History Matching of 3D Reservoir Models with Complex Non-Gaussian Distributions of the Model Parameters

Although the first application of the ensemble Kalman filter (EnKF) as a technique for sequential assimilation of noisy measurements was to a numerical weather prediction problem, remarkable research progress has been made in adapting this technique for application to data assimilation problems in reservoir engineering. Since its first application to a fairly simple parameter estimation problem in petroleum engineering less than a decade ago, the ensemble Kalman filter has been applied to fairly complex sequential model calibration problems in reservoir engineering with remarkable success. The reason for the rapid increase in the application of EnKF to data assimilation problems in reservoir engineering is partly due to the ease of implementing this technique; it is unnecessary to determine sensitivities from adjoint equations and the correlations between the model parameters and predicted data are estimated from the ensemble. Also the information from previously assimilated data are stored within the ensemble of conditional models such that it is unnecessary to repeat the history matching on previously assimilated data whenever new data are available for assimilation.Despite the encouraging performance of EnKF applied to sequential model calibration problems in reservoir engineering, the formulation of the ensemble Kalman filter is based on some critical assumptions (linear forward model and Gaussian model priors) that are generally not valid for reservoir engineering problems. The EnKF performance is optimal if at each data assimilation timestep, the prior state vector is linearly related to the predicted data and the distribution of the prior state vector is multivariate Gaussian. The state vector in reservoir engineering applications consists of the static model variables and the dynamic model variables, i.e., gridblock pressures and saturations for a black oil model. Some potential issues with EnKF applied to data assimilation problems in reservoir engineering include the following: non-Gaussian dynamic and/or static model parameters in the state vector, nonlinear model--data relationship, etc. Usually, the presence of severe nonlinearities is resolved by iteration, which also resolves the problem of non-Gaussian dynamic variables. However, for history matching problems with complex non-Gaussian model parameters, such as facies variables, vertical flow barriers, multimodal model variables, etc, the nonlinear effects are exacerbated and the performance of the EnKF in adjusting the models to obtain predictions that match production data is significantly degraded.In this dissertation, I focus on history matching problems with non-Gaussian model parameters for which the standard EnKF will perform very poorly without modifications. I identify some of the difficulties in the application of EnKF to the problem of updating facies models to match both production measurements and facies observations at the well locations and propose some modifications at the update step that improves the overall performance of the ensemble Kalman filter. I also introduce the concept of using pseudo-model variables for jointly updating the discrete facies variables and the multimodal rock properties in a way that is consistent with the EnKF updating scheme. The problem of updating reservoir models with vertical flow barriers using EnKF is also addressed in this dissertation. Estimation of vertical flow barriers is of practical importance in reservoir simulation studies as these flow barriers influence recovery mechanisms, gravity drainage processes and the selection of optimal well performance parameters. I outline three very efficient and fairly general methods for parameterizing the vertical transmissibility barriers between reservoir zones so that zonal communication can be shut off if production data indicate that there should be no communication. The EnKF will generally perform very poorly in generating conditional samples of the reservoir models if the posterior PDF is multimodal. I introduce a two-stage ensemble Kalman filter technique for application to history matching problems with multiple modes. I demonstrate the advantage of two-stage EnKF technique on a fairly complex low-order reservoir model with non-Gaussian model parameters and show that it converges to a better history match solution than the standard EnKF

Characterizing the Potential for Injection-Induced Fault Reactivation Through Subsurface Structural Mapping and Stress Field Analysis, Wellington Field, Sumner County, Kansas

Kansas, like other parts of the central U.S., has experienced a recent increase in seismicity. Correlation of these events with brine disposal operations suggests pore fluid pressure increases are reactivating preexisting faults, but rigorous evaluation at injection sites is lacking. Here we determine the suitability of CO2 injection into the Cambrian‐Ordovician Arbuckle Group for long‐term storage and into a Mississippian reservoir for enhanced oil recovery in Wellington Field, Sumner County, Kansas. To determine the potential for injection‐induced earthquakes, we map subsurface faults and estimate in situ stresses, perform slip and dilation tendency analyses to identify well‐oriented faults relative to the estimated stress field, and determine the pressure changes required to induce slip at reservoir and basement depths. Three‐dimensional seismic reflection data reveal 12 near‐vertical faults, mostly striking NNE, consistent with nodal planes from moment tensor solutions from recent earthquakes in the region. Most of the faults cut both reservoirs and several clearly penetrate the Precambrian basement. Drilling‐induced fractures (N = 40) identified from image logs and inversion of earthquake moment tensor solutions (N = 65) indicate that the maximum horizontal stress is approximately EW. Slip tendency analysis indicates that faults striking <020° are stable under current reservoir conditions, whereas faults striking 020°–049° may be prone to reactivation with increasing pore fluid pressure. Although the proposed injection volume (40,000 t) is unlikely to reactive faults at reservoir depths, high‐rate injection operations could reach pressures beyond the critical threshold for slip within the basement, as demonstrated by the large number of injection‐induced earthquakes west of the study area

Flashmob-Aktionen im Arbeitskampf

Flashmob-Aktionen im Arbeitskampf berühren den weiten Schutzbereich des Rechts am eingerichteten und ausgeübten Gewerbebetrieb. Diese Dissertation stellt Gesichtspunkte zur rechtlichen Bewertung des Einsatzes atypischer Arbeitskampfmittel vor, die den Gewerbeschutz komplettieren sollen. Ein Eingriff in das Recht am Gewerbebetrieb wird angenommen, wenn das beeinträchtigende Verhalten betriebsbezogen ist, eine erheblichen Schadensgefahr beinhaltet und keine bloße Bagatell-Beeinträchtigung ist. Die Rechtfertigung des Eingriffs erfordert eine Interessenabwägung. Als Rahmen der Abwägung empfiehlt die Arbeit folgende Punkte: 1. Welchen Bereich der gewerblichen Tätigkeit betrifft die Arbeitskampfaktion? 2. Handelt es sich um eine plötzliche, nicht-existenzielle Beeinträchtigung des Betriebsablaufes? 3. Welche Qualität und Quantität weist die Beeinträchtigung auf? 4. Welche finanziellen Nachteile sind infolge der Arbeitskampfaktion nachweisbar? Flashmob-Aktionen im Arbeitskampf sind das koordinierte, von Außen unvorhersehbare Tun einer Personenmehrzahl zur Verfolgung tariflicher Zwecke im räumlichen Umfeld eines Betriebes. Das BAG beurteilte Flashmob-Aktionen in seinem Urteil aus dem Jahr 2009 nicht als generell rechtswidrig. Diese Sichtweise bestätigte das BVerfG im Jahr 2014 auf eine Urteilsverfassungsbeschwerde hin. Die Bearbeitung stellt die zentralen Entscheidungsgesichtspunkte des BAG dar und prüft ihre Validität bei der Einordnung und Bewertung atypischer Arbeitskampfmittel. Zu ihnen zählen die Ausformung des Schutzbereichs der Koalitionsfreiheit, die Freiheit der Kampfmittelwahl, der Verhältnismäßigkeitsgrundsatz und die Parität. Die Dissertation erörtert ferner die Historie und Motivation der Nutzung atypischer Arbeitskampfmittel und setzt diese mit Konzepten des Organizings in Beziehung. Weiterhin stellt die Arbeit die jüngere Rechtsprechung nationaler sowie europäischer Gerichte zu atypischen Kampfmitteln dar.Atypical industrial action like flashmobs challenge business-owners'' long-established „Recht am eingerichteten und ausgeübten Gewerbebetrieb“ - a case-law based institute in German tort law that protects against interferences with individual and coporate economic activity. The book aims at refining the means to evaluate impairments of the „Recht am eingerichteten und ausgeübten Gewerbebetrieb“ in such cases. Up until now, interferences only qualified as such, if they were sufficiently related to the economic activity of the business, posed a relevant financial threat to it and did not qualify as bagatelles - as is usually the case during strikes. The further qualification of the interference as a breach requires a balancing of the opposing legal and factual positions. The following questions are designed to adjust the balancing-process across different scenarios of atypical industrial action: 1. Which part of business-activity is being affected by the industrial action? 2. Does the interference imply a sudden, non-existential impairment of the business procedures? 3. Of what quality and quantity is the impairment? 4. To which extent does the industrial action cause measurable financial damage for the business? A flashmob in the context of industrial action is a coordinated, externally unpredictable act of a multitude of people inside or around a business to the end of a trade agreement. In 2009 the Federal Labour Court of Germany ruled that this type of industrial action was not generally illegitimate, a view that the Federal Constitutional Court upheld in 2014. This book recounts central aspects of the former ruling and tests their validatity. Among them are the scope of the freedom of association, the free choice of means, the principle of proportionality and that of parity. The book further portrays history and motivation behind atypical industrial action and depicts recent corresponding German and European judicature

Review and experimental studies to evaluate the impact of salinity and wettability on oil recovery efficiency

Thesis (M.S.) University of Alaska Fairbanks, 2006Oil recovery efficiency is influenced by a myriad of interacting variables such as pore geometry, wettability, rock mineralogy, brine salinity, oil composition, etc. Reservoir wettability is known to have very significant influence on pore scale displacement and hence is a strong determinant of the final residual oil saturation. Recent studies have indicated the improved oil recovery potential of low salinity brine injection. Though the reason for this reported increase is still unclear, it is speculated that it may be due to wettability changes. In this work, coreflood studies were carried out to determine the recovery benefits of low salinity waterflood over high salinity waterflood and the role of wettability in any observed recovery benefit. Two sets of coreflood experiments were conducted; the first set examined the EOR potential of low salinity floods in tertiary oil recovery processes while the second set examined the secondary oil recovery potential of low salinity floods. Changes in residual oil saturation with variation in wettability and brine salinity were monitored. All the coreflood tests consistently showed an increase in produced oil and water-wetness with decrease in brine salinity and increase in brine temperature

Joint Updating of Petrophysical Properties and Discrete Facies Variables From Assimilating Production Data Using the EnKF

Summary The ensemble Kalman filter (EnKF), is a sequential data-assimilation technique that has been shown to work quite well in obtaining conditional facies models from assimilating production data. Because the problem of history matching geological facies is quite complex, most efforts at solving this problem typically assume that facies properties are constant and spatially homogeneous. In this paper, we propose a method for updating both the categorical facies variables and the spatially heterogeneous and nonuniform properties of the facies in a consistent manner within the EnKF framework. Tests of our proposed approach on two representative examples with different features of nonstationarity resulted in satisfactory history-match solutions and geologically consistent estimates of the nonuniform and heterogeneous petrophysical properties.</jats:p