Waterflooding using closed-loop control

To fully exploit the possibilities of “smart” wells containing both measurement and control equipment, one can envision a system where the measurements are used for frequent updating of a reservoir model, and an optimal control strategy is computed based on this continuously updated model. We developed such a closed-loop control approach using an ensemble Kalman filter to obtain frequent updates of a reservoir model. Based on the most recent update of the reservoir model, the optimal control strategy is computed with the aid of an adjoint formulation. The objective is to maximize the economic value over the life of the reservoir. We demonstrate the methodology on a simple waterflooding example using one injector and one producer, each equipped with several individually controllable inflow control valves (ICVs). The parameters (permeabilities) and dynamic states (pressures and saturations) of the reservoir model are updated from pressure measurements in the wells. The control of the ICVs is rate-constrained, but the methodology is also applicable to a pressure-constrained situation. Furthermore, the methodology is not restricted to use with “smart” wells with down-hole control, but could also be used for flooding control with conventional wells, provided the wells are equipped with controllable chokes and with sensors for measurement of (wellhead or down hole) pressures and total flow rates. As the ensemble Kalman filter is a Monte Carlo approach, the final results will vary for each run. We studied the robustness of the methodology, starting from different initial ensembles. Moreover, we made a comparison of a case with low measurement noise to one with significantly higher measurement noise. In all examples considered, the resulting ultimate recovery was significantly higher than for the case of waterflooding using conventional wells. Furthermore, the results obtained using closed-loop control, starting from an unknown permeability field, were almost as good as those obtained assuming a priori knowledge of the permeability field.     

A Direct Inverse Model to Determine Permeability Fields from Pressure and Flow Rate Measurements

The determination of the permeability field from pressure and flow rate measurements in wells is a key problem in reservoir engineering. This paper presents a Double Constraint method for inverse modeling that is an example of direct inverse modeling. The method is used with a standard block-centered finite difference method. With an a priori grid block permeability field as input, two forward runs are made: the first is constrained with the measured pressures; the second is constrained with the measured flow rates. We calculate the pressures in the grid block centers from the first run, while from the second run we calculate the fluxes through the faces between the grid blocks. Substitution of these pressures and fluxes into Darcy’s law then yields the transmissibilities at the faces and hence the permeabilities in the grid blocks. In this way the “hard” data (measured pressures and flow rates) are always honored while the “soft”, geological data can be incorporated at the discretion of the geologist. Using a synthetic example, we demonstrate the method and compare the results with another method: Ensemble Kalman Filtering. The two methods agree within the scope of their applicability. The Double Constraint method focuses initially on determining spatial distributions of the permeability field for single-phase, steady state flow. For history matching an extension is required to non-steady state, two-phase flow conditions, which is already possible with EnKF. We are currently investigating the possibility of combining the two methods, whereby the strengths of the two methods could be fully exploited.     

Nowcasting sunshine number using logistic modeling

In this paper, we present a formalized approach to statistical modeling of the sunshine number, binary indicator of whether the Sun is covered by clouds introduced previously by Badescu (Theor Appl Climatol 72:127–136, 2002). Our statistical approach is based on Markov chain and logistic regression and yields fully specified probability models that are relatively easily identified (and their unknown parameters estimated) from a set of empirical data (observed sunshine number and sunshine stability number series). We discuss general structure of the model and its advantages, demonstrate its performance on real data and compare its results to classical ARIMA approach as to a competitor. Since the model parameters have clear interpretation, we also illustrate how, e.g., their inter-seasonal stability can be tested. We conclude with an outlook to future developments oriented to construction of models allowing for practically desirable smooth transition between data observed with different frequencies and with a short discussion of technical problems that such a goal brings.     

Impact of Assimilation of Radiosonde and UAV Observations from the Southern Ocean in the Polar WRF Model

Weather forecasting in the Southern Ocean and Antarctica is a challenge above all due to the rarity of observations to be assimilated in numerical weather prediction(NWP)models.As observations are expensive and logistically challenging,it is important to evaluate the benefit that additional observations could bring to NWP.Atmospheric soundings applying unmanned aerial vehicles(UAVs)have a large potential to supplement conventional radiosonde sounding observations.Here,we applied UAV and radiosonde sounding observations from an RV Polarstern cruise in the ice-covered Weddell Sea in austral winter 2013 to evaluate the impact of their assimilation in the Polar version of the Weather Research and Forecasting(Polar WRF)model.Our experiments revealed small to moderate impacts of radiosonde and UAV data assimilation.In any case,the assimilation of sounding data from both radiosondes and UAVs improved the analyses of air temperature,wind speed,and humidity at the observation site for most of the time.Further,the impact on the results of 5-day-long Polar WRF experiments was often felt over distances of at least 300 km from the observation site.All experiments succeeded in capturing the main features of the evolution of near-surface variables,but the effects of data assimilation varied between different cases.Due to the limited vertical extent of the UAV observations,the impact of their assimilation was limited to the lowermost 1?2-km layer,and assimilation of radiosonde data was more beneficial for modeled sea level pressure and near-surface wind speed.