Maximum Information at Minimum Cost: A North Sea Field Development Study With an Experimental Design
Authors: Elvind Damsleth , Asmund Hage , Rolf Volden 
Published: December 2007

Statistical design of experiments is a technique to maximize the information obtained from a minimum number of experiments. This technique, however, has not been used extensively in the oil industry. With a well-designed setup, the same information obtained when one parameter is varied at a time can be obtained with significantly fewer simulation runs. Interactions among the various input parameters can be identified and estimated with a more elaborate design. The technique can be applied without profound statistical insight with commercially available packages for statistical analysis.

Introduction

In the evaluation and planning of a reservoir development, the common approach is to build the expected geological model with the most representative set of dynamic parameters and the best set of well locations. The platform and production facilities are optimized for this model. This combination of geological model, dynamic parameters, and technical design constitutes the base or reference case. A reservoir simulation is then performed, giving the base-case production profile and recovery factor. Finally, this production profile is combined with a fixed scenario for future oil and/or gas prices and investments to obtain the economic indicators [net present value (NPV) and return on investment (ROI)] for the project. Fig. 1 shows the different elements of this procedure.

Most factors in this process are uncertain. The geological model is wrong, the dynamic parameters are incorrect, the well locations and facilities are not optimal, and the price scenario certainly will not be fulfilled. Thus, only one thing is certain: the results from the base-case calculations are definitely wrong. To evaluate how the various parameters that enter the process influence the results, a sensitivity study usually is performed. The standard approach is to vary one parameter at a time, keeping all other parameters at the base-case value. Two runs (with an optimistic and a pessimistic setting) are required for most parameters.

The number of runs required for a full sensitivity study quickly becomes prohibitive. Fig. 1 gives an example (somewhat exaggerated) for a North Sea gas field and shows the sensitivities of potential interest. If there are 5 gas-sales scenarios, 5 handling capacities, 5 different numbers of wells, 2 different horizontal-well lengths, 2 vertical start positions, and 15 geological parameters with uncertainties of interest, it will take 15,500 simulations to investigate these sensitivities by varying one parameter at a time. Because a single run of this particular full-field reservoir model takes some 20 CPU hours on a Cray, the study would take about 40 years and would be finished just a few years before the scheduled field shutdown. Thus, any technique that can reduce the number of runs required will be very useful.

If two or more parameters differ from their base-case values simultaneously, the effect on production may differ from the cumulative effect of varying one parameter at a time. The effect of varying several parameters simultaneously cannot be investigated by varying one parameter at a time. Thus, a technique that can shed some light on these simultaneous effects will be of value.

In experimental design, several parameters are varied simultaneously according to a predefined pattern. With this technique, the same information as that obtained with the one-parameter-at-a-time method can be developed with significantly fewer simulation runs. Some understanding of the possible interactions among parameters also can be obtained.

The theory behind experimental design was developed in the 1920's for agricultural applications. Box et al.1 present a basic but more modern reference, while Ross2 presents the topic within the framework of modern Japanese ideas about quality control. Sacks et al.3 introduce experimental design to computer experiments, and Morris4 extends their ideas. Experimental design has not been applied widely in the petroleum industry. Sawyer et al.5 is a very early reference, and Chu6 shows a recent application. Egeland et al.7 extend the ideas presented here.

This paper presents the basic concepts of experimental design. The technique then is applied to a real case study from the North Sea, illustrating that it is possible to obtain the basic sensitivities with a minimum number of simulations and additional information about possible interaction effects from a few more runs. The results from the analysis also can be used as input to a simple Monte Carlo simulation to obtain approximate uncertainty ranges for the parameters under study. Øvreberg et al.8 present the context for such an analysis.