Boundary-Dominated Flow in Solutions-Gas-Drive Reservoirs

Camacho-V., Rodolfo; Raghavan, R.

doi:10.2118/18562-pa

Cited by 49 publications

(3 citation statements)

References 21 publications

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“…and the symbol t e represents material-balance time defined in Camacho-Velázquez and Raghavan (1989) as…”

Section: Pressure Tests: a And Bmentioning

confidence: 99%

A study in fractional diffusion: Fractured rocks produced through horizontal wells with multiple, hydraulic fractures

Raghavan

Chen²

2020

Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles

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The spatiotemporal evolution of transients in fractured rocks often displays unusual characteristics and is traced to multifaceted origins such as micro-discontinuity in rock properties, rock fragmentation, long-range connectivity and complex flow paths. A physics-based model that incorporates transient propagation wherein the mean square displacement of the diffusion front follows a nonlinear scaling with time is proposed. This model is based on fractional diffusion. The motivation for fractional flux laws follows from the existence of long-range connectivity that results in the mean square displacement of fronts moving faster than predicted by classical models; correspondingly, obstructions and discontinuities, local flow reversals, intercalations, etc. produce the opposite effect with fronts moving at a slower rate than classical predictions. The interplay of these two competing behaviors is quantified. We simulate transient production in a porous rock at the Theis scale as a result of production through a horizontal well consisting of multiple hydraulic fractures. Asymptotic solutions are derived and computations verified. The practical potential of this model is described through an example and the movement of fronts under the constraints of this model is demonstrated through the new expressions developed in this work. We demonstrate that this model offers a potential avenue to explain other behaviors noted in the literature. Though this work is developed in the context of applications to the earth sciences (production of hydrocarbons, extraction of geothermal resources, sequestration of radioactive waste and other fluids, groundwater flow), a minimal change in the Nomenclature permits application to other contexts. Ideas proposed here are particularly useful in the context of superdiffusion in bounded systems which until now, in many ways, has been considered to be an open problem.

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“…and the symbol t e represents material-balance time defined in Camacho-Velázquez and Raghavan (1989) as…”

Section: Pressure Tests: a And Bmentioning

confidence: 99%

A study in fractional diffusion: Fractured rocks produced through horizontal wells with multiple, hydraulic fractures

Raghavan

Chen²

2020

Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles

Self Cite

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“…If v ¼ 0, the solution presented in Eq. 7 is equivalent to the one introduced by Wattenbarger et al (1998) for tight reservoirs, and derived in Carslaw and Jaeger (1959) for linear heat-conduction problems. It has only two parameters, is valid for transient and boundary-dominated flow, and presents a continuous decline.…”

Section: Horizontal Wellmentioning

confidence: 99%

Combining Physics, Statistics, and Heuristics in the Decline-Curve Analysis of Large Data Sets In Unconventional Reservoirs

Holanda

Gildin

2018

SPE Reservoir Evaluation &Amp; Engineering

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Analytical single-well models have been particularly useful in forecasting production rates and estimated ultimate recovery (EUR) for the massive number of wells in unconventional reservoirs. In this work, a physics-based decline-curve model accounting for linear flow and material balance in horizontal multistage-hydraulically-fractured wells is introduced. The main characteristics of pressure diffusion in the porous media and the fact that the reservoir is a limited resource are embedded in the functional form, such that there is a transition from transient to boundary-dominated flow and the EUR is always finite. Analogously to the frequently used Arps (1945) hyperbolic model, the new model has only three parameters, where two of them define the decline profile and the third one is a multiplier. This model is applied to a large data set in a work flow that incorporates heuristic knowledge into the history matching and uncertainty quantification by assigning weights to rate measurements. The heuristic rules aim to lessen the effects of nonreservoir-related variations in the production data (e.g., temporary shut-in caused by fracturing in a neighboring well) and emphasize the reservoir dynamics to perform reliable predictions. However, there are additional degrees of freedom in the way these rules define the values of the weights; therefore, a criterion is established that "calibrates" the uncertainty in the probabilistic models by adjusting the parameters in the heuristic rules. Uncertainty quantification and calibration are performed using a Bayesian approach with hindcasts. This methodology is implemented in an automated framework and applied to 992 gas wells from the Barnett Shale. A comparison with the Arps (1945) hyperbolic model, the Duong (2011) model, and stretched exponential model for this data set shows that the new model is the most conservative in terms of estimated reserves.

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“…Fetkovich's type-curves provided the first method for analysis of constant-bottomhole-pressure production data on the basis of earlytransient analytical solutions combined with late-time BDF stems. Carter (1985) was able to improve Fetkovich's type-curves for the analysis of gas reservoirs by taking into account the evolution of gas viscosity and compressibility during pressure depletion. With finite-difference simulation, Carter developed a new set of typecurves on the basis of a newly defined parameter k, or viscositycompressibility ratio, which accounted for the impact of initial drawdown on the viscosity/compressibility product.…”

Section: Introductionmentioning

confidence: 99%

Rigorous and Explicit Determination of Reserves and Hyperbolic Exponents in Gas-Well Decline Analysis

Stumpf

Ayala

2016

SPE Journal

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Reservoir evaluation on the basis of rate-time data of gas wells producing under boundary-dominated flow (BDF) is often performed with the Arps' empirical hyperbolic decline model and associated type curves. In this study, we show that, for volumetric, single-phase, gas reservoirs produced at constant bottomhole pressure, the decline exponent, b, used in Arps' hyperbolic model can be calculated solely on the basis of fluid properties and the prevailing bottomhole specification-regardless of reservoir properties and before collecting any rate-time data. For the case of real gases produced under less-than wide-open decline, the assumption of a constant b necessary for the use of Arps' equations does not hold true throughout the production life of a reservoir. We show that during early BDF, a hyperbolic window may be defined for which the constant-b assumption may be valid. Within this window, we show that the application of type-curve and straight-line analysis techniques derived from the hyperbolic model can be used to successfully and explicitly determine reservoir properties, including original gas in place (OGIP). Several case studies based on numerical simulation and field data are presented to thoroughly validate and highlight the predictive capabilities of the proposed model.

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Boundary-Dominated Flow in Solutions-Gas-Drive Reservoirs

Cited by 49 publications

References 21 publications

A study in fractional diffusion: Fractured rocks produced through horizontal wells with multiple, hydraulic fractures

A study in fractional diffusion: Fractured rocks produced through horizontal wells with multiple, hydraulic fractures

Combining Physics, Statistics, and Heuristics in the Decline-Curve Analysis of Large Data Sets In Unconventional Reservoirs

Rigorous and Explicit Determination of Reserves and Hyperbolic Exponents in Gas-Well Decline Analysis

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