Simple Reservoir Model Research Articles

Progress in the hydrologic simulation of time variant recharge areas of karst systems – Exemplified at a karst spring in Southern Spain

A specific characteristic of karst systems is the occurrence of time variant recharge areas. In our study we present a new type of hydrological karst model and a new calibration approach both considering this specific characteristic. The new model type considers the spatial variability of karst system properties by distribution functions, and is compared to a simple reservoir model. Both models are applied to a karst system in Southern Spain where objective functions applied on hydrodynamic and hydrochemical information helped to determine model parameters playing a role for hydrodynamic response. Thereafter, the recharge area is determined separately for individual hydrological years and for the entire time series by calibrating the model to match the water balance. We show that hydrochemical information is crucial to find a reasonable set of parameters for both models. Considering different hydrological years, we find that the recharge area is changing significantly (from 28 to 53km2). The newly developed model is able to reproduce this variation and provide acceptable simulation results for the entire time series of available data. The classic reservoir model shows inferior performance concerning hydrodynamics and fails to reproduce the water balance because it does not consider variations of recharge area. Our calibration approach allows identifying a variable recharge area and our new model is able to reproduce its variability. Hence we obtain a more realistic system representation, which can be of high significance when models are used for prediction, i.e. beyond the conditions they were calibrated, e.g. for land-use or climate change scenarios.

Investigation of the sampling performance of ensemble-based methods with a simple reservoir model

The application of the ensemble Kalman filter (EnKF) for history matching petroleum reservoir models has been the subject of intense investigation during the past 10 years. Unfortunately, EnKF often fails to provide reasonable data matches for highly nonlinear problems. This fact motivated the development of several iterative ensemble-based methods in the last few years. However, there exists no study comparing the performance of these methods in the literature, especially in terms of their ability to quantify uncertainty correctly. In this paper, we compare the performance of nine ensemble-based methods in terms of the quality of the data matches, quantification of uncertainty, and computational cost. For this purpose, we use a small but highly nonlinear reservoir model so that we can generate the reference posterior distribution of reservoir properties using a very long chain generated by a Markov chain Monte Carlo sampling algorithm. We also consider one adjoint-based implementation of the randomized maximum likelihood method in the comparisons.

Reflection characteristics of linear carbon dioxide transition layers

Seismic monitoring of underground [Formula: see text] accumulations is a subject of growing interest in applied geophysics. Due to their large impedance contrasts, attention is focused on accumulations of high [Formula: see text] saturation in most cases. However, low-saturation zones with dispersed carbon dioxide, or saturation transition layers, may have an important role in the propagation of waves within the reservoir, giving rise to amplitude and phase changes of the seismic signals. With this motivation, we studied the reflectivity response of a simple reservoir model with a given [Formula: see text] saturation-depth profile, on a theoretical basis. We investigated the influence of the overall saturation, vertical extent, and spatial fluid distribution of a carbon dioxide transition zone in the reflectivity of a reservoir. The parametric analysis entails the computation of the generalized P-wave reflection coefficient and its variations with ray angle (AVA) and frequency (AVF). The combined analysis of AVA and AVF can help to characterize and monitor [Formula: see text] transition layers within geological storage sites.

Simple Deterministically Constructed Cycle Reservoirs with Regular Jumps

A new class of state-space models, reservoir models, with a fixed state transition structure (the "reservoir") and an adaptable readout from the state space, has recently emerged as a way for time series processing and modeling. Echo state network (ESN) is one of the simplest, yet powerful, reservoir models. ESN models are generally constructed in a randomized manner. In our previous study (Rodan & Tiňo, 2011), we showed that a very simple, cyclic, deterministically generated reservoir can yield performance competitive with standard ESN. In this contribution, we extend our previous study in three aspects. First, we introduce a novel simple deterministic reservoir model, cycle reservoir with jumps (CRJ), with highly constrained weight values, that has superior performance to standard ESN on a variety of temporal tasks of different origin and characteristics. Second, we elaborate on the possible link between reservoir characterizations, such as eigenvalue distribution of the reservoir matrix or pseudo-Lyapunov exponent of the input-driven reservoir dynamics, and the model performance. It has been suggested that a uniform coverage of the unit disk by such eigenvalues can lead to superior model performance. We show that despite highly constrained eigenvalue distribution, CRJ consistently outperforms ESN (which has much more uniform eigenvalue coverage of the unit disk). Also, unlike in the case of ESN, pseudo-Lyapunov exponents of the selected optimal CRJ models are consistently negative. Third, we present a new framework for determining the short-term memory capacity of linear reservoir models to a high degree of precision. Using the framework, we study the effect of shortcut connections in the CRJ reservoir topology on its memory capacity.

Self-potential anomalies induced by water injection into hydrocarbon reservoirs

The injection of cold water into a hydrocarbon reservoir containing relatively warmer, more saline formation brine may generate self-potential anomalies as a result of electrokinetic, thermoelectric, and/or electrochemical effects. We have numerically assessed the relative contributions of these effects to the overall self-potential signal generated during oil production in a simple hydrocarbon reservoir model. Our aim was to determine if measurements of self-potential at a production well can be used to detect the movement of water toward the well. The coupling coefficients for the electrochemical and thermoelectric potentials are uncertain, so we considered four different models for them. We also investigated the effect of altering the salinities of the formation and injected brines. We found that the electrokinetic potential peaked at the location of the saturation front (reaching values of 0.2 mV even for the most saline brine considered). Moreover, the value at the production well increased as the front approached the well, exceeding the noise level (∼ 0.1 mV). Thermoelectric effects gave rise to larger potentials in the reservoir (∼10 mV), but values at the well were negligible [Formula: see text] until after water breakthrough because of the lag in the temperature front relative to the saturation front. Electrochemical potentials were smaller in magnitude than thermoelectric potentials in the reservoir but were measurable [Formula: see text] at the well because the salinity front was closely associated with the saturation front. When the formation brine was less saline (∼1 mol/liter), electrokinetic effects dominated; at higher salinities (∼5 mol/liter), electrochemical effects were significant. We concluded that the measurement of self-potential signals in a production well may be used to monitor the movement of water in hydrocarbon reservoirs during production, but further research is required to understand the thermoelectric and electrochemical coupling coefficients in partially saturated porous media.

Population-Based Optimization Algorithms for History Matching and Uncertainty Quantification: PUNQ-S3

This article, written by Senior Technology Editor Dennis Denney, contains highlights of paper SPE 136861, ’Comparative Study of Novel Population-Based Op timization Algorithms for History Matching and Uncertainty Quantification: PUNQ-S3 Revisited,’ by Yasin Hajizadeh, SPE, Mike Christie, SPE, and Vasily Demyanov, Institute of Petroleum En gineering, Heriot-Watt University, prepared for the 2010 Abu Dhabi International Petroleum Exhibition & Conference, Abu Dhabi, UAE, 1-4 November. The paper has not been peer reviewed. Multiple history-matched models are essential for a realistic uncertainty estimate of the field’s future behavior. This study compared application of ant-colony optimization (ACO), differential evolution (DE), and neighborhood algorithms (NAs) for history matching and uncertainty quantification of the PUNQ-S3 reservoir, a synthetic benchmark case with challenging parameterization, history-matching, and uncertainty-quantification steps. Introduction History matching of reservoir models and uncertainty quantification of the predictions are two important steps in any field-management process. In the history-matching phase, simulation models are calibrated on the basis of the observed production history of the reservoir. Parameters of the reservoir model are perturbed, and the model’s output is compared with available fluid-production rates or pressure measurements. This procedure is repeated with new parameter values until good agreement is obtained between output of the simulation and observations. History matching is an inverse problem with nonunique solutions. Multiple combinations of reservoir properties can provide a good match to observed field behavior. To quantify the uncertainty of predictions realistically, multiple history-matched reservoir models are required. Diverse models are likely to show different production behavior in the future because of different reservoir parameters. Recently, ACO and DE algorithms have been applied to history matching of a simple reservoir model with a small number of unknowns (eight). The subject methods for history matching were applied to a more-complex reservoir with 45 uncertain parameters, and the results were compared to those from NA. Originally, ACO was proposed for problems with discrete parameter space, and it later was adopted to handle continuous-optimization problems. DE is a powerful global-optimization algorithm that is a parallel-population-based search algorithm. The NA is a recent stochastic-optimization method that uses simple geometrical constructs called Voronoi cells to find good-fitting regions of the search space. Voronoi cell is a method to decompose the search space into n cells around n points by centering on the generated points. Each of these cells is the nearest neighborhood region of the points. Case Study The PUNQ-S3 reservoir-simulation model is a five-layer model. The top depth of PUNQ-S3 reservoir is 2430 m. It has a 1.5° dip angle and is bounded by faults to the east and south. A relatively strong aquifer on the north and west provides pressure support. Because of this pressure support, no injection wells have been drilled in this reservoir. There also is a small gas cap in the reservoir in Layer 1, and no wells are completed in this layer because of the effect of free-gas production on recovery from the reservoir. There are six production wells, all near the initial gas/oil contact. Three producers are perforated in Layers 4 and 5. Two producers are completed in Layers 3 and 4, and one producer is perforated only in Layer 4. One of the producers is completed near the aquifer, and water breakthrough was observed in the seventh year. Free-gas production starts in Years 4 and 5 in two of the producers. There also are positions for five infill wells.

Groundwater response to leakage of surface water through a thick vadose zone in the middle reaches area of Heihe River Basin, in China

Abstract. The behavior of groundwater response to leakage of surface water in the middle reaches area of Heihe River Basin is significantly influenced by a thick vadose zone. The groundwater regime is a result of two recharge events due to leakage of Heihe River and irrigation water with different delay time. A nonlinear leakage model is developed to calculate the monthly leakage of Heihe River in considering changes of streamflow, river stage and agricultural water utilization. Numerical modeling of variable saturated flow is carried out to investigate the general behaviors of leakage-recharge conversion through a thick vadose zone. It is found that the recharge pattern can be approximated by simple reservoir models of leakages under a river and under an irrigation district with different delay-time and recession coefficient. A triple-reservoir model of relationship between surface water, vadose zone and groundwater is developed. It reproduces the groundwater regime during 1989–2006 with variable streamflow of Heihe River and agricultural water utilization. The model is applied to interpret changes of groundwater level during 2007–2008 that observed in the Watershed Airborne Telemetry Experimental Research (WATER).

Simplified Modeling of Turbidite Channel Reservoirs

Summary Effective properties can represent fine-scale geologic heterogeneities in simple full-field reservoir models without having to model them explicitly. A comprehensive simulation study tests the sensitivity of dynamic connectivity in turbidite channel reservoirs to a large number of stratigraphic and engineering parameters. Simulations performed using geologically realistic sector models at multiple levels of stratigraphic resolution show that dynamic connectivity is governed by large-scale architectural parameters, such as meander-belt size, net-to-gross ratio, degree of depositional-storey amalgamation, and stratigraphic parameters that describe the shale architecture at multiple scales (e.g., shale-drape coverage and shale-drape frequency of occurrence). We demonstrate how to rapidly generate effective properties at multiple geologic scales, incorporating the effect of channel architecture and reservoir connectivity into simple dynamic models. Use of simple dynamic models in conjunction with effective properties, principally geologically based pseudorelative permeabilities, accelerates the simulation workflow significantly. We show that a statistical distribution of the recovery factor (RF) can be produced within hours instead of days by the combined use of Monte Carlo simulation and a simple dynamic model with effective properties. Recovery factors estimated with our simplified modeling method agree well with observed RF distributions of turbidite channel reservoirs with significant production history.

Time-lapse seismic modeling assisted by numerical reservoir simulation of water and gas flooding scenarios in oil reservoirs

In this project, we link fluid flow simulation results to time-lapse seismic through rock physics and modeling. Our goal is to examine the main effects of permeability barriers on seismic response using fluid flow simulations to generate pressure and saturation fields. To explore this problem, we have carried out water and gas injection numerical experiments in a simple reservoir model which has vertical and horizontal variations of porosity as well as permeability barriers. In each experiment, we change the barrier permeability values. By using fluid substitution theory, Gassmann and patchy models, and Batzle and Wang's empirical relationship we model the main seismic parameters, such as acoustic impedance and compressional velocity. After that, we generate synthetics seismograms and some contrast sections to compare the seismic images prior and after fluid injection events in subsequent time periods to analyze possible differences in the seismic parameters due to changes in barriers properties. The results show that barriers can increase fluid pore pressure changing the bulk modulus in the regions with barriers. The results also show that water flow does not have significant impact on seismic response when the barrier is present. On the other hand, gas flow and the degree of impermeability of the barrier can help us to understand how the barriers act on the seismic response and thus to reduce uncertainty. Finally, this paper presents a methodology to examine barriers effects on seismic response.

Real-Time Reservoir Model Updating Using Ensemble Kalman Filter With Confirming Option

Summary The ensemble Kalman Filter technique (EnKF) has been reported to be very efficient for real-time updating of reservoir models to match the most current production data. Using EnKF, an ensemble of reservoir models assimilating the most current observations of production data is always available. Thus, the estimations of reservoir model parameters, and their associated uncertainty, as well as the forecasts are always up-to-date. In this paper, we apply the EnKF for continuously updating an ensemble of permeability models to match real-time multiphase production data. We improve the previous EnKF by adding a confirming option (i.e., the flow equations are re-solved from the previous assimilating step to the current step using the updated current permeability models). By doing so, we ensure that the updated static and dynamic parameters are always consistent with the flow equations at the current step. However, it also creates some inconsistency between the static and dynamic parameters at the previous step where the confirming starts. Nevertheless, we show that, with the confirming approach, the filter shows better performance for the particular example investigated. We also investigate the sensitivity of using a different number of realizations in the EnKF. Our results show that a relatively large number of realizations are needed to obtain stable results, particularly for the reliable assessment of uncertainty. The sensitivity of using different covariance functions is also investigated. The efficiency and robustness of the EnKF is demonstrated using an example. By assimilating more production data, new features of heterogeneity in the reservoir model can be revealed with reduced uncertainty, resulting in more accurate predictions of reservoir production. Introduction The reliability of reservoir models could increase as more data are included in their construction. Traditionally, static (hard and soft) data, such as geological, geophysical, and well log/core data are incorporated into reservoir geological models through conditional geostatistical simulation (Deutsch and Journel 1998). Dynamic production data, such as historical measurements of reservoir production, account for the majority of reservoir data collected during the production phase. These data are directly related to the recovery process and to the response variables that form the basis for reservoir management decisions. Incorporation of dynamic data is typically done through a history-matching process. Traditionally, history matching adjusts model variables (such as permeability, porosity, and transmissibility) so that the flow simulation results using the adjusted parameters match the observations. It usually requires repeated flow simulations. Both manual and (semi-) automatic history-matching processes are available in the industry (Chen et al. 1974; He et al. 1996; Landa and Horne 1997; Milliken and Emanuel 1998; Vasco et al. 1998; Wen et al. 1998a, 1998b; Roggero and Hu 1998; Agarwal and Blunt 2003; Caers 2003; Cheng et al. 2004). Automatic history matching is usually formulated in the form of a minimization problem in which the mismatch between measurements and computed values is minimized (Tarantola 1987; Sun 1994). Gradient-based methods are widely employed for such minimization problems, which require the computation of sensitivity coefficients (Li et al. 2003; Wen et al. 2003; Gao and Reynolds 2006). In the recent decade, automatic history matching has been a very active research area with significant progress reported (Cheng et al. 2004; Gao and Reynolds 2006; Wen et al. 1997). However, most approaches are either limited to small and simple reservoir models or are computationally too intensive for practical applications. Under the framework of traditional history matching, the assessment of uncertainty is usually through a repeated history-matching process with different initial models, which makes the process even more CPU-demanding. In addition, the traditional history-matching methods are not designed in such a fashion that allows for continuous model updating. When new production data are available and are required to be incorporated, the history-matching process has to be repeated using all measured data. These limit the efficiency and applicability of the traditional automatic history-matching techniques.

Is the groundwater reservoir linear? Learning from data in hydrological modelling

Abstract. Although catchment behaviour during recession periods is better identifiable than in other periods, the representation of hydrograph recession is often weak in hydrological simulations. Among the various aspects that influence model performance during low flows, in this paper we concentrate on those more inherently related to the modelling, such as the development of a suitable model conceptualization, and the choice of an appropriate calibration strategy. In this context we develop a methodology where the calibration procedure is combined with an iterative process of model improvement, to obtain an optimal model configuration that performs well both during low flows and high flows. The methodology starts by calculating a synthetic master recession curve that represents the long-term recession of a given catchment. Subsequently, using a simple reservoir model, we determine the storage-discharge relation that simulates the slow hydrograph component. This relation is determined without making any a-priori assumption on its form and is inferred from discharge data available through an iterative process. Next, high flow related parameters are recalibrated separately, to avoid that the simulation of low discharges is neglected in favour of a higher performance in simulating peak discharges. This methodology is applied on several catchments in Luxembourg, and as a result we determined that in all catchments except one (where human interference is high) within the chosen model structure a linear reservoir describes best the observed groundwater behaviour. This result is used to trigger a discussion as to the general suitability of the use of a linear groundwater reservoir in hydrological modelling.

FLOOD PREDICTIONS IN JAPAN AND PUB, PREDICTIONS IN UNGAUGED BASINS

Flood and sediment disasters are quite common in Japan. To establish countermeasures for flood and sedimentation disasters, the roles of rainfall-runoff models are significant. Various kinds of rainfall-runoff models have been developed and applied in Japan; however their comparative evaluations are still not well performed, especially from the view point of predictive uncertainties. A sound evaluation of rainfall-runoff models is indispensable to reduce the prediction uncertainties and to enhance the prediction accuracy. In 2003 the International Association of Hydrological Sciences (IAHS) initiated a global ten-year initiative: Predictions in Ungauged Basins (PUB). The PUB initiative (see www.iahs.info for details) aims at achieving major advances in the capacity to make reliable predictions in ungauged basins. Recently a PUB secretariat has been launched at the International Water Management Institute (IWMI) in Colombo, Sri Lanka. The thematic working groups (TWGs) and the national working groups (NWGs) are formed under the science steering committee of PUB. Japan, China, Korea, Nepal, and Thailand have actively promoted the PUB research to solve their problems in hydrology and water resources cooperatively. One of the PUB research topics in Japan is to develop a model evaluation method that accesses model performances and prediction uncertainties. This is a base to establish a rainfall-runoff modeling guideline to recommend a suitable hydrologic model in gauged and ungauged basins. The presentation includes flood disasters and flood runoff modeling in Japan, fundamental research issues to establish a hydrologic modeling guideline, and PUB activities especially in Asian countries. Flood runoff modeling in Japan Pioneering works for flood runoff modeling in Japan include the physically based hydrologic modeling by Ishihara and Takasao (1959, 1962), who achieved the theoretical development of the kinematic wave model for hillslope rainfall-runoff phenomena and proposed a variable sources area concept. Kimura (1960) proposed the storage function method, which is a simple nonlinear reservoir model. This model is still widely used for estimating design floods in Japanese river basins. The tank model proposed by Sugawara (1972, 1995) is another widely used model in Japan. In the last two decades, many studies have been conducted to analyze the relations between runoff and catchment properties such as topography, land use, soil types and so on. The relations between lumped and distributed hydrologic modeling structure have also been a major research topic. Physically based distributed models have been constructed and applied together with the development of numerical geographic information and radar rainfall observation technology. These models are extended to include dam reservoir operations to analyze human-nature interactions. To apply hydrologic models to continental scale basins with atmospheric general circulation models is also actively conducted to access water resources in global scale. Need of model evaluation method and modeling guideline To wisely apply hydrologic models, we need a modeling guideline that suggests a suitable model with settings such as model resolution, input data resolutions, parameter identifications and so on. The storage function method is still widely used in practical engineering works in Japan, though many models having more physically-based hydrologic background have been proposed. One of the reasons for not applying newly developed models in engineering purposes is that there exist no well-defined methods or indices that can intercompare the performances and predictive uncertainties among different models. The well defined evaluation method is also important to understand the insufficiency of existing models, which leads to develop an innovative next generation hydrologic model. Fundamental research issues for establishing modeling guideline The results of a hydrological model depend on many factors, including the forcing inputs, process descriptions, parameters and landscapes. It is not easy to define their importance and compare their influences in the modeling. Accurate descriptions of forcing inputs, process description, parameters and landscapes are practically impossible because of their heterogeneity in space and time. However, existing knowledge in hydrology has already identified important processes and their limitations in describing the rainfall runoff processes. In addition, scales and scaling effect are also significant in hydrological modeling. There exist certain thresholds in forcing inputs, parameter distributions, process recognitions and the landscapes that provides an acceptable accuracy in the modeling results. It is necessary to investigate these issues in detail and to identify the thresholds that define the appropriate scale of observation, process description, parameters and landscapes for establishing the modeling guideline. Annual Journal of Hydraulic Engineering, JSCE, Vol.50, 2006, February

Generation of Low-Order Reservoir Models Using System-Theoretical Concepts

Summary We present five methods to derive low-order numerical models of two-phase (oil/water) reservoir flow, and illustrate their features with numerical examples. Starting from a known high-order model, these methods apply system-theoretical concepts to reduce the model size. Using a simple but heterogeneous reservoir model, we illustrate that the essential information of the model can be captured by a limited number of state variables (pressures and saturations). Ultimately, we aim at developing computationally efficient algorithms for history matching, optimization, and the design of control strategies for smart wells. In this study we applied (1) modal decomposition, (2) balanced realization, (3) a combination of these two methods, (4) subspace identification, and (5) proper orthogonal decomposition (POD), also known as principal component analysis, Karhunen-Loève decomposition, or the method of empirical orthogonal functions. Methods 1 through 4 result in linear low-order models, which are only valid during a limited time span. However, the POD results in a nonlinear model that remains valid over a much longer period. Methods that result in linear low-order models are not very promising for speeding up reservoir simulation. POD, however, has the potential to improve computational efficiency in the case of multiple simulations of the same reservoir for different well operating strategies, but further research is required to quantify this scope. The potential benefit of low-order models is therefore mainly in the development of low-order control algorithms, and in history matching, where the use of reduced models may form an alternative to classical regularization methods.

Carbonate Reservoir Characterization

Technology Today Series articles are general, descriptive representations that summarize the state of the art in an area of technology by describing recent developments for readers who are not specialists in the topics discussed. Written by individuals recognized as experts in the area, these articles provide key references to more definitive work and present specific details only to illustrate the technology. Purpose: to inform the general readership of recent advances in various areas of petroleum engineering. During the past 15 years, methods and technology for predicting the performance of carbonate reservoirs have improved dramatically. This advance occurred in response to the realization that more than half of the oil that could be swept by waterflooding is not contacted and remains in the reservoir. Attempts to simulate this performance and locate the remaining oil by use of simple reservoir models and newly developed flow-simulation computer programs have failed mainly because of the extreme heterogeneity that characterizes carbonate reservoirs. It is, in fact, the extreme geologic and petrophysical heterogeneity typical of carbonate reservoirs that distinguishes carbonate from siliciclastic reservoirs. Research programs focused on understanding the nature of the heterogeneity and developing methods to characterize carbonate reservoirs, together with improvements in computer capability and simulation programs, have led to more reliable predictions of reservoir performance and to methods for locating volumes of unswept oil in reservoirs under waterflood. Reservoir characterization encompasses the understanding and methods used to characterize reservoir heterogeneity. It can be defined as the construction of realistic 3D images of petrophysical properties used to predict reservoir performance, and it is a multidisciplinary, integrated task involving expertise in reservoir geology, geophysics, petrophysics, well logging, geostatistics, and reservoir engineering. Three-dimensional images are obtained from geological models constructed with core, wireline-log, and geophysical data. Petrophysical properties, obtained from core, wireline-log, and production data, are distributed within the geological model by linking petrophysical properties to geologic fabrics and by use of advanced geostatistical and geophysical methods. Finally, the model is put into a numerical simulator for testing and predicting future performance. The extreme petrophysical heterogeneity found in carbonate reservoirs is clearly demonstrated by the wide variability observed in porosity-permeability crossplots of core-analysis data. Research has shown that basic rock fabrics dominate control of petrophysical heterogeneity; within a rock-fabric facies, porosity and permeability have little spatial correlation and are widely variable at the scale of inches and feet. Permeability, in particular, can vary by a factor of 10 or more at the small scale and is nearly randomly distributed (Fig. 1).1,2 This result suggests that much of the variability observed in core-analysis data is spatial noise and can be averaged within rock-fabric facies for the purposes of constructing a reservoir model. Only rock fabrics, not pore-throat size, permeability/porosity ratio, or flow-zone indicators, have vertical and lateral continuity. Therefore, rock-fabric facies are the basic elements for characterizing a carbonate reservoir.3 Rock fabrics are geologic descriptors that characterize pore size according to particle size and sorting, interparticle porosity, and various types of vuggy porosity. The main limestone rock fabrics are grainstone, grain-dominated packstone, and mud-dominated fabrics. Dolostone rock fabrics are similar but require a description of dolomite crystal size in mud-dominated dolostones as an added control on pore size. These basic fabrics are modified by the amount of fabric-selective vuggy pore space,4 and many rock fabrics can be linked directly to depositional facies. However, some rock fabrics cannot be linked to depositional facies because extensive modifications to the fabric have occurred since deposition through a geologic process known as diagenesis. Constructing models of reservoirs comprising complex fabrics, such as fracture and karst fabrics, is difficult and is the subject of current research. Each rock fabric has a specific porosity-permeability transform, and the vertical stacking of rock-fabric facies, together with interparticle porosity, provides the basis for estimating permeability in uncored wells. The wireline-log problem is determining interparticle porosity, as well as total porosity and rock fabric, for input into a general porosity-permeability transform. Porosity, acoustic velocity, resistivity, and saturation logs are used for this task, and calibrating wireline-log responses to core descriptions of rock fabrics is key to developing useful algorithms.5 Because rock-fabric and petrophysical data obtained from cores and wireline logs are one-dimensional, a geological framework is required to distribute the data in 3D space. In the past, geological models were constructed by identifying depositional facies from core data, then distributing those facies by use of depositional models on the basis of modern carbonate depositional processes. However, reservoirs described in this manner do not contain sufficient detail to capture basic reservoir heterogeneities, and facies correlations from well to well often are highly uncertain. Development of sequence stratigraphic methods greatly enhanced the accuracy of well-to-well correlations and provided the means of capturing basic scales of reservoir heterogeneity.

Oil field subsidence phenomena

Subsidence of an chalky oil field is described. The mechanical behaviour of the chalk partly saturated by oil and water is described and allows to model the compaction occurring within a simple reservoir model during the depletion as well as during the water injection.

Semi-Analytical Model for Thermal Effect on Gas Well Pressure-Buildup Tests

Summary This paper presents a semi-analytical wellbore/reservoir model1 that can describe general wellbore effects, especially the thermal effect, on high-temperature gas well pressure-buildup tests. A numerical simulator has been developed from the model. Using different combinations of wellbore and reservoir parameters, the simulator generated curve shapes that differed with wellbore thermal effects. Many of the curve shapes have been observed in the field.2,3 Using the results from this paper, engineers can distinguish between general wellbore effects and reservoir behavior in the pressure data, which will make the interpretation more accurate. Also, with the help of the simulator developed from the model, engineers can effectively design gas well pressure-buildup tests by running the simulator to determine the minimum time required to obtain the data not distorted by the wellbore effects.4 The governing equations of the wellbore model are based on mass, momentum, and energy balances for single-phase gas in one-dimensional space. The gas pressure/volume/temperature correlation was also used. Different flow regimes (laminar, transitional, and turbulent) inside the wellbore are modeled for calculating the friction factor. As one boundary condition, a simple analytical reservoir model was connected to the wellbore model at the bottomhole using Duhamel's principle. Heat-loss effects account for forced-convectional heat transfer inside the tubing, heat conduction between tubing and formation, natural convection and radiation heat transfer of annular fluid, and transient heat flow in the formation. Pressure, temperature, velocity, and gas properties inside the wellbore can be predicted at any depth during an entire pressure-buildup test. Variable wellbore storage, momentum, and thermal effects can be simulated.

Testing the USA EPA's ISCST-Version 3 model on dioxins: a comparison of predicted and observed air and soil concentrations

The central purpose of our study was to examine the performance of the United States Environmental Protection Agency's (EPA) nonreactive Gaussian air quality dispersion model, the Industrial Source Complex Short-Term Model (ISCST3) Version 98226, in predicting polychlorinated dibenzodioxins and polychlorinated dibenzofurans concentrations (subsequently referred to as dioxins and furans, or CDD/Fs) in both air and soil near the Columbus Municipal Solid Waste-to-Energy Facility (CMSWTE) in Columbus, OH. During its 11 yr operation, the CMSWTE was estimated to be emitting nearly 1 kg of CDD/F Toxic Equivalents (TEQs) per year, making it one of the highest single emitters of dioxin in the United States during its operation. An ambient air-monitoring study conducted in 1994, prior to its shutdown in December of 1994, clearly identified high dioxin air concentration in the downwind direction during two sampling events. In one of the events, the CMSWTE stack was concurrently monitored for dioxins. A soil sampling study conducted in 1995/1996 was similarly able to identify an area of impacted soil extending mainly in the predominant downwind direction up to 3 km from the CMSWTE. Site-specific information, including meteorological data, stack parameters and emission rates, and terrain descriptions, were input into ISCST3 to predict ground-level 48-h concentrations which could be compared with the 48-h measured air concentrations. Predicted annual average dry and wet deposition of particle-bound dioxins were input into a simple soil reservoir model to predict soil concentrations that would be present after 11.5 yr of emissions, which were compared to measured concentrations. Both soil- and air-predicted concentrations were generally within a factor of 10 of observations, and judged to be reasonable given the small number of observations and the uncertainties of the exercise. Principal uncertainties identified and discussed include: source characterization (stack emission rates of dioxins), meteorological data, and atmospheric and soil fate and transformation processes of the dioxins

Carbonate reservoir characterization

Technology Today Series articles are general, descriptive representations that summarize the state of the art in an area of technology by describing recent developments for readers who are not specialists in the topics discussed. Written by individuals recognized as experts in the area, these articles provide key references to more definitive work and present specific details only to illustrate the technology. Purpose: to inform the general readership of recent advances in various areas of petroleum engineering. During the past 15 years, methods and technology for predicting the performance of carbonate reservoirs have improved dramatically. This advance occurred in response to the realization that more than half of the oil that could be swept by waterflooding is not contacted and remains in the reservoir. Attempts to simulate this performance and locate the remaining oil by use of simple reservoir models and newly developed flow-simulation computer programs have failed mainly because of the extreme heterogeneity that characterizes carbonate reservoirs. It is, in fact, the extreme geologic and petrophysical heterogeneity typical of carbonate reservoirs that distinguishes carbonate from siliciclastic reservoirs. Research programs focused on understanding the nature of the heterogeneity and developing methods to characterize carbonate reservoirs, together with improvements in computer capability and simulation programs, have led to more reliable predictions of reservoir performance and to methods for locating volumes of unswept oil in reservoirs under waterflood. Reservoir characterization encompasses the understanding and methods used to characterize reservoir heterogeneity. It can be defined as the construction of realistic 3D images of petrophysical properties used to predict reservoir performance, and it is a multidisciplinary, integrated task involving expertise in reservoir geology, geophysics, petrophysics, well logging, geostatistics, and reservoir engineering. Three-dimensional images are obtained from geological models constructed with core, wireline-log, and geophysical data. Petrophysical properties, obtained from core, wireline-log, and production data, are distributed within the geological model by linking petrophysical properties to geologic fabrics and by use of advanced geostatistical and geophysical methods. Finally, the model is put into a numerical simulator for testing and predicting future performance. The extreme petrophysical heterogeneity found in carbonate reservoirs is clearly demonstrated by the wide variability observed in porosity-permeability crossplots of core-analysis data. Research has shown that basic rock fabrics dominate control of petrophysical heterogeneity; within a rock-fabric facies, porosity and permeability have little spatial correlation and are widely variable at the scale of inches and feet. Permeability, in particular, can vary by a factor of 10 or more at the small scale and is nearly randomly distributed (Fig. 1).1,2 This result suggests that much of the variability observed in core-analysis data is spatial noise and can be averaged within rock-fabric facies for the purposes of constructing a reservoir model. Only rock fabrics, not pore-throat size, permeability/porosity ratio, or flow-zone indicators, have vertical and lateral continuity. Therefore, rock-fabric facies are the basic elements for characterizing a carbonate reservoir.3 Rock fabrics are geologic descriptors that characterize pore size according to particle size and sorting, interparticle porosity, and various types of vuggy porosity. The main limestone rock fabrics are grainstone, grain-dominated packstone, and mud-dominated fabrics. Dolostone rock fabrics are similar but require a description of dolomite crystal size in mud-dominated dolostones as an added control on pore size. These basic fabrics are modified by the amount of fabric-selective vuggy pore space,4 and many rock fabrics can be linked directly to depositional facies. However, some rock fabrics cannot be linked to depositional facies because extensive modifications to the fabric have occurred since deposition through a geologic process known as diagenesis. Constructing models of reservoirs comprising complex fabrics, such as fracture and karst fabrics, is difficult and is the subject of current research. Each rock fabric has a specific porosity-permeability transform, and the vertical stacking of rock-fabric facies, together with interparticle porosity, provides the basis for estimating permeability in uncored wells. The wireline-log problem is determining interparticle porosity, as well as total porosity and rock fabric, for input into a general porosity-permeability transform. Porosity, acoustic velocity, resistivity, and saturation logs are used for this task, and calibrating wireline-log responses to core descriptions of rock fabrics is key to developing useful algorithms.5 Because rock-fabric and petrophysical data obtained from cores and wireline logs are one-dimensional, a geological framework is required to distribute the data in 3D space. In the past, geological models were constructed by identifying depositional facies from core data, then distributing those facies by use of depositional models on the basis of modern carbonate depositional processes. However, reservoirs described in this manner do not contain sufficient detail to capture basic reservoir heterogeneities, and facies correlations from well to well often are highly uncertain. Development of sequence stratigraphic methods greatly enhanced the accuracy of well-to-well correlations and provided the means of capturing basic scales of reservoir heterogeneity.

Waterflooding of Gas-Condensate Reservoirs

Summary Gas-condensate reservoirs are usually produced by primary depletion. This technique is normally an efficient means of producing the gaseous hydrocarbon components but can be very inefficient in producing the more valuable liquid components that are left in the reservoir in a condensed liquid phase (oil). The recovery efficiency of the liquid components decreases with increasing richness of the gas condensate, making for a large improved oil recovery (IOR) target in some reservoirs. The usual approach to improving liquid recovery is to recycle produced gas through the reservoir. However, this technique may not be economically attractive when there is the possibility of immediate gas sales because of the discounting applied to the gas value when sales are delayed. An alternative means of improving liquid recovery is to keep the reservoir pressure above the dewpoint for a period by injecting water. Depending on reservoir characteristics, water injection may be continued throughout field life or the reservoir may be pressure depleted after a period of injection. Special relative permeability data, describing the mobilization of waterflood trapped gas by expansion, are necessary for the latter case. This paper reports a simulation study that quantifies the potential benefits of the waterflood technique by use of simple reservoir models. For a fluid with a condensate to gas ratio (CGR) of 180 STB/ MMscf, total hydrocarbon recovery was optimized by injecting 0.25 hydrocarbon PV of water before pressure depletion. This increased the recovery efficiency of both the liquid and gaseous components, raising the total hydrocarbon recovery by 10% of the hydrocarbon mass initially present in the reservoir. For a richer, near-critical fluid with a CGR of 300 STB/MMscf, continued water injection gave the optimum total recovery, which was 21% of initial mass higher than for primary depletion. This improvement was achieved by greatly increasing the liquids recovery at the expense of a smaller reduction in the gas recovery. The results of this paper suggest that waterflooding of gas-condensate reservoirs might be a valuable IOR technique.

Use of long-term tritium records from the Colorado River to determine timescales for hydrologic processes associated with irrigation in the Imperial Valley, California

Tritium records were used to study hydrologic processes associated with irrigation and drainage in the Imperial Valley, a 2000-km 2 agricultural area in the southeastern California desert. Tritium was analyzed in surface water, ground water, soil-pore water and drain water, and the results were compared to the historical record of tritium in the Colorado River. The Colorado River record was reconstructed using a simple reservoir model and precipitation data in the Colorado River Basin for the period prior to 1965, and from continuous measurements in the river for 1965–1988. This historical record is especially useful in the arid Imperial Valley because recent agricultural development has been entirely dependent on irrigation water diverted from the Colorado River and local recharge is negligible. Results indicate that it takes about 5 a for irrigation drainage to move through the soil to a depth of 2–3 m. Drainwaters have a wide range in tritium concentrations because of varying degrees of influence from ground-water intrusion, and from rapid percolation of irrigation through preferred pathways. The net result is that drainwater from about 40 fields had a range in tritium concentration similar to that of the Colorado River over the last 9 a (1980–1988), a period during which tritium concentration was declining about 15% annually in the river.