Reduced Order Modeling In Reservoir Simulation Using the Bilinear Approximation Techniques

Ghasemi, Mohammadreza; Ibrahim, Ashraf; Gildin, Eduardo

doi:10.2118/169357-ms

Cited by 26 publications

(17 citation statements)

References 13 publications

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“…Bilinear models can characterise nonlinear properties over a wider range of operations, hence, broaden the range of adequate performances and they are considered to be significantly advantageous in applications to practical industrial systems (Martineau et al, 2002). In this paper, a bilinear model of the directional drilling tool is developed by applying the Carleman bilinearisation technique (Ghasemi et al, 2014;Krener, 1974;Rugh, 1981). The generalised state space representation of a Multiple-Input Multiple-Output (MIMO) continuous-time bilinear system is expressed as (Kim and Lim, 2003):…”

Section: Linearized Plantmentioning

confidence: 99%

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Bilinear modelling, control and stability of directional drilling

Inyang

Whidborne

2019

Control Engineering Practice

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This paper proposes an approach for the attitude control of directional drilling tools for the oil and gas industry. A bilinear model of the directional drilling tool is proposed and it characterises the nonlinear properties of the directional drilling tool more accurately than the existing linear model, hence broadens the range of adequate performance. The proposed bilinear model is used as the basis for the design of a Bilinear Proportional plus Integral (BPI) controller. The stability of the proposed BPI control system is proven using stability notions for LTI and LPV systems. The transient simulation results show that the proposed BPI controller is more effective, robust and stable for the attitude control of the directional drilling tool than the existing PI controller. The proposed BPI controller provides improved invariant azimuth responses and significantly reduces the adverse effects of measurement delays and disturbances with respect to stability and performance of the directional drilling tool.

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Section: Linearized Plantmentioning

confidence: 99%

“…In this subsection, the Carleman bilinearisation technique (Ghasemi et al, 2014;Krener, 1974;Rugh, 1981) is applied to the partially linearised and decoupled system, (4) and 5, to obtain a bilinear model of the directional drilling tool. Equations (4) and (5) are rewritten as:…”

Section: Proposed Bilinear Modelmentioning

confidence: 99%

Bilinear modelling, control and stability of directional drilling

Inyang

Whidborne

2019

Control Engineering Practice

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“…This leads to the notion of model reduction of large scale dynamical systems (Antoulas, 2005). Model reduction has been recently applied in reservoir simulation (Ghasemi et al, 2014(Ghasemi et al, , 2015. In this case, one can perform what is called balancing the system, whereby one determines the controllable and observable description of the system.…”

Section: Model (Variable 'S and J's) The Gentilmentioning

confidence: 99%

Improved Waterflood Analysis Using the Capacitance-Resistance Model Within a Control Systems Framework

Holanda

Gildin

Jensen

2015

SPE Latin American and Caribbean Petroleum Engineering Conference

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The Capacitance Resistance Model (CRM) is a fast way for modeling and simulating gas and waterflooding recovery processes, making it a useful tool for improving flood management in real-time. CRM is an input-output and material balance-based model, and requires only injection and production history, which are the most readily available data gathered throughout the production life of a reservoir. In this work, the CRM input-output relationship is explored by representing the CRM with state-space (SS) equations. The linear system SS equations define the relationship between inputs, outputs and states to completely describe system dynamics. The SS-CRM is a multi-input/multi-output (matrix) representation, which provides more insight into reservoir behavior than analyzing performance on a well-by-well basis. Thus, it is computationally faster and easier to apply in fields with large numbers of wells. The CRM parameters are estimated using a grey-box system identification algorithm. The matrix form of the CRM history matching and a sensitivity analysis to the CRM parameters estimates are presented. Minimal realizations and reduced order models are easily obtained with the SS-CRM approach. The performance of three CRM representations are analyzed: integrated (ICRM), producer based (CRMP) and injectorproducer based (CRMIP). The methodology developed here is tested in two reservoir systems, homogeneous with flow barriers and channelized. We find that the ICRM does not reproduce the rate fluctuations as well as the CRMP and CRMIP. The CRMP works well for wells in low heterogeneity regions but not as well as the CRMIP in more heterogeneous areas, e.g. near the flanks of channel deposits. This new approach facilitates closed-loop reservoir management by enabling CRM's use for linear control algorithms, which can improve tracking performance and predictability, and is amenable to real-time optimization.

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“…2 shows a schematic of the mass transfer between different porosity systems in our model. Various numerical approaches can be employed to reduce the computational cost of problems with high degrees of complexity and heterogeneity (Efendiev et al 2013;Ghasemi et al 2014).…”

Section: Review Of the Current Multiple Permeability Approachmentioning

confidence: 99%

How to Improve our Understanding of Gas and Oil Production Mechanisms in Liquid-rich Shale

Alfi

Yan

Cao

et al. 2014

SPE Annual Technical Conference and Exhibition

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Three phase oil, gas, and water flow in liquid-rich shale plays is investigated in this paper, using a state-of-the-art technique of dividing shale matrix into different sub-media. Shale reservoirs always present numerous challenges to modeling and understanding, from unintuitive, heterogeneous, and difficult to characterize rock properties, to limited understanding of the governing flow equations, lack of fundamental knowledge on related desorption mechanisms, and nearly impermeable formations with pores on the order of magnitude as the mean free path of gas molecules. This work proposes a partitioning scheme to divide porous media in shale into three different sub-media (porosity systems) with distinctive characteristics: inorganic matter and kerogen (in the shale matrix), along with fracture network (natural or hydraulic). The current model gives us the capability of better analyzing the complex nature of mass transfer in shale. Relative permeabilities in our model are accounted for by employing the functions specifically presented for shale reservoirs. Our model can also handle various flow and storage mechanisms corresponding with shales such as molecule/wall interactions and slippage of the gas phase, multicomponent desorption, and capillarities. Simulation results show that hydrocarbon production from shale reservoirs exhibits complicated dynamics that are controlled by a number of different factors. Because of very high capillary pressure in shale, water is observed to imbibe into the water-wet inorganic matter during the late production period. On the contrary, mass flow in the oil-wet kerogen is mostly limited to two-phase oil and gas flow. Although kerogen is considered to be a rich source of hydrocarbon, relatively high capillary pressure and very low rock permeability hinder oil production in organic-rich shale. We might be able to address such problems by employing an appropriate production enhancement technique compatible with the ultra-tight nature of such reservoirs.

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Reduced Order Modeling In Reservoir Simulation Using the Bilinear Approximation Techniques

Cited by 26 publications

References 13 publications

Bilinear modelling, control and stability of directional drilling

Bilinear modelling, control and stability of directional drilling

Improved Waterflood Analysis Using the Capacitance-Resistance Model Within a Control Systems Framework

How to Improve our Understanding of Gas and Oil Production Mechanisms in Liquid-rich Shale

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