Determination of lower and upper bounds of predicted production from history-matched models

We present a method to determine lower and upper bounds to the predicted production or any other economic objective from history-matched reservoir models. The method consists of two steps: 1) performing a traditional computer-assisted history match of a reservoir model with the objective to minimize the mismatch between predicted and observed production data through adjusting the grid block permeability values of the model. 2) performing two optimization exercises to minimize and maximize an economic objective over the remaining field life, for a fixed production strategy, by manipulating the same grid block permeabilities, however without significantly changing the mismatch obtained under step 1. This is accomplished through a hierarchical optimization procedure that limits the solution space of a secondary optimization problem to the (approximate) null space of the primary optimization problem. We applied this procedure to two different reservoir models. We performed a history match based on synthetic data, starting from a uniform prior and using a gradient-based minimization procedure. After history matching, minimization and maximization of the net present value (NPV), using a fixed control strategy, were executed as secondary optimization problems by changing the model parameters while staying close to the null space of the primary optimization problem. In other words, we optimized the secondary objective functions, while requiring that optimality of the primary objective (a good history match) was preserved. This method therefore provides a way to quantify the economic consequences of the well-known problem that history matching is a strongly ill-posed problem. We also investigated how this method can be used as a means to assess the cost-effectiveness of acquiring different data types to reduce the uncertainty in the expected NPV.     

Automated approaches for displaying spatially oriented time‐series data through image processing techniques

This study demonstrated the cartographic implications of automated image processing and computer graphics for the study of time‐series data. Automated statistical and image processing techniques were applied to a case study data set consisting of weekly Crop Moisture Index (CMI) values summarized at 174 state cooperative weather stations within Oklahoma for the time period between February and October, 1980. Computer generated isoline maps of the CMI values were interpolated and rescaled into a series of 32 grid matrices for input into a raster‐based ERDAS image processing software system. Principal Components Analysis (PCA) was used to develop graphic models that synthesized the multi‐temporal data into statistical dimensions that represented the most significant elements of CMI variability. Graphic models of the PCA statistical vectors were displayed individually, in conjunction with eigenvector loadings, and as composite images. Resultant images were analyzed statistically and graphically through the generated CMI grid matrices to ascertain the location, severity, and progression of drought represented in the CMI values. Traditional image processing techniques and devices were combined with the ERDAS software system to transform the multi‐temporal CMI data into multi‐dimensional images that represented the drought's spatial and temporal signature unobscured by redundant information.     

CODAR in Germany--A status report valid November 1985

The use of CODAR by the University of Hamburg has extended to a wide variety of experimental and oceanographic activities over the last three years. These have ranged from Arctic studies from land and ships to observations of the Dead Sea, all yielding surface current data. Hardware improvements have been investigated, including IF amplifier changes and loop-antenna arrays for shipboard operation.     

On the capability of an upward-looking ADCP deployed in the Iceland-Faeroe frontal area

Ocean Dynamics - An upward looking acoustic Doppler current profiler (ADCP), deployed in the Iceland-Faeroe area, recorded horizontal currents as function of depth over a period of some 200 days...     

Comparison of Remotely Measured and Modelled Currents in Coastal Areas of Norway and Spain

Data from two six-week current measurement campaigns at the coasts of Norway and Spain are presented. Spatial coverage of surface currents was obtained by an HF (High Frequency) radar. Subsurface currents were measured by bottom-mounted and ship-borne ADCPs (Acoustic Doppler Current Profiler). The HF data were assimilated by a fine gridded model with the aim of predicting currents for about 6 h. The objective of this article is twofold, to investigate the performance of the instruments and the model, and to show the high temporal and spatial variability of currents in the coastal zones under investigation.

Several strong storms occurred during the experiments with significant waveheights exceeding 11 m (Norway) and 8 m (Spain), respectively. High waves affected both the WEllen RAdar (WERA) (reduced ranges) and the ADCP (unreliable near-surface current velocities). The assimilation algorithm of the model worked well. The comparisons of measured and modelled maps of the surface-current velocity, time series and horizontal gradients reveal good agreement.

The analysis of current data shows similar features for both experimental areas. The dominant M2-tidal currents are weak (amplitudes of about 0.15 ms -1 ). The spatial distribution of the vector correlation between surface current and wind is homogeneous, although single current maps contain strong horizontal variabilities. The portion of current variance linearly forced by wind is about 30%.