Variations in Bounding and Scanning Relative Permeability Curves with Different Carbonate Rock Types

Spontaneous countercurrent imbibition into a finite porous medium is an important physical mechanism for many applications, included but not limited to irrigation, CO 2 storage, and oil recovery. Symmetry considerations that are often valid in fractured porous media allow us to study the process in a onedimensional domain. In 1-D, for incompressible fluids and homogeneous rocks, the onset of imbibition can be captured by self-similar solutions and the imbibed volume scales with ffiffi t p . At later times, the imbibition rate decreases and the finite size of the medium has to be taken into account. This requires numerical solutions. Here we present a new approach to approximate the whole imbibition process semianalytically. The onset is captured by a semianalytical solution. We also provide an a priori estimate of the time until which the imbibed volume scales with ffiffi t p . This time is significantly longer than the time it takes until the imbibition front reaches the model boundary. The remainder of the imbibition process is obtained from a selfsimilarity solution. We test our approach against numerical solutions that employ parametrizations relevant for oil recovery and CO 2 sequestration. We show that this concept improves common first-order approaches that heavily underestimate early-time behavior and note that it can be readily included into dual-porosity models. Key Points: New physically based model for spontaneous imbibition Model captures transition from earlytime to late-time imbibition Model validated for different applications Correspondence to: R. March, rafael.march@pet.hw.ac.uk Citation: March, R., F. Doster, and S. Geiger (2016), Accurate early-time and latetime modeling of countercurrent spontaneous imbibition, Water Resour.

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“…Five waterflooding simulations are carried out using experimental data from Dernaika et al . []. Viscosities are taken as

μ_{w} = 1

cP and

μ_{n} = 2.3824

cP, which are, respectively, reference values for pure water and crude Brent oil (kinematic viscosity of

ν = 2.86

{mm}^{2} / s

).…”

Section: Resultsmentioning

confidence: 99%

Accurate early‐time and late‐time modeling of countercurrent spontaneous imbibition

March

Doster

Geiger

2016

Water Resources Research

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“…In homogeneous systems, the hysteresis effect can be negligible. Due to the combined effects of different rock wettability and pore geometries, different types of rock samples exhibit different hysteresis patterns in imbibition relative permeability curves (Dernaika MR et al [58]). Salinity also affects the hysteresis effects of phase permeability experiments, with lower salinity conditions leading to more significant capillary hysteresis (Wang et al [59]).…”

Section: Direct Relative Permeability Measurementsmentioning

confidence: 99%

State of the Art on Relative Permeability Hysteresis in Porous Media: Petroleum Engineering Application

Lan,

Guo,

Liu

et al. 2024

Applied Sciences

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This paper delivers an examination of relative permeability hysteresis in porous media in the field of petroleum engineering, encompassing mathematical modeling, experimental studies, and their practical implications. It explores two-phase and three-phase models, elucidating the generation of scanning curves and their applications in various porous materials. Building on the research of traditional relative permeability hysteresis models, we have incorporated literature on forward calculations of relative permeability based on digital rock core models. This offers a new perspective for studying the hysteresis effect in relative permeability. Additionally, it compiles insights from direct relative permeability and flow-through experiments, accentuating the methodologies and key findings. With a focus on enhanced oil recovery (EOR), carbon capture, utilization and sequestration (CCUS), and hydrogen storage applications, the paper identifies existing research voids and proposes avenues for future inquiry, laying the groundwork for advancing recovery techniques in oil and gas sectors.

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“…Geological parameter uncertainties that affect immiscible CO2 WAG injection include the nature and flow significance of faults and subseismic fractures (Bourbiaux et al, 2002;Casabianca et al, 2007;Ramirez et al, 2009) and the role of wettability and hysteresis that control imbibition and drainage in the rock matrix (Okasha et al, 2007;Ferno et al, 2011;Dernaika et al, 2013;Blunt, 1997;Hui & Blunt, 2000;Ryazanov et al, 2009Ryazanov et al, , 2010Killough, 1976;Carlson, 1981;Larsen and Skauge, 1998;Spiteri et al, 2008;Schmid and Geiger, 2013).…”

Section: Introductionmentioning

confidence: 99%

“…The static DFNs are then upscaled to provide adequate permeability distributions for the fracture network (Bourbiaux et al, 2002;Makel, 2007). Knowledge of the wetting preference and its variation in a carbonate reservoir rock is fundamental to understanding flow behaviour during enhanced oil recovery but is difficult to quantify due to the intrinsic heterogeneity of carbonates (Okasha et al, 2007;Ferno et al, 2011;Dernaika et al, 2013;Agada et al, 2014b). Several authors (e.g., Blunt, 1997;Hui & Blunt, 2000;Al-Futaisi and Patzek, 2003, Ryazanov et al, 2009 have demonstrated how wettability changes alter relative permeability functions, using a number of drainage and imbibition simulations where the range of advancing and receding contact angles was modified.…”

Section: Introductionmentioning

confidence: 99%

Reduced Order Models for Rapid EOR Simulation in Fractured Carbonate Reservoirs

Agada¹,

Geiger²,

Elsheikh³

et al. 2015

SPE Reservoir Simulation Symposium

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Conventional simulation of fractured carbonate reservoirs is computationally expensive because multiscale heterogeneities and fracture-matrix transfer must be taken into account. The computational requirement increases exponentially when multiple simulation runs are required for sensitivity analysis and quantification of the uncertainty range. This can be prohibitive, especially for giant carbonate reservoirs. Yet, sensitivity analysis and uncertainty quantification are particularly important to analyse, determine and rank the impact of geological and engineering parameters on the economics and sustainability of different EOR techniques.We use experimental design to set up multiple screened simulations of a high-resolution model of a Jurassic Carbonate ramp, which is an analogue for the highly prolific reservoirs of the Arab D formation in Qatar. We consider CO 2 water-alternating-gas (WAG) injection, which has been shown to be a successful EOR method for carbonate reservoirs. The simulations are used as a basis for generating polynomial response surfaces for prediction of hydrocarbon recovery and net gas utilisation. We compare response surfaces from polynomial regression to response surfaces generated with polynomial chaos expansion (PCE). PCE allows for non-linear mapping of parameter uncertainty to the predicted results.In the current work, the geological parameter uncertainties affecting WAG modelling in fractured carbonates are evaluated. These include end-member fault transmissibility configurations, wettability scenarios, hysteresis models and fracture intensity. Effective fracture permeabilities are computed using discrete fracture networks (DFN) for sparsely distributed regional fractures. The results enable us to adequately explore the parameter space, quantify and rank the interrelated effect uncertain model parameters on CO2 WAG efficiency in fractured carbonate reservoirs. The results highlight the first order impact of fracture intensity, wettability and hysteresis on hydrocarbon recovery and net gas utilisation. Furthermore, reduced order (i.e. proxy) models enable us to calculate quick estimates of the probabilistic uncertainty range and achieve significant computational speed-up compared with the conventional Monte Carlo framework.

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Variations in Bounding and Scanning Relative Permeability Curves with Different Carbonate Rock Types

Cited by 13 publications

References 28 publications

Accurate early‐time and late‐time modeling of countercurrent spontaneous imbibition

Accurate early‐time and late‐time modeling of countercurrent spontaneous imbibition

State of the Art on Relative Permeability Hysteresis in Porous Media: Petroleum Engineering Application

Reduced Order Models for Rapid EOR Simulation in Fractured Carbonate Reservoirs

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