There are few published velocity and attenuation data for seafloor bedrocks at appropriate confining pressures (1 MPa to 10 MPa). Velocities and attenuations measured at low pressures are affected mainly by open microcracks. However, as the pressure is increased and the microcracks are closed, the effect of microcracks on the velocities and attenuations will be minimal. At elevated pressures, the velocities and attenuations in rocks depend primarily on the elastic moduli of the rock-forming minerals and porosity, which results from the degree of alteration and diagenetic processes that acted on the rocks. The aim of this paper is to investigate the effect of microcracks on the acoustic properties at low pressures (10 MPa effective pressure) and the relationship between the acoustic, petrophysical, and geological properties of seabed rocks at high pressure (40 MPa effective pressure), where the effect of microcracks is minimal. Laboratory measurements of acoustic velocity and attenuation of this kind give a better understanding of these properties at the appropriate pressure (depth) for rocks undergoing different geological (e.g., diagenesis) processes than those buried at greater depth.We measured compressional-and shear-wave velocity and attenuation on a suite of seabed sedimentary and igneous rocks of the northern U.K. continental shelf at effective pressures (confining less pore-fluid pressure) ranging from 10 MPa to 40 MPa. The measurement frequencies range from 0.5 MHz to 1 MHz. We used Winkler and Plona's (1) pulse-echo method to measure velocity and attenuation (quality factor). The porosity and permeability of the rocks range from 0% to about 20% and 0 to about 5 md, respectively. X-ray diffraction (XRD) analysis, petrological studies of polished thin-sections, and scanning electron microscope (SEM) observations show that most of the sandstones have a significant clay content (e.g., kaolinite, illite, and chlorite) and fractures. Most of the igneous rocks are chloritized.We show that the velocities and quality factors of the rocks studied are much lower than those of similar continental rocks. Microporosity formed by the alteration of feldspars, micas, and mafic minerals to clays (e.g., chloritization of pyroxenes) and the corresponding reduction of the elastic moduli are the major processes that result in low velocity and quality factors. Velocity and attenuation models of seabed rocks are critical for the interpretation of seismic data for rocks buried at greater depth. The results of this study suggest that values of velocities and quality factors used for modeling purposes should be lower than assumed normally.
The nature of nonlinear flow in porous media is analyzed by means of the volumetric averaging approach for a medium modeled by diverging/converging capillaries. To clarify the mechanism responsible for the nonlinearity, a physical explanation is deduced for the dispersion term in the averaged momentum equation. With the present periodical model, the numerically obtained microscopic flow fields, in association with the macroscopic coefficients calculated by the average momentum balance, indicated quantitatively that the microscopic inertial phenomena, which lead to distorted pore velocity and pressure fields, is the fundamental reason for the onset of nonlinear effects as filtration velocity increases.
Summary This paper presents a new general method for solving the pressure diffusion equation in laterally composite reservoirs, where rock and fluid properties may change laterally as a function of y in the x − y plane. Composite systems can be encountered as a result of many different types of depositional and tectonic processes. For example, meandering point bar reservoirs may be approximated as lateral composite systems. Reservoirs with edgewater encroachment are another example of such systems. The new solution method presented is based on the reflection-transmission concept of electromagnetics to solve fluid-flow problems in 3D nonhomogeneous reservoirs, where heterogeneity is in only one (y) direction. A general Green's function for a point source in 3D laterally composite systems is developed by using the reflection-transmission method. The solutions in the Laplace transform domain are then developed from the Green's function for the pressure behavior of specific composite reservoirs. The solution method can also be applied to many different types of wells, such as vertical, fractured, and horizontal in composite reservoirs. The pressure behavior of a few well-known laterally composite systems are investigated. It is shown that a network of partially communicating faults and fractures in porous medium can be modeled as composite systems. It is also shown that the existing solutions for a partially communicating fault are not valid when the fault permeability is substantially larger than the formation permeability. The derivative plots are presented for selected faulted, fractured, channel, and composite reservoirs as diagnostic tools for well-test interpretation. It is also shown that if the composite system's permeability varies moderately in the x or y direction, it exhibits a homogeneous system behavior. However, it does not yield the system's average permeability. Furthermore, the composite systems with distributed low-permeability zones behave as if the system has many two no-flow boundaries.
SummaryIn this work, we examine the behavior of pressure-transient data for single and multiphase flow in radially heterogeneous reservoirs. To illustrate multiphase flow behavior in these systems, we focus on heterogeneous gas-condensate reservoirs; however, we also consider other multiphase flow problems. It is well known1 that in some instances, e.g., water injection/falloff in homogeneous reservoirs, pressure-transient data from buildup (or falloff) tests cannot be obtained by superposition of drawdown (injection) pressure responses. In fact, drawdown and buildup reflect properties in different regions of the reservoir. This behavior is common to most occurrences of multiphase reservoir flow and is exaggerated in the presence of radial heterogeneity. This theoretical work describes the information contained in transient pressure derivative data and explains the fundamental difference in behavior between multiphase drawdown and buildup pressure-transient data in radially heterogeneous reservoirs. We show that multiphase buildup data may be treated like single-phase buildup data, but drawdown data is most indicative of properties in that region of the reservoir where mobility is changing most rapidly with time.
Summary Pulse testing is an effective way of understanding fluid reservoirs. Several noise components bias high-sensitivity pressure measurements so that a considerable part of the tests cannot be interpreted conventionally, thus impeding pulse testing's wide-range application. To improve noise filtering, we developed a computerized method of evaluation and noise suppression, which can enhance interpretability effectively. Only 17% of 617 tests performed in Hungary can be interpreted in the usual way, whereas 78% can be interpreted by the method reviewed in this paper. After an enumeration of the pressure changes (noises) disturbing pulse tests, we illustrate our cycle-sum-up method of noise suppressing and the related interpretation procedure. We also report on results of the reproducibility investigations, and we give a brief outline of the basic principles of interpreting reservoirs with multiple faults.
Summary Temperature logs commonly have been used to evaluate fracture height by locating cool anomalies that indicate the locations where cool fracture fluids were injected. Instead of cool anomalies, however, warm anomalies (called "warm noses") often occur on temperature logs run after fracture treatments. When interpreting fracture height from a temperature log, warm anomalies make it difficult to identify the top and bottom of the fracture. We believe that a plausible reason for warm anomalies is that the wellbore and the fracture are not coincident over the entire extent of the fracture; instead, away from the perforations, the fracture and the wellbore may be separated a finite distance that varies with depth. This paper investigates the effect of the existence and magnitude of the displacement between the wellbore and the fracture on wellbore temperature behavior after fracturing. The results obtained explain the "warm noses" on shut-in temperature logs run after a fracture treatment and, more generally, illustrate how fracture-wellbore separation can result in a variety of characteristic temperature log responses. A mathematical model has been developed to simulate the wellbore temperature after fracturing for cases where the wellbore and the fracture are not coincident for the entire extent of the fracture. The study shows that the temperature behavior strongly depends on the pattern and the magnitude of the displacement. When the fracture is perfectly connected with the wellbore, the cool region on the log indicates the top and bottom of the fracture clearly. However, the cool region is much smaller than the fracture height if the wellbore deviates from the fracture at a constant angle away from the perforations—a situation that may occur in a well that is deviated slightly from vertical, for example. Furthermore, "warm noses" appear on the log if the well spirals in a helical trajectory because the spacing between the wellbore and the fracture will vary with depth for this geometry. Therefore, when evaluating a postfracture temperature log, the possibility of a deviated wellbore-fracture system must be considered to avoid misinterpreting the fracture height. Longer shut-in times are shown to improve the fracture-height interpretation.
Summary We discuss and compare three different approaches for permeability determination from logs from a practical point of view. The three methods, empirical, statistical, and the recently introduced "virtual measurement," make use of empirically determined models, multiple variable regression, and artificial neural networks, respectively. We apply all three methods to well log data from a heterogeneous formation and compare the results with core permeability, which is considered to be the standard. Our comparison focuses on the predictive power of each method.
Summary Sonic while drilling has long been considered a major goal by the industry because of its potential applications: real-time determination of pore pressure and overburden gradients, improved lithology change determination, seismic calibration, and detection of seismic reflectors ahead of the bit. Until now, only two methods were available to perform sonic measurements while drilling—the use of continuous coring or a specific measurement while drilling (MWD) tool. Unfortunately, both methods remain very expensive and suffer from technical limitations. A new technology [named pulsed ultrasound on cuttings (PUC)] has been developed to measure both compressional and shear-wave velocities directly on cuttings with dimensions as low as 1 mm. Laboratory and field implementations of the method are presented along with its validation against reference measurements.
Summary The development of a strategy for the detailed three-dimensional (3D) description of permeability was a key ingredient of the recent reservoir characterization study of the Ekofisk field. Because the ultimate objective of this characterization effort was the construction of a new full-field 3D reservoir flow model, permeability and its heterogeneity received special focus. Permeability has a tremendous influence on history matching of reservoir fluid flow models and, in turn, reservoir-management decisions. This is particularly true in a mature, waterflooded field such as Ekofisk. The Ekofisk field is a high-porosity, low-matrix permeability naturally fractured chalk. Fluid-flow characteristics of the reservoir are largely governed by the distribution, orientation, and interconnectivity of the natural-fracture system. To honor this mechanism, an algorithm was developed based on the log linear relationship between fracture spacing (intensity) data from core and well-test effective permeability. To capture the intrinsic heterogeneity and complex nature of Ekofisk field, the basic relationship between fracture intensity and permeability was modified to incorporate variations associated with (1) chalk facies (2) fracture type; (3) porosity; (4) structural location; (5) structural curvature; and (6) silica content. To calibrate the algorithm, permeability determined from distributing total well-test flow capacity (kh) based on production log contribution was used as a tuning parameter. As a final step, geostatistical techniques were used to ensure that permeabilities derived from the algorithm matched those obtained from well-test analysis.
Summary Nuclear magnetic resonance imaging (NMRI) techniques were used for the measurement of the spatial distribution of apertures and two-phase fluid distributions in rock fractures. Rock models of known apertures were used to validate the NMRI technique. NMRI aperture values were in good agreement with nominal and hydraulic aperture values. The fracture signal in porous rock was isolated by NMR spin-spin relaxation times. Areal distributions of oil and water in an immiscible fracture flow were resolved on the basis of their NMR spin-lattice relaxation times.
Summary Systematic time-lapse pulsed-neutron capture (PNC) logging was conducted during a 2-year steam-foam mechanistic field trial in the steamflooded Monarch reservoir, which is composed of interbedded sandstones, conglomerates, siltstones, and diatomaceous mudstones. Observation wells were drilled with one continuously cored through the reservoir interval and two emptied to facilitate better temperature logging. Uncalibrated PNC log responses in the air-filled wells were normalized to water-filled conditions and were used to generate a series of steam/gas saturation profiles that indicate clearly the dynamics of the fluid and foam in the reservoir during the experiment. Correlations between neutron capture cross sections (sigma), mineralogy, and rock chemistry from core samples were examined for additional use of the PNC logs for steamflood reservoir characterization. Sigma was found to increase with increasing clay/mica content and diatomite content. This finding may result in improved stratigraphic correlations of the more laterally continuous diatomaceous mudstones based on PNC logs. The PNC log data from the field trial, when used in conjunction with core, temperature, and pressure data, were critical in developing a better understanding of foam generation and propagation in the reservoir. Furthermore, they minimized the time and cost required to complete the field trial successfully. They also led to opportunities for vertical expansion of steamflooding in the area.
Summary We present a new method to determine average pressure. This method is particularly suited for situations in which no record of the pseudoradial-flow period exists, which is the case in many low-permeability reservoirs. The assumptions of the method we propose are identical to conventional methods, except that the pseudoradial-flow period need not exist. The method may be used in channel-type reservoirs. Example illustrations are presented.
Summary For effective flow-simulation models, it may be important to estimate permeability accurately over several scales of geological heterogeneity. Critical to the data analysis and permeability prediction are the volume of investigation and sampling interval of each petrophysical tool and how each relates to these geological scales. We examine these issues in the context of the As Sarah Field, Sirte Basin, Libya. A geological study of this braided fluvial reservoir has revealed heterogeneity at a series of scales. This geological hierarchy in turn possessed a corresponding hierarchy of permeability variation. The link between the geology and permeability was found to be very important in understanding well logs and core data and subsequent permeability upscaling. We found that the small scale (cm) permeability variability was better predicted using a flushed-zone resistivity, Rxo, tool, rather than a wireline porosity measurement. The perm-resistivity correlation was strongest when the probe permeabilities were averaged to best match the "window size" of the wireline Rxo. This behavior was explained by the geological variation present at this scale. For the larger scale geological heterogeneity, the production flowmeter highlighted discrepancies between flow data and averaged permeability. This yielded a layered sedimentological model interpretation and a change in averaging for permeability prediction at the bedset scale (ms-10 × ms).
Summary Very thin, laminated sand-shale sequences pose a challenge to petrophysical evaluation. The poor vertical resolution of the log measurements results in pessimistic estimates of hydrocarbon volumes and producibility. An earlier proposal by Flaum1 to enhance the resolution of the analysis using a high-resolution clay indicator did not account for variations in clay mineralogy and porosity with clay content. We present a technique to incorporate results of core mineralogy measurements to ensure a geologically consistent resolution enhancement of the petrophysical analysis, and we compare the results in an actual field example.
Summary Discovered in 1955, the Lower Lagunillas member reservoir of the Miocene Lagunillas formation of Bloques III and IV of the Bachaquero field was originally estimated to contain 2 billion barrels of oil. This reservoir interval traditionally has been interpreted to have been deposited in a delta plain setting and to comprise three reservoir subdivisions that were developed as a single drainage unit. Field performance, however, has indicated that the reservoir is more complex; the present study was initiated to provide a revised development strategy. Sedimentological interpretation of four cored wells has led to the development of a new model of deposition in tidally influenced lower delta plain and delta-front settings. This model is supported by Fourier transform infrared (FT-IR) measurement of clay concentrations and prompt neutron capture boron measurements that are indicative of a brackish water-depositional setting. We used this geological model to guide correlation of wireline logs from 46 wells in the central part of Bloque IV and to provide a high-resolution sequence stratigraphic model of the Lower Lagunillas reservoir. Eleven genetic layers are identified that are separated by locally developed intraformational seals into up to eight drainage units. High permeability, tidally influenced channel-fill sands have acted as preferential conduits for gas influx, leaving bypassed oil in lower quality sands that were deposited as tidal deltas and bars. This reservoir model has been supported by re-examination of production data and by openhole measurements in a recent infill well and cased- hole logging of two other wells in the study area. The new model will form the basis for redevelopment of the Lower Lagunillas reservoir to increase recovery further from this mature field.
Summary This paper examines the sensitivities of interwell tracer and transient-pressure response to spatial distribution of permeability heterogeneity. On the basis of these sensitivities, we describe a formalism to quantify the resolution and spatial averaging associated with estimates of permeabilities derived through inversion of tracer and/or pressure data. The resolution is a measure of the effectiveness of the data in estimating local-scale (gridblock) permeabilities. The spatial averaging kernels quantify the inherent averaging associated with our estimates because of limited data or sampling. By examining the resolution and averaging kernels as a function of various data types, we can evaluate quantitatively the relative importance of tracer vs. pressure data for heterogeneity characterization and the improvement in estimates obtained by combining the data types. We illustrate the concepts by application to transient-pressure and tracer response from five-spot patterns and also to an experimental tracer response from a well-characterized slab of Antolini sandstone. Tracer data is found to yield much better resolution compared to transient-pressure response. Also, both transient-pressure and tracer data appear to resolve barriers to flow better rather than channels to flow.
Summary Drawdown tests are rarely interpreted unless accompanied by instantaneous surface or downhole rate measurements. Rate variations prevent a constant-rate analysis in most situations. Unsteady wellbore dynamics precipitated by progressive formation cleanup, multiphase fluid flow, and wellbore thermal effects influencing compressible fluids, to name a few, may prevent one from obtaining a stable surface rate. This reality compels an analyst to fall back upon buildup interpretation. Thus, one typically presupposes that the rate was held constant before shut-in. Drillstem tests and long-duration exploratory well tests are cases in point. This conventional practice raises an important question: Can we calculate a variable-rate history such that the drawdown analysis will be consistent with the buildup? This paper presents a method to interpret drawdown data whenever variable rates are encountered, either inherent in a test or induced by design, such as in a gas-lift well test. The method entails a stepwise procedure. First, buildup data are interpreted assuming a constant rate during drawdown. Second, the estimated parameters are used to compute instantaneous rate corresponding to each pressure data point by superposing constant-pressure solution with an appropriate pD model. The reconstructed rate history is then used to perform the variable-rate (convolution) analysis of drawdown data. Third, the new rate history is used to reinterpret buildup data. Parameters obtained from the two analyses provide the desired consistency. The proposed procedure is entirely general, in that any appropriate reservoir pD model may be used to compute the instantaneous rate values. However, best results are obtained when the late-time data are free from outer-boundary effects. We present field examples from various scenarios to show the usefulness of this approach. These examples include a short-duration onshore drillstem test (DST), a gas-lift well test involving a gas-vent period, a long-duration production test with suspected pressure-sensitive rock properties, and a slug/closed chamber test. In all cases, we have shown the synergy between the results of the two tests.
Summary In this paper, we discuss the influence of wellbore hydraulics in a horizontal wellbore on horizontal well pressure transient behavior. A finite-conductivity solution is obtained by a semianalytical method that incorporates three-dimensional (3D) flow in a reservoir and fluid flow inside a wellbore ranging from laminar to turbulent-flow regimes. On the basis of the finite-conductivity solution, finite-conductivity pressure transients are presented in terms of type curves, pressure derivatives, production distribution along a wellbore, and a pressure difference between the two ends of a wellbore. Furthermore, we provide a quantified criterion that allows us to approximate finite-conductivity solutions to an infinite-conductivity solution with respect to the following parameters: a formation flow capacity, a wellbore length, a wellbore radius, a relative pipe roughness, and the Reynolds number at the downstream end of a wellbore.
Summary We describe and demonstrate a method for the determination of three-phase relative permeability functions at reservoir conditions. Two- and three-phase displacement experiments are conducted on a low-permeability chalk sample, and estimates of the three-phase relative permeability and capillary pressure functions are obtained. We also calculate three-phase relative permeabilities with the Stone predictive model, and we evaluate them by simulating the experimental data.
Summary Reservoir simulations are limited to large-scale gridblocks because of prohibitive computational costs of fine-grid simulations. Rock properties, such as permeability, are measured on a scale smaller than coarse-scale simulation gridblocks. Therefore, the properties defined on a smaller scale are upscaled to a coarser scale. Few prior studies on permeability upscaling paid special attention to the problem of radial flow in the vicinity of a wellbore. This study presents an analytical method to calculate effective permeability of a coarse-grid wellblock from its constituent fine gridblocks. The method uses the incomplete-layer upscaling procedure, which is modified for radial flow around wellbore but applied to permeability heterogeneity defined in a Cartesian grid scheme. The method is validated by numerical simulations of primary and secondary recovery processes involving two-dimensional (2D) and three-dimensional (3D) systems. The simulation results with permeabilities from radial flow upscaling for wellblocks agreed better with the simulation results with the original permeabilities than results from linear-flow upscaling.
