Quantification of Uncertainty in Relative Permeability for Coarse-Scale 
Reservoir Simulation

Okano, Hirofumi

doi:10.2523/94140-ms

Cited by 5 publications

(13 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Neighbourhood Approximation (NA) Algorithm and NA-Bayes Algorithm. The Neighbourhood Approximation (NA) algorithm is a stochastic sampling algorithm, which was originally developed to solve an inverse problem in seismology, [4], and the application of the NA-algorithm to history-matching has recently been introduced to the petroleum industry, [2,3,9]. The algorithm uses information obtained from previous runs to bias the sampling of model parameters to regions of parameter space where a good fit is likely.…”

Section: Theorymentioning

confidence: 99%

“…This approximation allows us to avoid calculating the real PPD of the new proposed models at each step of MCMC. In this paper we used this scheme of the MCMC with the Neighbourhood Approximation to evaluate the posterior expectation and P10 and P90 cut-offs, [2,3,9].…”

Section: Theorymentioning

confidence: 99%

“…The introduction of knots in an interval gives flexibility in defining the function over that interval. This characteristic of B-spline functions leads to local flexibility for adjusting curves during history-matching, [18,9]. As in our previous paper [9], we parameterise the relative permeability with the fourth order (cubic) B-spline function in the following way.…”

Section: Parameterisation Of Relative Permeabilities B-splinementioning

confidence: 99%

“…After generating multiple history-matched models, we estimate the uncertainty envelope in a Bayesian framework. Our previous paper [9] demonstrated the ongoing framework in a 1D coarse-scale model. Extending the previous work, we used a 2D synthetic reservoir model for the numerical experiments in the current study, which mimics a five spot pattern waterflooding.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Quantification of Uncertainty Due to Subgrid Heterogeneity in Reservoir Models

Okano¹,

Pickup²,

Christie³

et al. 2006

All Days

View full text Add to dashboard Cite

Due to the lack of data, a reservoir engineer needs to calibrate unknown petrophysical parameters based on production history. However, because the observations cannot constrain all the subsurface properties over a field, production forecasts for reservoirs are essentially uncertain. In general, many parameters of the model must be adjusted in the historymatching process, and the amount of computation required to solve the inverse problem may be prohibitive. To address this issue, we proposed a new methodology which restricts the parameter ranges of the calibration by using physically based prior information, extracted from geological and petrophysical input. The aim of the work is to have a sound basis for forecasting uncertainty in reservoir production. We demonstrate the applicability of the methodology using quarter five-spot pattern waterflooding models. The petrophysical properties to be adjusted in this paper are coarse-scale relative permeabilities. Coarse-scale models have the disadvantage of omitting the effects of fine-scale heterogeneity and suffering from solution errors, although in practice they are often employed in field-scale simulation because of the computational cost. Here, we history-match relative permeabilities at the coarse scale in order to encapsulate physical dispersion and compensate for numerical dispersion. The prior information was estimated from a range of possible geostatistical parameters. It allowed us not only to determine the parameterisation of the grouped relative permeabilities but also to set up the bounds of each type of curve. We used a synthetic data set for which the true solution is known. The resulting posterior expectations and P10 / P90 cutoffs of the production data and the relative permeabilities were examined in comparison with the reference results. We conclude that this new approach enabled us to quantify the uncertainty of sub-grid heterogeneity through the use of coarse-scale relative permeabilities without refining the model.

show abstract

Section: Theorymentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

Section: Parameterisation Of Relative Permeabilities B-splinementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Quantification of Uncertainty Due to Subgrid Heterogeneity in Reservoir Models

Okano¹,

Pickup²,

Christie³

et al. 2006

All Days

View full text Add to dashboard Cite

show abstract

“…Generally, geological factors and dynamic factors are the two main classes. Relative permeability curve reflects reservoir characteristics and fluid characteristics [1] [2]. So, relative permeability Journal of Geoscience and Environment Protection curve is one of the main factors affecting water cut [3].…”

Section: Introductionmentioning

confidence: 99%

The Influence Law of Oil Relative Permeability on Water Cut

Zhang¹,

Liu²,

Zhang³

et al. 2018

GEP

View full text Add to dashboard Cite

Water cut is a key evaluation parameter for reservoir development evaluation. Relative permeability curve reflects reservoir characteristics and fluid characteristics. It is important to figure out the influence law of oil relative permeability on water cut. Based on the 269 relative permeability curves of Bohai oilfields, the distribution of oil index of Bohai oilfields were studied. On the basis, combined with Corey expression of relative permeability and fractional flow equation, the theoretical relationship between oil index and water cut increasing rate was established. Three end points of water cut increasing rate curve were proposed and the influence law between three end points and oil index was studied. The results show that the oil index has a linear relationship with three end points. When the value of water oil mobile ratio is large than 1, with the increase of oil index, maximum value of water cut increasing rate gradually increase. When the value of water oil mobile ratio is less than 10, oil index has great effect on recovery percent when water cut increasing rate reaches to the maximum value as well as water cut when water cut increasing rate reaches to the maximum value. The application of SS field shows that the theoretical value is consistent with the field data.

show abstract

Quantitative Prediction Model for the Water–Oil Relative Permeability Curve and Its Application in Reservoir Numerical Simulation. Part 1: Modeling

et al. 2011

View full text Add to dashboard Cite

The waterÀoil relative permeability curve has a great effect on the rules of water cut increase and production variation. It is one of the most important data in reservoir development. With regard to a reservoir with a high degree of heterogeneity, the flow properties are various in different positions of the reservoir. Therefore, neither a single average relative permeability curve for the whole reservoir nor different curves for different sedimentary facies can precisely describe the reservoir flow characteristics, which will cause great difficulties for the remaining oil prediction and potential tapping. Therefore, it is of great importance to build a prediction model for the waterÀoil relative permeability curve, which can provide a calculation theory of the relative permeability curve for reservoir simulation using different relative permeability curves in different grid cells. The existing prediction models for the relative permeability curve have established the correlations between petrophysical properties and endpoint values of the relative permeability curve and between end-point values of the relative permeability curve and the relative permeability curve independently. However, the relationship between petrophysical properties and the relative permeability curve has not been developed. For this reason, it is impossible to achieve the spatial distribution of the relative permeability curve according to petrophysical properties. Furthermore, the end-point values of the relative permeability curve are usually calculated directly by petrophysical properties, which may result in all predicted relative permeability curves shifting to the left or right unrealistically compared to the reservoir average relative permeability curve. As a result of the above-mentioned problems, taking into consideration the correction effect of the average relative permeability curve on predicting relative permeability curves in different positions of the reservoir, this paper obtains a correlation between petrophysical properties and the relative permeability curve on the basis of the statistical analysis technique and normalization method of the reservoir average relative permeability curve. Finally, a prediction model for the waterÀoil relative permeability curve is established. A test based on the basic data of the relative permeability curve is performed to verify the effect of this model. The test result shows that the prediction procedure of this model is quick, easy, and reliable. It also indicates that the spatial distribution of the relative permeability curve satisfying the migration rule can be generated from petrophysical properties, which provides a basic calculation theory of the waterÀoil relative permeability curve for reservoir simulation using different relative permeability curves in different grid cells.

show abstract

Quantification of Uncertainty in Relative Permeability for Coarse-Scale Reservoir Simulation

Cited by 5 publications

References 18 publications

Quantification of Uncertainty Due to Subgrid Heterogeneity in Reservoir Models

Quantification of Uncertainty Due to Subgrid Heterogeneity in Reservoir Models

The Influence Law of Oil Relative Permeability on Water Cut

Quantitative Prediction Model for the Water–Oil Relative Permeability Curve and Its Application in Reservoir Numerical Simulation. Part 1: Modeling

Contact Info

Product

Resources

About