[1] The superimposition of rhythmic bed forms of different spatial scales is a common and natural phenomenon on sandy seabeds. The dynamics of such seabeds may interfere with different offshore activities and are therefore of interest to both scientists and offshore developers. State-of-the-art echo sounding accuracy allows for the analysis of bed form dynamics on unprecedented spatial and temporal scales. However, the superimposition of bed forms complicates the automated determination of morphodynamic parameters of individual bed form components. In this research we present the extension and comparison of two well-known, automated signal-processing methods for the 1-D and 2-D separation of bathymetric data derived from multibeam echo soundings into different components that each represents a bed form of a particular length scale. One method uses geostatistical filtering, and the other uses a Fourier decomposition of the bathymetric data. The application of both methods in two case studies of the North Sea shows that both methods are successful and that results correspond well. For example, megaripples up to 0.83 m height could be separated from 1.49-2.28 m high sand waves, and regionally averaged lengths and heights of sand waves, as calculated in either method, differ only 0.42-8.2% between methods. The obtained sand wave migration rates differ 7-11% between methods. The resulting morphometric and morphodynamic bed form quantification contributes to studies of empirical behavior and morphodynamic model validation and is valuable in risk assessments of offshore human activities.Citation: van Dijk, T. A. G. P., R. C. Lindenbergh, and P. J. P. Egberts (2008), Separating bathymetric data representing multiscale rhythmic bed forms: A geostatistical and spectral method compared,

We address the problem how to operate the injectors and producers of an oil field so as to maximize the value of the field. Instead of agressively producing and injecting fluids at maximum rate aiming at large short term profits, we are after optimizing the total value (e.g. discounted oil volume) over the whole lifecycle of the field. An essential tool in tackling this optimization problem is the adjoint method from optimal control theory. Starting from a base case reservoir simulation run, this extremely efficient method makes it possible to compute the sensitivities of the total (lifecycle) value with respect to all (time-dependent) well control variables in one go, at a cost less than that of an extra reservoir simulation run. These sensitivities can be used in an optimization loop to iteratively improve well controls. We implemented the adjoint method and an associated optimization algorithm in our in-house reservoir simulator. In addition to conventional well control options based on the well's pressure or total rate, we have also implemented smart well control options which allow the separate control of individual inflow intervals. Special adaptations of the optimization algorithm were required to allow the inclusion of inequality constraints on well control (pressure and rate constraints). We applied the optimization algorithm to a number of cases, and found interesting, non-trivial solutions to some optimal waterflood design problems, that would not easily have been found otherwise. In this paper, we also present a self-contained elementary derivation of the adjoint method, which is different from, but equivalent to the well-known derivation based on the Lagrange formalism. Introduction We focus on the problem of designing an optimal waterflood for an oil field. We limit ourselves to the situation where the well configuration and well types are given, so the only degree of freedom left is the way the injector and producer wells are operated. The waterflood design we are looking for should be optimal in the lifecycle sense, i.e., it should maximize the lifecycle integral Equation (1) where the integrand is a weighted sum of field rates, Equation. Here the weights are denoted by the letter and the field rates by the letter . The subscripts and refer to "oil" and "water", while the superscripts "prod" and "inj" refer to "production" and "injection", respectively. We note that the weights, which are given functions of time, can have arbitrary sign. This makes it possible to combine oil revenues and water costs in the lifecycle integral. Well control is modeled with one or more time-dependent well control variables per well. For conventional wells, there is just one control variable, which can be tubinghead pressure (THP), bottomhole pressure (BHP) or a rate. For smart wells there are generally more control variables corresponding to the setting of downhole inflow or outflow devices which can be controlled independently. Well control is not completely free as it should take into account certain operational limits such as rate and pressure constraints. These operational limits correspond to inequality constraints, either directly on the control variables or indirectly, in terms of certain state variables of the well/reservoir system. Apart from constraints on individual wells, there can also be global constraints dealing with several wells. Examples can be (equality or inequality) constraints imposed by surface facilities, or constraints imposed by reservoir management considerations (e.g., voidage balance constraints). The mathematical optimization problem to be solved is to maximize the lifecycle integral by choosing the optimal well control while satisfying all constraints.

Estimates of recovery from oil fields are often found to be significantly in error, and the multidisciplinary SAIGUP modelling project has focused on the problem by assessing the influence of geological factors on production in a large suite of synthetic shallow-marine reservoir models. Over 400 progradational shallow-marine reservoirs, ranging from comparatively simple, parallel, wave-dominated shorelines through to laterally heterogeneous, lobate, river-dominated systems with abundant low-angle clinoforms, were generated as a function of sedimentological input conditioned to natural data. These sedimentological models were combined with structural models sharing a common overall form but consisting of three different fault systems with variable fault density and fault permeability characteristics and a common unfaulted end-member. Different sets of relative permeability functions applied on a facies-by-facies basis were calculated as a function of different lamina-scale properties and upscaling algorithms to establish the uncertainty in production introduced through the upscaling process. Different fault-related upscaling assumptions were also included in some models. A waterflood production mechanism was simulated using up to five different sets of well locations, resulting in simulated production behaviour for over 35 000 full-field reservoir models. The model reservoirs are typical of many North Sea examples, with total production ranging from c . 15×10 6  m 3 to 35×10 6  m 3 , and recovery factors of between 30% and 55%. A variety of analytical methods were applied. Formal statistical methods quantified the relative influences of individual input parameters and parameter combinations on production measures. Various measures of reservoir heterogeneity were tested for their ability to discriminate reservoir performance. This paper gives a summary of the modelling and analyses described in more detail in the remainder of this thematic set of papers.

It is neither straightforward nor simple to estimate the capacity of a geological formation to store CO 2 . In a recent attempt to list the various estimates of CO 2 storage capacity for the world and regions of the world (Bradshaw et al., 2006), the estimates are often merely given as "very large", with ranges in the order of 100s to 10,000s Gt CO 2 . It is clear that there is a general lack of definitions, rules and general procedures for calculating storage potentials.Having conducted studies in the past, TNO is convinced that we now need a more uniform and standard method to calculate the storage potential of any subsurface location -be it a gas or oil field (whether totally or partially depleted) or an aquifer. In any calculation of storage capacity, TNO prefers to include the concept of total affected space i.e. the entire space whose state or qualities change during the total storage time as a result of the storage operation. Furthermore, in the storage calculations we consider the injectivity of the selected injection location, and the pressure and fluid conductivity of the total affected storage space.. The intended free CO 2 storage location must have enough storage space or enough sealing capacity to contain the CO 2 for at least 10,000 years and prevent it from migrating to the surface. And finally, it must be taken into account that as a result of gravity segregation, the heavier CO 2 -saturated formation water will sink to deeper parts of the affected space.We describe a standard method we have devised to be used for any storage location to calculate the maximum storage volume based on affected space and maximum pressurization, the storage potential based on injectivity, and finally the storage efficiency of the geological trap.

Several simple examples are presented that demonstrate the application of an ensemble-based method to production optimization. In particular, some practical aspects of the method such as ensemble size, perturbation, regularization and smoothing, and robust gradient estimation are discussed by comparison with an adjoint approach. The controls in the presented examples are inflow control valve settings for fixed time intervals or well position. We find that the performance of the method is clearly affected by the correlation time scale that is assumed for the controls, as reflected both by the quality of the gradient estimation and the subsequent optimization. The well placement optimization problem is studied for two cases: one is a homogenous reservoir with a sealing fault, and the other a non-homogeneous case. The ensemble optimization method is found to work well for both these simple well placement problems.

Summary Simplified analytical relations derived for homogeneous formations are usually applied to the determination of the productivity of horizontal wells, regardless of the presence of heterogeneities in the reservoir. Furthermore, complex well architectures and the wealth of completion options currently available cannot be taken into account properly because the well trajectory can only be schematized as a single horizontal wellbore. However, the use of numerical reservoir simulators to reliably forecast the productivity of horizontal wells draining heterogeneous reservoirs may be time-prohibitive or not feasible because of a lack of sufficiently detailed information, especially during the appraisal phase or the early stages of production. A new semianalytic technique is proposed in this paper to solve the inflow equations in an approximate yet reliable manner. A solution to 3D problems of single-phase flow into a horizontal well, taking into account friction in the wellbore, is provided for both single-layer reservoirs and reservoirs comprising two interfering layers. The method also has been extended to describe the fluid flow when the well intercepts one or more fractures. The presented technique allows very fast calculation of the well productivity in oil and gas reservoirs, offering great flexibility in the placement and architecture of the wells. The method has been applied to two field cases for which the well productivity under pseudosteady-state conditions was measured. One of these is a 200-m-long horizontal well draining an isotropic carbonatic reservoir and intersected by a natural low-conductivity fracture. The other is a similar well, intercepting a natural high-conductivity fault, but the oil-bearing formation is anisotropic. Good correspondence was found between the actual productivity and the predictions obtained by application of the proposed semianalytic technique. Introduction Horizontal wells are common practice in the present hydrocarbon industry, and smart wells (including multilateral completions and wells with selective access of different zones) are becoming increasingly commonplace. The modeling of such wells is, in many cases, not ideal. Areas in which improvements are welcome are well testing, well models in reservoir simulators, and fast models for quick assessment of many field-development options. Further, the handling of natural or hydraulic fractures is often suboptimal. In reservoir simulation, fine grids need to be selected to properly capture the flow behavior close to the well. Moreover, most reservoir simulators are not equipped with extensive well models, which are required when friction in the well becomes important or when two-phase flow develops in the well. This situation has prompted the development of a number of analytical and semianalytical tools, some of which are intended for implementation in a reservoir simulator. Most of the first models, as well as many of the more recent models, assume either constant influx density along the well or infinite well conductivity in a single homogeneous layer. Dikken introduced the effect of well conductivity for a single horizontal well in a homogeneous formation. He started with the assumption that the flow is mainly perpendicular to the wellbore, which allowed him to reduce the reservoir to a 2D flow domain, coupled to a friction model in the well. Others followed this approach, but 3Dmodels were developed as well. A second kind of extension are the multilayer models. Lee and Milliken and Kuchuk and Habashy used a method of reflection and transmission, while Basquet et al. used a "quadrupole" method relating the pressures between the various layers. The multilayer models are also, however, still limited to constant-influx or infinite-conductivity wells.

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