In field trials including large numbers of varieties, it is often impossible or impractical to replicate each variety. In these situations, the researcher may choose to use only one replicate of each test variety and to include a "check" variety every so often so that the spatial variability of the field may be determined. Five different check patterns were purposefully designed, each possessing distinct characteristics. The purpose of this study is to determine which spatial patterns for the check variety are better able to identify the spatial structure in a field and to rank the experimental varieties accurately. The problem was approached in two ways. First, the check patterns were compared using optimality criteria. Then, the patterns were applied to an actual field experiment, and the data collected was used to identify the spatial structure of variation in the field and to test for experimental variety differences. It is shown that the results from the optimality criteria were not necessarily comparable to what was actually observed in the field.

Crop researchers performing germplasm screenings are often unable to replicate their plots due to scarcity of seed and the large numbers of genotypes being evaluated. The use of known check varieties is a common method of overcoming the difficulties associated with unreplicated trials. In this simulation, we explored the effect of check plot density on the effectiveness of the resulting analysis. We also explored the effect of analyzing treatments as random versus fixed. Our study considers ten different designs with check densities ranging from 5% of the plots to 50%. The designs and analyses were then compared on the basis of the correlation of the actual treatment effects with the following: "observed" yield, LSMEANs for treatments fixed, and BLUPs for treatments random. Finally, we observed the frequency with which the analysis ranked the top 10% of the treatments within the top 15% of the LSMEANs or BLUPs. It was found that the LSMEANs and BLUPs from the spatial analysis provide more accurate results than the observed Y-values. Also, if the treatments are analyzed as fixed and the LSMEANs are used as estimates, then there seems to be a certain point beyond which not much additional information is gained by adding more check plots. This plateau is reached near a check plot density of approximately 30%. Finally, the BLUPs seem to be a more accurate estimate of the true treatment effects than are the LSMEANs at the lower densities; in fact, the BLUPs perform relatively well even at check densities of only 5% or 10%.

-In the planning of new wells, typically the same trajectory is used for conventional wells and wells with smart completions. This study demonstrates that the economically optimized trajectory for smart and conventional wells can be very different. Two new well trajectory optimization algorithms were developed using Stochastic Pattern Search (SPS) principles. In both algorithms random perturbations are made starting from an initial well trajectory, which are sent to a reservoir simulator whereafter the perturbation with the highest Net Present Value (NPV) is selected. New perturbations of the selected well trajectory are made and simulated to, again, select the highest NPV. This process is repeated until a certain stopping criteria is met. The two methods differ in the selection of the perturbations used to initiate the new iteration. In the SPS1 method every subsequent iteration starts from the perturbation with the highest NPV which may be the starting well from the previous iteration. In the SPS2 method the starting well from the previous iteration is excluded. This does not allow the SPS2 method to converge, but it avoids one of the main risks of the SPS1 method, i.e. that the optimization remains stuck in a local optimum. To demonstrate the difference between the optimal well trajectory of well with a conventional and smart completion, both the SPS1 and SPS2 method were evaluated using a realistic, but slightly simplified reservoir model. Both methods were able to optimize the trajectory for both conventional and smart completions. The SPS1 method quickly converged to a local optimum, whilst the SPS2 method was able to determine a trajectory with a significantly higher NPV for both the conventional and smart wells. Moreover, the optimal well trajectory with the smart completion, as found by the SPS2 algorithm, had a NPV that was 40% higher than the optimal trajectory for the conventional completion. It can therefore be concluded that when smart completions are assessed, well trajectory optimization can have very significant value impact and may be crucial in evaluating the full potential of the completion. Furthermore it was shown that, for the example considered, the SPS2 procedure is a good method for well trajectory optimization in a three-dimensional reservoir and although more testing is needed it is believed that is has potential to work with any type of completion.