History Matching by Spline Approximation and Regularization in Single-Phase Areal Reservoirs

Lee, T. Y.; Kravaris, Costas; Seinfeld, John H.

doi:10.2118/13931-pa

Cited by 33 publications

(11 citation statements)

References 13 publications

(1 reference statement)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Over the last two decades, the oil and gas industry has employed optimization techniques for a variety of purposes such as determining optimal well location and spacing of fracture stages, [4][5][6] field development under uncertainty, 7 resource scheduling, 8,9 maximization of net present value, 10,11 optimization of water management in shale oil and gas production process, [12][13][14][15] shale oil and gas supply chain optimization, 16,17 history matching of reservoir parameters, [18][19][20][21][22][23] and development of well and reservoir simulators. [24][25][26][27] Specifically, for a given amount of proppant to be injected, a unified fracture design (UFD) that provides the optimal fracture geometry was proposed by Ref.…”

Section: Introductionmentioning

confidence: 99%

Feedback control of proppant bank heights during hydraulic fracturing for enhanced productivity in shale formations

et al. 2017

View full text Add to dashboard Cite

In hydraulic fracturing of shale formations, compared to conventional reservoirs, the fracturing fluid injected is of lowviscosity and hence during pumping the proppant settles significantly, forming a proppant bank. Motivated by this consideration, we initially develop a high-fidelity process model of hydraulic fracturing to describe the dominant proppant settling behavior during hydraulic fracturing process. Second, a novel remeshing strategy is developed to handle the high computational requirement due to moving boundaries. Third, a section-based optimization method is employed to obtain key fracture design parameters for enhanced productivity in shale formations subject to given fracturing resources. Fourth, a reduced-order model is constructed to design a Kalman filter and to synthesize a real-time model-based feedback control system by explicitly taking into account actuator limitations, process safety and economic considerations. We demonstrate that the proposed control scheme can regulate the uniformity of proppant bank heights along the fracture at the end of pumping.

show abstract

Section: Introductionmentioning

confidence: 99%

Feedback control of proppant bank heights during hydraulic fracturing for enhanced productivity in shale formations

et al. 2017

View full text Add to dashboard Cite

show abstract

“…A third way to parameterize is based on prior knowledge. Approaches include the use of pilot points [Wen et al, 2006], spline interpolation [Lee et al, 1986], wavelets [Sahni and Horne, 2005], or sparsity information [Jafarpour et al, 2010]. More complex methods and applications can be found in Liu and Oliver [2005], Zhao et al [2008], and Agbalaka and Oliver [2008].…”

Section: Literature Reviewmentioning

confidence: 99%

Estimation of plume distribution for carbon sequestration using parameter estimation with limited monitoring data

Espinet

Shoemaker

Doughty

2013

Water Resources Research

View full text Add to dashboard Cite

[1] This study develops and evaluates an integrated methodology including parameter zonation, efficient global optimization, and multiple aquifer realizations that gives a useful forecast of the pressure distribution and the CO 2 plume migration through a heterogeneous storage formation, over time, using only a few monitoring locations in a feasibly short amount of computing time, while dealing with data error. Geological characteristics of the example application are similar to a CO 2 sequestration pilot test conducted in a fluvialdeltaic geological setting. In the example, the CO 2 injection problem is simulated with the TOUGH2 code, a numerical simulator for multiphase (gas and aqueous), multicomponent flow and transport. The inverse problem is difficult because the GCS optimization estimation problem has multiple local minima and the simulation is computationally expensive. The efficient surrogate response surface global optimization algorithm ''Stochastic RBF'' (stochastic radial basis function) is used to calibrate the model parameters. Results are averaged over three saline aquifer realizations. In the third numerical experiment using only pressure data, the CO 2 plume could be determined with an average correlation coefficient compared to the actual plume of up to R 2 ¼ 0.916 (for current plume at t ¼ 1.5 years) and average R 2 ¼ 0.80 (for forecasted plume estimated at t ¼ 7.5 years years, using only the first 1.5 years of monitoring data). Adding gas saturation data improved the 6 year forecast somewhat (increasing average R 2 ¼ 0.85) but it was not significantly helpful in estimating the current plume. Both our inverse methodology and findings can be broadly applicable to GCS in heterogeneous sedimentary formations.Citation: Espinet, A., C. Shoemaker, and C. Doughty (2013), Estimation of Plume distribution for carbon sequestration using parameter estimation with limited monitoring data, Water Resour. Res., 49,

show abstract

“…Since GCV requires parametric sensitivity information, this method is not practical for such a large scale problem like reservoir parameter estimation. Lee and Seinfeld (1986) developed an algorithm based on Miller's idea that determines the regularisation parameters automatically during the estimation process without requiring a a priori information.…”

Section: Euclidean Norm Term (Comentioning

confidence: 99%

“…The properties are determined as those that produce the closest possible match of the observed and predicted histories. This so-called history-matching process has been addressed in the petroleum, hydrology and mathematics literature for some 20 years or so (Jacquard andJain 1965, Neuman 1973, Carter et Van den Bosch and Seinfeld 1977, Shah et a1 1978, Seinfeld and Chen 1978, Neuman and Yakowitz 1979, Yakowitz and Duckstein 1980, Yeh and Yoon 1981, Yeh et a1 1983, Tang and Chen 1984, Watson et a1 1984, Neuman and Carrera 1985, Sun and Yeh 1985, Yeh 1986, Carrera and Neumann 1986, Lee et a1 1986, Lee and Seinfeld 1986).…”

Section: Introductionmentioning

confidence: 99%

“…The first step of the regularisation formulation is to measure the non-smoothness of the parameter by its norm in an appropriate Hilbert space, called the stabilising functional, and then to seek the value of the parameter that minimises the weighted sum of the least-squares discrepancy term and the stabilising functional. In previous applications of regularisation to the petroleum reservoir inverse problem, Lee et a1 (1986) estimated absolute permeability and porosity in a single-phase reservoir and Lee and Seinfeld (1986) estimated the absolute permeability in a two-phase reservoir.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Estimation of absolute and relative permeabilities in petroleum reservoirs

Lee

Seinfeld

1987

Inverse Problems

Self Cite

View full text Add to dashboard Cite

Abstract. The estimation of absolute and relative permeabilities for petroleum reservoirs on the basis of noisy data at wells is considered. The spatially varying absolute permeability is estimated by regularisation combined with a bi-cubic spline approximation. Relative permeability is represented by a given function of saturation with unknown coefficients. Numerical results provide an indication of the estimability of the two permeabilities in conventional petroleum production operations.

show abstract

History Matching by Spline Approximation and Regularization in Single-Phase Areal Reservoirs

Abstract: An automatic history matching algorithm is developed based on bi-cubic spline approximations of permeability and porosity in a single-phase, twodimensional areal reservoir from well pressure data.The regularization feature of the algorithm, the theoretical details of which are described by

Cited by 33 publications

References 13 publications

Feedback control of proppant bank heights during hydraulic fracturing for enhanced productivity in shale formations

Feedback control of proppant bank heights during hydraulic fracturing for enhanced productivity in shale formations

Estimation of plume distribution for carbon sequestration using parameter estimation with limited monitoring data

Estimation of absolute and relative permeabilities in petroleum reservoirs

Contact Info

Product

Resources

About