Wilko Rohlfs

Valuation of CCS-ready coal-fired power plants: a multi-dimensional real options approach

In this paper, we develop a multi-factor real options model for a two-stage investment problem where a coal-fired power plant is later retrofitted with carbon capture and storage (CCS). A capture-ready power plant with lower retrofit costs is compared with a conventional one and higher CCS retrofit costs. The stochastic variables considered are the price of electricity, the price of CO2 permits, capturing, transporting and storing (CTS) costs and CCS retrofit investment costs. Fuel costs are disregarded due to the constant boiler size in case of a retrofit, resulting in constant fuel consumption but lower electricity output of the CCS plant. Two retrofit options that reduce the power plant’s net efficiency from 46% to 30% and 35%, respectively, and an integrated CCS power plant with an efficiency of 38.5% are investigated. In a numerical simulation with realistic parameterization, we find a low probability for a retrofit even after fifteen to twenty years, caused by the high uncertainty and the adverse impact of the electricity price and the CO2 permit price. This renders the capture-ready option unattractive and calls for investments in conventional coal-fired power plants with later CCS investments at higher costs than for the case of a capture ready pre-installation.

Cost Effectiveness of Carbon Capture-Ready Coal Power Plants with Delayed Retrofit

In this paper we investigate the cost effectiveness of coal-fired CCS plants. Two different model approaches are used. First, we consider marginal costs to determine the impact of fuel and CO2 certificate prices on electricity generation cost. Second, we apply a net present value evaluation to identify the main factors influencing the NPV, using projections for the price of electricity and CO2 as well as the costs of capturing, transporting and storing CO2. The NPV assessment shows that the threshold price of CO2 is highly sensitive with respect to the electricity price. Incorporating the possibility to postpone the CCS investment leads to much higher threshold prices, rendering the investment less attractive from today’s perspective. Finally, with a risk-adjusted discount rate for all CCS options it turns out to be more attractive than with a predefined discount rate of 10%, providing evidence that typical practitioner’s assumtions may indeed be too pessimistic.

Challenges in the Evaluation of Ultra-Long-Lived Projects: Risk Premia for Projects with Eternal Returns or Costs

The economic evaluation of ultra-long-lived investment projects is not only challenging due to the choice of the planning horizon but also due to the discounting of future uncertain cash flows. Thus, for real world investment decisions a better understanding of the project’s risks and their effect on the project’s value is crucial. If long-term investments are modeled, stochastic processes may be used to reflect the uncertain development of future prices and cash flows. The choice of the stochastic process is consequently an essential assumption in the modeling process. This paper critically discusses the risk of ultra-long-lived investment projects implied if future pay-off’s are assumed to follow geometric Brownian motion processes. In our analysis, we distinguish between projects driven by costs and such driven by revenues. For both kind of projects we compare the value at risk with the returns of a risk-free asset. Therein, the value at risk describes the threshold value of the confidence levels of the uncertain cash flow’s probability density function. The comparison for long time horizons shows that the lower confidence interval exceeds the returns of a risk-free asset used as a benchmark for any choice of the confidence level, which implies that the returns of a “worst-case” scenario (within the assumed confidence interval) will still exceed the returns of a risk-free asset in the long-term perspective. For the case of uncertain future cost, the risk measure is defined as the difference between the expected value and the boundary of the confidence interval. This value is also found to become negative in the long-term perspective.

Optimal Power Generation Investment: Impact of Technology Choices and Existing Portfolios for Deploying Low-Carbon Coal Technologies

In this paper we identify optimal strategies for the investment in power generation assets. The investments are characterized by multiple available technologies whose economic value is driven by a technology-specific combination of several underlying assets, such as the price of fuel, electricity, and CO2. The correlation between the development of those underlying assets allows for diversification and thus to reduce the overall risk by holding a portfolio of different technologies. This yields an investor-dependent strategy for the deployment of new energy generation assets. The modeling framework developed is based on stochastic real options analysis that enables to account for the additional value of waiting which arises from uncertain commodity price development. In the presentation, we increase the model’s complexity stepwise, in order to depict the influences of various aspects, as for instance the interaction of technologies, value of waiting, or modification of an existing power plant portfolio. We find that including the value of waiting in the decision process not only delays the investment but also leads to an asymmetric risk distribution which features a much lower probability for losses. In addition, the results where the value of waiting is incorporated are more robust with respect to a variation of the investor’s risk- and time-preferences compared to the results gained with the classical net present value model. Finally, we investigate the required market conditions needed for the deployment of carbon capture and storage (CCS) technologies. We find that a carbon dioxide price of 60 e/tCO2 and an electricity price of 70 e/MWh is required in the year 2015 in order to reach a probability of at least 50% for the deployment of CCS in 2022.

Critical inclination for Absolute/Convective instability transition in inverted falling films

Liquid films flowing down the underside of inclined plates are subject to the interaction between the hydrodynamic and the Rayleigh-Taylor (R-T) instabilities causing a patterned and wavy topology at the free surface. The R-T instability results from the denser liquid film being located above a less dense ambient gas, and deforming into an array of droplets, which eventually drip if no saturation mechanism arises. Such saturation mechanism can actually be provided by a fluid motion along the inclined plate. Using a weighted integral boundary layer model, this study examines the critical inclination angle, measured from the vertical, that separates regimes of absolute and convective instability. If the instability is of absolute type, growing perturbations stay localized in space potentially leading to dripping. If the instability is of convective type, growing perturbations move downwards the inclined plate, forming waves and eventually, but not necessarily, droplets. Remarkably, there is a minimum value ...

On the stabilizing effect of a liquid film on a cylindrical core by oscillatory motions

Liquid films on cylindrical bodies like wires or fibres disintegrate if their length exceeds a critical size (Plateau-Rayleigh instability). Stabilization can be achieved by an axial oscillation of the solid core provided that a suitable combination of forcing amplitude and frequency is given. To investigate the stabilizing effect, direct numerical simulations (DNS) of the axisymmetric problem are conducted with a height function based solver. It is found that the mechanism of film stabilization is caused by the interaction between an inertia dominated region (high film thickness) and a viscosity dominated region (low film thickness). Replenishing of the thin film region is thereby supported while depleting is suppressed, finally leading to a stable film flow on an oscillating cylinder. To the end, a systematic variation of the main system parameters, e.g., the Weber number, the ratio between the radius of the inner core and the average film coating thickness, and the oscillation frequency is presented an...

Influence of micro-scale aspects and jet-to-jet interaction on free-surface liquid jet impingement for micro-jet array cooling

Arrays of impinging jets can cool large areas with good thermal uniformity and are often used in industrial processes, such as drying and electronics cooling. However, due to cross-flow of the spent liquid and interference between adjacent jets, a significant amount of the available cooling performance is lost. Under free-surface jet impingement the area beyond the hydraulic jump is associated with significantly reduced heat transfer, and locally increased temperatures, therefore the hydrodynamics in this area must be better understood. Specifically, the interaction of jets in the vicinity of this location is expected to shed light on improving multi-jet array cooling uniformity and performance. Beyond this, it has been shown that micro-scale (sub-millimeter) jets tend to behave somewhat differently from larger jets, due to the increased significance of surface tension, pumping noise and edge-effects (such as small recirculation zones, and jet widening due to contact-angle at the nozzle exit, noise and nozzle imperfections due to manufacturing). These become much more dominant at the micro-scale. These effects cannot usually be accounted for by traditional scaling laws or numerical simulations, and are preferably investigated experimentally. Moreover, at these scales a micro-machined fixed-geometry array of jets is typically used, leaving no possibility for geometric variation, optimization and limited observation.

A simple hydrodynamic model of a laminar free-surface jet in horizontal or vertical flight

A useable model for laminar free-surface jet evolution during flight, for both horizontal and vertical jets, is developed through joint analytical, experimental, and simulation methods. The jet’s impingement centerline velocity, recently shown to dictate stagnation zone heat transfer, encompasses the entire flow history: from pipe-flow velocity profile development to profile relaxation and jet contraction during flight. While pipe-flow is well-known, an alternative analytic solution is presented for the centerline velocity’s viscous-driven decay. Jet-contraction is subject to influences of surface tension (We), pipe-flow profile development, in-flight viscous dissipation (Re), and gravity (Nj = Re/Fr). The effects of surface tension and emergence momentum flux (jet thrust) are incorporated analytically through a global momentum balance. Though emergence momentum is related to pipe flow development, and empirically linked to nominal pipe flow-length, it can be modified to incorporate low-Re downstream diss...

The Influence of Subsurface Temperature Measurements on the Determination of Transient Wall-Side Boundary Conditions: An Analytical Tool

Abstract An analytical approximation for the two-dimensional heat conduction problem with temporally and spatially oscillating thermal boundary conditions is presented. In addition, simplified expressions for the damping and phase shift of the temperature signal between the surface and a “measurement” position inside the wall are derived and their validity in dependency on the inverse Fourier number is shown. The solution algorithm is implemented in a MATLAB program and made available for other researchers. In two case studies, the analytical solution is applied in order to evaluate the ability of experimental systems to measure instantaneous and local heat transfer coefficients as well as temperatures on a boundary.

Direct numerical simulations of a thin liquid film coating an axially oscillating cylindrical surface

Liquid films on cylindrical bodies like wires or fibers disintegrate into droplets if their length exceeds a critical measure (Plateau–Rayleigh instability). Stabilization of such films can be achieved by an axial oscillation of the solid core provided that a suitable combination of forcing amplitude and frequency is given. To investigate the stabilizing effect, direct numerical simulations of the axisymmetric problem are conducted in this study. Thus, a modified volume-of-fluid solver is employed based on the open source library OpenFOAM®. The effect of film stabilization is demonstrated and the required conditions for a stable film configuration are found to be in accordance with other studies. Finally, parameter variations are conducted to investigate the influence on the long-term shape of the stabilized film surface.