This paper compares the output of several available empirical black oil model correlations against compositional model results. In this process, the limitations of these models became apparent.
Even acknowledging the imperfections of black model implementation, it is possible to improve the quality of the outputs by means of making the definitions consistent and coherent across the prediction ranges.
A new method is outlined in order to extend the validity of the models in predicting both reservoir and multiphase flow simulations.
This new method is presented here and will be extended in a separated paper.
The behavior of black oil fluid is commonly inferred from two PVT laboratory procedures: flash (or separator test) and differential liberation. Oil formation volume factor and gas solution ratios are calculated as explained by McCain. On the other hand, given a particular EOS is possible to obtain PVT fluid parameters by simulating the same laboratory procedures or making direct flash calculations at any particular condition.
The traditional calculation method outlined in 1 can be modified in a simple way to extend the validity of black oil model correlations by accounting the dew point curve. Negative gas solution ratios indicate liquid vaporization, and need not to be masked by any correction method. If we follow definitions literally, Rs diminish towards dew point and reaches a constant negative minimum at dew point and inside monophasic gas area. Oil formation volume factor can be lower than unity and in fact should be zero at dew point.
As modern calculations take into account both reservoir and multiphase wellbore and pipeline calculations, is of paramount importance to be able to accurately predict fluid properties in a wider range of pressure and temperature conditions.
The first objective of this paper is to make apparent the limitations of current PVT laboratory calculations and propose a revision.
A second objective is to present black oil model standard correlations phase diagrams together with phase diagrams calculated with EOS and acknowledge the differences and limitations of empirical correlations.
The third objective is to outline a new mathematical method to improve black oil correlations.
The following definitions extracted from Dake will be taken as references:
These parameters enable converting fluid volumes at any conditions to volumes at standard conditions.
This paper describes the implementation of a petroelastic model (PEM) based on Gassmann's equation to calculate seismic attributes into a commercial reservoir flow simulator. This implementation is the first step of a project to integrate time-lapse (4D) seismic attributes into an assisted history matching tool developed in a previous project.
The paper includes the description of the PEM and some implementation issues, such as the coupling of the model with the flow simulator with the purpose of using its basic calculated properties, discuss some user options (such as properties input through correlation or geoestatisticaly obtained maps) and the model variants and extensions (such as lithology influence and pressure effects). Three applications of this petroelastic model are shown: the first is a synthetic model based on outcrop data; the second is a 4D feasibility study for water injection monitoring in an offshore field; and the last one is a comparison between observed and calculated pressure impedances for an offshore field.
The resulting tool is applicable, for example, in 4D seismic feasibility studies, in seismic modeling for comparison with observed surveys and makes possible further implementations for incorporating the seismic data in assisted history matching.
The use of petroelastic attributes has several useful purposes1, such as feasibility of applying 4D seismic monitoring, optimize 4D seismic monitoring program and prepare more accurate production forecasts.
A possible workflow for applying 4D seismic in the monitoring of fluid flow in porous media follows the iterative steps2:
Steps 3 and 4 are unnecessarily cumbersome because most flow simulators do not calculate reservoir seismic attributes. As a result, information from the flow simulation Step 3 must be converted to a format suitable for analysis in the PEM Step 4.
In addition, errors may be introduced into the calculation of seismic attributes if fluid properties in the PEM do not match the corresponding fluid properties in the flow simulator, like using standard correlations of fluid properties.
These problems can be avoided if the PEM is incorporated into the flow simulator, eliminating the need of a third-party software to calculate the seismic attributes, so that it uses exactly the same fluid property model.
Fanchi1 shows the results for some reservoir management scenarios, applying successfully the petroelastic properties information calculated through an integrated flow simulator using the Gassmann's equation3, improving the reservoir management and monitoring processes.
Gosselin et al.4 also implemented an integrated flow simulator tool5 using the Gassmann's equation in a project to integrate 4D data into an assisted history matching process.
The ultimate aim of this project is to incorporate time-lapse seismic attributes into an assisted history match (AHM) tool, which combines efficient derivative calculation and robust optimization techniques, already developed in a previous project6 through an integrated reservoir flow simulator, facilitating a lot the viable use of this kind of data.
The use of seismic attributes has increased, especially when extracted from interpreted horizons. The various available attributes are not independent from each other but represent, in fact, different ways of presenting and studying fundamental information from seismic data (time, amplitude, frequency and attenuation). However, statistical analysis using attributes must be based on geological knowledge and not only on mathematical correlation. Petrophysical studies and seismic modeling are sources of understanding. Such knowledge is necessary to improve confidence in observed correlations with reservoir parameters and must be part of all attribute analysis.
However, the use of seismic attributes leads to several questions, for example, what do they all mean? When to use one or another? How to use them on geologic modeling? How reliable those data are? The answers to these questions are not easy, but considering about petrophysical modeling (Porosity, NTG and permeability) what is the best approach: to consider only well data, that are punctual and need to be interpolated, or try to find correlation with physical measurements (seismic data)? Not to consider seismic attributes makes one feel coming back in time, when this important tool was not available.
On a giant oilfield offshore Brazil seismic attributes (‘conventional', complex trace, polynomial decomposition, geometric and coherence) have been used to create geological models and to reduce uncertainties. The attribute choice must be performed by the geophysicist and the geologist working together, in order to check geological meaning of attribute maps, possible physical meaning of the attribute, etc. Plots of the highest correlation values should be visually inspected in order to choose the attribute with best correlation to the desired parameters.
The results show attributes have been favourable to porosity and NTG prediction, but regular (at maximum) to permeability. For permeability even if the results are not so good, the correlation are improving for the latest models (as long as new wells are used). Polynomial decomposion and complex trace attributes have shown better results.
Introduction: seismic attribute definitions and discussions
The use of seismic attribute data for prediction of detailed reservoir properties began more than 30 years ago.
In fact, a seismic attribute is any property derived from seismic reflection signal. Attributes may be compared to lithology in an attempt to devise a method of property prediction away from well control. The method of prediction can vary from a simple linear correlation to multi-attribute analysis, geostatistical methods, etc.
As an evidence of current proliferation the use of attributes, Chen and Sidney (1997) have catalogued more than 60 commom seismic attributes along with a description of their apparent significance and utility.
Although there is a rich history of seismic attributes use in reservoir prediction, the practice remains a difficult and uncertain task. The bulk of this uncertainty arises from the nature of the physics connecting a number of attributes to a corresponding reservoir property. Due to the complex and varied physical processes responsible for various attributes the unambiguous use of attributes for direct prediction will probably remain a challenge for the years to come.
In addition to the fact above described, there is the possibility of coming across statistical pitfalls while using multiple attributes for empirical reservoir property prediction. In addition, many attributes are derived using similar signal processing methods and can, in some cases, be considered largely redundant with respect to their description of the seismic signal.
Successful design and implementation of a miscible gas injection project depends upon the minimum miscibility pressure (MMP) and other factors such as reservoir and fluid characterization. The experimental methods available for determining MMP are both costly and time consuming. Therefore, the use of correlations that prove to be reliable for a wide range of fluid types would likely be considered acceptable for preliminary screening studies. This work includes a comparative evaluation of MMP correlations and thermodynamic models using an equation of state by PVTsim1 software. We observed that none of the evaluated MMP correlations studied in this investigation is sufficiently reliable. EOS-based analytical methods seemed to be more conservative in predicting MMP values.
Following an acceptable estimate of MMP, several compositional simulation runs were conducted to determine the sensitivity of the oil recovery to variations in injection pressure (at pressures above, equal to and below the estimated MMP), stratification and mobility ratio parameters in miscible and immiscible gas injection projects. Simulation results indicated that injection pressure was a key parameter that affects oil recovery to a high degree. MMP determined to be the optimum injection pressure. Stratification and mobility ratio could also affect the recovery efficiency of the reservoir in a variety of ways.
Through the past decades, miscible displacement processes have been developed as a successful oil recovery method in many reservoirs. The successful design and implementation of a gas injection project depends on the favorable fluid and rock properties. The case studies using Eclipse2 compositional simulator considered the effect of key parameters, such as injection pressure, stratification and mobility ratio on the performance recovery in miscible and immiscible flooding of the reservoir. However, accurate estimation of the minimum miscibility pressure is important in conducting numerous simulation runs. MMP is the minimum miscibility pressure which defines whether the displacement mechanism in the reservoir is miscible or immiscible.
Thermodynamic models using an equation of state and appropriate MMP correlations were used in determining the MMP.
Compositional simulation runs determined the sensitivity of the oil recovery to the variations in above mentioned parameters. Significant increase in oil recovery was observed when interfacial tension dependent relative permeability curves were used. These relative permeability curves provide an additional accounting for miscibility by using a weighted average between fully miscible and immiscible relative permeability curves. The local interfacial tension determines the interpolation factor which is used in obtaining a weighted average of immiscible and miscible (straight line) relative permeabilities.
Simulation runs were performed at pressures below, equal to, and greater than estimated MMP for reservoir fluid/ injection gas system. Oil recovery was greatest when miscibility achieved.
To investigate the effect of stratification on the performance recovery of the reservoir, the base relative permeability of two layers changed. Location of the high permeable layer (up or bottom layer) in the stratified reservoir greatly influenced the efficiency of the reservoir.
Understanding the effect of interfacial tension and adverse mobility ratio on the efficiency of the gas injection project was the last case study. Injection gas and reservoir fluid compositions differed in such a way to have interfacial tension and mobility dominated mechanism. To investigate the effect of interfacial tension water was considered as a fluid with much higher surface tension values with the oil. Lower surface tension values between rich gas and reservoir fluid (interfacial tension dominated) made gas injection project a more competitive recovery method than waterflooding. In mobility dominated displacement mechanism (lean gas/reservoir fluid system) the viscous instabilities were more important than the interfacial tension effect. For this case, waterflooding with favorable mobility ratio resulted in higher oil recoveries.
In well testing, the subject of study is composed by the reservoir, wellbore and piping.
The traditional well testing interpretation approach focuses in the transient behavior of the pressure inside the reservoir. Flow rates are considered input information; generally assumed instantaneously constant during each flow period.
On the other side, the traditional nodal analysis concentrates in the pressure drops inside the wellbore and pipelines reducing the behavior of the reservoir to a pseudo-stationary state.
These simplifications can be applied for a limited period of time in high potential wells.
However, especially in low potential wells, the productivity index varies continuously, flow rates can not be approximated by constant values; the effects of liquid loading, slugging, and other regimes of multiphase pipe flow affect decisively the conditions in the reservoir. Understanding system's operation implies the analysis of every component and the relations between them.
The models can be concatenated in series so that the output of one model becomes the input of the next.
The purpose of this paper is to show that integrating the tools each method provides, solving the models as a system in a dynamic and simultaneous way, significant advantages are obtained:
A typical well testing procedure consists in measuring transient pressures and flow rates simultaneously while inducing changes to the flow conditions.
As can be seen in Figure 1 the hydraulic system is composed of the reservoir, connected to the wellbore that conveys the fluid to surface, a flow control device such as a Choke or restriction, a surface pipe line to derive the flow to a separator or other metering device where rates are measured.
Pressures are taken at several points: at bottom, using a pressure and temperature gauge, at the well head, after the choke or start of surface pipe line and at the separator. Flow rates are commonly measured after separation.
The analysis of alternatives of development of gas deposits and condensed is usually carried out by using the coupling between the balance of materials in predictive mode and the nodal analysis or also using numerical simulation models. In both cases it is required a suitable model of the multiphase flow behavior in vertical pipes in order to be able to predict with accuracy the flowrates the wells will produce through the different life stages of the reservoir.
The correlations for the multiphase flow, with which it is modeled the flow in vertical tubes, show a big dispersion of results in flowrates less than 50 km3std/d with gas - liquid relationships less than 10000 m3/m3. This area of low flowrates and low gas - liquid relationships is usually observed in the gas and condensed reservoirs final phase due to the decline in the production because of the fall of the static pressure and the fall of the gas - liquid relationship and the increase of the water cut.
Consequently, the dispersion in the correlations generates important differences in the production forecasts, with the associated high economic impact, because the pressures for abandonment of the wells are very different according to the multiphase correlation used.
In this work we show an exhaustive statistical analysis of the behavior of the multiphase flow correlations in vertical tubes, contrasted with measurements of pressure gradients in wells, in the majority of the cases within the ranges of flowrates and gas - liquid relationships mentioned in the previous paragraph.
From the results of this analysis, it is developed a new correlation of multiphase flow for gas - condensed - water systems that allows predicting the pressure gradients in vertical tubes within the reasonable error ranges.
We show the methodology used for the development of the correlation and the statistical analysis of the results of the application of it based on the data from the studied cases.
A numerical model for the analysis of multiphase flow on vertical or slightly inclined wells has been developed. The model calculates flow properties (velocity of each phase, volumetric fraction of each phase, pressure and fluids properties) on gas-oil-water wells as function of depth. Fluids properties are obtained under the assumption of black oil
model by means of correlations taken from literature, requiring only petroleum °API and the gas specific gravity as
The model may be applied to simulate both liquid flow and gas-liquid flow. In this case, different flow patterns are taken
into account: -bubble, slug, dispersed bubble and annulardepending on flow conditions, which are determined from fluid properties and production rates of oil, gas and water. Flow in tubings consisting of several sections with different diameters and inclinations may also be simulated.
The model was validated by comparisons of measured and calculated the pressure variation along the well Good agreement was found between the numerically predicted pressure drop and measurements taken from different
databases from open literature. As a consequence the proposed model proves to be a reliable tool to describe the
flow on oil-gas-water wells.
The developed numerical model takes into account the most relevant effects that take place in a production well including multiphase flow, presence of different flow pattern, mass transfer from gaseous to liquid phase and influence of
gas-liquid flow pattern on wall friction. Special attention is paid to the velocity profile of each phase along the well. Ishii's
model for two-fluid flow is used to prescribe the slip velocity between liquid and gaseous phases and to determine the
acceleration term contribution to the pressure gradient. This model is actually being employed for corrosion rate calculations inside production wells.
The study of the multiphase flows (water - oil - gas) is of major importance in oil industry since it is found quite frequently during the production process. The physics involved in these flows is very complex due to interactions between the different phases. In order to deal with this complexity, sophisticated numerical models with several parameters (most of them determined from experiments) are required.
The complexity of the problem leads to a number of simplifying assumptions and to the use of correlations to model some terms of the equations. Many numerical methods have been proposed in order to prescribe flow variables (velocities of each phase, volume fraction of each phase, flow pattern, pressure gradient) along the tubing for vertical upward flow. There is a wide variety of numerical methods, including simple models where liquid and gas are supposed to have same velocity [1-3], models that account for slippage between gas and liquid but do not consider the existence of different flow patterns [4-6], models that take into account different flow patterns [7-12] to complex mechanistic models [13-17].
In this work an alternative numerical model to estimate the flow characteristics along a vertical or near vertical pipe is presented. The proposed method belongs to the class of models described in references [7-12]. However, instead of using a correlation for liquid hold up we use a correlation for the slip velocity between liquid and gaseous phases and
calculate the hold up from conservation equations. It was codified in a FORTRAN code named GOWflow.
In the next section the general equations of the model are introduced. Then the modeling of different terms taking part in the equations is presented, followed by the description of the algorithm. There is a section devoted to the validation and another one to the application. In the last section conclusions and future work are discussed.
Governing equations were obtained from mass conservation for each component and global momentum conservation
principles in steady state . The equations were averaged across the -assumed circular- section S of the pipe in order to obtain a one-dimensional model.
Modern viscosity prediction methods have to satisfy the requirements for flow assurance and reliable reservoir characterization by demonstrably predicting accurate, reliable and internally consistent viscosity data. The best way to achieve this is by employing predictive methods based on the best available theory, simplified, just sufficiently to allow ready application and validated against a critical set of primary experimental data of proven accuracy.
The presented VW methodology is one such method, that is based on the kinetic theory of rigid spheres, modified to take into account the behavior of real fluids. It has no adjustable parameters, and requires no dense mixture viscosity data. In this work, the VW method was validated against a new set of natural gas viscosity data of very high accuracy. The experimental data were predicted with an rms deviation of the order of 0.5%-1%, commensurate with the experimental accuracy of the data. Overall, it is estimated that the VW method can predict the viscosity of natural gas within ±2% in the temperature region 260 K - 400 K and pressures up to 200 bars, with the accuracy deteriorating slightly at higher pressures and lower temperatures. It can be used to predict the viscosity of CO2-rich, sour and wet natural gas.
Increasing demand for natural gas has led to the need to develop a more reliable reservoir characterization and simulation. The upstream gas industry, through the gas suppliers, is also being faced with increasing demand for precision in the monitoring of gas supplies. For the exploitation and usage to be optimal, an accurate and reliable knowledge of viscosity, along with other thermophysical properties of natural gas is a prerequisite. The large number of possible natural gas mixtures, and the wide range of relevant conditions, precludes obtaining data by experimental means alone; accordingly, predictive methods are required.
The petroleum industry currently bases its prediction of viscosity on the Lohrentz-Bray-Clarke (LBC) correlation produced in the 1960's1. As is well documented in the SPE literature2-3 and elsewhere4-5, such an approach does not produce reliable and accurate viscosity predictions. For natural gas the failure of the method is mostly evident at high pressures, since the underlying assumption of the LBC method, that the residual viscosity is only a function of density, no longer holds true4,6. A number of methods have been proposed to address this structural failure with varying degrees of success2,4. Furthermore, a number of empirical correlations have been proposed for natural gas (see Ref 3 for details), as a replacement of the LBC method. They usually rely on fitting to a limited set of experimental viscosity data. The data do cover natural gas and similar hydrocarbon mixtures, but invariably a limited number of compositions is available. Also, the viscosity data used for this purpose, are not always obtained in primary instruments.
A primary instrument7 is a well-characterized experimental apparatus, with a well-defined uncertainty level, which produces data that cannot be demonstrated to be inconsistent with other data or with theory. The use of such viscometers requires knowledge of a full, fluid mechanics, working equation and requires a number of corrections to be applied to the experimental data, making the analysis expensive and time-consuming. This makes use of empirically based correlations difficult to justify unless they are fitted to the data obtained in a number of primary instruments. Even then the possibility of systematic errors in the primary data set could not be discounted. More importantly any extrapolation to mixtures and conditions outside the range they were fitted to is fraught with difficulty. Thus, currently neither the empirical correlations nor LBC type methods produce optimal, accurate and reliable viscosity values over the whole range of conditions and compositions of interest to the natural gas industry. Hence, they do not satisfy the modern industrial requirements for flow assurance and reliable reservoir characterizations, which are likely to become even more stringent in the not-so-distant future.
Reaching dew-point conditions upon depletion in a near-critical gas reservoir results in the precipitation of a liquid hydrocarbon phase or condensate dropout. Condensate dropout is usually immobile and impairs the flow of the other phases, adversely affecting reservoir productivity and ultimate recovery in this type of gas reservoirs. In the case of fissured reservoirs, the high-conductivity channels supplied by the fracture network will be prone to faster depletion upon fluid withdrawal. Condensate dropout would then occur in the fracture network first and then in the external edges of the matrix blocks. Even though condensate dropout in the fracture may have considerable mobility, this is not the case for the liquid formed at the external portions of the matrix. In this scenario, liquid buildup will hinder the flow of hydrocarbons from the inner portions of the matrix blocks and severely obstruct their recovery. This study aims at the numerical tracking of the liquid barrier, which requires a fine discretization of the inner portions of the matrix blocks, and the analysis of the interplay between the condensate barrier and hydrocarbon flow within the surrounding matrix/fracture system. While traditional wisdom dictates that reservoir condensate dropout is undesirable because this valuable condensate may be completely lost to the formation, this study analyzes if the situation is even worse for the case of fissured systems. In addition to low surface condensate recoveries, condensate appearance in fissured systems may also indicate that the inner-block gas stored in the matrices—where the bulk of the reservoir storage resides—might be also unrecoverable. In this study, guidelines for the development of this class of reservoirs are presented by identifying the controlling parameters of system behavior and ultimate recovery and analyzing the depletion characteristics of near critical fluids in fissured systems.
An Artificial Neural Network (ANN) was designed and tested in the present study to examine the correlation between permeability estimations and porous medium properties, such as porosity, specific surface area, and irreducible water saturation. The network developed in this work is a predictive tool that uses soft computing techniques to estimate absolute permeability of carbonate reservoirs. The Artificial Neural Network toolbox of MATLAB® R2006b and the Feed Forward Error Back Propagation methodology were used in the construction of the network. Carbonate reservoir field data presented in the literature were utilized in the training, testing, and validation of the proposed model. The present study indicates that ANN generated permeability values are consistent with those obtained from core analysis. Results from this study confirm the complex relationship among permeability, porosity, specific surface area and irreducible water saturation of carbonate reservoirs, and suggest that variations in specific surface area affect the magnitude of irreducible water saturations, thus creating an apparent dependence of permeability on irreducible water saturation.
Additional observations support a direct relationship between porosity and permeability, and an inverse relationship between specific surface area and permeability.
Porosity-permeability relationships are of great importance for the reservoir engineer because of the difficulties and uncertainties associated with direct permeability interpretations from well-log data. Accurate permeability predictions provide engineers with the ability to design and manage efficient processes in the development of oil and gas fields. Although it is generally accepted that permeability is closely related to porosity, their relationship cannot be captured by a simple expression. Absolute permeability is a dynamic flow property, while porosity is a measure of the storage capacity of a rock, a static rock property. The absolute permeability of a porous medium varies with grain size, sorting, cementing, direction, and location; thus the scatter quality of permeability plots.
A wide range of permeability correlations using pore- and field-scale models are presented in the literature1-3. Starting with the seminal works by Kozeny4 and Carman5, many different correlations have been proposed between porosity and permeability. The Kozeny-Carman equation was developed for a porous medium represented by a bundle of uniform capillary tubes and introduces a direct dependence between porosity and permeability, while accounting for specific surface area and tortuosity as a measure of flow resistance.
For unconsolidated porous media with variable particle size, Panda and Lake6 propose a modification of the Kozeny-Carman equation to express permeability in terms of particle-size distribution characteristics and the bulk physical rock properties. They found reasonable agreement between predicted and experimental permeability, relying on appropriate estimations of surface area, and demonstrated the modest impact of sorting on the quality of their predictions. With respect to sorting, porosity tends to increase for perfectly sorted media and decrease as sorting becomes poorer7, thus affecting permeability.