Numerical Reservoir Simulation Research Articles

Support Vector Regression for Petroleum Reservoir Production Forecast Considering Geostatistical Realizations

Summary Decision analysis related to petroleum field development and management phases with complex models can be time-consuming, especially in highly heterogeneous fields. Probabilistic approaches require a large number of simulation runs to cover all possible solutions, and this can be slow. In this study, we present a methodology to include high-dimensional spatial attributes (geostatistical realizations) in proxy modeling, based on support vector regression (SVR), for building risk curves with decreased run time. The proposed workflow accomplished the following: definition of uncertain inputs, such as porosity and horizontal and vertical permeabilities; selection of outputs from the simulator (cumulative oil, water and gas productions) to be mimicked by the proxies; sample inputs to generate scenarios for training and proxy building; and consistency check to evaluate if the proxy model is reliable to mimic simulator output. We then used proxy models to generate risk curves at the final forecast period (7,305 days) as an application. Using the SVR with high-dimension inputs, we show that the proxy was able to provide reliable results with 300 scenarios, which represent 35% less computational effort compared with using only a reservoir numerical simulator. As a result, we can use this proxy to perform a risk analysis with a high level of accuracy [mean absolute percentage error (MAPE) lower than 0.5%] to predict the production curves. In conclusion, we can use the SVR proxy model technique as an alternative to a reservoir simulator when spatial uncertainty attributes (geostatistical realization) are present.

A Conjugate Gradient Method for Inverse Problems of Non-linear Coupled Diffusion Equations

In many fields there are many problems called inverse problems, which infer the reasons from the observations. The inverse problem of nonlinear diffusion equations plays a crucial role in the numerical simulation of reservoirs. This article constructs a conjugate gradient method to solve the inverse problem of a nonlinear diffusion equation within oil reservoir simulation. The numerical simulation is performed, and the results show the effectiveness of the method.

An extended trajectory-mechanics approach for calculating two-phase flow paths

A technique originating in quantum dynamics is used to derive a trajectory-based, semi-analytical solution for two-phase flow. The partial differential equation governing the evolution of the aqueous phase is equivalent to a family of ordinary differential equations defined along a path through the porous medium. The trajectories may be found by solving the differential equations directly or by post-processing the output of a numerical solution to the full set of governing equations. The trajectories, which differ from conventional streamlines, are found to bend downward in response to gravitational forces. The curvature is more pronounced as the dip of the porous layer containing the flow increases. Subtle changes in the relative permeability curve can lead to significant variations in the trajectories. The ordinary differential equation for the trajectory provides an expression for the travel time along the path. The expression produces a semi-analytical approximation to the model parameter sensitivities, the partial derivatives of the travel times with respect to changes in the permeability model. The semi-analytical trajectory-based sensitivities generally agree with those computed using a numerical reservoir simulator and a perturbation approach. The sensitivities are useful in tomographic imaging algorithms designed to estimate the spatial variation in permeability within a porous medium using multiphase observations.

Numerical simulation of three dimensional flow in Yazidang Reservoir based on image processing

In order to study the water flow movement of the Yazidang Reservoir, this paper generates the initial terrain for the researched water area with the image stitching technology and image edge detection technology, establishes a 3D k - ɛ mathematical model, solves the equations discretely by FVM and SIMPLEC algorithms, studies the numerical simulation of the water flow movement of the reservoir under four working conditions, and analyzes the flow field on the surface and at the bottom of the reservoir. The results show the improved terrain pre-processing accuracy and efficiency of the researched water area and the rationality of the water flow field and rate simulation results, which means that the established 3D turbulence mathematical model can be applied to the numerical simulation of the reservoirs similar to the Yazidang Reservoir. The numerical simulation of 3D turbulence in Yazidang Reservoir provides a theoretical basis and practical application value for the numerical simulation of similar reservoirs.

A semi-analytical model for simulation of multiple vertical wells with well interference

Hydraulic fracturing is widely applied to develop tight oil reservoirs, and it is significant to diagnose fracture hit to determine optimal well spacing. Pressure test is an effective method to determine fracture hit in a multi-well system. In this study, we developed a semi-analytical model to quickly identify fracture hit in multiple vertical well system in tight oil reservoir. This semi-analytical model involves several steps, i.e., prior production step of parent wells, pressure build-up step, and interference test step. The model was verified by a numerical reservoir simulator for single well and multiple wells. Then, based on the model, the well interference by fracture hit in a three-well system (two parent wells and one child well) is discussed. Results show that the developed semi-analytical model could efficiently simulate the entire production process of a multi-well system, quickly diagnose fracture hit by using pressure interference test data and determine the optimal shut-in time of parent well. The practicability of model lies in that the reservoir pressure depletion by prior production of parent wells is considered. Besides, it is found shutting down the parent well is very necessary to diagnose fracture hit when the child well is infilled. When the shut-in parent well is connected to producing child well, the pressure build-up process of parent well is terminated with the bottom hole pressure reducing continuously. What is more, the shut-in time of parent wells should be sufficient to better detect the fracture hit, especially under the condition that parent wells have produced for a long time or the connectivity among wells is weak. This work can provide critical insights into understanding the mechanism of well interference by fracture hit in a multi-well system.

End-Point Model for Optimization of Multilateral Well Placement in Hydrocarbon Field Developments

Drilling cost is one of the most critical aspects in the reservoir management plan. Costs may exceed a million dollars; thus, optimal designing of the well trajectory in the reservoir and completion are essential. The implementation of a multilateral well (MLW) in reservoir management has great potential to optimize oil production. The object of this study is to develop an integrated workflow of end-point multilateral well placement optimization integrated with the reservoir simulator supported by artificial intelligence (AI) methods. The paper covers various types of MLW construction, including: horizontal, bi-, tri-, and quad-lateral wells. For quad-lateral wells, the capital expenditure is highest; nevertheless, acceleration of oil production affects the project’s NPV (net present value), indicating the type of well that is most promising to implement in the reservoir. Tri- and quad-lateral wells can operate for 12.1 and 9.8 years with a constant production rate. The decreasing hydrocarbon production rate is affected by reservoir pressure and the reservoir water production rate. Other well design patterns can accelerate water production. The well’s optimal trajectory was evaluated by the genetic algorithm (GA) and particle swarm optimization (PSO). The major difference between the GA and PSO optimization runs is visible with respect to water production and is related to the modification of one well branch trajectory in a reservoir. The proposed methodology has the advantage of easy implementation in a closed-loop optimization system coupled with numerical reservoir simulation. The paper covers the solution background, an implementation example, and the model limitations.

Air assisted in situ upgrading via underground heating for ultra heavy oil: Experimental and numerical simulation study

In situ upgrading (ISU) via underground heating and thermal cracking is regarded as an effective technique for exploiting ultra heavy oils, in which the heavy oil components can be cracked into light oils and gases for production. However, the slow heating rate via conduction from wellbore to oil formation is the main issue concerned in the conventional ISU process. Herein, an air injection assisted ISU technique (AAISU) is proposed to improve heat transfer by gas convection and along with the thermal effect of oil oxidation due to the oxygen in the injected air. Air injection can also provide extra energy for oil production and reservoir pressure maintenance. To illustrate the advantage of the proposed AAISU technique, thermal cracking experiments of ultra heavy oil samples in the presence of air under high pressure were conducted to investigate the reaction mechanisms and to establish the kinetics models of the oxidation and cracking reactions. Moreover, reservoir numerical simulation studies are performed to evaluate the effects of air injection during the ISU process. The experiment results indicate that the ultra heavy oil can be effectively cracked into gases, light oils and coke-like substances in the presence of air at temperature over 350 °C. The activation energy of the thermal cracking derived is around 248 kJ/mol. The numerical simulation results show that the heat transfer rate can be effectively enhanced by air injection because of the heat convection of the air flow and the thermal effect of the low temperature oxidation reactions of oil components. The total oil recovery factor can be increased via air injection with improved energy conversion efficiency from 6.51 GJ/GJ to 8.42 GJ/GJ.

Numerical simulation of shale gas reservoirs considering discrete fracture network using a coupled multiple transport mechanisms and geomechanics model

Shale has typical characteristics of multi-scale space for gas storage and migration. It is suitable for description by a triple medium model composed of double continuous medium and discrete fracture model, and need to consider multiple migration mechanisms. Besides, during gas production, effective stress and desorption will cause the deformation of shale, leading to the dynamic changes in porosity and permeability. In this paper, a fully coupled model was established to evaluate the shale gas production dynamics, including the governing equation of shale deformation and the governing equation of gas migration in the matrix, micro-fractures, and hydraulic fractures, respectively. All processes are coupled by the dynamic models of porosity and permeability for matrix and micro-fractures, and by the gas exchange between different systems. The fully coupled model was solved by the finite element method through the PDE solver software named COMSOL Multiphysics. The rationality of this fully coupled model is verified by the production data of Barnett shale. The validated model was applied to study the effects of adsorption and geomechanics parameters on dynamic changes of porosity and permeability, and gas production. Moreover, the impact of primary fracture geometry and secondary fracture distribution parameters on production were also analyzed. Simulation results show that the adsorption parameters have essential effects on both gas flow and production; that the geomechanics parameters have important influences on the evolution of porosity and permeability; that optimizing the distribution and development of hydraulic fracture and secondary fracture is beneficial to the efficient development of shale gas.

Experimental studies of shear-induced changes in two-phase relative permeability

Numerical reservoir simulation is often used as a tool to forecast the production performance of oil and gas fields. Multi-phase flow functions including relative permeability and capillary pressure relationships are important components for modeling fluid distribution and movement in a porous medium, and they are strongly influenced by the pore structure. Often, relative permeability curves are habitually modified, without consideration of geomechanics effects, during the history match process. However, the depletion or injection of oil and gas reservoirs generally alters the effective stress of the system as a result of either decreasing or increasing of pore pressure. This causes changes in grain arrangement or pore structure. In this paper, a series of isotropically consolidated drained triaxial compression tests were conducted to investigate the behavior of very dense, reconstituted specimens at low effective stress conditions. After restoring the specimens to the desired reservoir conditions, the specimens were sheared under a drained compression-loading path. At various levels of axial strain, steady-state process, absolute and relative permeability tests were performed. Our results showed that in two-phase flow, the oil relative permeability was more sensitive to stress in comparison to the water relative permeability. This change of oil relative permeability was up to about 30%. Also, it was noticed from preliminary capillary pressure measurements that both cycles of drainage were significantly affected by the shear-induced contractive and dilative volume changes. This study supports the notion that relative permeability curves, instead of being kept constant, should be updated depending on the in situ stress-strain behavior.

Technology Focus: Simulation (July 2020)

As the world struggles through the COVID-19 crisis and our industry suffers from linked oversupply and demand reduction, we are all forced to refocus on what makes a difference to the bottom line.In the numerical reservoir simulation space, that is generally, "How do we answer a decision-related question in the least amount of time with an acceptable degree of confidence?" Simulation has always been a double-edged sword - a method that, when well-used in fit-for-purpose ways to answer specific questions, can deliver real value. Conversely, when it is used as a substitute for understanding, perhaps to justify a development decision or simply to convince ourselves that we understand a system far better than we really do, many staff years of effort can be quickly lost while not delivering very much. Fit-for-purpose approaches likely will be of ever-increasing focus going forward. If it is not adding value, it should not be done. But "fit for purpose" encompasses a wide range of possibilities - leveraging new approaches as well as learning from old approaches and improving current approaches. It is these three prongs that have guided my paper selections for this edition. While the rapid rise to prominence of methods that eschew conventional numerical modeling approaches in favor of data-driven proxy approaches provides us with some new tools to answer these questions, these tools are unlikely to be reliably predictive unless they incorporate governing physics. It is for this reason that one of the following papers spells out just such a solution, marrying fundamental material-balance governing equations with analytics-driven clustering techniques to deliver what appears to be a fit-for-purpose approach to a complex problem. Keeping in mind the quote attributed to George Santayana - "Those who cannot learn from history are doomed to repeat it" - the second paper is an interesting look back at different attempts to simulated unconventional plays, while the third paper is an interesting extension of a current approach to well deconvolution. I hope you enjoy reading this selection of papers and look forward to what the future may hold in the numerical simulation space.

A New Method of Predicting the Distribution of Remaining Oil by the Composite Index of Heterogeneity

As the Xingbei Development Zone gradually goes into the extra high water cut stage, the difficulty of residual oil tapping is becoming harder and harder. Heterogeneity not only controls the injection agent’s sweep coefficient, but also controls the injection displacement efficiency, which is the key factor affecting the formation and distribution of residual oil.Characterization of reservoir macroscopic heterogeneity by parameters such as sedimentary microfacies, oil layer structure, permeability, porosity and net thickness ratio. The heterogeneous comprehensive index obtained by the wave superposition method can not only quantitatively evaluate reservoir heterogeneity, but also explain the distribution characteristics of the residual oil.Using this method to fit the eastern part of a district of Xingbei Oilfield, The obtained heterogeneous composite index (IRH) distribution map is compared with the reservoir numerical simulation residual oil saturation map, and the correlation between the two is good. Statistically fit the production of new wells in the simulated area, wells with heterogeneous composite index between 0.55 and 0.75 have higher cumulative oil production, average daily oil production, and the water content is 2-5 percent lower than the average. According to the comprehensive analysis, the remaining oil enrichment area is in the IRH [0.55, 0.75] region. Guided by this method, we repart Well B1; let free its S II 8 accompanying water blocking layer, so as to strengthen liquid supply to Well B2 and Well B3, which are rich in residual oil through this method. The production plan proves to be effective, Well B2’s daily oil production increases by 1.5t, and Well B3’s daily oil production increases by 1.2t. Till now, the accumulated increasing oil production has up to 1324t, which equals to economic benefits of 3840,000 RMB.Through quantitative characterization of reservoir heterogeneity, we find that the remaining oil enrichment zone is mostly located in the IRH [0.55, 0.75] region, which has important guiding significance for the future development.

Matrix-fracture transfer shape factor for modeling multimechanisitc multicomponent shale gas flow

Numerical simulation of multimechanisitc multicomponent shale gas flow is computationally intensive and a challenging task. Upscaling of pore scale phenomena to Darcy scale simulations is highly desirable to cut down the computational time. Mass transfer between matrix and fracture in dual-porosity simulators has been traditionally upscaled through a pseudo steady state shape factor, which can be obtained analytically thanks to the linear nature of the pressure diffusion in conventional reservoirs. The use of such a shape factor is well established in modeling of fluid flow and transport in conventional reservoirs. However, the shape factor for multimechanisitc multicomponent shale gas flow is not fully realized and its determination is not straightforward due to the non-linear nature of the governing equations. In this work, we present detailed numerical simulation of multimechanisitc multicomponent shale gas flow to obtain shape factor required for Darcy scale numerical simulation of unconventional reservoirs. It is shown that shape factor can be presented as a function of dimensionless pressure (pseudo pressure), which makes application of transient shape factor independent of time. The dependence of the derived shape factor on pressure drawdown, reservoir temperature, Darcy permeability and fluid composition are also investigated. The theoretical analysis improves our knowledge of shale gas flow dynamics and the results find applications in reservoir simulation of gas production from unconventional reservoirs.

Practical workflow to improve numerical performance in time-consuming reservoir simulation models using submodels and shorter period of time

Numerical reservoir simulation is a valuable tool to support the decision-making process in oil field projects. For this purpose, current reservoir engineering studies request numerous simulations runs for complex workflows, such as numerical reservoir characterization, data assimilation process, strategy optimisation, well placement studies, production management and supplementary project support. Thus, providing efficient and effective simulation numerical models is a critical task in reservoir simulation studies before starting the daily run demands.In this work, we propose, test and evaluate a practical workflow to improve the numerical performance of time-consuming reservoir simulation models. We provide a procedure to select representative numerical submodels and representative snapshots interval from simulation time (RSIST) to reduce the total time spent in numerical optimisation. The first approach allows the optimisation of the numerical parameters without the drawback of simulating long execution runtime. The second enables to select a range of simulation time where typical convergence problems of timestep cuts occur. The numerical parameters are then optimised using submodels and RSIST, where we highlight a workflow to reduce runtime of the optimisation of slow reservoir models. Following, the resultant set of parameters is applied to the entire (original) reservoir numerical model, improving its performance and allowing more effective execution of several simulation-runs in reservoir engineering studies.To conclude, we provide a workflow to be applied to any reservoir simulation model, especially those with complex structural grid and high-time consuming to run. Our results demonstrated remarkable improvements in the numerical performance of simulation models, with a high potential of saving days of work during probabilistic evaluations. Furthermore, we recommend this workflow as a first step before starting studies using reservoir simulation to avoid unphysical and time-demanding simulation runs that may affect future decisions.

Potential for Evaluation of Interwell Connectivity under the Effect of Intraformational Bed in Reservoirs Utilizing Machine Learning Methods

Machine learning method has gradually become an important and effective method to analyze reservoir parameters in reservoir numerical simulation. This paper provides a machine learning method to evaluate the connectivity between injection and production wells controlled by interlayer in reservoir. In this paper, Back Propagation (BP) and Convolutional Neural Networks (CNNs) are used to train the dynamic data with the influence of interlayer control connectivity in the reservoir layer as the training model. The dataset is trained with dynamic production data under different permeability, interlayer dip angle, and injection pressure. The connectivity is calculated by using the deep learning model, and the connectivity factor K is defined. The results show that compared with BP, CNN has better performance in connectivity, average absolute relative deviation (AARD) below 10.01% higher. Moreover, CNN prediction results are close to the traditional methods. This paper provides new insights and methods to evaluate the interwell connectivity in conventional or unconventional reservoirs.

Study on the Development Effect Standard of Classified Well Groups for Polymer Flooding in Class II Reservoirs

Because of the development characteristics of the second type reservoir, the heterogeneity of the reservoir is obvious, and the development effect of polymer flooding in different well groups is quite different, which is not conducive to the adjustment and evaluation of later development. Therefore, it is necessary to classify the polymer flooding well groups in the second type reservoir according to the dynamic and static physical parameters, and evaluate the development effect of different types of polymer flooding well groups on this basis. By analyzing the dynamic and static data of polymer flooding blocks in type II reservoirs, this paper determines the influencing factors of well group classification evaluation, establishes the method of well group classification combined with grey correlation method and mathematical statistics analysis, uses reservoir numerical simulation technology to predict the development effect of polymer flooding for different types of well groups, gives the development effect standards of polymer flooding for different types of well groups, and plays a certain role in adjusting the development effect of polymer flooding in oilfields.

Integrating Fiber Optic Data in Numerical Reservoir Simulation Using Intelligent Optimization Workflow.

A novel workflow is presented for integrating fiber optic Distributed Temperature Sensor (DTS) data in numerical simulation model for the Cyclic Steam Stimulation (CSS) process, using an intelligent optimization routine that automatically learns and improves from experience. As the steam–oil relationship is the main driver for forecasting and decision-making in thermal recovery operations, knowledge of downhole steam distribution across the well over time can optimize injection and production. This study uses actual field data from a CSS operation in a heavy oil field in California, and the value of integrating DTS in the history matching process is illustrated as it allows the steam distribution to be accurately estimated along the entire length of the well. The workflow enables the simultaneous history match of water, oil, and temperature profiles, while capturing the reservoir heterogeneity and the actual physics of the injection process, and ultimately reducing the uncertainty in the predictive models. A novel stepwise grid-refinement approach coupled with an evolutionary optimization algorithm was implemented to improve computational efficiency and predictive accuracy. DTS surveillance also made it possible to detect a thermal communication event due to steam channeling in real-time, and even assess the effectiveness of the remedial workover to resolve it, demonstrating the value of continuous fiber optic monitoring.

Production data analysis of gas reservoirs with edge aquifer drive: A semi-analytical approach

Production data analysis is proved to be an efficient reservoir engineering tool that can be utilized to estimate some important reservoir parameters including fluid in place and, average reservoir pressure. Among the available production data methods, flowing material balance is more popular. In spite of the development of this method for volumetric gas and, oil reservoirs over the past years, non-volumetric effect doesn't feature the equations. In this paper, modified flowing material balance equations are proposed for production data analysis of gas reservoirs subjected to finite-extended edge aquifer. The validity of the presented equations is performed using analytical solutions. For the development of analytical solutions, special simplifying assumptions are considered. To evaluate these assumptions, a comparison is performed using a commercial numerical reservoir simulator for some models with different rock and, fluid properties. Moreover, the introduced flowing material balance equation is combined with material balance equation in order to find a simple equation to calculate average reservoir pressure. Detailed steps are presented to determine gas in place of and, average reservoir pressure of this kind of reservoirs. Furthermore, for a better match between analytical and numerical outputs of gas flow rates, a correction coefficient is recommended which depends on the strength of aquifer.

Warmback analysis to determine fracture geometry of a single-stage hydraulic fracturing stimulation

Significant variation in hydraulic fracturing efficiency over the length of horizontal wells has been observed in the field. Monitoring and diagnosis of the fracture treatment is a critical step to evaluate the efficiency of the fracturing stimulation and the fracture geometry. Different diagnostic tools have been used to determine fracture placement and fracture effectiveness such as pressure decline analysis, microseismic, and tiltmeter fracture mapping technology. Recently, temperature monitoring has been evolved as a new technique can be analyzed to infer fracturing zone and fracture characteristics. Temperature behavior during fracture propagation and the subsequent warmback period can reveal important information about the dimensions and flow characteristics of developed fracture. In this work, we present forward and inverse modelling approaches to determine the fracture geometry using the temperature measured at the horizontal lateral. An analytical model is first developed to obtain the transient temperature in the fracture-matrix system during injection/propagation and the subsequent warmback period. The analytical solutions are developed by solving mass conservation equation along with energy balance equation in the fracture and the surrounding matrix assuming linear fluid flow and negligible leak-off effect which can be feasible for ultra-tight formations with low filtration coefficient. The developed solutions are validated against a thermally coupled numerical reservoir simulator as well as published field data. The solutions for warmback period are obtained and presented in the form of graphical type curves. The temperature measurements obtained during warmback period along with the developed solutions are used to estimate fracture width, fracture half-length, and geothermal reservoir temperature. The analytical results provide good agreement with the numerical results during forward and inverse modelling.

A fast method of waterflooding performance forecast for large-scale thick carbonate reservoirs

Due to the severe heterogeneity of carbonate reservoirs, the traditional reservoir engineering methods for waterflooding performance forecast, mainly including the material balance equation, waterflooding characteristic curve and production decline curve, suffer from less reliability. The fine-scale reservoir numerical simulation is extremely time-consuming, because petrophysical properties in carbonate geological models change so drastically. To predict the development performance rapidly, a new method for large-scale thick carbonate reservoirs is proposed. By combining the geological characteristics and dynamic performance of each well, vertical stacking pattern of the reservoir are classified, and also good insights into the lateral distribution of typical stacking patterns are also gained. The stacking pattern distributions are further projected onto the waterflooding well pattern, followed by rapid evaluation of production and injection rate of every block. Based on the simulation results for typical stacking pattern blocks, type curves of water flooding on different stacking pattern reservoirs are workout. Then the waterflooding performance for the whole carbonate reservoir is step-by-step quickly predicted at a constant liquid rate so as to keep the reservoir injection-production balance with voidage replacement ratio 1. Finally, a large-scale thick porous carbonate reservoir in the Middle East is taken as an example to show the workflow of the proposed method. The accuracy is further validated by comparing the predicted results from numerical simulation, indicating that the proposed method can save a lot of calculation time while ensuring the accuracy of performance forecast.

An experimental study on the viscosity of SPAM solutions with a new correlation predicting the apparent viscosity of sulfonated polyacrylamides

Abstract Being one of the most commonly performed EOR methods, polymer injection is used to increase the mobility ratio and decrease water relative permeability to allow the injected fluid to sweep more oil towards the production well. Before the polymer solution is injected into the reservoir through the injection wells, the process of polymer injection must be simulated using commercial numerical reservoir simulators. In order to be able to simulate the process, the viscosity behavior of the solution must be known. Therefore, a model is required to estimate the viscosity of the injected fluids versus shear rate and polymer concentration. In this study, a new mathematical function based on the power-law fluid equation is presented, which can be applied to predict the viscosity of SPAM solutions. The two required parameters of the power-law equation are obtained by fitting a power-law function to the viscosity-shear rate data. Samples in different polymer concentrations (using two SPAM polymers with different molecular weights) were prepared and their viscosity was measured against different shear rates. The results were fitted to the power-law equation and their corresponding power-law parameters were recorded. A mathematical function was introduced and tested for each parameter. The new functions combined with the power-law equation were used to estimate the viscosity of different polymer solutions with different SPAM concentrations. The results showed that the model is capable of estimating the viscosity with acceptable precision. Furthermore, it is applicable in various temperatures and water salinities.