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Modern permanent downhole gauges have the capability to measure both pressure and flow rate, which provides data with the potential for a wider range of reservoir analysis applications than just pressure data alone. It is important to pair the data analysis of pressure and flow rate streams together. Reservoir physics imposes a relationship between the two data sets. Investigation into the interrelation of data pairs provides a better way of characterizing the true reservoir response. Deconvolution is an important tool for understanding the interrelationship between variable pressure and flow rate. Using convex optimization approaches to achieve deconvolution in the time domain was found to be successful in extracting the constant rate pressure response. We evaluated the noise model of pressure and flow rate data for each pair of measurement points. We were able to estimate pairs of noise-reduced pressure and flow rate data according to the interdependence of the original data streams, thus honoring the reservoir physics. Analysis of the interrelation allowed us also to update the estimate of the constant rate reservoir response. Investigating pressure and flow rate pairs simultaneously may improve the match and accuracy of the reservoir model. The ability to incorporate and retain interrelations suggested by true pressure and flow rate pairs is useful to the interpretation of reservoir behavior. Cointerpreting the two data streams simultaneously provides better information about the reservoir. Following noise reduction by cointerpretation, the data can then be used in more complex reservoir engineering functions, such as closed loop optimization.

Permanent downhole gauges (PDGs) provide a continuous source of downhole pressure, temperature and sometimes rate data. Until recently, the measured temperature data have been largely ignored. However, a close observation of the temperature measurements reveals that the temperature responds to changes in flow rate and pressure, which implies that the temperature data may be a source of reservoir information. In this work, the Alternating Conditional Expectations (ACE) technique was applied to temperature and flow rate signals from PDGs to establish the existence of a functional relationship between them. Then, performing energy, mass and momentum balances, reservoir temperature transient models were developed for flow of single- and multiphase fluids, as functions of formation parameters, fluid properties, and changes in rate and pressure. The pressure fields in oil and gas bearing formations are usually transient. This gives rise to pressure-temperature effects appearing as temperature changes in the porous medium when the pressure field changes. The magnitudes of these effects depend on the properties of the formation, flow geometry, time and other factors and result in a reservoir temperature distribution that is changing in both space and time. Therefore, in this study, reservoir thermometric effects were modeled as convective, conductive and transient phenomena with consideration for time and space dependencies. This mechanistic model included the Joule-Thomson effects due to fluid compressibility, and viscous dissipation in the reservoir during fluid flow in accounting for the reservoir temperature dependence on changing pressure/flowrate fields. Numerical solution schemes as well as the semianalytical scheme – Operator Splitting and Time Stepping (OSATS) were used to solve the models, and the solutions closely reproduced the temperature profiles seen in real measured data. By matching the models to different temperature transient histories obtained from PDGs, reservoir parameters namely porosity and saturation and fluid Joule-Thomson coefficient could be estimated. Hence the normally unused temperature data record can be used to estimate reservoir parameters not usually available from conventional well test analysis. Analysis of temperature may also provide a less expensive substitute for downhole flow rate measurement.

SummaryThis paper presents generalized procedures to interpret pressure injection and falloff data following cold-water injection into a hot-oil reservoir. The relative permeability characteristics of the porous medium are accounted for, as is the temperature dependence of the fluid mobilities. It is shown that the saturation and temperature gradients have significant effects on the pressure data for both the injection and falloff periods. The matching of field data to type curves generated from analytical solutions provides estimates of the temperature-dependent mobilities of the flooded and uninvaded regions. The solutions also may be used to provide estimates of the size of the invaded region, the distance to the temperature discontinuity, heat capacities, and wellbore-storage and skin effects.

Summary. This paper describes techniques for the identification of well-test interpretation models from pressure-derivative data. Artificial pressure-derivative data. Artificial intelligence (AI) techniques are used to separate the derivative response from signal and differentiation noise, and a rule-based recognition system characterizes the response using a symbolic representation. Introduction The use of computers for well-test analysis has played an important role in the development and application of new interpretation techniques. With nonlinear regression, algorithms have been developed that can perform automated type-curve matching when perform automated type-curve matching when given a specific model and a first estimation of its parameters. Such algorithms not only speed the interpretation procedure but also increase the confidence in the results by allowing quantification of the quality of the match obtained. Correct application of these methods, however, depends on the choice of the interpretation model. An interpretation procedure that uses the pressure derivative is regarded as the pressure derivative is regarded as the most appropriate tool for the diagnosis of an interpretation model for well-test data. The derivative is not only more sensitive to the different flow regimes and flow-regime transitions but also is more generally applicable and therefore provides a substitute for all the specialized analyses. In traditional graphical analysis, the choice of an interpretation model is essentially a visual process. Based on a log-log plot of the pressure derivative, an expert can perform model identification by recognizing features that are specific to particular analytical models. The combination of the various models then gives an interpretation model. Although the human visual perception process is not fully understood, significant process is not fully understood, significant work in AI has been conducted to develop machine vision systems. These systems operate not on the image itself but on a symbolic representation containing the information needed for the task under consideration. This paper describes the development of techniques to automate the modelidentification step of well-test interpretation by use of AI. The computer's choice of a model is based on the pressure-derivative curve and simulates the visual diagnosis performed by a human expert. The reasoning performed by a human expert. The reasoning involved in such a diagnosis uses a symbolic representation of the derivative curve, which in the case of a human expert is built almost unconsciously. Techniques were developed to replicate this visual-perception step. A major difficulty in the analysis of real data, particularly when the pressure derivative is used, is the separation of the true reservoir response from signal or differentiation noise. Again, this is relatively simple for a human observer, but difficult to implement in a computer program. This paper describes an algorithm developed to overcome this problem. The algorithm was able to distinguish response from noise correctly, thereby allowing for correct model identification. In a manner analogous to a human expert, the technique constructs an interpretation model for the duration of the data by combining the features of the different flow periods of the response. The adequacy of a periods of the response. The adequacy of a model is determined by qualitative and quantitative information. Once a model is chosen, its parameters are estimated with a correlation or an appropriate table. The system developed in this work can perform model identification on real or perform model identification on real or hypothetical data. Because the method also provides parameter estimation, it can be provides parameter estimation, it can be used with an automated type-curve-matching analysis, allowing full automation of welltest interpretation. The task of identifying an interpretation model by use of the derivative of well-test data can be separated into three components:observation-extraction of the features present on the data derivative and present on the data derivative and representation of these features,knowledge of the models-methods for the construction and description of interpretation models, andmatching-criteria for choosing appropriate interpretation models for given data. The development of the specialized rule base and logical approach for these three components took considerable work before the algorithms were able to interpret real data reliably. The purpose of this paper is to describe this development as an aid to others who may wish to attempt a similar approach. JPT P. 342

Permanent downhole gauge data provide us with reservoir information in space and time and aid in well and reservoir management. Interpretation of permanent downhole gauge data is a fairly new problem and several outstanding issues remain in this area. This paper addresses some of the challenges in analyzing flow rate data and pressure data from permanent downhole gauges - development of improved algorithms for reliable and accurate identification of transient break points (to separate transients into relevant subsections), and investigating the impact of continuous downhole rate data in analyzing well tests. We tested four different algorithms, one based on the stationary Harr wavelet transform method and others based on nonwavelet approaches such as Savitzky-Golay Smoothing Filters and a novel pattern recognition approach called the Segmentation Method. These four methods were developed for accurate and reliable identification of break points using both pressure and rate data. The new methods developed in this paper were applied to real field data and the results were compared to the spline wavelet-based approach. All the nonwavelet approaches showed significant improvement over the wavelet-based method in identifying the true break points and avoiding false break points, thus reducing manual editing of break points. Also, significant difference in the estimates of permeability and skin was observed by using continuous rate information instead of average rate data for interpreting transient pressure data. These new algorithms find their application in the interpretation of permanent downhole gauge data using conventional well test interpretation methods, to obtain dynamic information about changes in properties of the well and reservoir. The use of continuous downhole rate data can have significant advantage in well test interpretation.

This work develops a generalized wavelet-based methodology for stochastic data integration in complex reservoirs models. This is an extension of our earlier work for simpler reservoir descriptions (Sahni 2003; Sahni and Horne 2005, 2006). A single history-matched reservoir permeability model is combined with a stochastic geological description to obtain multiple equiprobable reservoir descriptions using wavelet transforms of the parameter distribution (permeability). In this paper the algorithm has been extended and generalized to be usable with commercial reservoir simulation software and to enable handling of complex three-dimensional models and production scenarios. We also conducted a study of sensitivity coefficient distributions, thresholding and averaging techniques, and a comparison of different Haar wavelet implementations.Wavelet coefficients of reservoir parameter distributions are decoupled into sets of history-matching and geologic coefficients and modified independently. Inverse transformation of these coefficients yields multiple reservoir model results, all of them matched to history. A significant reduction in time is obtained for stochastic modeling of reservoirs by use of this decoupling of production data and other parameters, since only a single history match is required.Thus the proposed algorithm addresses the issue of stochastic modeling of complex reservoirs by integrating all available sources of information. From a single history-matched model we obtain a set of distinct equiprobable reservoir models that can then be used to evaluate uncertainty and make future production predictions and reservoir management decisions.

Gas-condensate reservoirs exhibit complex phase and flow behaviors due to the appearance of condensate banking in the near-well region. A good understanding of how the condensate accumulation influences the productivity and the composition configuration in the liquid phase is very important to optimize the producing strategy, to reduce the impact of condensate banking, and to improve the ultimate gas recovery. This study addressed several issues related to the behavior of the composition variation, condensate saturation build-up and condensate recovery during the gas-condensate producing process. A key factor that controls the gas-condensate well deliverability is the relative permeability, which is influenced directly by the condensate accumulation. The accumulated condensate bank not only reduces both the gas and liquid relative permeability, but also changes the phase composition of the reservoir fluid, hence reshapes the phase diagram of reservoir fluid and varies the fluid properties. Different producing strategies may impact the composition configuration for both flowing and static phases and the amount of the liquid trapped in the reservoir, which in turn may influence the well productivity and hence the ultimate gas and liquid recovery from the reservoir. Changing the manner in which the well is brought into flowing condition can affect the liquid dropout composition and can therefore change the degree of productivity loss. In this study, compositional simulations of multicomponent gas-condensate fluids were conducted at field scale to investigate the composition and condensate saturation variations. Different producing strategies have been compared, and the optimum producing sequences are suggested for maximum gas recovery. A core flooding experiment with two- component synthetic gas-condensate was designed and constructed to model gas-condensate production behavior from pressure above the dew-point to below. Experimental observations of gas-condensate production confirm the dramatic changes in the liquid composition seen in the simulations.

[1] The Brooks and Corey relative permeability model has been accepted widely as a way to calculate relative permeability using capillary pressure data. However, the Purcell model was found to be the best fit to the experimental data of the wetting-phase relative permeability in the cases studied here, as long as the measured capillary pressure curve had the same residual saturation as the relative permeability curve. The differences between the experimental data of relative permeability and the data calculated using the Purcell relative permeability model for the wetting phase were almost negligible. A physical model was developed to explain the insignificance of the effect of tortuosity on the calculation of the wetting-phase relative permeability. For the nonwetting-phase, the relative permeabilities calculated using the models were very close to the experimental values in drainage except for the Purcell model. However, in the case of imbibition, the relative permeabilities calculated using the models were different from the experimental data. This study showed that relative permeability could be calculated satisfactorily by choosing a suitable model, especially in drainage processes. In the reverse procedure, capillary pressure could also be computed once relative permeability data are available.

[1] Despite some successful studies of two-phase or unsaturated flows in ideal smooth-walled fractures, the more realistic issues regarding fundamentals of two-phase interactions in rough-walled fractures are still poorly understood. In this study, we suggest a new approach to describe relative permeability behavior in rough-walled fractures based on experimental observations of two-phase flow structures. This approach lumps the microscale physical mechanism (viscous and capillary forces) into an apparent observable parameter, the channel tortuosity, which was found to dominate the reduction of the relative permeabilities from the values that would be expected based on the linear X curve (i.e., relative permeability equals saturation). Two analog fractures, the homogeneously rough-walled and randomly rough-walled fractures, combined with a smooth-walled fracture investigated previously were studied to represent distinct surface geometry and heterogeneity. The uncertainty and quality of measured relative permeabilities in the fractures were discussed in the aspects of high-resolution relative permeability and different averaging techniques. The experimental results from these three fractures could be described successfully by the proposed approach. Furthermore, we found that the magnitude of the channel tortuosity increases when the heterogeneity of the fracture surface increases. We also showed that the rates' (velocities) effects on flow structures within the experimental ranges were insignificant. Generalizing from channel tortuosities occurring in these three fractures, we were able to derive empirical, tortuous channel models. These models represent the current experimental data as well as observations from earlier studies with good agreement.

A semianalytical model was developed to infer relative permeability from resistivity data. Although it would still be necessary to conduct experimental measurements of resistivity, these are easier than measuring capillary pressure. On the other hand, resistivity data are commonly available from routine well logging. The semianalytical model was tested against experimental data. The results demonstrated that the relative permeabilities calculated from resistivity data were close to those calculated from capillary pressure data. The model developed in this study may also provide an approach to estimate permeability using both the resistivity well logging and well testing.

Field production data from Kern County acquired from the California state database was analyzed for production decline. A decline curve methodology based on fluid flow mechanisms was used. The model reveals a linear relationship between the oil production rate and the reciprocal of the oil recovery. Existing decline curve methods often either overestimate or underestimate reserves, and are mostly empirical in origin. The current approach not only provides a method to estimate reserves, but because of its basis on fluid flow mechanisms, can also be used to infer regional reservoir properties that may be useful in production decisions. Oil wells from six producing oil fields in Kern County were analyzed using this decline curve method and two parameters, a0, the production rate index, which measures the recovery rate, and b0, the gravity index, were mapped regionally. Since the two parameters are associated with capillary pressure and relative permeability, conclusions can be made about the geological properties of the reservoirs from the derivation of the a0 and b0 parameters. This will aid in determining which regions are more prolific, and provide a correlation based on physics to infer reserves, and reservoir rock and fluid properties. It was found that fields with higher a0 and b0 values have higher oil recovery. This study demonstrates the applicability of this decline curve analysis and provides an alternative to empirical methods.

Determining the optimum location of the wells is a critical and crucial decision to be made during a field development plan. The quality of the decision is strongly dependent upon the amount of the information available to the decision-maker at the time the decision is made. Knowing that the development phase of a reservoir is a dynamic period in which different categories of information are added to system from distinct sources, one should make the well placement decisions considering these time-dependent contributions of information. This study proposes an approach that addresses the value of time-dependent information to achieve better decisions in terms of reduced uncertainty and increased probable Net Present Value (NPV). A Hybrid Genetic Algorithm1 (HGA) was used as the optimization method to find the best locations of the wells. A utility framework, that enables the assessment of the uncertainty of the well-placement decisions, was used to find the optimum decisions for different risk attitudes. Through this new approach, production history data obtained from the wells, as they are drilled, are integrated into the well placement decisions. Unlike previous approaches, well placement optimization is coupled with recursive history matching steps. To test the results of the proposed approach, an example reservoir was investigated with multiple realizations, all of which match the history response of the reference. At each step of optimization, a reduction in the uncertainty of the multiple realizations was observed, as production history became available.

This paper focuses on an automated way to generate multiple history-matched reservoir models with the inclusion of both geological uncertainty and varying levels of trust in the production data, using wavelet methods. As opposed to previously developed automated history-matching algorithms, this methodology not only ensures geological consistency in the final models, but also includes uncertainty in the production data.A data distribution, say a permeability field, can be (reversibly) transformed into wavelet space where it fully described by a set of wavelet coefficients. It was found that different subsets of the collection of wavelet coefficients can be constrained separately to: (a) the production history, and (b) the geological constraints. This means the history match need only be performed once, after which multiple realizations can be generated by adjusting just the second subset of coefficients.The ability to include both geological and production data uncertainty into reservoir model automatically is of great consequence to reservoir modeling and hence to reservoir management, risk analysis and making key economic decisions. The more complete and realistic reservoir model will lead to better reservoir production and development decisions.

Phase transformation affects multiphase flow in geothermal and gas-condensate reservoirs due to the same substance occurring in different phases. These effects change the phase behavior and the flow characteristics. The goals of this research were to compare the flow behavior and relative permeabilities difference between two-phase flow with and without phase transformation effects in smooth-walled and rough-walled fractures. During this research, an experimental apparatus was built to capture the unstable nature of the two-phase flow fractures and display the flow structures in real time. Two-phase flow experiments with phase transformation effects (steam-water flow) and without phase transformation effects (nitrogen-water flow) were conducted. The porous medium approach was used to calculate two-phase relative permeabilities. From the results in this study, steam-water relative permeabilities are different from nitrogen-water relative permeabilities. The enhanced steam-phase relative permeability is due to the effects of phase transformation. This shows consistency with some earlier studies in porous media. The nitrogen-water relative permeability is described most appropriately by using the viscous coupling model. However, steam-water flow in the rough-walled fracture, which is coupled with strong phase transformation effects, seems to be represented better by Brooks-Corey relative permeability functions for fractured media (λ →∞). The results from this study suggest that relative permeabilities accounting for phase transformation effects have to be used in simulations of geothermal and solution gas reservoirs to represent two-phase interactions adequately.

Abstract Direct comparisons between steam-water and air-water capillary pressures have been few because of the difficulty in experimental measurement. An experimental method was developed to measure both steam-water and air-water capillary pressures using an X-Ray CT technique. Spontaneous water imbibition and gravity drainage tests were conducted in ceramic core samples for steam-water and air-water systems, respectively. The results were compared, and it was found that the steamwater capillary pressures were less than the air-water capillary pressures. Introduction Steam-water flow is of importance during steam injection into heavy oil reservoirs and water injection into geothermal reservoirs in which steam is produced. In these reservoirs, steam-water capillary pressure plays an important role in controlling fluid distribution, transfer of liquid between fracture and matrix, and well productivity. The study of steam-water flow in porous media may also be useful for other single-component two-phase systems or even some multicomponent gas-liquid systems such as solution gas-oil and gas-condensate systems in which there is also significant mass transfer between the two phases as pressure changes. However, it is difficult to measure steam-water capillary pressure using routine techniques (for example, semipermeable porousplate and centrifuge methods) due to the phase transformation and the significant mass transfer between the two phases. In situ fluid saturation measurement techniques, such as X-Ray CT, γ-ray, and NMR techniques, may be useful to overcome the difficulties. Many papers(1–4) have been published in oil-gas and oil-water flow, but few in the measurement of both steam-water and airwater capillary pressures. A similar fluid flow to steam-water flow is gas-condensate flow. Although a lot of papers(5–8) have been published on the measurement of relative permeability for gas-condensate systems, reports on the direct measurement of gas-condensate capillary pressure have been few. On the other hand, there has been some argument regarding the differences between steam-water and air-water flow through porous media in recent years. If there are no differences between the two, we could represent steam-water flow by air-water flow in which capillary pressure can be measured easily. Sanchez and Schechter(9) reported that the differences between steam-water and nitrogen-water relative permeabilities were almost negligible in an unconsolidated core sample. However, Horne et al.(10) found significant differences in experiments using Berea sandstone with a much lower permeability than that of the core sample used by Sanchez and Schechter(9). Accordingly, there may also be significant differences between steam-water and nitrogen-water capillary pressures. Very few direct comparisons of steam-water and air-water capillary pressures are available due to the scarcity of methods available to measure them. Li and Horne(11) developed a technique based on the Kelvin equation to calculate steam-water capillary pressure using the data from steady-state steam-water flow experiments. This method is suitable for steam-water systems but not for air-water systems. Therefore, we developed another method that could measure both steam-water and air-water capillary pressures in order to identify the differences between the two in this study. We conducted spontaneous water imbibition and gravity drainage in ceramic core samples for steam-water and air-water systems. The core sample was positioned vertically.

Mathematical models to predict oil production accurately by gravity drainage have been few. To this end, an analytical model was developed to determine the ultimate oil recovery by free-fall gravity drainage. An empirical oil recovery model was proposed accordingly to match and predict oil production. The model was tested against experimental, numerical, and field data of oil production by free-fall gravity drainage. The results demonstrated that the oil recovery model could work satisfactorily in the oil-gas cases studied. Initial oil production rate, entry capillary pressure, and average residual oil saturation can be estimated using the oil recovery model. An approach was also developed to infer capillary pressure curves from the oil production data by free-fall gravity drainage.

An approach was developed to extract the imbibition capillary pressure and the global mobility data from spontaneous water imbibition tests in oil-water-rock systems. Capillary pressure and global mobility data were calculated using this method with the experimental data of countercurrent spontaneous water imbibition tests in different rocks and at different interfacial tensions. The calculated capillary pressures were consistent with the change in interfacial tension. The oil-water-rock systems with greater interfacial tensions had greater capillary pressures. However the oil-water-rock systems with greater capillary pressure may not have greater imbibition rate. The calculated values of the global mobility and the imbibition index explain why the oil recovery or the imbibition rate in systems with high interfacial tension was smaller than that in systems with low interfacial tension, which has been considered a paradoxical result for many years.

Decline curve analysis models are frequently used but still have many limitations. Approaches of decline curve analysis used for naturally-fractured reservoirs developed by water flooding have been few. To this end, a decline analysis model derived based on fluid flow mechanisms was proposed and used to analyze the oil production data from naturally-fractured reservoirs developed by water flooding. Relative permeability and capillary pressure were included in this model. The model reveals a linear relationship between the oil production rate and the reciprocal of the oil recovery or the accumulated oil production. We applied the model to the oil production data from different types of reservoirs and found a linear relationship between the production rate and the reciprocal of the oil recovery as foreseen by the model, especially at the late period of production. The values of the maximum oil recovery for the example reservoirs were evaluated using the parameters determined from the linear relationship. The results demonstrated that the analytical decline analysis model is not only suitable for naturally-fractured reservoirs developed by water flooding but also for other types of water drive reservoirs. An analytical oil recovery model was also proposed. The results showed that the analytical model could match the oil production data satisfactorily. We also demonstrated that the frequently-used nonlinear type curves could be transformed to linear relationships in a log-log plot. This may facilitate the production decline analysis.

Methods that can be used to determine the wettability in both gas-liquid-rock and liquid-liquid-rock systems have been few. To this end, a method is proposed to evaluate the wettability in either gas-liquid-rock systems or liquid-liquid-rock systems. The method can be used to evaluate the wettability at a specific wetting phase saturation if the capillary pressure and relative permeability at this fluid saturation are known. The validity of the proposed technique was tested qualitatively and quantitatively using experimental data of capillary pressure and relative permeability from different systems. The wettability index calculated using the proposed technique was greater in the drainage case than that in the imbibition case, which is reasonable and consistent with the present understanding. The calculated wettability indices in gas-oil-rock systems were greater than in oil-water-rock systems as expected. Results also showed that the wettability index calculated using the proposed method may or may not be independent of fluid saturation in the cases studied.

This study proposes a numerical simulation approach without direct specification of relative permeability functions. Using this approach, it is not necessary to impose relative permeability functions as input to the simulator in order to conduct the numerical simulations of two-phase fluid flow. Instead only capillary pressure data need to be imposed and the relative permeabilities can be calculated consistently using specific models. Example numerical simulations at both core and reservoir scales were conducted to test the technique without the direct input of relative permeability functions from experimental data. The results showed that the production performance calculating from the numerical simulations without the input of relative permeability functions was almost the same as the experimental data. Using the method proposed in this study, the effects of pore size distribution index and entry capillary pressure on oil recovery by gravity drainage were investigated at both core scale and reservoir scale. The technique may be especially suitable for reservoirs in which it is difficult to measure relative permeability curves. Such reservoirs include gas-condensate reservoirs, extremely low permeability reservoirs, and geothermal reservoirs. The proposed technique may also be useful to upscaling, numerical simulation while drilling, and other areas.

Decisions have to be made at every level of petroleum reservoir development. For many cases, optimal decisions are dependent on many nonlinearly correlated parameters, which makes intuitive judgement difficult. In such cases automated optimization is an option. Decisions should be based on the most relevant and accurate tools available. For the well placement problem a numerical simulator that computes the movement and interaction of subsurface fluids is the most accurate tool available to engineers. However, numerical simulation is most often computationally expensive making direct optimization prohibitive in terms of CPU requirements. To overcome the computational infeasibility, one can try to utilize mathematical proxies (surrogates) to replace numerical simulators. Although these proxies are very cheap to compute, they often require an initial investment in computation for calibration purposes. The magnitude of this initial computational investment is unclear. Also the calibration points, that are used to calibrate the proxy, are chosen synchronously; that is, the choice of a particular point to be simulated is independent of the others even though in real life the choice of later experiments would be based on the experience of earlier observations. In this study, an approach is proposed which employs direct optimization and proxy approaches simultaneously. The Genetic Algorithm (GA) forms the basis of the approach. The proxy ought to evolve intelligently as the GA iterates. This work investigated the design of a composite and adaptive algorithm, and tested its effectiveness in a range of artificial test problems and real field cases. Kriging was considered as the proxy. The polytope method was also utilized to help with local search. The composite algorithm was applied to the highly non-linear problem of an offshore Gulf of Mexico hydrocarbon reservoir development and significant improvement in efficiency was observed.

Scaling the experimental data of spontaneous imbibition without serious limitations has been difficult. To this end, a general approach was developed to scale the experimental data of spontaneous imbibition for most systems (gas-liquid-rock and oil-water-rock systems) in both cocurrent and countercurrent cases. We defined a dimensionless time with almost all the parameters considered. These include porosity, permeability, size, shape, boundary conditions, wetting and nonwetting phase relative permeabilities, interfacial tension, wettability, and gravity. The definition of the dimensionless time was not empirical, instead, was based on theoretical analysis of the fluid flow mechanisms that govern spontaneous imbibition. The general scaling method was confirmed against the experimental data from spontaneous water imbibition conducted at different interfacial tensions in oil-saturated rocks with different sizes and permeabilities. A general analytical solution to the relationship between recovery and imbibition time for linear spontaneous imbibition was derived. The analytical solution predicts a linear correlation between the imbibition rate and the reciprocal of the recovery by spontaneous imbibition in most fluid-fluid-rock systems.

This paper proposes a subcell technique for modeling geometry and spatial distribution of channels in a fluvial reservoir by history matching of production and 4-D seismic data while constraining to well log and 3-D seismic information. The method developed here is capable of processing any number of geological objects with arbitrary geometric shapes and results in a fast and feasible inversion. The application of the proposed technique is presented in this work through several two- and three-dimensional examples in a two-phase water-oil case. The results of this work also show that the ntegration of production and 4-D seismic data can give us a better understanding of the reservoir geology and geophysics.

The effect of initial water saturation on gas recovery by cocurrent spontaneous water imbibition and imbibition rate was investigated both theoretically and experimentally. Equations correlating initial water saturation, gas recovery, imbibition rate, rock/fluid properties, and imbibition time were derived and used to conduct the theoretical analysis. These equations foresee that gas recovery and imbibition rate could increase, remain unchanged, or decrease with increase in initial water saturation, depending on rock properties, the quantity of residual gas saturation, the range of initial water saturation, and the units used in the definitions of gas recovery and imbibition rate. The theoretical predictions were verified experimentally by conducting spontaneous water imbibition at five different initial water saturations, ranging from 0 to about 50%. Water phase relative permeabilities and capillary pressures were calculated using the experimental data of spontaneous imbibition. The effects of initial water saturation on residual gas saturation, water phase relative permeability, and capillary pressure were also studied experimentally. The results in different rocks were compared. It was found that the residual gas saturation by spontaneous imbibition in a fired Berea sandstone sample (clay was removed by firing) was lower than in a natural Berea sandstone sample (clay was not removed). This demonstrates significant wettability alteration caused by firing. In other words, there may be significant wettability differences among different gas-liquid-rock systems.

The Brooks and Corey model has been accepted widely to calculate relative permeability using capillary pressure data. However the Purcell model was found to be the best fit to the experimental data of the wetting phase relative permeability for the cases studied, as long as the measured capillary pressure curve had the same residual saturation as the relative permeability curve. The differences between the experimental and the Purcell model data were almost negligible. A physical model was developed to explain the insignificance of the effect of tortuosity on the wetting-phase. For nonwetting phase relative permeability, the model results were very close to the experimental values in drainage except for the Purcell model. However, calculated data in imbibition were different than the experimental data. This study showed that relative permeability could be calculated satisfactorily by choosing a suitable capillary pressure technique, especially in drainage processes. In the reverse procedure, capillary pressure could also be computed once relative permeability data are available.

A method has been developed to scale the experimental data of spontaneous water imbibition (cocurrent) for gas-liquid-rock systems. In this method, a dimensionless time has been defined with the effects of relative permeability, wettability, and gravity included. The definition was not empirical but based on a theoretical derivation. Using this dimensionless time, experimental data from spontaneous water imbibition in different rocks with different size, porosity, permeability, initial water saturation, interfacial tension, and wettability might be scaled. The scaling model proposed in this study for gas-liquid-rock systems was verified experimentally for different rocks (Berea, chalk, and graywacke from The Geysers) with significantly different properties; it was also verified experimentally at different initial water saturations in the same rock. The scaling results from this study demonstrated that the cocurrent spontaneous water imbibition in gas-liquid-rock systems could be scaled and predicted.

Determining the best location for new wells is a complex problem that depends on reservoir and fluid properties, well and surface equipment specifications, and economic criteria. Numerical simulation is often the most appropriate tool to evaluate the feasibility of well configurations. However, since the data used to establish numerical models have uncertainty, so do the model forecasts. The uncertainties in the model reflect themselves in uncertainties of the outcomes of well configuration decisions. We never possess the true and deterministic information about the reservoir but we may have geostatistical realizations of the truth constructed from the information available. An approach that can translate the uncertainty in the data to uncertainty in the well placement decision in terms of monetary value was developed in this study. The uncertainties associated with well placement were addressed within the utility theory framework using numerical simulation as the evaluation tool. The methodology was evaluated using the PUNQ-S3 model, which is a standard test case that was based on a real field. Experiments were carried on 23 history-matched realizations and a truth case was also available. The results were verified by comparison to exhaustive simulations. Utility theory not only offered the framework to quantify the influence of uncertainties in the reservoir description in terms of monetary value but also provided the tools to quantify the otherwise arbitrary notion of the risk attitude of the decision maker. A Hybrid Genetic Algorithm (HGA) was used for optimization. In addition a computationally cheaper alternative was also investigated. The well placement problem was formulated as the optimization of a random function. The GA was used as the optimization tool. Each time a well configuration was to be evaluated, a different realization of the reservoir properties was selected randomly from the set of realizations all of which honored the geologic and dynamic data available from the reservoir. Numerical simulation was then carried out with this randomly selected realization to calculate the objective function value. This approach had the potential to incorporate risk attitudes of the decision maker and was observed to be approximate but computationally feasible.

Technological achievements in the area of well testing, such as permanent downhole gauges, demand automated techniques to cope with the large amounts of data acquired. In such an application, the need to interpret large quantities of data with little human intervention suggests the desirability of automated model recognition. Also in some cases the characteristic behavior of the pressure or its derivative curves for specific models may be hidden behind noise or human bias may lead to the selection of an invalid or inappropriate model. This paper demonstrates an approach based on Genetic Algorithm (GA) that is able to select the most probable reservoir model among a set of candidate models, consistent with a given set of pressure transient data. The type of reservoir model to be used is defined as a variable and is estimated together with the other unknown model parameters (permeability, skin, etc.). Several reservoir models are used simultaneously in the regression process. GA populations consist of individuals that represent parameters for different models. As the GA iterates, individuals that belong to the most likely reservoir model dominate the population, while less likely models become extinct. Since different models may require different numbers of parameters, the solution vectors have varying lengths. The GA is able to cope with such solution vectors of differing size. Information exchange (GA crossover operator) is allowed only between parameters that are physically related. Alternatively, we illustrate the use of GA as a preprocessor for conventional gradient-based algorithms such as LevenbergMarquardt. When combined with the GA, the dependency of such conventional algorithms to the initial guess is reduced and the overall regression performance is improved. For automated interpretations where the model is already known this method allows to virtually eliminate the initial guess determination step. Tests on real and synthetic pressure transient data indicated that the proposed method was able to select the correct reservoir model. The method revealed hidden implications of the pressure transient that may otherwise have been overlooked due to noise. As a preprocessor for more conventional nonlinear regression approaches, applying GA to a number of noisy pressure transient tests demonstrated that the method is robust and efficient.

Gas slippage in single-phase gas flow (Klinkenberg Effect) has been investigated extensively. Few papers, however, have been published on the gas slippage in gas-liquid two-phase flow. The gas relative permeabilities at water saturations close to the residual value have been found to be significantly greater than one in both nitrogen-water and steam-water flow through rocks. These values became less than one after the calculation was calibrated by taking the two-phase gas slip effect into consideration. The gas relative permeabilities have been measured at different mean pore pressures and the values of two-phase gas slip factor have been computed at different water saturations. The effects of temperature on both nitrogen and steam slip factors have also been studied and compared. These data have then been used to conduct a calibration in order to obtain intrinsic gas relative permeabilities that do not vary with the test pressures. It has been found from the present work that neglecting the two-phase gas slip effect may overestimate gas relative permeabilities. It is the intrinsic gas relative permeabilities instead of those measured at low test pressure that should be utilized in numerical simulation or other reservoir engineering calculation.

An experimental method was developed to measure both steam-water and air-water capillary pressures using an X-ray CT technique. We conducted spontaneous water imbibition and gravity drainage in ceramic core samples for steam-water and air-water systems respectively. The results were compared, and it was found that the steam-water capillary pressures were significantly less than the airwater capillary pressures in both imbibition and drainage cases.

To use pressure transient test data in computerised methods for integrated reservoir charcterisation numerical simulations of the well tests are typically required. Numerical artifacts occurring in the simulation must be avoided as much as possible so that they do not adversely affect the reservoir characterisation. This work explores the advantages of a hybrid boundary element method known as the Green element method for modeling pressure transient tests. Boundary element methods are a natural choice for the problem because they are based on Green's functions, which are an established part of well test analysis. The classical boundary element method is limited to single phase flow in homogeneous media. This works presents formulations which give computationally efficient means to handle heterogeneity. The accuracy of the scheme is further enhanced by incorporating singularity programming. Comparisons of the proposed Green element approach to standard finite difference simulation show that both methods are able to model the pressure change in the well over time. When pressure derivative is considered however the finite difference method produces very poor results which would give misleading interpretations. The Green element method in conjunction with singularity programming reproduces the derivative curve very accurately.

The Fifth SPE Colloquium on Petroleum Engineering Education (CPEE),, held 23–28 July 2000, was a very successful gathering of educators, technical leaders, engineers, and scientists from academia, industry, and government. The purpose was to address the critical issue of industry-university-government partnership in education, technology development, and technology transfer. The ultimate goal was to identify ways to develop the engineers and technology that the industry will need for the future. This paper reports the consensus of the Colloquium pertaining to: 1) the industry's current expectations for new petroleum engineering graduates (B.S., M.S., and Ph.D.) and 2) the future of research and development (R&D) activity in academia. Other subjects such as petroleum engineering education, curricula, technology transfer, and ABET (Accreditation Board for Engineering and Technology) issues are presented in a companion paper. In the context of this paper, academia refers to the U.S. petroleum engineering schools, and industry means the upstream segment of the U.S. petroleum industry. While this presentation has a U.S. framework, some findings may certainly apply globally elsewhere.

In this paper, a new multiresolution approach is proposed for reservoir parameter estimation, i.e., to estimate the spatial distribution of the reservoir properties by proper integration of all types of data available (either static or dynamic). We considered the integration of production history data, seismic data and well test data in this work.One of the key issues in parameter estimation is to develop an efficient and reliable nonlinear regression procedure. We adapted wavelet analysis to describe the distribution of sensitivity coefficients, since wavelet analysis is a powerful tool in multiresolution analysis and is widely used in signal and image processing. Wavelet analysis can compress the parameter space, stabilize the algorithm and avoid local minima. This new approach also improves the computational efficiency significantly by varying the resolution of the estimation at different regression stages.Wavelet analysis also has the capability to integrate different types of data efficiently, using different levels of wavelets to incorporate different data types. We can account explicitly for the resolving power of different data and estimate reservoir properties with nonuniform resolution.We have applied the procedure to multiphase reservoir examples that demonstrate the reliability and flexibility of the approach. We also gained very good convergence and excellent computational efficiency compared to conventional methods. The most important conclusion of this paper is that wavelet analysis is a very useful tool for reservoir parameter estimation and can speed up the computation and improve the performance. The nonlinear regression procedure integrating wavelet analysis has substantial advantages over the conventional algorithms.

Steam-water capillary pressure is very important in numerical simulation and reservoir engineering for steam injection into petroleum reservoirs and water injection into geothermal reservoirs. The significant mass transfer between steam and water phases makes it very difficult to measure steam-water capillary pressure using routine methods such as the semipermeable porous plate method and centrifuge method. Due to the difficulties in measuring steam-water capillary pressure, very few steam-water capillary pressure data are available. A steady-state flow method was deployed to measure steam-water capillary pressure curves using a modified X-ray CT technique to monitor and measure the water saturation and its distribution in the core sample. Experiments were conducted under near-adiabatic conditions controlled automatically by a computer. Steam-water capillary pressure was calculated using a formula derived from Kelvin's equation with the measured pressures and temperatures of the water phase. Both drainage and imbibition steam-water capillary pressure curves were obtained. The drainage and imbibition steam-water capillary pressures of the Berea sample used in this study were about 10 psi and 3.5 psi, respectively, at a water saturation of 30% and a temperature of 120°C. It was also confirmed experimentally that the lowering of vapor pressure was very small but the capillary pressure was significant for the experimental system used. This observation is consistent with thermodynamic analysis.

The Fifth SPE Colloquium on Petroleum Engineering Education (CPEE), held 23–28 July 2000, focused on partnership among industry, education, and government. Attendees determined how each partner can develop the people and technology that the industry will need in the 21st century. Significantly, the group suggested ways of enhancing interaction between universities and industry by encouraging greater cooperation in identifying and funding research projects that will benefit both. Proposed collaborative efforts among universities, possibly working with government laboratories, could meet some of the growing need as research programs move away from industry settings. Universities requested assistance from industry in identifying competencies that will serve students leaving academic programs. Included in the continuous feedback industry could provide the schools might be identification of needs for continuing education or distance degree programs, including coursework that would better prepare geoscientists to work in the petroleum industry. In addition, industry could provide data sets from real fields for students to use in capstone design courses. Educators agreed to seek a means for systematic sharing of those data.

Spontaneous water imbibition into gas-saturated rocks is an important physical process during water injection into highly fractured petroleum and geothermal reservoirs. Few methods, however, are available for characterizing the process of spontaneous water imbibition into gas-saturated rocks. To this end, a method has been developed. Water relative permeability and capillary pressure can be calculated separately from water imbibition data using this method. A linear relationship between imbibition rate and the reciprocal of the gas recovery by spontaneous water imbibition was found and confirmed both theoretically and experimentally, even at different initial water saturations. The effect of initial water saturation on imbibition rate, residual gas saturation, and the gas recovery has been investigated. There was almost no effect of initial water saturation on residual gas saturation by spontaneous water imbibition. The higher the initial water saturation, the lower the water imbibition rate and the ultimate gas recovery. It was found that the capillary pressure did not vary with initial water saturation in a certain range. The capillary pressure calculated using the new method was approximately equal to the values measured using an X-ray CT technique in a glass-bead pack. The computed water relative permeability was consistent with published experimental results. The method developed in this paper is also of importance for scaling-up experimental data.

This work deals with the problem of estimating reservoir permeability and porosity distribution from multiple sources, including production data and well logging data. The work focuses on integrating long-term resistivity data into the parameter estimation problem, investigating its resolution power both in the depth direction and in area. The resistivity logging tool considered in this project is a new tool proposed for permanent installation. The tool is installed in the cement around the well when the well is completed, and is capable of recording the long-term resistivity variation around the wellbore. In this work, the Poisson equation with mixed boundary condition was used to model the infinite potential field around the resistivity logging tool. The behavior of the reservoir was modeled with a standard three-dimensional, two-phase, black-oil model. The resistivity response simulator was integrated into the flow simulator through Archie's law. The Gauss-Newton algorithm was used to solve the inverse problem. This algorithm requires the calculation of the derivatives of the observation data with respect to the unknown parameters. These derivatives are called the sensitivity coefficients. By running several simple inverse problems, it was concluded that the resistivity data has high resolution power in the depth direction and is capable of sensing the areal heterogeneity.

The ambition of modern reservoir modeling is to make integrated use of dynamic data from multiple sources to infer the reservoir properties. The process of inferring the reservoir properties from indirect measurement is an inverse or parameter estimation problem. The parameters of interest in this work are porosity and absolute permeability. These parameters have important influence in determining the performance of the reservoir and in reservoir optimization. This work represents a way of estimating such parameters from a variety of indirect measurements such as well test data, long-term pressure and water-oil ratio history, and 4-D seismic information. The work also considers the effect of the data on the uncertainty and resolution of reservoir parameters. In particular, since earlier work has addressed two-dimensional problems, this study focuses on the estimation of parameters in three dimensions where properties vary as a function of depth. The study determined that depth-dependent properties can be estimated to varying degrees of precision, depending on the resolution of the data used to constrain the model. Seismic data generally has poor depth resolution, hence it was found that parameter estimates are better determined areally.

Summary The parameters that govern fluid flow through heterogeneous reservoirs are numerous and uncertain. Even when it is possible to visualize all the parameters together, the complex and nonlinear interaction between them makes it difficult to predict the dynamic reservoir responses to production. A flow simulator may be used to evaluate the responses and make reservoir management decisions, but normally only one deterministic set of parameters is considered, and no uncertainty is associated with the responses or taken into account for the decisions. This paper introduces the concept of a "quality map," which is a 2D representation of the reservoir responses and their uncertainties. The quality concept may be applied to compare reservoirs, to rank stochastic realizations, and to incorporate reservoir characterization uncertainty into decision making (such as choosing well locations) with fewer full-field simulation runs. The data points necessary to generate the quality map are obtained by running a flow simulator with a single vertical well completed in all the layers and varying the location of the well in each run to have good coverage of the entire horizontal grid. The quality of the horizontal cell in which the well is located is the cumulative oil production after a long production time. The geological model uncertainty is captured by generating multiple stochastic realizations and building a quality map for each realization. The quality maps of all the realizations provide a distribution of quality values for each cell of the map grid. A mean quality map can be obtained by taking the expected value for each cell, and a map of quality uncertainty can be obtained by taking the standard deviation of the distribution for each cell. If a loss function is specified, an L-optimal quality map can be generated by retaining, for each cell, the quality value that minimizes the expected loss. This map allows us to locate wells accounting for the geological uncertainty as well as for the risk profile of the decision maker. The methodology for building the quality map is presented in detail, and the applications of the map are demonstrated with 50 realistic reservoir models.

Long-term data from permanent gauges have the potential to provide more information about a reservoir than data from traditional pressure transient tests that last for a relatively small duration. Besides reducing ambiguity and uncertainties in the interpretation, long-term data also provide an insight on how reservoir properties may change as the reservoir is produced. This type of long-term surveillance provides the opportunity to look at the reservoir information in four dimensions rather than obtaining a glimpse or snapshot in time. However, the installation of permanent downhole gauges is only a recent phenomenon, and a methodology for the interpretation of the data has yet to be developed. The use of long-term data requires special handling and interpretation techniques due to the instability of in-situ permanent data acquisition systems, extremely large volume of data, incomplete flow rate history caused by unmeasured and uncertain rate changes, and dynamic changes in reservoir conditions and properties throughout the life of the reservoir.This study developed a multistep procedure for the processing and interpretation of long-term pressure data. The procedure was tested with several sets of simulated and actual field data. It was found to be an effective approach for the analysis of long-term pressure data from permanent gauges.

Abstract This study presents a new way to integrate flow rate history and pressure history data in well-test analysis. The method used is an extension of the deconvolution principle to a chosen period of time before the well-test. It is based on the recovery of missing parts of the pressure history by taking into account the flow rate history and the available sections of measured pressure history. The method has the advantage of working without making any assumption about the reservoir by using the data itself to define the "model". A real example with 71 pressure points and 70 corresponding flow rate points shows how it is possible to recover the first 20 pressure points correctly considering that only the flow rate history and the last 51 pressure points are known. The main purpose of this procedure is to have an alternative to treat the problem of flow rate variations both before and during the well-test. In such a case, neither the deconvolution (only applicable for flow rate variations during the well-test, when flow rate and pressure are both known), nor the multirate superposition plots (too constraining on the shape of the flow rate history and on the late time reservoir behavior) can be applied properly. In addition, the principle of the method enables us to extend its use to the analysis of well-tests with pressure recording errors or missing pressure recording. Examples show that it is possible to make a good analysis of a well-test with missing pressure regions when current methods give only parts of the information. P. 91^

Optimization of reservoir development requires many evaluations of the possible combinations of the decision variables, such as well locations and production scheduling parameters, to obtain the best economic strategies. Running a simulator for such a large number of evaluations may be infeasible due to the computation time involved. This study investigated two multivariate interpolation algorithms, Least Squares and Kriging, to generate new realizations from a limited number of simulations in order to predict the optimal strategies in a field development scheduling project and a waterflood project. The result was a significant reduction in the simulation effort required. The recommended solutions were obtained by searching for the optimal objective function values among the interpolation realizations. Additional simulation runs were performed to refine the search for the final optimal solution in the vicinity of the intermediate optimal region. The net present value was used as the objective function in both projects. The field development scheduling simulation was achieved by an economic model taking account of all the costs and profits during the time period being studied. In the waterflooding application, movement of the waterfront was tracked and the oil and water production at each production well was calculated, after which the optimum well placement strategy was determined. The results obtained using the interpolation methods showed that the algorithms are able to reduce the number of simulation runs, to provide a global sketch of the objective function surface, to avoid possible failure at local optima, and to reach the absolute optimum by refining the grids near the intermediate optima. The approaches were shown to be practical, and will be useful in full-scale optimization problems in which simulation costs would be prohibitive for iterative nonlinear optimization methods.

Abstract Optimization of reservoir development requires many evaluations of the possible combinations of the decision variables, such as the reservoir properties, well locations and production scheduling parameters. to obtain the best economical strategies. Running a simulator for such a large number of evaluations may be impractical due to the computation time involved. In this study, a hybrid Genetic Algorithm (GA) was developed. The optimization algorithm integrated economic analysis, simulation and project design. The layout of 33 new wells for a real oil field development project was proposed by the company's project team. The algorithm was used to determine an optimal relocation of the wells, by evaluating an objective function from a cash flow analysis for the production profile obtained from simulation at each iteration. The wells were allowed to be placed anywhere in the reservoir and could be vertical or horizontal and, if horizontal. any direction in the same layer could be considered. A total of 99 decision variables were used to solve this problem. All the real restrictions were included. Based on the cost of the sea bottom flowlines a second level optimization found the best platform location. The results were compared against the proposed solution, and showed that the algorithm performed very well finding an optimized well distribution. A reduction of the total number of new wells was found as part of the solution. An improvement of about 6% in the project profit was found. representing about US$70 million additional income. Introduction The main task of a reservoir engineer is to develop a scheme to produce as much hydrocarbon as possible within economic and physical limits. The solution of this kind of problem encompasses two main entities: the field production system and the geological reservoir. Each of these entities presents a wide set of decision variables and the choice of their values is an optimization problem. In view of the large number of decision variables it is not feasible to try to enumerate all possible combinations. Analysis tools encoded in computer programs can spend hours or days of processing for a single run, depending on their sophistication and features. Also, it can be costly to prepare the input data if many hypotheses are going to be considered. A typical reservoir development involves many variables that affect the operational schedule involved in its management. These variables are usually used as input to a reservoir simulator that generates a forecast of the production profile. Using this forecast, the production engineer has to consider several hypotheses to achieve the best strategy for the field development. Also, each hypothesis can generate others, and so the overall process is one of generating a hypothesis tree. More and more data are generated and analyzed. The solution of these problems requires the effort of several people as well as considerable computer work and physical time. An optimization procedure requires the characterization of the function to be optimized (minimized or maximized), known as the objective function. as well as the choice of an appropriate optimizing method. The complexity of predicting hydrocarbon production profiles requires the use of reservoir simulators. So, the simulator must be part of the evaluation of the objective function. This work concerns the optimization of characteristic petroleum production problems considering economic factors. A hybrid algorithm based on direct methods such as Genetic Algorithm (GA). polytope search and Tabu search was developed. Hybrid techniques were found to improve the overall method. The objective function consisted of a cash flow analysis for production profiles obtained from simulation runs. The optimizing procedure was able to interface with commercial simulators (generating their input data and retrieving the results) that worked as data generators for the objective function evaluation. These hybrid mathematical approaches were found to be successful in obtaining the optimal solution with less time and work than existing techniques. P. 545^

This paper deals with the problem of estimating the distributions of permeability and porosity in heterogeneous and multiphase petroleum reservoirs by matching the dynamic behavior. The dynamic data is in the form of field measurements from well testing, production history, interpreted 4-D seismic information, and other data such as correlations between permeability and porosity, geostatistics in the form of a variogram model and the inference of large scale geological structure. The issue was posed as an inverse problem and solved by using nonlinear parameter estimation. The procedure developed here is capable of processing all the information simultaneously and this results in a fast and efficient method. The procedure is also able to determine the uncertainty associated with the estimated permeability and porosity fields. Examples of different parameter types that may be estimated by this approach include: (a) individual block permeabilities and porosities; (b) geological objects such as channels and faults; (c) pilot points that form the basis of a kriged distribution; and (d) seismic attenuation values from 3D seismic images. An important conclusion of this work is that the value of each piece of information does not reside in its isolated use but in the value it adds to integrated analysis of the complete set of information. Thus data that traditionally was considered to be of low information content for reservoir characterization becomes useful and enhances the value of the data set as a whole.

This paper describes a new method of analyzing the cost of uncertainty in reservoir data. The method is based on the use of nonlinear optimization techniques. Nonlinear optimization techniques are mathematical or heuristic methods of determining the set of decision variable values that maximizes an objective function value. Given the appropriate model, optimization techniques can be used to determine the best set of production engineering parameters for an oil or gas field. The optimization technique considered is the Genetic Algorithm (GA). However, the optimized engineering parameters depend largely upon the input reservoir rock and fluid properties. If the reservoir property values differ from the expected values, the engineering parameters selected as optimal by numerical optimization will probably be suboptimal. This leads to a new technique for assessing the cost of uncertainty in reservoir data. The cost of uncertainty in a reservoir parameter depends upon the discrepancy between the optimal net present value (NPV) for the actual parameter value and the NPV realized when optimization is performed for the expected value of the parameter. For a parameter, such as porosity or permeability, a probability distribution is determined. From this distribution, five representative values are chosen to discretize the distribution. The engineering parameters are optimized for the expected property value (the third representative value). The NPVs based on these engineering parameter values and the other four reservoir parameter values are determined. Then the optimal NPVs are determined for the four remaining reservoir parameter values. Combining the probability of each representative parameter value and the discrepancy between optimal and suboptimal NPVs for that parameter value yields the cost of uncertainty for that reservoir parameter. When the cost of uncertainty has been established for each reservoir parameter, the engineer will be able to decide which parameter should be further tested, and to what extent. This allows careful weighing of the cost of testing procedures, including seismic, logging, and transient testing, against the cost of uncertainty in the reservoir parameter values.

Abstract This paper describes numerical techniques developed to determine the wellbore configuration that will optimize the life-time value of a property. The production history of a reservoir can be predicted by integrating a reservoir model, a well-bore flow model, a choke model, and a separator model. Changes in any production parameter, including the gas-lift configuration, will cause changes in the predicted production history. The numerical methods can find the combination of production parameters that optimizes the net present value of the flowstream. The control parameters sampled in this work include tubing diameter, separator pressures, depth of gas injection, and volume of gas injected. Each of these parameters can be variable with time. The influence of these parameters upon the net present value is complicated by the feed-back nature of the gas-injection loop. This nonlinearity requires robust, efficient routines for optimization. Genetic Algorithm optimization techniques are shown to be both stable and efficient when used to optimize these sorts of nonlinear problems. Introduction Petroleum engineers face a wide variety of parameter estimation and optimization problems. Every time a transient test is analyzed or a location for a well is chosen, an optimization or parameter estimation problem has been solved. Yet it is surprising how rarely a formal optimization technique is used to solve these problems. Mathematical and heuristic methods are available which can find optimal solutions for a given model. This paper describes the application of formal optimization techniques to a realistic petroleum engineering problem. With the improvement of computer modeling over time, it is now feasible to apply optimization techniques to petroleum engineering models. In 1990, Carroll and Horne applied multivariate optimization techniques to a model of a field produced by a single well. However, only the separator model was compositional, and no wellbore parameters were allowed to vary with time. Carroll and Horne used two types of optimization routines, gradient methods and polytope methods. In 1992, Ravindran followed and allowed engineering parameters to be varied with time. Fujii continued this line of study in 1993, by including a network of wells connected at the surface. Fujii also studied the utility of genetic algorithms for petroleum engineering optimization. This project expands on Ravindran's work by replacing all black-oil components with fully compositional models. In addition, all three major types of optimization techniques were considered. Model Construction The model developed for this project was designed to test optimization algorithms for petroleum engineering problems. In addition to being robust, the model is a simplification of a real petroleum engineering problem. If the tested optimization algorithms are to be useful for real applications, the test problem should include challenging nonlinear relationships. The field model constructed for this work provides these challenges. The field model is an integration of smaller components. The complete model represents an oil reservoir with a single gas-lifted well. The individual components include:reservoir model;well model with gas lift;choke model;and separator model. Fig. 1 illustrates the fashion in which these components are combined. In the integrated model, each component influences the other components. Produced fluid flows into the tubing. At the point where the lift gas enters the tubing, the two streams commingle, and the flow continues up the wellbore. At the surface, the commingled fluid passes through the choke into the first separator. Gas from the first separator goes into the gas line and the liquid phase moves into the second separator. Gas from the second separator passes into the gas line, and the liquid goes into the third separator. The gas in the third separator goes into the gas line, and the liquid goes into stock tanks to be sold. Some of the separated gas is compressed, and injected into the tubing-casing annulus for gas lift. The remainder of the gas is sold. Notice the nonlinear relationships between the various components. P. 341^

Spotlight on R&D series - This is the second of a series of articles on the state of research and development (R&D) in the major upstream technological disciplines. The Spotlight on R&D Series, comprising articles published in JPT during 2004 and 2005, is available as a collection on OnePetro (SPE-101432-JPT).