1,721,039 research outputs found
Matlab files used to produce the figures in the publication: Insights from closed-form expressions for injection- and production-induced stresses in displaced faults.
No full textSet of Matlab files to create most of the figures in manuscript:
Jansen, J.D., Singhal, P. and Vossepoel, F.C., 2019: Insights from closed-form expressions for injection- and production-induced stresses in displaced faults. Submitted for publication to JGR Solid Earth
System-Theoretical Model Reduction for Reservoir Simulation and optimization
No full textThis thesis is concerned with low-order modelling of heterogeneous reservoir systems for the purpose of efficient simulation and optimization of flooding processes with multiple injection and production (smart) wells. Typically, one is initially equipped with a physics-based ('white-box') model consisting of O(103-106) equations and parameters representing a (coupled) system of discretized PDEs defined on a geometric grid. The model-order reduction (MOR) methodology undertaken in this research is fundamentally different from the traditional, 'grid-coarsing' approximation methods, in that no coarse-grid approximation of the fine-grid problem is employed at all. Instead, the reduced-order models are here based on 'system-theoretic' and dynamically intrinsic properties of the fine-scale system. In single-phase flow problems that can be modelled as linear time-invariant state-space systems these properties are, e.g., the system's transfer function in the Laplace domain, the eigenstructure of the system matrix, or controllability and observability of the (particular state-space realization of the) system. For multi-phase flow problems resulting in nonlinear state-space models, intrinsic information needs to be sought in data obtained by simulating the fine-scale model. The contribution of this thesis can be divided into three themes: 1) Standard 'projection-based' MOR: assessment of the performance of modal truncation, singular perturbation, balanced truncation, transfer function moments maching (inc. Krylov-subspaces), and proper orthogonal decomposition (POD), 2) Acceleration of solving the fine-scale problem: use of MOR as a 'shadow simulation' to determine an improved fine-scale initial guess, and 3) Acceleration of waterflooding optimization: use of POD in the inner-loop of an adjoint-based optimization scheme.Civil Engineering and Geoscience
Control-Relevant Upscaling
No full textAn ‘upscaling/order-reduction’ solution transfers the relevant features of a geological model to a flow simulation model such that cost-efficient simulation, prediction and control of the fluid flow in an oil reservoir become feasible. In addition to the computational issues, in most reservoir applications and for a given configuration of wells, there is only a limited amount of information (output) that can be observed from production data, while there is also a limited amount of control (input) that can be exercised by adjusting the well parameters. From a system-theoretical point of view, this means that a large number of combinations of the state variables (pressure and saturation values) are not actually controllable and observable from the wells, and accordingly, they are not affecting the input-output behavior of the system. In this research, therefore, we aim at adjusting (reducing) the level of model complexity (order) to the level of relevant dynamics in terms of input-output behaviour. In particular, we present a multi-level selective (i.e. non-uniform) grid coarsening method, in which the criterion for grid size adaptation is based on the spatial quantification of the controllability and observability properties of the reservoir system. Based on the numerical examples, this method can accurately reproduce the flow response of the fine scale models.GeotechnologyCivil Engineering and Geoscience
Data assimilation in reservoir management
No full textThe research presented in this thesis aims at improving computer models that allow simulations of water, oil and gas flows in subsurface petroleum reservoirs. This is done by integrating, or assimilating, measurements into physics-bases models. In recent years petroleum technology has developed rapidly. Nowadays wells can be drilled to a depth of up to 10 km, not just vertically, but also at an angle, horizontally or with branches. Moreover, downhole valves can be installed which can be opened or closed from the surface and advanced sensors can be placed in the subsurface. This technology has the potential to drain petroleum reservoirs much more efficiently. In order to do so, the technology needs to be used sensibly, which requires adequate knowledge of subsurface physical processes. Large amounts of measurements can contribute to this, but conventional methods are often ad hoc and not suited to handle the large amounts of data that are available nowadays. Good "data assimilation" methods are very important to ensure that the growing demand for energy in the near future can be met. The objective of this thesis is to apply data assimilation techniques, invented and developed in other areas of research, to petroleum reservoir engineering, to modify them to be better suited for their new application, and to investigate how they can help to integrate both production data and seismic data to support decision-making in petroleum reservoir management.Civil Engineering and Geoscience
Feature-based estimation for applications in geosciences
No full textA reservoir simulator mimics the movement of fluids in the presence of each other through a porous medium under some specified conditions. It is a numerical model of a real-life physical process, therefore, subject to uncertainty. Some uncertainties can be lowered by improving model-parameter estimates. This is where data assimilation plays an important role. Automated data assimilation, using sophisticated techniques, is a widely researched topic in today's applied science. We investigated two research topics in data assimilation that are closely connected to the area of image processing. Images are an integral part of reservoir engineering application in the form of property or variable fields. Reservoir engineering, image processing and data assimilation are the leading themes here. First, we applied an ensemble multiscale filter as a permeability estimator and concluded that the filter can be an efficient localizing tool especially for spatially large observations. Second, we developed a grid deformation technique inspired by grid generation and image warping methods. We presented two- and three-dimensional versions of the method in reservoir and groundwater flow models, and concluded that the grid distortion proved cost efficient and effective.Applied mathematicsElectrical Engineering, Mathematics and Computer Scienc
Quantification of the impact of data in reservoir modeling
No full textGlobal energy use is increasing. As societies advance, they will continue to need energy to power residential and commercial buildings, in the industrial sector, for transportation and other vital services. To satisfy this rising demand, liquid, natural gas, coal, nuclear power and renewable fuel sources are extensively developed. Particularly fossil fuels (i.e. oil, natural gas and coal) remain the largest source of energy for the world. Petroleum exploration and production companies continuously develop new and enhance current production technologies to increase recovery from the existing fields. These companies rely on various tools to support their production and development decisions. Reservoir modeling is a standard tool used in the decision making process allowing analysis and prediction of the reservoir flow behavior, identification of beneficial production strategies and evaluation of the associated risks. The models used for reservoir simulation contain a large number of imperfectly known parameters characterizing the reservoir flow, e.g. permeability and porosity of the reservoir rock. Therefore the predictive value of such models is limited and tends to deteriorate in time. History matching is employed to update the values of poorly known model parameters in time with the help of the production data which become available during the production life of the reservoir, i.e. to adapt parameters such that simulated results are consistent with measured production data. Such an approach generally improves estimates of the model parameters and the predictive capability of the model. Remarkably, the information extracted from the measurements in the history matching phase is repeatedly found as not enough to provide well-calibrated model with a high predictive value. Hence, consideration of additional data can be of particular help. To optimize the costs and effort associated with collection of new data and computations, up-front selection of the most influential measurements and their locations is desirable. Methods to assess the impact of measurements on model parameter updating are therefore needed. The research objective of this thesis was to develop efficient tools for quantifying the impact of measured data on the outcome of history matching of reservoir models, i.e. tools that provide a meaningful quantification of the impact of observations, while requiring limited time and effort to be incorporated in the history matching algorithms. This research addressed history matching two-dimensional two-phase reservoir model representing water flood with production data (bottom hole pressure at injection well and oil and water flow rates at production wells). First, the applicability and implementation of a number of history matching algorithms were investigated. The representer method (RM) has been considered as an example of variational techniques. The algorithm’s key feature is the computation of a set of so-called representers describing the influence of a certain measurement on an estimation of the state and/or parameter. The RM was found to provide a reasonable parameter estimate, although it is computationally inefficient for dealing with large data sets. This fact yielded testing of the accelerated representer method (ARM), where direct computation of representers is avoided. The results indicate that the accuracy of the ARM can be controlled to provide an outcome of the same accuracy as the RM, and that the ARM outperforms the classical RM in terms of computational speed when the number of assimilated measurements increases. In this thesis we developed a strategy to evaluate the number of operations performed by the methods to assess the amount of data for which the ARM becomes beneficial to use. The RM and the ARM require the model adjoint and are not intended for continuous (sequential) history matching, namely for incorporating obtained data in the model on the fly. Instead they perform history matching over a rather long time window using all available observations. The ensemble Kalman filter (EnKF) has been discussed as it is the algorithm for continuous history matching. The EnKF schemes do not require the model adjoint, which makes them very attractive for data assimilation with complex non-linear models. The use of the EnKF in reservoir engineering however is prone to producing physically unreasonable values of the state variables. The problem can be overcome by including a so-called confirmation step in the algorithm. The EnKF, particularly with a confirmation step, is often computationally demanding for large-scale applications. The asynchronous EnKF (AEnKF) is a modification of the EnKF which offers a practical way to perform history matching in such cases by updating the system with batches of measurements collected at the times different to the time of the update. Hence, all observations collected during a certain time-window can be history-matched at once at the end of observational period. This allows for comparison of the influence of the observations collected at different times. Furthermore, it does not rely on an adjoint model, though it resembles the approach usually followed in variational methods. Both the EnKF and the AEnKF demonstrated considerable improvement of the model parameter estimates compared to the prior and gave acceptable history matches. Since the AEnKF allows for history matching all the data gathered throughout the observational period at once, it permits comparison of the effect of observations collected at different time instances. The equivalence of the AEnKF to variational techniques (e.g. the RM) yields the possibility to evaluate if ensemble Kalman filtering and variational methods utilize the observations in a similar manner. The representer method and the AEnKF were selected to be used as platforms for quantification of the measurements impact on history matching. Secondly, in this thesis we developed a tool to quantify the impact of measured data on the outcome of history matching. The method has been inspired by the recent advancements in meteorology and oceanography, and is based on a so-called sensitivity matrix. This matrix can be used to evaluate the amount of information extracted from available data during the data assimilation phase and identify the observations that have contributed to the parameter update the most. In particular, we used the diagonal elements of the matrix, known as self-sensitivities, as a quantitative measure of the influence of observed measurements on predicted measurements. Additionally, we have proposed a way to use the norm of the sensitivity matrix for assessing the magnitude of possible change in the accuracy of the model due to the respective change in the accuracy of collected observations. The observation sensitivity matrix is fast and easy to compute both for adjoint-based and EnKF types of history matching algorithms. The analysis performed with the aid of the observation sensitivity matrix has confirmed that the RM and the AEnKF utilize the data with comparable effectiveness. Remarkably, for a simple test case the global averaged influence of the observed measurements is only 4%. This is a rather low value compared to the 96% global averaged influence of the prior. The observation sensitivity matrix can be also used to investigate the dependency between the measurement location / type and its importance to history matching.Applied mathematicsElectrical Engineering, Mathematics and Computer Scienc
Model-based lifecycle optimization of well locations and production settings in petroleum reservoirs
No full textThe coming years there is a need to increase production from petroleum reservoirs, and there is an enormous potential to do so by increasing the recovery factor. This is possible by making better use of recent technological developments, such as horizontal wells, downhole valves and sensors. However, actually making better use of these improved capabilities is difficult because of many open problems in reservoir management and production operations processes. Consequently, there is significant scope to increase the recovery factor of oil and gas fields by tailoring tools from the systems and control community to efficiently perform dynamic optimization of wells (e.g. number, locations) and their production settings (e.g. bottom-hole pressures, flow rates, valve settings) based on uncertain reservoir models, in the sense that they lead to good decisions while requiring limited time from the user. This thesis aims at developing these tools, and the main contributions are as follows. Many production setting optimization problems can be written as optimal control problems that are linear in the control. If the only constraints are upper and lower bounds on the control, these problems can be expected to have pure bang-bang optimal solutions. The adjoint method to derive gradients of a cost function with respect to production settings can be combined with robust optimization to efficiently compute settings that are robust against uncertainty in reservoir models. The gradients used in production setting optimization can be used to efficiently compute directions in which to iteratively improve upon an initial well configuration by surrounding the to-be-placed wells by pseudo wells (i.e. wells that operate at a negligible rate). The controllability and observability properties of single-phase flow reservoir model are analyzed. It is shown that pressures near wells in which we can control the flow rate or bottom-hole pressure are controllable, whereas pressures near wells in which we can measure the flow rate or bottom-hole pressure are observable. Finally, a new method of regularization in history matching is presented, based on this controllability and observability analysis.Mechanical Maritime and Materials Engineerin
Model-reduced gradient-based history matching
No full textSince the world's energy demand increases every year, the oil & gas industry makes a continuous effort to improve fossil fuel recovery. Physics-based petroleum reservoir modeling and closed-loop model-based reservoir management concept can play an important role here. In this concept measured data are used to improve the geological model, while the improved model is used to increase the recovery from a field. Both problems can be formulated as optimization problem, i.e. history matching identifies the parameter values that minimize an objective function that represents the mismatch between modeled and observed data while production optimization identifies wells controls that maximize the total oil recovery or monetary profit. One of the most efficient class of methods to solve history matching and production optimization problems are gradient-based methods where the gradients are calculated with the use of an adjoint method. The implementation of the adjoint method for parameter estimation and control optimization is, however, very difficult if no Jacobians of the model are available. This implies that there is a need for gradient-based, but adjoint-free optimization methods. A requirement becomes even more pressing if reservoir simulation is combined with another simulation, e.g. simulation of geomechanics or rock physics, with a code for which no Jacobians are available. The research objective of this thesis was to evaluate the performance of a model-reduced gradient-based history matching routine that does not require a difficult implementation and involves the reduction of the reservoir system. Additionally, the use of model-reduced method for production optimization of a reservoir operating under induced fracturing conditions was considered. In history matching problems one deals with a large number of uncertain parameters and very sparse observations, while in the production optimization one controls a large dimensional system by adjusting a limited number of controls. Consequently, the values of many model parameters cannot be verified with measurements due to a relatively few information content present in them, while in the production optimization only a limited part of the system can be indeed controlled. In this thesis we proposed a new method inspired by the results in reduced order modeling (ROM) and system-theoretical concepts of controllability and observability of the reservoir system. The new approach assumes that the reservoir dynamics relevant for history matching or production optimization can be represented accurately by a much smaller number of variables than the number of grid cells used in the simulation model. Consequently, the original (nonlinear and high-order) forward model is replaced by a linear reduced-order forward model and the adjoint of the tangent linear approximation of the original forward model is replaced by the adjoint of a linear reduced-order forward model. The reduced-order model is constructed by means of the Proper Orthogonal Decomposition (POD) method or Balanced Proper Orthogonal Decomposition (BPOD) method. The reduced-order model is not, however, obtained by the projection of the nonlinear system of equations as in the conventional projection-based ROM techniques, but instead it is approximated in the reduced subspace. The conventional POD method requires the availability of the high-order tangent model, i.e. of the Jacobians with respect to the states which are not available. The model-reduced method obtains a reduced-order approximation of the tangent linear model directly by computing approximate derivatives of the reduced-order model. Then due to the linear character of the reduced model, the corresponding adjoint model is easily obtained. The gradient of the objective function is approximated and the minimization problem is solved in the reduced space; the procedure is iterated with the updated estimate of the parameters if necessary. The POD-based approach is adjoint-free and can be used with any reservoir simulator, while the BPOD-based approach requires an adjoint model but does not require the Jacobians of the model with respect to uncertain parameters or controls. At first the model-reduced method was applied to history matching problems and was evaluated based on its computational efficiency and robustness. In order to make a valuable judgment this approach was compared to the classical adjoint-based method, which was available for the estimation of the permeability field. Permeabilities are described at each cell of the model, and therefore they need to be re-parameterized. The KL-expansion was used to reduce the parameters space. The significant reduction of the dimension of the dynamic reservoir model and parameter space made the approximation of the reduced-order system feasible in acceptable computation time. The pressure field required relatively low number of patterns which modeled mostly the changes around the wells. The saturation field required much more patterns and they modeled mostly the moving front of the saturation field. In the first studies simplistic reservoir models were used, for which the model-reduced approach showed to perform very well. The obtained estimates of the permeability field significantly improved compared to the prior fields and gave the acceptable history-matches; the quality of the prediction capabilities of the estimated models were very high and comparable to those obtained by the classical adjoint-based approach. The POD-based method was approximately twice as expensive as the classical approach, but the BPOD-based method was comparable to the adjoint-based method. Moreover, both methods were considerably cheaper than the finite difference approach. These preliminary results were the first applications of the model-order reduction to history matching problems. After this proof of concept, further studies were carried on more complex and larger models. The proposed method was capable to obtain satisfactory match with a computational efficiency about five times lower than the adjoint-based method. Similarly, an improvement in the prediction was obtained. The second problem considered in this research was to apply the adjoint-free methods to production optimization of the reservoir operating under special conditions that required coupling of two simulators and for which the adjoint code is not available. The model-reduced method could not be applied because of a low accuracy of the simulation solution which in case of long time simulations resulted in large approximation errors. Therefore, simultaneous perturbation stochastic algorithm (SPSA) was applied together with the finite difference gradient-based method to solve the production optimization problem. SPSA is a gradient-based method where the gradients are approximated by random perturbations of all controls in once, while the finite difference method approximates the gradients by perturbation of each control separately. Both approaches were very simple to implement, they resulted in the improvement of the production, but they were computationally relatively expensive.Applied mathematicsElectrical Engineering, Mathematics and Computer Scienc
Using Distributed Fiber-Optic Sensing Systems to Estimate Inflow and Reservoir Properties
No full textRecent developments in the deployment of distributed fiber-optic sensing systems in horizontal wells carry the promise to lead to a new, cheap and reliable way of monitoring production and reservoir performance. Practical applicability of distributed pressure sensing for quantitative inflow detection will strongly depend on the specifications of the sensors, details of which are currently not yet publicly available. We therefore theoretically examined the possibility to identify reservoir inflow from distributed measurements in the well. The first chapter gives a common definition of ‘smart wells’ concept, as used in hydrocarbon production. Conventional and newly-emerging well monitoring and reservoir surveillance techniques are briefly reviewed and the advantages of recent fiber-optic sensing systems are addressed. The significance of filling the gap between advanced monitoring and control technology by means of robust interpretation methods is discussed. In the second chapter a single-phase transient model for the fluid flow in the wellbore is used to investigate the time span in which dynamic phenomena in the wellbore occur. The model is based on a numerical method utilizing a flux splitting scheme and standard first-order-accurate upstream discretization is presented. Moreover the most important parameters influencing the pressure drop over a long horizontal well are investigated. The results suggested that the dynamics of the wellbore are significantly faster than the dynamics of the reservoir. Therefore in coupling a (numerical/analytical) reservoir simulator with a wellbore model, the dynamics of the wellbore can be neglected for the sake of simplicity and higher computational speed. Furthermore, the presented numerical experiments illustrated that the duration of transient-state in the wellbore was affected by the fluid compressibility. The well length, wellbore diameter and total production rate were the most important parameters to influence the total pressure-drop over the entire length of the well. The third chapter the possibility to identify reservoir inflow from distributed pressure measurements in the well is theoretically examined. The wellbore and near-wellbore are described by semi-analytical steady state models, and a gradient-based inversion method is applied to estimate the specific productivity index (SPI) as a function of along-well position. To obtain the gradients the adjoint method is used and results in a computationally very efficient inversion scheme. With the aid of two numerical experiments, the effects of well and reservoir parameters, sensor spacing, sensor resolution and measurement noise on the quality of the inversion results are investigated. The results showed that under single-phase steady-state conditions in the reservoir and the wellbore, SPIs and the associated inflow profile can be estimated from distributed pressure sensors. However, the inversion results are affected by sensor resolution, measurements noise and by the number of measurements compared to the number of unknown parameters. The negative effects of measurement noise and low sensor resolution are strongest in those areas of the well where the influx is smallest i.e. usually close to the toe. This is mainly due to the small pressure gradients along the wellbore which makes estimation of the flow rate and thus of the specific influx and of the SPI very inaccurate. The low computational time required for the proposed inversion methodology is of potential importance for applications in the real-time control of smart wells, e.g. to control coning behavior using measurements of gas or water influx. In the chapter four, the gradient-based minimization technique utilizing the adjoint method, as described in chapter three, is extended to the transient problem. Transient semi-analytical reservoir models are combined with adjoint-based minimization algorithms to estimate reservoir properties from dynamic recording of distributed pressure sensors in the well. Methods of instantaneous sink-source functions along with principle of superposition are employed to create a dynamic forward model for the coupled well-reservoir system. Aanalyzing measurements taken by distributed pressure sensor systems under dynamic conditions enables identifying properties of reservoir zones i.e. permeability and reservoir dimensions. By applying the proposed inversion methodology to transient pressure measurements, reservoir properties that influence the specific productivity index of each individual zone are independently estimated. In chapter five, the inversion methodology of chapter three is extended to multi-phase fluid flow condition. Resistivity measurements in addition to distributed pressure measurements are employed to estimate water and oil inflow of reservoir zones. In this approach, semi-analytical two-phase oil and water flow in the reservoir and wellbore is used to estimate two-phase specific productivity indices. Through several synthetic examples the effects of measurement noise and wellbore-reservoir geometry on the inversion results are investigated. Under steady-state conditions, the SPIs corresponding to oil and water phases and the associated oil and water inflow profiles can be estimated from distributed pressure and resistivity sensors. Combination of pressure and resistivity measurements leads to a fairly accurate estimation of the location and amount of different phases entering the wellbore from the reservoir.Geoscience & EngineeringCivil Engineering and Geoscience
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