Faruk O. Alpak

Validation of a Modified Carman-Kozeny Equation To Model Two-Phase Relative Permeabilities

This paper presents a validation of an internally consistent, physically based model for relative permeability based on an extension of the Carman-Kozeny (CK) equation. The modified CK (MCK) expression is a function of surface areas of fluid-fluid and fluid-rock interfaces, as well as fluid saturations and tortuosity. The model uses interfacial and surface areas determined from capillary pressure measurements and, by this means, can incorporate variable wettability and hysteresis as well as assuring consistency of petrophysical properties. To validate the MCK approach, the model is fit to experiments where both capillary pressure and relative permeability are measured simultaneously during flow. The MCK model is further fit to literature-reported water-oil experimental data. Besides the MCK model, each data set is fit with a modification of the commonly used Brooks-Corey (MBC) model to compare the performances of the two. The surface areas derived from capillary pressure relationship used in the MCK model provide a good description of the experimental relative permeabilities measured under the same conditions. The investigated MCK model fits experimental data almost as well as the MBC model. Furthermore, the MCK model is physically based and appears to agree with the wetting characteristics of the investigated porous media when these are known.

The impact of fine-scale turbidite channel architecture on deep-water reservoir performance

This article concentrates on the question, Which parameters govern recovery factor (RF) behavior in channelized turbidite reservoirs? The objective is to provide guidelines for the static and dynamic modeling of coarse reservoir-scale models by providing a ranking of the investigated geologic and reservoir engineering parameters based on their relative impact on RF. Once high-importance (H) parameters are understood, then one can incorporate them into static and dynamic models by placing them explicitly into the geologic model. Alternatively, one can choose to represent their effects using effective properties (e.g., pseudorelative permeabilities). More than 1700 flow simulations were performed on geologically realistic three-dimensional sector models at outcrop-scale resolution. Waterflooding, gas injection, and depletion scenarios were simulated for each geologic realization. Geologic and reservoir engineering parameters are grouped based on their impact on RF into H, intermediate-importance (M), and low-importance (L) categories. The results show that, in turbidite channel reservoirs, dynamic performance is governed by architectural parameters such as channel width, net-to-gross, and degree of amalgamation, and parameters that describe the distribution of shale drapes, particularly along the base of channel elements. The conclusions of our study are restricted to light oils and relatively high-permeability channelized turbidite reservoirs. The knowledge developed in our extensive simulation study enables the development of a geologically consistent and efficient dynamic modeling approach. We briefly describe a methodology for generating effective properties at multiple geologic scales, incorporating the effect of channel architecture and reservoir connectivity into fast simulation models.

A phase-field method for the direct simulation of two-phase flows in pore-scale media using a non-equilibrium wetting boundary condition

Advances in pore-scale imaging (e.g., μ-CT scanning), increasing availability of computational resources, and recent developments in numerical algorithms have started rendering direct pore-scale numerical simulations of multi-phase flow on pore structures feasible. Quasi-static methods, where the viscous and the capillary limit are iterated sequentially, fall short in rigorously capturing crucial flow phenomena at the pore scale. Direct simulation techniques are needed that account for the full coupling between capillary and viscous flow phenomena. Consequently, there is a strong demand for robust and effective numerical methods that can deliver high-accuracy, high-resolution solutions of pore-scale flow in a computationally efficient manner. Direct simulations of pore-scale flow on imaged volumes can yield important insights about physical phenomena taking place during multi-phase, multi-component displacements. Such simulations can be utilized for optimizing various enhanced oil recovery (EOR) schemes and permit the computation of effective properties for Darcy-scale multi-phase flows.We implement a phase-field model for the direct pore-scale simulation of incompressible flow of two immiscible fluids. The model naturally lends itself to the transport of fluids with large density and viscosity ratios. In the phase-field approach, the fluid-phase interfaces are expressed in terms of thin transition regions, the so-called diffuse interfaces, for increased computational efficiency. The conservation law of mass for binary mixtures leads to the advective Cahn–Hilliard equation and the condition that the velocity field is divergence free. Momentum balance, on the other hand, leads to the Navier–Stokes equations for Newtonian fluids modified for two-phase flow and coupled to the advective Cahn–Hilliard equation. Unlike the volume of fluid (VoF) and level-set methods, which rely on regularization techniques to describe the phase interfaces, the phase-field method facilitates a thermodynamic treatment of the phase interfaces, rendering it more physically consistent for the direct simulations of two-phase pore-scale flow. A novel geometric wetting (wall) boundary condition is implemented as part of the phase-field method for the simulation of two-fluid flows with moving contact lines. The geometric boundary condition accurately replicates the prescribed equilibrium contact angle and is extended to account for dynamic (non-equilibrium) effects. The coupled advective Cahn–Hilliard and modified Navier–Stokes (phase-field) system is solved by using a robust and accurate semi-implicit finite volume method. An extension of the momentum balance equations is also implemented for Herschel–Bulkley (non-Newtonian) fluids. Non-equilibrium-induced two-phase flow problems and dynamic two-phase flows in simple two-dimensional (2-D) and three-dimensional (3-D) geometries are investigated to validate the model and its numerical implementation. Quantitative comparisons are made for cases with analytical solutions. Two-phase flow in an idealized 2-D pore-scale conduit is simulated to demonstrate the viability of the proposed direct numerical simulation approach.

Petrophysical inversion of borehole array-induction logs: Part I — Numerical examples

We have developed a new methodology for the quantitative petrophysical evaluation of borehole array-induction measurements. The methodology is based on the time evolution of the spatial distributions of fluid saturation and salt concentration attributed to mud-filtrate invasion. We use a rigorous formulation to account for the physics of fluid displacement in porous media resulting from water-base mud filtrate invading hydrocarbon-bearing rock formations. Borehole array-induction measurements are simulated in a coupled mode with the physics of fluid flow. We use inversion to estimate parametric 1D distributions of permeability and porosity that honor the measured array-induction logs. As a byproduct, the inversion yields 2D (axial-symmetric) spatial distributions of aqueous phase saturation, salt concentration, and electrical resistivity. We conduct numerical inversion experiments using noisy synthetic wireline logs. The inversion requires a priori knowledge of several mud, petrophys-ical, and fluid param...

Petrophysical inversion of borehole array-induction logs: Part II — Field data examples

We describe the application of Alpak et al.s (2006) petrophysical inversion algorithm to the interpretation of borehole array induction logs acquired in an active North American gas field. Layer-by-layer values of porosity and permeability were estimated in two closely spaced vertical wells that penetrated the same horizontal rock formation. The wells were drilled with different muds and overbalance pressures, and the corresponding electromagnetic induction logs were acquired with different tools. Rock-core laboratory measurements available in one of the two wells were used to constrain the efficiency of gas displacement by water-based mud during the process of invasion. Estimated values of porosity and permeability agree well with measurements performed on rock-core samples. In addition to estimating porosity and permeability, the petrophysical inversion algorithm provided accurate spatial distributions of gas saturation in the invaded rock formations that were not possible to obtain with conventional procedures based solely on the use of density and resistivity logs.

A kinematic trishear model to predict deformation bands in a fault-propagation fold, East Kaibab monocline, Utah

Well core with numerous deformation bands in the reservoir interval may or may not be indicative of reduced effective reservoir permeability at the scale of well drainage areas. Many dense concentrations of deformation bands are related to the damage zone of a larger fault. However, some populations are more broadly distributed. We analyze one such population associated with the East Kaibab monocline in southern Utah. A kinematic trishear analysis is compared with field-based strain measurements. We find that the widespread dense deformation-band populations correspond to a broad zone of relatively high strain across the structure. Fault-damage zone models are inadequate to explain these occurrences. Our results show that, where deformation bands are known to occur from core in a folded reservoir, finite strains can be used to estimate their lateral and volumetric extents. However, we also find that the orientations of deformation bands predicted by our modeling are highly sensitive to the strain path. This indicates that path-independent methods for estimating strain such as curvature analysis are not fully appropriate for application to deformation bands. Ultimately, any such method requires information relating rock properties with propensity to form deformation bands to be predictive.

Joint inversion of transient‐pressure and dc resistivity measurements acquired with in‐situ permanent sensors: A numerical study

We develop a quantitative methodology to interpret jointly in‐situ transient‐pressure and dc resistivity measurements acquired in a hypothetical water injection experiment, with the goal of displacing oil in a hydrocarbon‐bearing formation. The assumed measurement acquisition system consists of enforcing time‐variable flow rates while injecting water into the surrounding rock formations, thereby producing a sequence of repeated transient‐pressure pulses. In‐situ dc resistivity measurements are acquired at the end of every flow‐rate pulsing sequence. The objective of the experiment is to estimate the spatial distributions of absolute fluid permeability and electrical resistivity. Geophysical inverse theory is used to account for the presence of noisy measurements.Synthetic data with noise are inverted to assess the relative benefits of different types of sensor geometries in axisymmetric models of permeability and electrical resistivity. Results strongly suggest that cooperative inversion of in‐situ transi...

Assessment of Mud-Filtrate-Invasion Effects on Borehole Acoustic Logs and Radial Profiling of Formation Elastic Properties

Despite continued improvements in acoustic-logging technology, sonic logs processed with industry-standard methods often remain affected by formation damage and mud-filtrate invasion. Quantitative understanding of the process of mud-filtrate invasion is necessary to identity and assess biases in the standard estimates of in-situ compressionaland shear-wave (Pand S-wave) velocities. We describe a systematic approach to quantify the effects of mudfiltrate invasion on borehole acoustic logs and introduce a new algorithm to estimate radial distributions of elastic properties away from the borehole wall. Radial saturation distributions of mud filtrate and connate formation fluids are obtained by simulating the process of mud-filtrate invasion. Subsequently, we calculate radial distributions of the elastic properties using the Biot-Gassmann fluid-substitution model. The calculated radial distributions of formation elastic properties are used to simulate array sonic waveforms. Finally, estimated Pand S-wave velocities for homogeneous, stepwise, and multilayered formation models are compared to quantify mud-filtrate-invasion effects on sonic measurements. We use a nonlinear Gauss-Newton inversion algorithm to estimate radial distributions of formation elastic parameters in the presence of invaded zones using normalized spectral ratios of array waveform data. Inversion examples using synthetic and field data indicate that physically consistent distributions of formation elastic properties can be reconstructed from array waveform data. In turn, radial distributions of formation elastic properties can be used to construct more-realistic near-wellbore petrophysical models for applications in reservoir simulation and production.

Retaining geological realism in dynamic modelling: a channelized turbidite reservoir example from West Africa

ABSTRACT A comprehensive simulation study tested and analysed the sensitivity of dynamic connectivity in turbidite channel reservoirs to a large number of stratigraphic and engineering parameters. The study showed that subseismic shale architecture has a significant effect on reservoir connectivity. However, representing the complete spectrum of fine-scale architectural details in full-field simulation models is beyond the limits of existing computational capabilities. Previous work demonstrated that incorporating geologically based pseudo-relative permeabilities into relatively coarse full-field reservoir models renders practically intractable simulation cases tractable. We developed a methodology for generating pseudo-relative permeabilities at multiple geological scales, incorporating the effect of channel architecture and reservoir connectivity into fast simulation models. We describe a dynamic modelling workflow that integrates geologically based pseudo-relative permeabilities into a two-stage automatic history-matching algorithm. The history-matching problem is posed as one of data conditioning in the Bayesian framework. We show the application of the workflow to a channelized turbidite reservoir in West Africa. It is demonstrated that multiple geologically consistent models that are conditioned to production data can be generated rapidly thanks to optimally coarse simulation models that capture the effect of subseismic channel architecture on recovery behaviour, and run efficiently as the forward model within a Bayesian inference framework. Proof-of-concept tests carried out using field data indicate that the history-matched models predict well-by-well future recovery response with good accuracy.

Estimation of Permeability and Permeability Anisotropy From Straddle-Packer Formation-Tester Measurements Based on the Physics of Two-Phase Immiscible Flow and Invasion

We describe the successful application of a new method to estimate permeability and permeability anisotropy from transient measurements of pressure acquired with a wireline straddle-packer formation tester. Unlike standard algorithms used for the interpretation of formation-tester measurements, the method developed in this paper incorporates the physics of two-phase immiscible flow as well as the process of mudcake buildup and invasion. An efficient 2D (cylindrical coordinates) implicit-pressure explicit-saturation finitedifference algorithm is used to simulate both the process of invasion and the pressure measurements acquired with the straddle-packer formation tester. Initial conditions for the simulation of formation-tester measurements are determined by the spatial distributions of pressure and fluid saturation resulting from mud-filtrate invasion. Inversion is performed with a Levenberg-Marquardt nonlinear minimization algorithm. Sensitivity analyses are conducted to assess non-uniqueness and the impact of explicit assumptions made about fluid viscosity, capillary pressure, relative permeability, mudcake growth, and time of invasion on the estimated values of permeability and permeability anisotropy. * Currently with TOTAL