Discrete Optimization of Oil Production in Thin Oil Rim Reservoir under Geological Uncertainty

Abstract

Abstract A control system that distributes fluids from an injection to a production well at an adjustable rate has attracted considerable interest in recent years. Several optimization algorithms have been developed for this system and these techniques have proved to be beneficial in reservoir development. In this study, we propose a discrete optimization approach to increase oil production from thin oil rim reservoirs by smart horizontal wells under waterflooding. The smart well was equipped with several on-off control valves that can be adjusted to reach optimum oil production by maximize sweep efficiency and delay water breakthrough. This bring into optimization problem that involves discrete possible choices with valves settings as decision variables. We perform Binary Integer Programming (BIP) in order to decide valves settings in the injection and production well. BIP is one of linear programming problem where variable required being 0 or 1. These variables correspond with on-off control valves. Preliminary results obtained with this methodology show a significant improvement in the oil recovery factor, and the water saturation at breakthrough is observed to be more uniformly distributed across the reservoir, when compared with the reference non-optimized case. In the second stage of this study we add uncertainty in the geological description of the reservoir (permeability distribution), and perform robust optimization. To this end, we consider statistics of the Net Present Value (NPV) in the optimization objective function. We maximize an average of the NPV, and we control the risk attitude by means of a penalty term that involves the standard deviation of that quantity. Introduction Oil was formed by geological processes millions of years ago and is typically found in underground reservoirs of dramatically different sizes, at varying depths, and with widely varying characteristics. The largest oil reservoirs are called "Super Giants", many of which were discovered in the Middle East. Because of their size and other characteristics, Super Giant reservoirs are generally the easiest to find, the most economic to develop, and the longest lived. The last Super Giant oil reservoirs discovered worldwide were found in 1967 and 1968. Nowdays large oil fields are already at a mature stage and the number of new significant oil fields found per year decreases gradually. Smaller fields are still regularly found, but at the current oil price it is often not economical to exploit them. As a direct result it becomes more and more difficult to maintain economic reserves at a desirable level. In the past, a variety of secondary oil recovery methods have been developed and applied to mature and depleted oil reservoirs. These methods help to improve oil recovery compared to primary depletion. The oldest secondary recovery method is waterflooding, since water is usually readily available and inexpensive. Fundamentally, waterflood involves pumping water through a well (injector) into the reservoir. The water is forced through the pore spaces and sweeps the oil towards the producing wells (producers). It is becoming increasingly necessary to produce these fields as efficiently as possible in order to meet the global increase in demand for oil and gas. Production optimization problems involving reservoir modeling with time was first attempted by Lee and Aronofsky [Lee 1958]. The purpose of their study was to apply linear programming procedure to oil production scheduling problems. Jansen [Jansen 02] found that for the Smart Stinger Completion (SSC) in thin oil rims, the optimum valve-settings changed over time, due to a drop in reservoir pressure caused by production. The SSC was both effective in delaying water and gas breakthrough and in coning control for the post water breakthrough stage. For optimal design of the SSC a reasonable knowledge on the permeability distribution along the well is required. Brouwer and Jansen [Brouwer 2004] studied the optimization of water flooding with fully penetrating, smart horizontal wells in 2-dimensional reservoirs with simple, large-scale heterogeneities. They used optimal control theory as an optimization algorithm for valve settings in smart wells.