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ECMOR XVI - 16th European Conference on the Mathematics of Oil Recovery
- Conference date: September 3-6, 2018
- Location: Barcelona, Spain
- Published: 03 September 2018
81 - 100 of 172 results
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A Numerical Model to Characterize the Flow and Heat Transfer Behaviors of Compressed Air in High-Pressure Air Injection Wells
Authors N.C. Feng, S.Q. Cheng, W.Y. Shi, J.Z. Qin and J. ZhangSummaryHigh-pressure air injection (HPAI) is a significant EOR technology of light oils especially in deep, thin, low-permeability reservoirs. With the rapid development of technology, concentric dual-tubing injection technique was employed in multi-layer HPAI wells to overcome the influence of heterogeneity and to adjust the uneven suction in each layer. The objective of this study is to better characterize wellbore pressure and temperature distribution of compressed air along wellbore in HPAI wells with concentric dual-tubing injection technique. Based on mass, momentum and energy balance equations, mathematical model was established and solved by finite difference method and iterative technique. The pressure drop in both inner tubing and annulus is calculated based on the momentum balance equation, and the temperature drop along wellbore is calculated based on the energy balance equation. The heat conduction between inner tubing and annulus, and the dynamic behaviors of injected air are taken into consideration. The effect of injection temperature on distribution of air temperature and pressure in inner tubing are conducted.
It is found out that: (1) . As well depth increasing, temperature difference between formation and wellbore tends to become constant, and the radial heat transfer tends to reach an equilibrium state. The lower the injection temperature is, the deeper the equilibrium depth is. (2) . The air pressure in both inner tubing and annulus is mainly dominated by the hydrostatic pressure and increases with well depth. The pressure gradient in the annulus is larger than that in inner tubing. (3) . Decreasing the injection temperature can increase the temperature gradient increases in inner tubing, which is caused by the increasing of heat transfer rate between formation and wellbore fluid. (4) . Increasing the injection temperature can decreases the air pressure in inner tubing. This is because the air density decreases with increasing of injection temperature, which causes the decrease of hydrostatic pressure and increase of friction losses.
This paper proposed a novel model to predict the pressure and temperature distribution along wellbore in HPAI wells. The theoretical studies in this paper provides following researchers with the very basic theory for the application of concentric dual-tubing injection technique in HPAI wells and can be taken as a reference for engineers in optimization of injection parameters.
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Architecture Characterization And Remaining Oil Distribution Pattern Of A Fluvial Point Bar Reservoir
More LessSummaryAfter integrating results from all these methods, some interesting observations were found. Six facies were identified in the point bar strata studied, including massive sandstone with clasts at the base of point bar sequence, cross-stratified sandstone, various interbedded sandstone and siltstone unites that comprise IHS packages, and bioturbated siltstone and mudstone. The dips of IHS deposits were 3–8 degree with the average width of 80m. The thickest and coarsest-grained sediments were deposited near the channel-bend apex, occurring as a circular body when channel bends mainly increase in sinuosity. Extensive finer-grained deposits were accumulated in concave-bank areas when meanders migrated downstream, forming an elongate body parallel to the channel-belt axis. The numerical simulation suggested that channel belts with downstream translation constituted reservoir with higher recovery factors than those with only increase in sinuosity. The abandoned channel and IHS package were the main barriers or baffles in the meandering system. The width, dip angle of IHS package and the direction of water injection could all effect the final swept volume.
The study offers a comprehensive case study that helps geologists and reservoir engineers for better understanding the reservoir and optimizing production plan in the future. Moreover, it provides an integrated method for understanding and characterizing point bar reservoir in detail, which can be used in other similar oilfields.
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Well Interference Test Analysis In Stochastic Porous Media
Authors D.V. Posvyanskii and A.V. NovikovSummaryInterference well test analysis provides valuable information about reservoir characteristics such as permeability and hydraulic diffusivity coefficient. Interference well test analysis is based on solution of the diffusivity equation which describes mass transfer in a porous medium. Generally, analytical solutions are used for interpreting interference test data. However all these solutions were obtained under the condition of reservoir homogeneity. In heterogeneous reservoirs with spatially variable permeability, the exact analytical solutions are not known. A heterogeneous permeability field can be represented as the sum of two terms. The first term is the constant mean permeability value and the second one is the random function with known statistical properties. The second term is considered as a perturbation. The possibility to evaluate geostatistical parameters from well test analysis was considered by various authors and it is still a challenging problem. In heterogeneous reservoirs, a flow equation is formulated for the pressure which is averaged over all the permeability realizations. It can be solved using Green’s function techniques, where the ensemble-averaged Green’s function is represented as an infinite perturbation series. This series expansion can be written graphically using Feynman diagrams and its summation can be performed following the rules that are well known in quantum theory. This approach was first introduced to reservoir simulation in [1], where the stochastic pressure equation was solved for the steady-state case.
In this study we use diagrammatic analysis to obtain the solution of the time dependent stochastic pressure equation. This solution was used in interpretation of well test interference data. The calculations were carried out assuming the statistics of the random permeability field are Gaussian and the covariance of the logarithm of the permeability is exponentially decaying. The two limiting cases were considered: (i) the distance between wells is much bigger than the permeability correlation length, (ii) the opposite case when the correlation length is the smallest length parameter. Using different realizations of a synthetic reservoir model with fixed statistical parameters, the ensemble of well interference data was numerically generated. The mean value and correlation length of the permeability distribution were estimated so that the solution for stochastic pressure reproduced the averaged results of numerical simulations.
[1] King P.R. J .Phys. A: Math. Gen 20 p. 3935 – 3947 1987
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Application Of Xu-White And Critical Porosity Models To A Carbonate Reservoir Using An Optimization Algorithm
Authors A. Heidari, N. Amini, H. Amini and M. Emami NiriSummaryPetro-elastic modeling plays a crucial role in closing the loop between the reservoir model and seismic data by means of relating elastic properties to the reservoir model properties. Accordingly, precise estimation of elastic parameters leads to a more reliable petro-elastic model and helps to reduce uncertainties related to reservoir model construction. One of the pitfalls in petro-elastic modeling is the values of mineral elastic properties, which are conventionally considered constant for most of the reservoirs. Disregarding the lithological characteristics may increase uncertainty in the estimation of parameters and can be misleading especially in 4D studies on saturation effects. Carbonate rocks as the most predominant rocks in the reservoirs show a more complex behavior in comparison to sandstone reservoirs; hence, the effects of physical properties such as aspect ratio and critical porosity should be considered with more care. In this paper, solving the multivariate optimization problem is addressed via very fast simulated annealing algorithm. The optimum values of elastic moduli are determined considering two rock physics models, Nurs’ critical porosity, and the simplified Xu-White model. Depending on dry rock physics relation, the correspondent physical parameter (critical porosity or aspect ratio) is optimised as well. The case study is a carbonate reservoir located in the southwest of Iran. The variation of lithological characteristics with depth for each rock type necessitates constraining the physical parameters of each rock physics model to lithology during the optimization workflow. The output of the optimization workflow is The output of the workflow is the optimised elastic moduli of the mineral components and the regression coefficient of the fitting parameters to effective porosity. In addition, the optimised fitting parameters provide some insights into pores shape and diagenesis processes of the rock in the target zone. Comparison of the modeled and observed elastic logs confirms the accuracy of the proposed workflow.
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Application Of Hydraulic Flow Units Approach In Permeability Prediction: Case Study, Abu Roash G Member, Sitra Field, Egypt
Authors A. Abu Mostafa, A. Abu Khadrah, A. Refaat and E. AbdelmoutySummaryPermeability prediction is necessary to develop an effective reservoir characterization program. Permeability is controlled by the pore throat size, which in turn is a function of the pore type. The latter is determined by the depositional facies and the subsequent diagenetic processes. Statistical analyses including histogram, probability plot, and hierarchical clustering algorithm of conventional core data based on Hydraulic Flow Units approach (HFU) were used to evaluate the reservoir characteristics of the Abu Roash “G” Member. Probability plot and Hierarchical clustering analyses show 7 and 5 clusters for grouping the core data in the two studied wells, corresponding to 7 and 5 hydraulic flow units can be considered. The Hydraulic Flow Units in the Abu Roash “G” Member nearly reflect the depositional facies. Since each flow unit is characterized by unique values of porosity, permeability, and pore throat distribution, the lateral and vertical distribution of the Hydraulic Flow Units in the two analyzed wells reflect the high heterogeneity of the reservoir in the Abu Roash “G” sandstones and could be attributed to the changes in the local sedimentary structures and the diagenetic processes, which enhance or reduce the reservoir properties. High correlation coefficients between the core permeabilities and the predicted permeability values from average flow zone indicator data reflect the accuracy of the probability plot and clustering methods and the suitable number of clusters for grouping the flow zone indicator data.
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A Case Study Of A New Time-Depth Conversion Workflow Designed For Optimizing Recovery
Authors J.M. Chautru, N. Nosjean-Gorgeu, D. Renard, H. Binet and P. CorreiaSummaryTo optimize hydrocarbons recovery and quantify future production risks, it is necessary to accurately characterize traps geometry. This geometry is estimated from both seismic and well data, using Time-Depth conversion methods. This characterization is a critical issue in reservoirs with thin beds, as the uncertainty on horizons depth can lead to large variations of beds thickness.
The paper presents an application on real data of a new Time-Depth conversion integrated workflow which is based on advanced geostatistical estimation and simulation multivariate algorithms and on automatic Spill Point recognition. It enhances horizons depth estimation and minimizes the uncertainty on the consecutive horizons. This workflow is extremely efficient in faulted layer-cake deposits, especially when reservoirs are thin.
First, the theoretical background of the geostatistical multivariate algorithm is briefly summarized, including its version in the Bayesian framework. Then, the application example is used to highlight the differences between the simultaneous conversion of consecutive horizons and the standard conversion where horizons are considered as independent to each other. Focus is put on the vertical evolution of uncertainty and on the Geophysicist input allowed by the Bayesian framework.
The workflow is versatile enough to convert directly Time in Depth or to compute intermediate enhanced velocity models when required. Practical examples are presented to illustrate the characteristics of each method. The impact of the different conversion options on Spill Points location and on the reservoirs Gross Rock Volumes are highlighted.
One of the most original and useful features of the workflow is its ability to include faults location uncertainty in the global Gross Rock Volumes uncertainty quantification. The implementation of this capability is explained and illustrated from its application to real data.
In the end, the impact on ultimate recovery uncertainty is analyzed and illustrated from a practical case study.
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Conditioning Spectral Simulation Method By Horizontal Well Data
Authors N.S. Ismagilov and M.A. LifshitsSummarySpectral simulation is a relatively new geostatistical approach to 3D probabilistic reservoir property simulation. In spectral method simulated property is considered as a realization of a stochastic field, and well logs as realizations of stochastic processes. Well logs are decomposed into Fourier series of coefficients w.r.t. some L2 basis. Coefficients among different wells are grouped according to the basis function, each group representing samples of 2D stochastic fields (surfaces) of coefficients. For each group stochastic surfaces of coefficients are simulated, based on obtained samples and full 3D stochastic field is reconstructed as sum of Fourier series at each lateral point.
One of the features of the spectral method is conditioning simulation results (i.e. reproducing hard data) only on data along vertical wells, which is considered as a limitation in practical applications when reservoirs with large number of horizontal wells are modeled. Hard data on non-vertical wells impose different type of conditioning on simulated stochastic fields of coefficients. In order to satisfy the new type of conditions, generalization of kriging and new type of conditioning of stationary fields, based on this generalization, is proposed. The new type of conditioning is proved to modify simulated surface-coefficients such that conditions imposed on resulting 3D stochastic field on any finite set of points (including points on trajectories of horizontal wells) can be satisfied while preserving statistical parameters of the stochastic field.
Numerical algorithms are provided for analytical derivations, which are confirmed by illustrative simulation experiment for a simple one-dimensional model. The new algorithm is implemented in experimental software and demonstrated to be scalable by conducting conditional simulation for real-field geophysical parameter on a full-scale reservoir model. The results are compared to those of more traditional methods and shown to be more adequate from geological point of view and better reproduce statistical parameters of well data.
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Experimental And Mathematical Study Of Multi-Component Gas/Oil Displacement With Constant Pressure Boundaries
Authors L.A. James, H.N. Nekouie and T.J. JohansenSummaryIn this paper multi-component gas/oil displacements with constant pressure boundaries are studied mathematically and experimentally. Mathematically, a novel generation of Buckley-Leverett’s classic fractional flow theory is applied to analytically solve the problem of multi-component gas/oil displacements under constant pressure boundaries. Experimentally, slim tube tests under constant pressure boundary condition are conducted to validate the assumptions made in the mathematical section and thus confirm the innovative analytical solution. All the previous studies in gas/oil displacement problems have been accomplished under the assumption of constant flux boundaries. In practice however, gas flooding projects are often conducted with constant injection pressure and constant producing well pressure. Therefore, a fast and accurate analytical solution will be a powerful tool for IOR/EOR scenario simulations.
Conservation of mass in a one-dimensional, dispersion-free medium, for a multi-component gas/oil displacement system leads to a set of partial differential equations. The solution of the corresponding initial value problem under constant flux boundary conditions consists of rarefaction waves, shock waves and constant states connecting the injection state to the production state. In incompressible systems with constant pressure boundaries, the total volumetric flux is a function of time and hence, the classical Buckley-Leverett theory is not valid. However, the saturation wave structure obtained from the constant flux boundary condition problem can be used in the solution of the associated problem with constant pressure boundaries by determining the flux analytically as a function of time.
The experimental and analytical solution for a multi-component gas/oil displacement case study is presented. The determination of time dependent volumetric flux from the analytical solution of the constant flux problem is demonstrated. Experimental results are analyzed and compared with the analytical solution. This indicates that analytical solutions match with the experimental results if reliable relative permeability data are used.
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Measurement Of Physical Dispersion In Random Correlated Permeability Fields And Its Application For Upscaling
Authors S. Ghanbari, E.J. Mackay, G.E. Pickup and S. GeigerSummaryAn algorithm is developed to measure local dispersion within the model. The algorithm is based on solving the solution of convective-diffusive equation between two neighbouring cells in a 1D model to identify the relevant Peclet number describing dispersion between them. The algorithm may be applied for the entire pair of grid blocks located in the transition zone; for each pair of grid blocks a Peclet number may be measured. Properly averaging these measured Peclet numbers could provide an estimate of the total system dispersion coefficient. Measurement of dispersion in systems with known numerical and physical dispersions also confirmed algorithm’s accuracy.
The algorithm is later applied to 2D heterogeneous random correlated permeability fields. As with the 1D model, measurement of Peclet numbers may be carried out between all pair of neighbouring cells located only in the transition zone for either horizontal or vertical orientations. This in turn provide estimate regarding dispersion coefficient for that respective orientations.
For each respective orientation, the measured dispersion coefficients can be matched with equivalent numerical grid block sizes replicating the same physical mixing. This provides a rapid tool for estimating the approximate number of grid blocks for different orientations particularly for a miscible simulation.
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A Pattern-Based Approach For Geologic Scenario Identification And Reservoir Model Calibration
Authors A. Golmohammadi and B. JafarpourSummarySubsurface flow model calibration is often formulated to adhere to a given prior geologic scenario for describing th econtinuity in rock property distributions while minimizing the mismatch between predicted and observed flow responses. In probabilistic model calibration, the prior geologic continuity model is given either through parametric distributions with known parameters (e.g. Gaussian priors with known covariances) or through empirical distributions with sample realizations that share the same statistical attributes or spatial patterns (e.g., a training image). The conventional assumption is to use the prior model as a geologic constraint to maintain consistency with descriptions provided by the geologist. However, geologists often deal with various sources of uncertainty that complicate the construction of prior models to describe the variability in the spatial distribution of subsurface properties. A natural question to ask is whether dynamic data can help geologists to constrain or narrow down the number of possible scenarios. The purpose of this paper is to evaluate the feasibility of using dynamic data to accept or reject prior geologic scenarios using a pattern-based approach. We develop a twostage calibration process, where in the first stage dynamic data is used to identify plausible geologic scenarios using approximate parametric solutions while in the second stage geologic feasibility is ensured through a pattern-based mapping with a supervised machine learning technique. A series of model calibration problems are used to evaluate the performance of the proposed formulation and to discuss its properties. These examples show the value of incorporating dynamic data in selecting consistent geologic scenarios prior to performing full model calibration and uncertainty quantification.
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Digital Core Analysis: A Collaborative Cloud-Based Environment Leveraging High-Performance Computing
Authors N. Koliha, J. Bautista, D.M. Freed, B. Crouse and C.A. Santos MolinaSummaryDigital Core Analysis: A Collaborative Cloud-based Environment
Leveraging High-Performance Computing
Finely resolved single and multi-phase pore-scale flow simulation has emerged as a complimentary technique to laboratory Routine and Special Core Analysis (RCAL/SCAL) methods. Digital core analysis is faster, given adequate computational resources, and provides detailed insight into the mechanics of oil displacement and recovery at the micro-scale, even for samples not suitable for RCAL/SCAL. Sensitivities to flow conditions and properties of the rock-fluids system can be explored in a self-consistent way without sample-to-sample error. However, the high-performance computing (HPC) environment required for the digital core analysis approach represents a potential barrier to entry due to infrastructure cost and IT support. Pre- and post-processing of the data can necessitate expert knowledge and/or training, complicating the workflow and creating a steep learning curve for new practitioners.
Here we present a fully automated, on-demand, cloud-based digital core analysis system that overcomes these entry barriers and makes a complex scientific computing application easily and readily accessible. From a web-based UI, the system allows users to upload pore-scale micro-CT or FIB-SEM images of rock samples, explore the pore space characteristics, and perform single and multi-phase lattice-Boltzmann simulations to obtain absolute and relative permeability curves. An example use case and results are presented for an operator leveraging this application for petrophysical property analysis of a sandstone rock sample. While the system carries out the highly complex algorithms, the user achieves all this with a few mouse clicks – expert supervision and manual parameter selection are avoided. Users can share the resulting information throughout their organization, from the field to remote managers, allowing unprecedented collaboration in evaluating and using core analysis results. The advantages of this cloud-based approach are not application specific; they represent a disruptive technology that can be replicated to other complex, computationally intensive workflows within and beyond the oil and gas industry. In this way, the digital core analysis system presented serves as an example of democratizing the power of high performance computing.
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A Fractal Model For Oil Recovery By Spontaneous Water Imbibition In Tight Oil Reservoirs
More LessSummaryDeveloping tight oil reservoirs is challenging due to ultra-low permeability and porosity. Oil recovery through spontaneous water imbibition into water-wet tight matrix is an important mechanism of tight oil development. This paper develops a novel semi-analytical model for spontaneous imbibition (SI) in tight oil reservoirs with fractal theory. Firstly, pore structures of tight sandstones were characterized with fractal geometry, and pore space of tight sandstones are assumed to be bundles of tortuous capillary tubes with fractal characteristics. Then, considering the boundary-layers of initial water and residual oil, the SI in a single tortuous capillary tube was studied. With the assumption of pore size distribution following fractal distribution, the model of SI on core scale were developed and the model reliability was verified with experiment data. Finally, the effects of pore structure parameters, contact angle, IFT, oil-water viscosity ratio on SI oil recovery were quantitatively evaluated.
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Impact Of Cell-To-Cell Scale Variability On Flow In Reservoir Models
By H.O. OsmanSummaryReservoir models typically contain hundreds-of-thousands to millions of grid cells in which petrophysical properties such as porosity and permeability vary on a cell-to-cell basis. Moreover, the petrophysical properties and flow equations are discretized on the same grid. We investigate the impact of decoupling the grid used to model the petrophysical properties from that used to solve the flow equations. The aim is to test whether cell-tocell variability in petrophysical properties has a significant impact on fluid flow. We test the decoupling in two ways using a number of grid-based models. First, we keep the initial distribution of petrophysical properties, but solve flow equations on a finer grid. Second, we remove cell-to-cell variability to yield models containing just a few tens of unique porosity and permeability values grouped into a few hundred, internally homogeneous domains, but use the same initial grid to solve the flow equations. In both approaches, the flow behaviour of the original model is used as a reference. We find that the impact of cell-to-cell variability on predicted flow is small, and smaller than the error introduced by discretizing the flow equations on the same grid as the petrophysical properties. Cell-to-cell variability is not necessary to capture flow in reservoir models; rather, it is the spatially correlated variability in petrophysical properties that is important. Reservoir modelling effort should focus on capturing the geologic domains in the most realistic and computationally efficient manner.
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A Unified Convection-Diffusion Layered Model For Non-Ideal Rarefied Gas Flow In Nanoscale Porous Media
More LessSummaryExisting rarefied gas flow models cannot accurately characterize gas flow behaviors in nano-porous media by coupling various empirical rarefaction and diffusion coefficients. Also, almost all models overlook the importance of non-ideal gas effect on the flux and apparent permeability. In this work, a unified model for nonideal rarefied gas flow in nano-porous media has been developed. More specifically, a straight capillary tube consisting of a viscous flow zone and a Knudsen diffusion zone is sectioned by an analytically derived boundary. Subsequently, the apparent permeability is obtained by coupling weighted flow mechanisms and extended to the porous media considering the roughness, rarefaction, and real gas effect. It has been found the apparent permeability hardly change when pressure is over 10.0 MPa and pore size is larger than 100 nm. Sensitivity analysis shows the apparent permeability is strongly dependent on pore size and weakly dependent on roughness. Finally, it is observed that real gas effect decreases the flux of the new model at high pressures. The developed model is an easy-to-use tool for gas transport in tight porous media and can be integrated in large-scale simulations to optimize the long-term production performance of unconventional reservoirs.
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Permeability Indexes For Defining Tight Oil Reservoirs
More LessSummaryIn recent years, the tight oil production increased dramatically in the U.S. thanks to the advances in large-scale hydraulic fracturing of horizontal wells, which has not just restructured this country’s energy supply pattern to some extent, but also drawn extensive attention around the world. Significant progress was also made in China in respect of tight oil exploration and development. Nonetheless, there are no standards available yet in China for assessing tight oil reserves. Because of the uniqueness of tight oil, standards for assessing the reserves of conventional oil are not applicable to tight oil. Therefore, both CNPC and the China national reserves regulator attach great importance to the standards defining tight oil.
Indeed, there are two types of tight oil definitions – one in broad sense, and the other in narrow sense, which are distinguished mainly by whether or not the shale reservoirs are included. The concept of tight oil in narrow sense (reservoir consists of tight sandstone or carbonate rock) is normally adopted in the exploration and development practices in China. In consideration of the existing standards, data availability, traditional practices and the relationship between formation permeability under overburden pressure and surface permeability, it is recommended to use the air permeability at surface condition as the key index to define tight oil.
Tight oil reservoirs differ from conventional reservoirs with extremely low permeability mainly in three aspects: the pore structure, the porosity-permeability relationship and the porosity-irreducible water saturation relationship. After analysis by such methods as evaluation of the reservoir productivity, investigation of the relative permeability of cores in laboratory, and assessment of the core displacement pressure and from such aspects as the core porosity versus permeability relationship, it is proposed that the air permeability of 1 mD be used as the threshold to divide tight oil reservoirs and conventional reservoirs. The Standards for Estimation of Tight Oil Reserves (Q/SY1834-2015) (CNPC Standards) were stipulated based on the achievement of this project to help CNPC to report over 1.0 billion tons of proved, probable and possible tight oil reserves.
Besides permeability indexes, two supplementary methods for characterizing tight oil reservoirs, i.e. the seepage rate and the pore throat radius, are analyzed by referring to the research results in China and abroad, for the reference of other scholars.
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Total Organic Carbon Prediction In Barnett Shale Gas Reservoir Using The Multilayer Perceptron Neural Network
Authors S.A. Ouadfeul and L. AliouaneSummaryIn this paper, we predict the Total Organic Carbon from raw well-logs data recorded in two horizontal wells drilled in the Lower Barnett shale formation using the Multilayer Perceptron neural network machine. A comparative study between the Levenberg-Marquardt and the Conjugate Gradient learning algorithms shows the power of the Levenberg-Marquardt to predict the Total Organic Carbon in case of lake in the measurement of the Bulk density log, this can help to resolve the lake of the Schmoker’s method which requires continuous measurement of the bulk density log
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Hybrid Coupled Discrete-Fracture And Continuum Models For Low Permeability Reservoir Simulation
Authors J. Xu, C. Bailian, Z. Wei, S. Baojiang and W. ShiSummaryIt is an important and hot issue to simulate flows in tight reservoirs with complex fractures. Large work has been done to study the transport between the matrix and fracture. However, pseudo-steady-state transfer encounters difficulty due to extremely low matrix permeability for tight reservoirs. Transient transfer shape factor between matrix and fracture should be considered. Considering the transient transfer, a simulation workflow is developed using Discrete-Fracture and Continuum Models, i.e., embedded-discrete-fracture model (EDFM) and dual porosity (DP) model. We consider the SRV region and USRV region respectively. In the SRV region, the EDFM+DP model is used while for USRV, the single porosity model is used. The DP concept allows the hybrid model to handle the transient transfer between matrix and secondary fracture in SRV region. The model is verified by comparing with EDFM+MINC model. The effect of some parameters on oil production are analyzed. The prediction capacity of the new hybrid model is better when replacing pseudo steady state transfer to transient transfer between matrix and secondary fracture in SRV region.
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Field Development Plan Optimization With Structural Uncertainty
Authors G. De Paola, P. Koryuzlov, R. Rodriguez Torrado, A. Fernandez, E. Reding, M. Bartnik and M. SeignoleSummaryField development plan optimization under uncertainty requires a consistent analysis of well placement across the geological realizations to evaluate the selected cost function. Special care has to be taken in the well trajectory description in the target zone, to allow in the same formulation vertical, deviated and directional well assessment for a more effective decision making. In case of structural uncertainty well trajectories will cross different grid elements in each realization. The workflow proposes a methodology to screen well trajectories based on the expected productivity overall the realizations and the fulfillment of user defined constrains. Well constrains can include, inter-well distance, well length, distance from the closest fault. For a consistent uncertainty propagation and an efficient optimization a nested optimization loop has also been proposed to allow the well screening before the actual reservoir simulation evaluation and allow only the most promising strategies to be evaluated and, therefore, reducing the overall computational burden. The workflow has been tested on a real reservoir case showing the strength of the methodology in assessing the location for an infill and a sidetrack well and improving the understanding of the reservoir dynamic behavior.
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Refined Ensemble-Based Waterflooding Optimization Subject To Field-Wide Constraints
Authors J. Rojas Tueros, B. Horowitz, R. Willmersdorf and D. OliveiraSummaryA refined ensemble-based method for constraints waterflooding optimization is presented. The problem of determining life-cycle rate controls for both producer and injector wells that maximize the Net Present Value, NPV, subject to well and field-wide capacity constraints is solved using an SQP algorithm. The required gradient is approximately computed by an ensemble-based method. Field NPV is decomposed as the sum of the NPVs of each well. Sensitivity matrix of well NPVs with respect to controls of all wells is obtained from ensemble-based covariance matrices of controls and of well NPVs to controls. For efficiency reasons ensemble size should be kept small which results in sampling errors. The effective approximate gradient is the sum of the columns of the refined sensitivity matrix. Using small-sized ensembles introduces spurious correlations that degrades gradient quality. Novel non-distance based localization technique are employed to mitigate deleterious effects of spurious correlations to refine sensitivity of NPV of production wells with respect to injector controls. The localization technique is based on the connectivity of each injector/producer pair using a Producer-based Capacitance Resistance Model (CRMP). Competitiveness factors are developed to refine sensitivity of NPV of production wells with respect to producer controls, obtained using an Interference Test. A new procedure is proposed for consideration of maximum water-cut limit resulting in producer shut-in during the optimization process. Smoothing techniques are also proposed to avoid excessive abrupt jumps in well controls and to improve the overall optimization efficiency. Proposed procedures and refinements are applied to two realistic reservoirs taken from the literature, Brush Canyon Outcrop Field and Brugge Field Case, to demonstrate the resulting level of objective function improvement and variability reduction of the obtained solutions. NPV solution statistics are obtained for twenty independent runs. Using refinements, smoothing and water cutting techniques, we obtained 15% and 28% gains with respect to the median values of unrefined solutions of the two example cases with much smaller variability.
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Software For Industrial Scale Oil Production Optimization
Authors S. Horsholt, H.M. Nick and J.B. JørgensenSummaryOil production optimization of petroleum reservoirs under uncertainty give rise to large-scale optimization problems.
Ensemble-based methods for production optimization are used in combination with gradient-based optimization algorithms.
Use of commercial-grade simulators able to handle real-scale reservoir models and compute the gradient by the adjoint method is essential for implementing such methods in real-life.
However, the simulation time for a single ensemble model renders the problem computationally intractable. Therefore, model reduction is needed.
We introduce a grid coarsening method that maintains the overall dynamics of the flow, by preserving the geological features of the model.
In this paper, we present a software tool for oil production optimization and a semi-automated workflow for grid coarsening and property upscaling.
The software tool integrates state-of-the-art optimization algorithms, ensemble-based optimization strategies and reservoir simulators with adjoint capability.
The software is based on the Eclipse input file-format, which enables use of existing reservoir models for production optimization.
This allows for oil production optimization of both black-oil and compositional flow models and brings model based production optimization a step closer to routinely implementation in reservoir management workflow.
We present the workflow of the optimization software and numerical examples that demonstrates the application of ensemble-based production optimization.
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