Numerical Reservoir Simulation Research Articles

Copula Modeling and Uncertainty Propagation in Field‐Scale Simulation of CO2 Fault Leakage

AbstractSubsurface storage of is an important means to mitigate climate change, and the North Sea hosts considerable potential storage resources. To investigate the fate of over decades in vast reservoirs, numerical simulation based on realistic models is essential. Faults and other complex geological structures introduce modeling challenges as their effects on storage operations are subject to high uncertainty. We present a computational framework for forward propagation of uncertainty, including stochastic upscaling and copula representation of multivariate distributions for a storage site model with faults. The Vette fault zone in the Smeaheia formation in the North Sea is used as a test case. The stochastic upscaling method reduces the number of stochastic dimensions and the cost of evaluating the reservoir model. Copulas provide representation of dependent multidimensional random variables and a good fit to data, allow fast sampling and coupling to the forward propagation method via independent uniform random variables. The non‐stationary correlation within the upscaled flow functions are accurately captured by a data‐driven transformation model. The uncertainty in upscaled flow functions and other uncertain parameters are efficiently propagated to leakage estimates using numerical reservoir simulation of a two‐phase system of CO2 and brine. The expectations of leakage are estimated by an adaptive stratified sampling technique which effectively allocates samples in stochastic space. We demonstrate cost reduction compared to standard Monte Carlo of one or two orders of magnitude for simpler test cases, and factors 2–8 cost reduction for stochastic multi‐phase flow properties and more complex stochastic models.

Numerical simulation for low permeability reservoirs based on POD-TPWL method

ABSTRACT Numerical simulation is a key technology to improve the development efficiency of low-permeability and tight oil reservoirs. In this paper, in order to improve the speed of reservoir numerical simulation, a complex two phase flow model was presented considering the threshold pressure gradient and stress sensitivity, and the application process of POD-TPWL method is derived and summarized. Furthermore, the computational accuracy and efficiency based on the POD-TPWL method was investigated. The simulation time and error of production data of POD-TPWL method and other methods were statistically analyzed and compared. The results reveal that the POD-TPWL method not only ensures accuracy and stability but also significantly improves computational speed. The calculation time of the full order model is 487 s, the calculation time of the POD method is 284 s, and the calculation time of the POD-TPWL method is 122 s. The calculation speed of the POD-TPWL method is almost 4 times faster than the full order model, the POD-TPWL method is more efficient in the numerical simulation of low permeability nonlinear seepage.

Research on Composite 3D Well Pattern for Blocky Heavy Oil in Offshore Areas: Transition from Huff-and-Puff to Displacement-Drainage

In view of the deep burial depth, high formation pressure, and presence of top and bottom water in offshore extra-heavy-oil reservoirs, this paper conducts a study on the production performance and flow field variation law of steam huff-and-puff to steam flooding conversion in thick heavy-oil reservoirs based on physical simulation, and analyzes the development effect of the conversion from steam huff-and-puff to steam flooding. On this basis, by comprehensively considering the advantages of gravity-assisted steam flooding and a three-dimensional HHSD well pattern obtained from physical simulation experiments, this paper proposes a well pattern development mode of steam huff-and-puff to composite displacement and drainage, and analyzes the development effect of this well pattern mode using the reservoir numerical simulation method. The research results show that, compared with the planar well pattern of steam huff-and-puff to steam flooding conversion, the adoption of the three-dimensional well pattern can significantly improve the degree of reservoir production and the expansion dynamics of the steam chamber, and mitigate adverse effects such as the increase in water cut caused by top and bottom water on thermal recovery. The composite development of steam huff-and-puff to composite displacement and drainage can be divided into three stages: thermal communication, gravity drainage-assisted steam flooding, and thermal breakthrough erosion and oil washing. The steam chamber presents a development mode of “single-point development–rapid longitudinal expansion–rapid transverse expansion upon reaching the top–polymerization into a sheet”, and simultaneously possesses the oil displacement mechanisms of both steam displacement and gravity drainage. The proposed composite mode of steam huff-and-puff to composite displacement and drainage has guided the implementation of adjustment wells in the Bohai L Oilfield, and the recovery factor has been increased by about 20% compared with the steam huff-and-puff development of the basic well pattern. This study has reference and guiding significance for the efficient thermal recovery development of this oilfield.

Experimental Study and Molecular Dynamics Simulation of Oil Displacement Using Different Microemulsions in the Fang2 Block of Songfangtun Oilfield.

After many years of mining in the Fang2 block of the Songfangtun oilfield, the conventional water drive development method can no longer meet the requirement of greatly improving the recovery rate, and ternary composite drive (TCD) technology is adopted for this purpose. TCD is one of the most important methods to further improve crude oil recovery, and it has entered the industrialization and promotion stage, but there are still problems of fouling in the injection and extraction system and high production and maintenance costs. In order to reduce formation damage and improve recovery in the Songfangtun oilfield, an alkali-free microemulsion system was developed by replacing the weak base sodium carbonate with sodium chloride, but its emulsification capacity was weak and the recovery enhancement value was lower than that of the weak base TCD. In order to improve the emulsification performance of the alkali-free microemulsion and enhance the effect of oil repulsion, an alkali-free microemulsion oil-repellent system was developed on the basis of the alkali-free ternary system by using the compounding of surfactant, alcohol, and sodium chloride. Through indoor physical modeling experiments, it was concluded that the SDBS alkali-free microemulsion system had the best effect on improving crude oil rheology and viscosity reduction, and the lowest interfacial tension of 9.4 × 10-4 mN/m in the solution system when the mass fraction was 4%, with the maximum recovery rate of 47.03%, and the decrease in water content of 9.3%. Through molecular dynamics simulation and microemulsion oil-repellent coefficient, it is concluded that the alkali-free SDBS microemulsion system can greatly reduce the interaction force between crude oil and rock, with the lowest peak value of radial distribution function of 4.21, and the oil-repellent coefficient of F p of 5.85; CMG reservoir numerical simulation software is adopted to verify the chemical repellent numerical simulation of Fang2 block, which shows that the recovery degree of SDBS alkali-free microemulsion system is 24.8% higher than that of water repellent, with the cumulative increase of 213.6 thousand tons of oil. The developed alkali-free microemulsion system not only realizes the goal of ternary composite alkalinity-free but also achieves the purpose of greatly improving the recovery rate and reducing the cost and increasing efficiency. It has a broad application prospect and can also provide a technical reference for the efficient development of other old oilfields with land-phase sandstone.

A transient source-function-based embedded discrete fracture model for simulation of multiscale-fractured reservoir: Application in coalbed methane extraction

The classic embedded discrete fracture model (EDFM) may cause certain errors when simulating the transient flow process within the multi-scale fractured system. In this study, the transient transmissibility was derived by using the point (matrix-fracture) and line (fracture-fracture) source functions. The transient source-function-based EDFM (tSEDFM) is established via this method. Then, based on the dual criteria that dNNC is less than a certain distance and its projection point is within the corresponding fracture domain, a 3D fracture meshing method for arbitrary fracture geometry and orientation is established. The finite volume method is used to discrete the fluid flow equations for matrix and fracture systems, considering the multi-deformation-induced permeability evolution. Consequently, the numerical simulation framework of FVM-tSEDFM is proposed to investigate the transient mass transfer characteristics. Compared with the current pEDFM, the pressure drop near fractures of the proposed model is higher and the gap narrows as pressure wave further spreads. Compared with AEDFM, the Tmf of tSEDFM is almost the same, but AEDFM's Tff is substantially higher in the initial stage and the attenuation rate is slower, resulting in an error of nearly 15% at the hydraulic fracture location. As fracture density increases, more transient flow makes AEDFM- and EDFM-calculated BHP values deviate from tSEDFM. History matching using the tSEDFM with only 10000 meshes shows better results where the mismatching rate is larger than 90%. Simulation of CBM extraction indicate that sharp pressure decline occurs near the fractures, resulting in gas desorption enhancement and rapid productivity increment. The tSEDFM demonstrates good practicality in calculating the production and long-term permeability evolution. Results also show that the tSEDFM can correct the underestimation of mass exchange in the early stage and overestimation since the pseudo-steady stage, and can be better applied to the numerical simulation of multi-scale fractured reservoirs. As the dominant factor for gas extraction, sensitivity analyses of fracture properties are also documented.

Exact Solutions and Upscaling for 1D Two‐Phase Flow in Heterogeneous Porous Media

AbstractUpscaling of 1D two‐phase flows in heterogeneous porous media is important in interpretation of laboratory coreflood data, streamline quasi 3D modeling, and numerical reservoir simulation. In 1D heterogeneous media with properties varying along the flow direction, phase permeabilities are coordinate‐dependent. This yields the Buckley‐Leverett equation with coordinate‐dependent fractional flow f = f(s, x), which reflects the heterogeneity. So, an x‐dependency is considered to reflect microscale heterogeneity and averaging over x—upscaling. This work aims to average or upscale the heterogeneous system to obtain the homogenized media with such fractional flow function F(S) that provides the same water‐cut history at the reservoir outlet, x = 1. Thus, F(S) is an equivalent property of the medium. So far, the exact upscaling for 1D micro heterogeneous systems has not been derived. With the x‐dependency of fractional flow, the Riemann invariant is flux f, which yields exact integration of 1D flow problems. The novel exact solutions are derived for flows with continuous saturation profile, transition of shock into continuous wave, transition of continuous wave into shock, and transport in heterogeneous piecewise‐uniform rocks. The exact procedure of upscaling from f = f(s, x) to F(S) is as follows: the inverse function to the upscaled F(S) is equal to the averaged saturation over x of the inverse microscale function s = f −1(f, x). It was found that the Welge's method as applied to heterogeneous cores provides the upscaled F(S). For characteristic finite‐difference scheme, the fluxes for microscale and upscaled‐numerical‐cell systems, coincide in all grid nodes.

Phase Behavior and Rational Development Mode of a Fractured Gas Condensate Reservoir with High Pressure and Temperature: A Case Study of the Bozi 3 Block

The Bozi 3 reservoir is an ultra-deep condensate reservoir (−7800 m) with a high temperature (138.24 °C) and high pressure (104.78 MPa), leading to complex phase behaviors. Few PVT studies could be referred in the literature to meet such high temperature and pressure conditions. Furthermore, it is questionable regarding the applicability of existing condensate production techniques to such a high temperature and pressure reservoir. This study first characterized the phase behavior via PVT experiments and EOS tuning. The operating conditions were then optimized through reservoir numerical simulation. Results showed that: (1) the critical condensate temperature and pressure of Bozi 3 condensate gas were 326.24 °C and 43.83 MPa, respectively; (2) four gases (methane, recycled dry gas, carbon dioxide, and nitrogen) were analyzed, and methane was identified as the optimal injection gas; (3) gas injection started when the production began to fall and achieved higher recovery than gas injection started when the pressure fell below the dew-point pressure; (4) simultaneous injection of methane at both the upper and lower parts of the reservoir can effectively produce condensate oil over the entire block. This scheme achieved 8690.43 m3 more oil production and 2.75% higher recovery factor in comparison with depletion production.

A novel model for low-permeability reservoir numerical simulation considering dynamic capillary force

ABSTRACT Capillary force is not only affected by water saturation but also affected by fluid flow velocity, which is necessary to modify the prior numerical simulation methods. First, a dynamic capillary force testing device was developed, then, an experimental procedure was adopted to measure the dynamic capillary force curve. Three dynamic capillary force curves were obtained under different displacement velocity conditions. Finally, the dynamic capillary force was introduced into the flow equation of low-permeability reservoir numerical simulation. The oil-phase equation and water-phase equation were discretized in three-dimensional space, and the IMPES method was used to solve the water saturation and pressure difference. The calculation results between the traditional numerical simulation method and the novel method under heterogeneous and inhomogeneous conditions were analyzed. The results reveal that the difference in water cut is mainly reflected in the rapid rise of water cut. In the early stage of rapid increase, the water cut calculated by the new method is slightly higher than traditional method. When the water cut is more than 65%, the water cut calculated by the new method is slightly lower than the traditional method.

Comparative Study on Artificial Fracture Modeling Schemes in Tight Reservoirs—For Enhancing the Production Efficiency of Tight Oil and Gas

In order to improve the reliability of the deployment of production schemes after artificial fracturing in tight reservoirs, it is urgent to carry out research on the description of fractures after artificial fracturing. In this study, taking the Chang 61 oil formation group in the Wangyao South area of Ordos Basin as an example, three different fracture modeling schemes are used to establish the geological model of fractured reservoirs, and the fitting ratios of the respective reservoir models are calculated by using the method of reservoir numerical simulation of the initial fitting, and the optimal fractured reservoir modeling scheme is screened in the end. The research area adopts three types of fracture prediction results based on FMI fracture interpretation data, seismic fracture prediction data, and rock mechanics artificial fracturing simulation data. On this basis, geological models of fractured reservoirs are established, respectively. The initial fitting of reservoir values of each geological model are compared, and the highest initial fitting rate of reservoir values is 88.44%, which is based on rock mechanics artificial fracturing simulation data. However, the initial fitting rate of the reservoir model was the lowest at 75.76%, which was established based on the fracture random modeling results of FMl fracture interpretation data. Under the constraints of seismic geostress prediction results and microseismic monitoring data, the simulation results of rock mechanics artificial fracturing fracture are used as the basis, on which the geological model of artificially fractured reservoirs is thus established, and this scheme can more realistically characterize the characteristics of fractured reservoirs after artificial fracturing in the study area.

Numerical simulation of shale gas reservoir based on ILU-GMRES method

ABSTRACT The numerical simulation of shale gas reservoirs requires transforming mathematical models into large linear equation systems, and solving large linear equation systems requires a lot of time. A novel ILU-GMRES method for solving large linear equations is presented, which treats the sub matrix discretized at nodes as the basic elements of the coefficient matrix. By combining the incomplete LU decomposition method (ILU) with the generalized minimum residue method (GMRES), the discretized large linear equations are iteratively solved. A comparison was made between the new method and other methods for calculating the actual shale gas reservoir model. The results reveal that the new method has a faster calculation speed in solving linear equation systems. The calculation time of the novel ILU-GMRES method is 1029s, the calculation time of the generalized minimum residual method (GMRES) method is 2709s, the calculation time of the Gauss–Seidel method (GS) is 3786s, and the calculation time of the successive over relaxation method (SOR) method is 3386s, the calculation time of the preprocessing conjugate gradient method (PCG) is 3115s. The calculation speed of the novel method is almost 2.6 times faster than the GMRES method, the novel method is more effective in the numerical simulation of shale gas.

Modeling unobserved geothermal structures using a physics-informed neural network with transfer learning of prior knowledge

Deep learning has gained attention as a potentially powerful technique for modeling natural-state geothermal systems; however, its physical validity and prediction inaccuracy at extrapolation ranges are limiting. This study proposes the use of transfer learning in physics-informed neural networks to leverage prior expert knowledge at the target site and satisfy conservation laws for predicting natural-state quantities such as temperature, pressure, and permeability. A neural network pre-trained with multiple numerical datasets of natural-state geothermal systems was generated using numerical reservoir simulations based on uncertainties of the permeabilities, sizes, and locations of geological units. Observed well logs were then used for tuning by transfer learning of the network. Two synthetic datasets were examined using the proposed framework. Our results demonstrate that the use of transfer learning significantly improves the prediction accuracy in extrapolation regions with no observed wells.

A novel meshless method for numerical simulation of fractured-vuggy reservoirs

This paper proposes a novel meshless numerical simulation method for fractured-vuggy reservoirs. Initially, model discretization involves extracting fracture and vug feature nodes along the contours of the reservoir bodies and in alignment with fracture orientations, tailored to the characteristics of the fractured-vuggy oil deposit. Subsequently, a connection element model is established within the influence domain. Based on the seepage equations of the connection system, a computational method for the parameters of the connection elements (connection transmissibility and connection volume) is defined. In addition, a sequential method is employed to solve for the pressure and saturation, achieving rapid prediction of the reservoir's production dynamics. On this basis, an automatic history matching algorithm is utilized for real-time fitting of oil–water dynamic indicators, inverting the characteristic parameters of the connection element model, and quantitatively characterizing the injection–production connection elements. The research findings indicate that the method is capable of rapidly fitting and predicting the dynamics of oil reservoir production. Furthermore, conceptual model examples have substantiated that it achieves comparable computational efficiency and superior computational accuracy when compared to the traditional finite difference (volume) method under the same nodal conditions. Additionally, the node arrangement for fractures and vugs is comparatively flexible, and it can ensure the integrity of the flow paths with a limited number of nodes to enhance predictive accuracy. Therefore, this method can effectively meet the rapid prediction requirements for fractured-vuggy reservoirs and also provides a novel meshless computational approach for the numerical simulation of such reservoirs.

Reservoir numerical simulation method considering time-varying relative permeability during polymer flooding process

Abstract In response to the abnormal decline in liquid production capacity during the middle and later stages of chemical flooding in Chinese offshore oil fields, in-depth analysis was conducted using reservoir engineering, dynamic analysis, and reservoir simulation methods. Because of the viscoelasticity of polymer solution, the relative permeability curve of oil/water during polymer flooding is different from that during water flooding, including the minimum mobile water saturation and residual oil saturation. In this study, an interpolation coefficient ‘f’ related to polymer solution concentration was firstly proposed for simplicity. Then, reservoir numerical simulation with the self-developed simulator ‘SIMFAST’ were conducted to investigate the influence of the interpolation coefficient ‘f’ on the injector and producer performance and the applications in actual field production history matching. The results indicated that compared with the commercial simulators, the self-developed simulator with the interpolation factor could more reliably describe the characteristic of the injected polymer solution in controlling water cut rise, and more efficiently simplify the combination of parameters on relative permeability curves during polymer flooding in offshore oilfields. Finally, above reservoir simulation method considering the change of the relative permeability curves during chemical flooding, was successfully conducted in the production history matching in J oilfield in Bohai Bay China, in terms of oil rate & water cut parameters. The research results give an efficient method to investigate the fluid seepage behaviour variation and its influence on oil rate and water cut during polymer flooding in China offshore reservoirs, which offers very useful technical support for the accurate design of chemical flooding schemes.

Prediction Method for Hydraulic Fracturing Effect of Producing Well Based on Machine Learning Methods

Abstract Accurate prediction of producing fracturing oil enhancement is a prerequisite for decision-making on the implementation of production enhancement measures in producing wells. The traditional reservoir numerical simulation method requires accurate reservoir geological parameters and fracturing construction parameters, which makes the calculation process complicated and the on-site application effect unsatisfactory. Therefore, a method for predicting fracturing effect of producing well based on machine learning is proposed. A combination of correlation coefficient analysis and gray correlation analysis was used to determine the main controlling factors affecting fracturing effectiveness; Considering the nonlinear mapping relationship between the fracturing effect and the main control factors, a prediction model was established using a support vector machine. The model is applied with an actual block of an oil field as an example, and the evaluation of potential wells is completed with the analysis of economic benefits of fracturing measures. The results show that the model prediction results meet the accuracy requirements for engineering application, and the screened fracturing potential wells have achieved better oil enhancement results after the implementation of measures. The prediction model of oil enhancement effect established by this method is based on the actual production data of producing wells, with reliable prediction results and simple model solution, which has the value of popularization and application in the same type of blocks.

Research and Practice on EOR Development Strategy of Water Drive Followed by Gas Drive in Fractured Carbonate Reservoir in Bohai Sea

Abstract Focusing on the issues of high comprehensive water cut and low recovery degree following water flooding in the CFD 2-2 carbonate buried hill reservoir in the Bohai Sea, the productivity variation law, water cut rising characteristics and development effect of horizontal wells were analyzed based on different types of reservoir classification systems. The reservoir numerical simulation model of dual media coupling of matrix and fracture is established, and the analysis is done on the matrix and fracture production state, the distribution pattern of the residual oil, and the primary governing parameters.. The physical simulation experiment of water flooding to gas flooding is carried out. In conjunction with the distribution characteristics of fractures and matrix residual oil in low, middle and upper tiers of the framework, the development strategy of nitrogen injection pressure water cone in low water-flooded area, nitrogen flooding in middle inter-well residual oil enrichment area and nitrogen huff and puff in high well point residual oil enrichment area is put forward. The recovery rate is increased by 5-8 %, which successfully enhances the high water cut stage development effect, and provides reference for similar oilfield development.

A geothermal doublet in a single well: application of the recirculation well concept to reuse wells to be abandoned

The depletion of oil and gas reservoirs leaves many deep and expensive wells with no option but to be abandoned. However, these wells could have a second chance to extend their life as a source of geothermal energy, especially if they are located next to urban or industrial areas in need of heating. This article shows a technical analysis of the well recirculation or geothermal doublet in a single well approach as a strategy to reuse wells that cross aquifers. Different aspects of this strategy are highlighted, including the technical conditions required for the application, the well completion, and the geothermal performance. The latest is assessed via numerical reservoir simulations using geological data from an existing well. The results show that vertical petrophysical heterogeneities play an important role in the performance and feasibility of this approach.

The Time-Varying Characteristics of Relative Permeability in Oil Reservoirs with Gas Injection

Relative permeability is a critical parameter in reservoir numerical simulation and production prediction, intimately associated with reservoir architecture and fluid property. During gas injection development, substantial alterations in reservoir properties and fluid phase behavior induce dynamic changes in relative permeability. Clearly characterizing the time-varying features of relative permeability is very useful for an understanding of how gas injection influences fluid mobility within the reservoir and enhances recovery rates. In this paper, core displacement experiments are firstly conducted to obtain the characteristics of the relative permeability of oil and gas under various development stages and displacement conditions, further delineating the comprehensive shifts in reservoir properties at different gas injection stages. Subsequently, a novel reservoir numerical simulation method is proposed that considers the spatial and temporal segmentation of relative permeability curves in the reservoir simulation. Finally, a practical application is presented to clarify the effects of injection and production parameters on the development performance of gas flooding oil reservoirs. The results show the following: (i) Significant time-varying characteristics of relative permeability occur throughout gas injection development, in the early stages of gas injection, where most of the reservoir is at the gas injection front, and a rightward shift in relative oil and gas permeability indicates that gas injection promotes oil mobility. Conversely, in the later stages of gas injection, as the reservoir reaches the trailing edge of gas injection, the change trend in relative oil and gas permeability reverses, shifting leftward, thereby exacerbating the gas breakout phenomena. (ii) Increasing the rate of gas injection causes relative oil and gas permeability to move leftward, effectively enhancing the gas volume sweep coefficient and microscopic oil displacement efficiency at lower injection speeds while reducing development performance at higher injection speeds. (iii) An increase in gas injection pressure causes relative oil and gas permeability to shift rightward, and although it reduces residual oil saturation and enhances microscopic oil displacement efficiency, it also intensifies gas breakout phenomena and lowers the gas volume sweep coefficient. This paper provides theoretical guidance and technical support for the design of gas injection strategies, optimization of injection and production parameters, and production forecasting.

Inverse Problem of Permeability Field under Multi-Well Conditions Using TgCNN-Based Surrogate Model

Under the condition of multiple wells, the inverse problem of two-phase flow typically requires hundreds of forward runs of the simulator to achieve meaningful coverage, leading to a substantial computational workload in reservoir numerical simulations. To tackle this challenge, we propose an innovative approach leveraging a surrogate model named TgCNN (Theory-guided Convolutional Neural Network). This method integrates deep learning with computational fluid dynamics simulations to predict the behavior of two-phase flow. The model is not solely data-driven but also incorporates scientific theory. It comprises a coupled permeability module, a pressure module, and a water saturation module. The accuracy of the surrogate model was comprehensively tested from multiple perspectives in this study. Subsequently, efforts were made to address the permeability-field inverse problem under multi-well conditions by combining the surrogate model with the Ensemble Random Maximum Likelihood (EnRML) algorithm. The research findings indicate that modifying the network structure allows for improved integration of the outputs, resulting in prediction accuracy and computational efficiency. The TgCNN surrogate model demonstrated outstanding predictive performance and computational efficiency in two-phase flow. By combining the surrogate model with the EnRML algorithm, the inversion results closely aligned with those from the commercial simulation software, significantly improving the computational efficiency.

Combined mechanistic and machine learning method for construction of oil reservoir permeability map consistent with well test measurements

We introduce a novel method for estimating the spatial distribution of absolute permeability in oil reservoirs, consistent with well logging and well test measurements. The primary objective is to create a permeability map, incorporating the well test interpretation results and achieving hydrodynamic similarity to the actual permeability distribution around each well. This enhancement aims to improve the accuracy of reservoir modeling outcomes in reproducing real data. We utilize Nadaraya-Watson kernel regression to parameterize the two-dimensional spatial distribution of rock permeability. The kernel regression parameters are optimized by minimizing the discrepancies between actual and predicted values of permeability at well locations, the integral permeability of the reservoir domain around each well, and skin factors. This inverse optimization problem is addressed by repeatedly solving forward problems, where an artificial neural network (ANN) predicts the integral permeability of the formation surrounding a well and skin factor. The ANN is trained on a physics-based dataset generated through a synthetic well test procedure, which includes the numerical modeling of the bottomhole pressure decline curve in a reservoir simulator and its interpretation using a semi-analytical reservoir model. The proposed method is tested on the “Egg Model”, a synthetic reservoir with significant heterogeneity due to highly permeable channels. The permeability map created by our approach demonstrates hydrodynamic similarity to the original map. Numerical reservoir simulations, corresponding to the constructed and original permeability maps, yield comparable pore pressure and water saturation distributions at the end of the simulation period. Additionally, we observe a notable match in flow rates and total volumes of produced oil, water, and injected water between simulations. The developed approach outperforms kriging in terms of numerical reservoir modeling outcomes. This research advances existing geostatistical interpolation techniques by fusing well logging and well test data to build the reservoir permeability map through an optimization framework coupled with machine learning. Unlike traditional variogram-based geostatistical simulation algorithms, our method provides a permeability distribution that is hydrodynamically similar to the actual one, enhancing initial guess in the history matching process. The novel incorporation of well test interpretation results into the permeability map represents a significant improvement over existing methods, offering an innovative approach that can benefit the petroleum industry. We also provide recommendations for further development of the proposed algorithm to account for geological realism.

Weighted mapping of productivity potential based on simulated annealing algorithm for well placement optimization

In the realm of reservoir development, the optimization of well placement constitutes a cornerstone challenge with significant implications that directly determine the recovery rate and economic benefits of oil and gas production. This research proposes a novel approach to optimizing well placement in reservoirs by integrating reservoir numerical simulations with intelligent optimization algorithms. The quintessence of this inquiry revolves around the strategic placing of wells amidst the complex geological fabric of reservoirs, where the objective function landscape often manifests with non-smooth, multimodal characteristics. To address those issues, the Weighted Mapping of Productivity Potential (WMPP) technique, fortified by the Simulated Annealing algorithm to judiciously ascertain specific weighting coefficients for the computation of WMPP across reservoirs is introduced in this study. Furthermore, an emblematic carbonate reservoir model serves to corroborate the adaptability and viability of WMPP for well placement optimization, underscoring its efficacy as a swift, economically viable instrument for the delineation of prospective reservoir zones and the guidance of drilling initiatives. The optimization results show that the well placement scheme guided by WMPP, which required 7 fewer wells than the oil initially in place (OOIP)-based scheme, improved 21.74% oil production over the twenty years production period. This comprehensive workflow proffers invaluable insights and benchmarks for the formulation of well placement strategies, with the proposed methodology, in its apparent simplicity, showcasing remarkable efficiency.