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Optimizing Workover Rig Fleet Sizing and Scheduling Using Deterministic and Stochastic Programming Models.

ABSTRACT: We present deterministic and stochastic programming models for the workover rig problem, one of the most challenging problems in the oil industry. In the deterministic approach, an integer linear programming model is used to determine the rig fleet size and schedule needed to service wells while maximizing oil production and minimizing rig usage cost. The stochastic approach is an extension of the deterministic method and relies on a two-stage stochastic programming model to define the optimal rig fleet size considering uncertainty in the intervention time. In this approach, different scenario-generation methods are compared. Several experiments were performed using instances based on real-world problems. The results suggest that the proposed methodology can be used to solve large instances and produces quality solutions in computationally reasonable times.

SUBMITTER: Fernandez Perez MA

PROVIDER: S-EPMC6156096 | biostudies-literature | 2018 Jun

REPOSITORIES: biostudies-literature

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Optimizing Workover Rig Fleet Sizing and Scheduling Using Deterministic and Stochastic Programming Models.

Fernández Pérez Miguel A MA Oliveira Fabricio F Hamacher Silvio S

Industrial & engineering chemistry research 20180511 22

We present deterministic and stochastic programming models for the workover rig problem, one of the most challenging problems in the oil industry. In the deterministic approach, an integer linear programming model is used to determine the rig fleet size and schedule needed to service wells while maximizing oil production and minimizing rig usage cost. The stochastic approach is an extension of the deterministic method and relies on a two-stage stochastic programming model to define the optimal r ...[more]

PMID: 30270974

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Project description:Experimental studies of the flowering of Arabidopsis thaliana have shown that a large complex gene regulatory network (GRN) is responsible for its regulation. This process has been mathematically modelled with deterministic differential equations by considering the interactions between gene activators and inhibitors (Valentim et al. in PLoS ONE 10(2):e0116973, 2015; van Mourik et al. in BMC Syst Biol 4(1):1, 2010). However, due to complexity of the model, the properties of the network and the roles of the individual genes cannot be deducted from the numerical solution the published work offers. Here, we propose simplifications of the model, based on decoupling of the original GRN to motifs, described with three and two differential equations. A stable solution of the original model is sought by linearisation of the original model which contributes to further investigation of the role of the individual genes to the flowering. Furthermore, we study the role of noise by introducing and investigating two types of stochastic elements into the model. The deterministic and stochastic nonlinear dynamic models of Arabidopsis flowering time are considered by following the deterministic delayed model introduced in Valentim et al. (2015). Steady-state regimes and stability of the deterministic original model are investigated analytically and numerically. By decoupling some concentrations, the system was reduced to emphasise the role played by the transcription factor Suppressor of Overexpression of Constants1 ([Formula: see text]) and the important floral meristem identity genes, Leafy ([Formula: see text]) and Apetala1 ([Formula: see text]). Two-dimensional motifs, based on the dynamics of [Formula: see text] and [Formula: see text], are obtained from the reduced network and parameter ranges ensuring flowering are determined. Their stability analysis shows that [Formula: see text] and [Formula: see text] are regulating each other for flowering, matching experimental findings. New sufficient conditions of mean square stability in the stochastic model are obtained using a stochastic Lyapunov approach. Our numerical simulations demonstrate that the reduced models of Arabidopsis flowering time, describing specific motifs of the GRN, can capture the essential behaviour of the full system and also introduce the conditions of flowering initiation. Additionally, they show that stochastic effects can change the behaviour of the stability region through a stability switch. This study thus contributes to a better understanding of the role of [Formula: see text] and [Formula: see text] in Arabidopsis flowering.

Project description:BackgroundGillespie's stochastic simulation algorithm (SSA) for chemical reactions admits three kinds of elementary processes, namely, mass action reactions of 0th, 1st or 2nd order. All other types of reaction processes, for instance those containing non-integer kinetic orders or following other types of kinetic laws, are assumed to be convertible to one of the three elementary kinds, so that SSA can validly be applied. However, the conversion to elementary reactions is often difficult, if not impossible. Within deterministic contexts, a strategy of model reduction is often used. Such a reduction simplifies the actual system of reactions by merging or approximating intermediate steps and omitting reactants such as transient complexes. It would be valuable to adopt a similar reduction strategy to stochastic modelling. Indeed, efforts have been devoted to manipulating the chemical master equation (CME) in order to achieve a proper propensity function for a reduced stochastic system. However, manipulations of CME are almost always complicated, and successes have been limited to relative simple cases.ResultsWe propose a rather general strategy for converting a deterministic process model into a corresponding stochastic model and characterize the mathematical connections between the two. The deterministic framework is assumed to be a generalized mass action system and the stochastic analogue is in the format of the chemical master equation. The analysis identifies situations: where a direct conversion is valid; where internal noise affecting the system needs to be taken into account; and where the propensity function must be mathematically adjusted. The conversion from deterministic to stochastic models is illustrated with several representative examples, including reversible reactions with feedback controls, Michaelis-Menten enzyme kinetics, a genetic regulatory motif, and stochastic focusing.ConclusionsThe construction of a stochastic model for a biochemical network requires the utilization of information associated with an equation-based model. The conversion strategy proposed here guides a model design process that ensures a valid transition between deterministic and stochastic models.

Dataset Information

Optimizing Workover Rig Fleet Sizing and Scheduling Using Deterministic and Stochastic Programming Models.

Publications

Optimizing Workover Rig Fleet Sizing and Scheduling Using Deterministic and Stochastic Programming Models.

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