primary stage utilizes the reservoir's natural pressure to bring oil to the surface, and during this stage (which typically extracts about 5–20% of the total oil originally present in the reservoir) the decline in pressure over time constrains the rate of oil production. The secondary stage involves injection of water into the reservoir to augment or maintain pressure. During this stage (which typically extracts another 10–30% of the oil) maximum production declines over time because water is progressively less able to “flush” additional oil out of tiny connected pore spaces in the reservoir rock. In both stages, once a producer has developed a field (i.e., put wells and other equipment in place), the decline rate of maximum oil production is essentially exogenous. By contrast, during EOR, which is typically applied in a tertiary stage, the producer is able to affect the rate at which oil production declines by varying the rate of CO2 injection. This ability effectively endogenizes the physical constraint and complicates the producer's problem in a number of non-trivial ways.
First, CO2 is not a costless input. Significant up-front investments are required to make production and injection wells suitable for CO2 use. In addition, maintaining a given injection rate over time requires continuous purchases to make up for the fraction of injected CO2 that is retained in the reservoir. Separating the remaining fraction that resurfaces with the produced oil, and then dehydrating and recompressing it, is costly as well.
Second, even at a constant injection rate, the decline in oil recovery over time implies a similar decline in the fraction of injected CO2 that is retained in the reservoir. Both the producer's revenue stream and cost stream are therefore time varying.
Third, while sequestration of CO2 currently yields no economic benefits in jurisdictions without carbon emissions restrictions, future regulations of CO2 emissions in the context of climate-change policies may generate such benefits if EOR projects are allowed to earn credits for units of CO2 sequestered. The producer will then receive revenue streams from both oil production and CO2 sequestration.
Fourth, carbon policies affect the producer's revenue and cost streams in multiple ways. While a carbon tax (or an equivalent tradeable permit scheme – hereafter we take this equivalency as understood) effectively reduces the input cost for EOR and increases the value of the CO2-storage potential of the oil field, the incidence of the tax on the price of oil reduces the value of the traditional use of the asset.
Fifth, in addition to these economic tradeoffs, fluid-dynamic interactions of CO2, water, and oil inside the reservoir give rise to a further, physical tradeoff faced by the producer. Whereas injecting pure CO2 maximizes oil recovery from the area of the reservoir that the CO2 sweeps through, that area itself may be small, as pure CO2 tends to “finger” or “channel” between injection and production wells, bypassing some of the oil. In comparison, injecting pure water increases the area that is swept, but reduces recovery from that area. Reservoir-engineering studies indicate that both oil recovery and CO2 sequestration are maximized when a mix of CO2 and water is injected (though the CO2 fraction that maximizes oil recovery typically differs from that which maximizes sequestration).5
These five factors combined present the producer with a problem of co-optimizing oil production and CO2 sequestration. Three earlier studies have investigated different components of this problem. Kovscek and Cakici (2005), for example, use a reservoir simulation model to investigate the impact of varying the fraction of CO2 in the injection stream. However, their analysis is limited by the choice of objective function (an arbitrary weighted sum of cumulative oil recovery and cumulative CO2 sequestration) and by the imposition of an exogenous termination time. McCoy and Rubin (2009), on the other hand, explicitly optimize the termination time to maximize an EOR project's net present value at different oil and CO2 prices. However, they do not allow for an endogenously selected fraction of CO2 in the injection stream, assuming instead that it is exogenously set at 100%. Finally, in a recent working paper, Bandza and Vajjhala (2008) compare four CO2 injection strategies that producers might choose: focus on profits from oil production alone; on profits from sequestration alone; on profits from oil production with sequestration profits considered only later, as an “afterthought”; or on combined profits from oil production and sequestration from the outset. While Bandza and Vajjhala pay attention to the role of prices, there is no explicit model of dynamic optimization – a shortcoming shared by all three papers. By considering how the operator of an EOR project might maximize the project's net present value through its choice of the optimal time path of the fraction of CO2 in the injection stream, as well as the optimal time to terminate the project, our paper addresses this shortcoming in the extant literature.
We start by analyzing the dynamic co-optimization problem theoretically, using an optimal control framework in which the CO2 fraction in the injection stream is the control variable, the stock of oil remaining in the reservoir is the state variable, and the terminal time is determined by a transversality condition. Using this model, we find that the optimal CO2 fraction will typically decline over time, and may eventually drop to zero before it becomes optimal to terminate the project.
Next, we conduct a series of simulations of the model, after calibrating it to an ongoing EOR project, namely the Lost Soldier-Tensleep project in Wyoming. The simulations generate time paths of CO2 injection and implied time paths of oil production and CO2 sequestration, for a range of oil prices and carbon taxes. A key finding is that cumulative sequestration is more responsive to the oil price than to the price of carbon.
Section snippets
The model
Our model of oil production is based on the physical reality that input injections (water, gas, or some mixture of the two) must balance with fluid output (oil, water, and gas).6 In addition, the rate of oil
Analysis
In the context of our model, the firm's choice variables are the time path of the CO2 fraction c(t) in its injection stream (or equivalently, by our normalization that qi = 1, the time path of the CO2 injection rate ), the terminal time T at which to cease injection altogether, and the resulting terminal state R(T). Note that, by Eqs. (2), (3), the firm's choice of c(t) directly determines both its oil production rate and CO2 sequestration rate . The firm's goal is to maximize
Simulation framework
In order to add greater context to the results derived above, we have implemented the model numerically to solve for optimal time paths of carbon injection and oil production at various combinations of the oil price and carbon tax. Specifically, we compute the solution for scenarios with oil prices of $50, $100, $150, and $200 per barrel (bl), taking $100/bl as our baseline price,21
Simulation results
The first element of behavior that we wish to define is the optimal extraction and sequestration path for our benchmark assumptions. Here, we use an oil price of $100 with no carbon tax. Panel (a) of Fig. 2 shows the optimal paths of CO2 injection , CO2 production , oil production , and flow CO2 sequestration .
The optimal initial injection rate is 0.485 million barrels/year, somewhat smaller than either the instantaneous oil-production maximizing rate of 0.625 or the myopic
Conclusion
In this paper, we have examined how the standard resource-economics problem of optimizing the rate of oil extraction from a field is altered when the producer has the option of increasing the rate of oil extraction through continuous injections of a mix of CO2 and water into the reservoir. Our focus in the paper is on the producer's problem of determining the optimal CO2 fraction in the injection stream and thus the effects of carbon taxes and oil prices on oil production and carbon
Acknowledgement
This research was funded in part by the U.S. Department of Energy and the National Energy Technology Laboratory through Award number: DE-FC26-05NT42587. The authors thank, without implicating, participants at the NBER Summer Institute workshop on Energy and Environmental Economics, an anonymous referee and the Editor for constructive comments.
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