Assessing the Non-Uniqueness of a Well Test Interpretation Model Using a Bayesian Approach

Cumming, Jonathan A.; Botsas, Themistoklis; Jermyn, Ian H.; Gringarten, Alain C.

doi:10.2118/200617-ms

Cited by 3 publications

(1 citation statement)

References 17 publications

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“…Gringarten source function and Valko volume source function can only simulate single heavy media oil reservoir seepage problems, and Ozkan source function is more suitable for solving seepage problems in tight oil reservoirs containing a large number of natural fractures [10][11][12][13][14]. Scholars have used the Ozkan source function as a theoretical basis to model seepage in a large number of single volume fracturing horizontal wells in tight oil reservoirs [15][16][17][18][19][20][21]. In order to study the seepage pattern of multiple volume fracturing horizontal wells, scholars have developed mathematical models of seepage when multiple volume fracturing horizontal wells are produced simultaneously [22].…”

Section: Introductionmentioning

confidence: 99%

Transient Pressure Behavior of Volume Fracturing Horizontal Wells in Fractured Stress-Sensitive Tight Oil Reservoirs

Li¹,

Yan²,

Wen³

et al. 2022

Processes

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Tight oil reservoirs tend to contain more natural fractures, and the presence of natural fractures leads to a greater stress sensitivity in tight oil reservoirs. It is a very challenging task to model the seepage in the volume fracturing horizontal wells considering the stress-sensitive effects. Based on the Laplace transform, Perturbation transform and Stefest numerical inversion, this paper establishes a horizontal well seepage model for volume fracturing in fractured stress-sensitive tight oil reservoirs. This model allows us to analyze and study the effect of stress sensitivity, fracture interference, dual media and complex fracture network on seepage flow in tight oil reservoirs. We apply the model to delineate the seepage stages of volume fracturing horizontal wells, it can be divided into seven seepage stages I wellbore storage flow, II surface flow stage, III transition flow, IV natural fracture system proposed radial flow, V interporosity flow, VI system proposed radial flow and VII stress-sensitive flow stage. Wellbore storage coefficient mainly affects the flow in the wellbore storage stage. The larger the wellbore storage coefficient is, the longer the duration of wellbore storage flow will be. The higher the skin coefficient is, the greater the pressure drop is. The storage capacity ratio has a greater influence on the flow before the occurrence of channeling flow, and the “groove” depth on the derivative curve of dimensionless pressure drop becomes shallower with the increase in storage capacity ratio. The higher the channeling coefficient is, the earlier the channeling occurs from the matrix system to the natural fracture system and the more leftwing the “groove” position is.

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Section: Introductionmentioning

confidence: 99%

Transient Pressure Behavior of Volume Fracturing Horizontal Wells in Fractured Stress-Sensitive Tight Oil Reservoirs

Li¹,

Yan²,

Wen³

et al. 2022

Processes

View full text Add to dashboard Cite

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Using Deconvolution to Estimate Unknown Well Production from Scarce Wellhead Pressure Data

Aluko¹,

Cumming

Gringarten

2020

SPE Annual Technical Conference and Exhibition

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Well test analysis requires the knowledge of bottomhole pressure and rates from the well of interest, and from any other well involved in the case of interferences. Sometimes, bottomhole pressures are not available and must be estimated from wellhead pressures, which usually are of lower quality, due to multiphase flow and possible tubing leaks. Converting flowing wellhead pressures to bottomhole pressures can be performed with a number of models, all of which assumes knowledge of the well production rate, which is usually determined with flowmeters or separators at the surface. In some cases, for instance when there is a blow out, production rate information is not available. The question is then how to determine well production rate in the absence of rate measurements when only wellhead pressures are available. In this paper, we use an iterative process based on well test deconvolution (von Schroeter et al. 2001-2004) to estimate unknown well production from wellhead pressure data. The procedure is as follows: (1) we assume a constant unit production rate and apply deconvolution to wellhead pressures: this yields a deconvolved wellhead pressure derivative and corrects the rates to make them compatible with the wellhead pressures; (2) we calibrate the rates with permeability from a trusted source e.g. core measurements or sampling wireline formation test analysis; (3) we use the calibrated deconvolved rates to convert wellhead pressures into bottomhole pressures; (4) we again assume a constant unit production rate and apply deconvolution to calculated bottomhole pressures: this yields a deconvolved bottomhole pressure derivative and corrects the rates to make them compatible with the calculated bottomhole pressures; and (5) we calibrate the calculated rates with trusted permeability information. We have applied the procedure described above to DST data from an oil well for which a complete data set is available, including permeabilities from cores, wellhead pressures, production rates, bottomhole pressures and well test analysis results. For the purpose of this study, we assume that we only know wellhead pressures, and we compare calculated results with measurements, i.e. calculated vs. measured bottomhole pressures, calculated vs. measured rates, and calculated vs. measured cumulative production. We assess the uncertainty in the results by applying a Bayesian approach to deconvolution (Cumming et al. 2020) which accounts for uncertainties in all input parameters, including permeability from different sources, and also uncertainty in deconvolution. In all cases, good to excellent agreement is reached between calculated results and measured data, thus validating the approach and providing confidence in the validity of the results. The procedure described in this paper provides a very good estimate of production rates from only wellhead measurements and permeability estimates: rather than using a welltest to determine reservoir properties knowing the rates and pressures, we do the inverse i.e. we use known reservoir properties and pressures to determine the rates. This approach can be used with confidence when measured rates are not available.

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Application of an Ensemble Based Method for Pressure-Rate Deconvolution

Piccinini,

Kubota,

Galvão

et al. 2024

SPE Annual Technical Conference and Exhibition

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This paper employs an ensemble-based method to address and assess the uncertainty in solutions to the single- and multi-well pressure-rate deconvolution problem. The method is implemented in two field cases from the Campos Basin. The first field case comprises a single vertical well producing from a virgin reservoir with continuous recording of bottom-hole pressure but uncertain flow-rate history. The second field case comprises a pair of horizontal wells, one acting as a producer and the other as an injector, with similar uncertainties in the flow-rate history and the additional complexity of a multi-well problem. We extend the investigation into the solution of the pressure-rate deconvolution proposed in a previous work (Kubota and Piccinini, 2022), which relies on the fundamental solution of the diffusion equation for bounded domains. In the present study, the deconvolved pressure response is obtained using the Ensemble Smoother with Multiple Data Assimilation (ES-MDA), a popular method for history matching numerical reservoir simulation models. ES-MDA provides an uncertainty quantification of the deconvolved pressure response and the investigated porous volume, along with other reservoir properties. Because ES-MDA uses a Bayesian formulation, data are weighted according to the inverse of the error variance. We explore this feature to include data from flowing periods, a desirable feature for the analysis of long-term pressure data with few well shut-ins. The results obtained for the two field cases consist of the posterior ensemble of model parameters, estimated flow rates, investigated pore volume, productivity index, single-well deconvolved response, as well as interference responses for the multi-well case.

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Assessing the Non-Uniqueness of a Well Test Interpretation Model Using a Bayesian Approach

Cited by 3 publications

References 17 publications

Transient Pressure Behavior of Volume Fracturing Horizontal Wells in Fractured Stress-Sensitive Tight Oil Reservoirs

Transient Pressure Behavior of Volume Fracturing Horizontal Wells in Fractured Stress-Sensitive Tight Oil Reservoirs

Using Deconvolution to Estimate Unknown Well Production from Scarce Wellhead Pressure Data

Application of an Ensemble Based Method for Pressure-Rate Deconvolution

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