We demonstrate how key geological uncertainties in a giant onshore carbonate reservoir in the Middle East, most notably fracture permeability and saturation distribution, impact the quality of the history match and change the performance forecasts of a planned Miscible Water Alternating Gas (MWAG) injection process. To achieve this, we used a history matching and multi-objective optimisation (MOO) workflow that was tightly integrated with an innovative reservoir modelling workflow that paid particular attention to the fracture and saturation modelling.
Different geological models for the reservoir were designed by integrating static and dynamic data. These data indicated the need to consider fault-related fractures and to update the saturation distribution in the reservoir model. The effective medium theory was therefore used to estimate effective permeability in order to capture the presence of low-intensity fault-controlled fractures in the reservoir. The integration of Special Core Analysis (SCAL) and log-derived J-functions allowed us to build alternative saturation models that honoured well data with great accuracy. The resulting history matched models therefore accounted for the key geological uncertainties present in the reservoir. Afterwards, MOO was applied for each history matched model to identify well controls that optimally balanced the need to maximise the time on the plateau rate while adhering to the field's gas production constraints.
Our results clearly show that including low-intensity fault-controlled fractures in the reservoir model improved the quality of the history match for the gas oil ratio (GOR), bottom hole pressure (BHP) and water cut. This is especially true for wells located near faults, which were difficult to match in the past. Moreover, our results further show that the updated saturation model improved the quality of the history match for the water cut, particularly for wells located in the transition zone. These different history matched models yielded different production forecasts, where the time at which the reservoir can be produced at the plateau rate varied by up to ten years.
Applying MOO for each history matched model then allowed us to identify well controls for the MWAG injection that could extend the time at which the reservoir would be produced at the plateau rate for up to nine years and the risk of losing production plateau down to two years, while always adhering to the current field operational constraints.
We demonstrate how the integration of MOO with an innovative workflow for fracture and saturation modelling impacts the prediction of a planned MWAG injection in a giant onshore carbonate reservoir. Our work clearly illustrates the potential of integrating MOO with new reservoir characterisation methods to improve the quantification of uncertainties in reservoir performance predictions in carbonate reservoirs.
Al-Jenaibi, Faisal (ADNOC - Upstream) | Shelepov, Konstantin (Rock Flow Dynamics) | Kuzevanov, Maksim (Rock Flow Dynamics) | Gusarov, Evgenii (Rock Flow Dynamics) | Bogachev, Kirill (Rock Flow Dynamics)
The application of intelligent algorithms that use clever simplifications and methods to solve computationallycomplex problems are rapidly displacing traditional methods in the petroleum industry. The latest forward-thinking approaches inhistory matching and uncertainty quantification were applied on a dynamic model that has unknown permeability model. The original perm-poro profile was constructed based on synthetic data to compare Assisted History Matching (AHM)approach to the exact solution. It is assumed that relative permeabilities, endpoints, or any parameter other than absolute permeability to match oil/water/gas rates, gas-oil ratio, water injection rate, watercut and bottomhole pressure cannot be modified.
The standard approach is to match a model via permeability variation is to split the grid into several regions. However, this process is a complete guess as it is unclear in advance how to select regions. The geological prerequisites for such splitting usually do not exist. Moreover, the values of permeability and porosity in different grid blocks are correlated. Independent change of these values for each region distortscorrelations or make the model unphysical.
The proposed alternative involves the decomposition of permeability model into spectrum amplitudes using Discrete Cosine Transformation (DCT), which is a form of Fourier Transform. The sum of all amplitudes in DCT is equal to the original property distribution. Uncertain permeability model typically involves subjective judgment, and several optimization runs to construct uncertainty matrix. However, the proposed multi-objective Particle Swarm Optimization (PSO) helps to reduce randomness and find optimal undominated by any other objective solution with fewer runs. Further optimization of Flexi-PSO algorithm is performed on its constituting components such as swarm size, inertia, nostalgia, sociality, damping factor, neighbor count, neighborliness, the proportion of explorers, egoism, community and relative critical distance to increase the speed of convergence. Additionally, the clustering technique, such as Principal Component Analysis (PCA), is suggested as a mean to reduce the space dimensionality of resulted solutions while ensuring the diversity of selected cluster centers.
The presentedset of methodshelps to achieve a qualitative and quantitative match with respect to any property, reduce the number of uncertainty parameters, setup ageneric and efficient approach towards assisted history matching.
The traditional trial and error approach of history matching to obtain an accurate model requires engineers to control each uncertain parameter and can be quite time consuming and inefficient. However, automatic history matching (AHM), assisted by computers, is an efficient process to control a large number of parameters simultaneously by an algorithm that integrates a static model with dynamic data to minimize a misfit for improving reliability. It helps to reduce simulation run time as well.
Particle Swarm Optimization (PSO) is a population based stochastic algorithm that can explore parameter space combined with the least squares single objective function. The process of AHM can adopt parameterization and realization methods to reduce inverse problems. In this study, realizations of various reservoir properties such as porosity, net to gross, relative permeability, horizontal and vertical permeability, and aquifer size were chosen for controlling throughout the AHM. History matching was conducted to validate the efficiency of each method. The guidelines for optimized AHM with a stochastic algorithm are also disccussed.
The realization and parameterization methods improved matching results in a full-field application with resulting in a reduced misfit and in less. A stochastic algorithm generates multiple models to deduce control parameters to reduce a misfit. In this study we identified that PSO converged effectively with updated control parameters. The optimized AHM improved the accuracy of a full-field model although some misfit remained in the match to bottomhole pressure.
We found that updating with too many parameters makes the problem difficult to solve while using too few leads to false convergence. In addition, while the simulation run time is critical, a full-field simulation model with reduced computational overhead is benefitial.
In this study, we observed that the PSO was an efficient algorithm to update control parameters to reduce a misfit. Using the parameterization and realization as an assisted method helped find better results. Overall this study can be used as a guideline to optimize the process of history matching.
This study examines which is the margin of usability for Artificial Intelligence (AI) algorithms related to the rock properties distribution in static modeling. This novel method shows a forward modeling approach using neural networks and genetic algorithms to optimize correlation patterns among seismic traces of stack volumes and well rock properties. Once a set of nonlinear functions is optimized in the well locations, to correlate seismic traces and rock properties, spatial response is estimated using the seismic volume. This seismic characterization process is directly dependent on the error minimization during the structural seismic interpretation process, as well as, honoring the structural complexity while modeling. Previous points are key elements to obtain an adequate correlation between well data and seismic traces. The joint mechanism of neural networks and genetic algorithms globally optimize the nonlinear functions and its parameters to minimize the cost function. Estimated objective function correlates well rock properties with seismic stack data. This mechanism is applied to real data, within a high structural complexity and several wells. As an output, calibrated petrophysical time volumes in the interval of interest are obtained. Properties are used initially to generate a geological facies model. Subsequently, facies and seismic properties are used for the three-dimensional distribution of petrophysical properties such as: rock type, porosity, clay volume and permeability. Therefore, artificial intelligence algorithms can be widely exploited for uncertainty reduction within the rock property spatial estimation.
Park, Jaeyoung (Texas A&M University) | Iino, Atsushi (Texas A&M University) | Datta-Gupta, Akhil (Texas A&M University) | Bi, Jackson (Anadarko Petroleum Corporation) | Sankaran, Sathish (Anadarko Petroleum Corporation)
The objective of this study is to develop a workflow to rapidly simulate injection and production phases of hydraulically fractured shale wells by (a) incorporating fracture propagation in flow simulators using a simplified physical model for pressure-dependent fracture conductivity and fracture pore volume (b) developing a hybrid Fast Marching Method (FMM) and 3D Finite Difference(FD) model for efficient coupled simulation and (c) automating the entire workflow for rapid analysis in a single simulator domain.
Pressure-dependent fracture transmissibility and pore volume multiplier models are assigned to predefined potential hydraulic fracture paths to mimic geomechanical behavior of fractures (i.e. opening and closure). The multipliers are based on empirical equations (e.g., Barton-Bandis model) and theoretical models (e.g., linear elastic fracture mechanics and cubic law). The FMM-based simulation transforms an original 3D reservoir model into an equivalent 1D simulation grid leading to orders of magnitude faster computation and is utilized to efficiently history-match field production and pressure data. A population-based history matching algorithm was used to minimize data misfit and quantify uncertainties in tuning parameters.
We demonstrate the effectiveness and efficiency of the proposed method using synthetic and field examples. First, we validated our proposed simplified fracture propagation model with a comprehensive coupled fluid flow and geomechanical simulator, ABAQUS. The results showed close agreement in both injection pressure response and fracture geometry. Next, the method was applied to a field case to history-match injection pressure and production data. Fracture geometry and properties were inferred from the injection phase and are input to the production phase modeling. After history matching, the misfit and uncertainty ranges in reservoir and fracture properties were substantially reduced.
The proposed workflow enables rapid analyses of hydraulically fractured wells and does not require computationally demanding geomechanical simulations to generate fracture geometry and properties. The FMM-based simulation further improves computational efficiency and allows us to automate the workflow using population-based history matching algorithms to quantify and assess parameter uncertainty.
Proper characterization of heterogeneous rock properties and hydraulic fracture parameters is essential for optimizing well spacing and reliable estimation of EUR in unconventional reservoirs. High resolution characterization of matrix properties and complex fracture parameters requires efficient history matching of well production and pressure response. We propose a novel reservoir model parameterization method to reduce the number of unknowns, regularize the ill-posed problem and enhance the efficiency of history matching of unconventional reservoirs.
Our proposed method makes a low rank approximation of the spatial distribution of reservoir properties taking into account the varying model resolution of the matrix and hydraulic fractures. Typically, hydraulic fractures are represented with much higher resolution through local grid refinements compared to the matrix properties. In our approach, the spatial property distribution of both for matrix and fractures is represented using a few parameters via a linear transformation with multiresolution basis functions. The parameters in transform domain are then updated during model calibrations, substantially reducing the number of unknowns. The multiresolution basis functions are constructed by eigen-decomposition of an adaptively coarsened grid Laplacian corresponding to the data resolution. High property resolution at the area of interest through the adaptive resolution control while keeping the original grid structure improves quality of history matching, reduces simulation runtime and improves the efficiency of history matching.
We demonstrate the power and efficacy of our method using synthetic and field examples. First, we illustrate the effectiveness of the proposed multiresolution parameterization by comparing it with traditional method. For the field application, an unconventional tight oil reservoir model with a multi-stage hydraulic fractured well is calibrated using bottom-hole pressure and water cut history data. The hydraulic fractures as well as the stimulated reservoir volume (SRV) near the well are represented with higher grid resolution. In addition to matrix and fracture properties, the extent of the SRV and hydraulic fractures are also adjusted through history matching using a Multiobjective Genetic Algorithm. The calibrated ensemble of models are used to obtain bounds of production forecast.
Our proposed method is designed to calibrate reservoir and fracture properties with higher resolution in regions that have improved data resolution and higher sensitivity to the well performance data, for example the SRV region and the hydraulic fractures. This leads to a fast and efficient history matching workflow and enables us to make optimal development/completion plans in a reasonable time frame.
Objective/scope – This paper is an extension of the work presented in URTeC paper #2856750, 2018, where a decline curve reproducing the standard transition from linear flow to pseudo steady state flow regimes was proposed for fractured horizontal wells in unconventional reservoirs. In this new work, the formulation was generalized to a succession of flow regimes. This enables the new decline curve to reproduce a succession of periods with power-law behavior, as predicted by recent work on anomalous diffusion models. By construction, this decline curve is fully consistent with RTA concepts and the predictions of physical models.
Method/Procedures/Process – The decline curve is obtained by numerically integrating, in the material balance time domain, a “base function” defined as a succession of straight lines reproducing the successive flow regimes, linked with continuous transition periods. By construction, the base function follows the characteristic evolution of the rate-normalized pressure derivative on a loglog plot, which ensures the physical consistency of the obtained decline curve. Once the curve is matched, its parameters can then be used to infer combinations of physical parameters. Two approaches are possible: (1) In the absence of bottomhole pressures, a classical match and forecast of the instantaneous rate or of the cumulative can be performed in the real time domain directly, with only 3 parameters. (2) If a bottomhole pressure history is available, the evolution of the rate-normalized pressure and its derivative can first be displayed on a loglog plot, where the different regimes emerging can be rigorously identified, and the corresponding lines traced. Once the different straight lines have been positioned, they are automatically linked with continuous transition periods, and seamlessly integrated into the final decline curve. The forecast can be made either by extending the last observed flow regime, or by using a more conservative regime.
Results/Observations/Conclusions – The calculation steps leading to the decline curve are detailed. Comparisons of the results from the decline curve and from various physical models (including analytical anomalous diffusion models with different flow regimes paths) show excellent agreement. Several application examples are shown and the estimation of physical parameters from the parameters of the decline curve is demonstrated.
Applications/Significance/Novelty - The proposed decline curve reproduces the successive emergence of expected flow regimes and is fully consistent with the predictions of currently available physical models – including recent anomalous diffusion models. The parameters of the curve can be used to estimate combinations of the corresponding physical model parameters. As a consequence, the proposed approach bridges the gap between empirical decline curve techniques and the physical concepts used for rate transient analysis.
The petro-elastic model (PEM) represents an integral component in the closed-loop calibration of integrated four-dimensional (4D) solutions incorporating time-lapse seismic, elastic and petrophysical rock property modeling, and reservoir simulation. Calibration of the reservoir simulation model is needed so that it is not only consistent with production history but also with the contemporaneous subsurface description as characterized by time-lapse seismic. The PEM requires dry rock properties in its description, which are typically derived from mechanical rock tests. In the absence of those mechanical tests, a small data challenge is posed, whereby all necessary data is not available but the value of reconciling seismic attributes to simulated production remains. A seismic inversion-constrained n-dimensional metaheuristic optimization technique is employed directly on three-dimensional (3D) geocellular arrays to determine elastic and density properties for the PEM embedded in the commercial reservoir simulator.
Ill-posed dry elastic and density property models are considered in a field case where the seismic inversion and petrophysical property model constrained by seismic inversion exist. An n-dimensional design optimization technique is implemented to determine the optimal solution of a multidimensional pseudo-objective function comprised of multidimensional design variables. This study investigates the execution of a modified particle swarm optimization (PSO) method combined with an exterior penalty function (EPF) with varied constraints. The proposed technique involves using n-dimensional design optimization to solve the pseudo-objective function comprised of the PSO and EPF given limited availability of constraints. In this work, an examination of heavily and reduced-order penalized metaheuristic optimization processes, where the design variables and optimal solution are derived from 3D arrays, is conducted so that constraint applicability is quantified. While the process is examined specifically for PEM, it can be applied to other data-limited modeling techniques.
Integration of time-lapse seismic data into dynamic reservoir model is an efficient process in calibrating reservoir parameters update. The choice of the metric which will measure the misfit between observed data and simulated model has a considerable effect on the history matching process, and then on the optimal ensemble model acquired. History matching using 4D seismic and production data simultaneously is still a challenge due to the nature of the two different type of data (time-series and maps or volumes based).
Conventionally, the formulation used for the misfit is least square, which is widely used for production data matching. Distance measurement based objective functions designed for 4D image comparison have been explored in recent years and has been proven to be reliable. This study explores history matching process by introducing a merged objective function, between the production and the 4D seismic data. The proposed approach in this paper is to make comparable this two type of data (well and seismic) in a unique objective function, which will be optimised, avoiding by then the question of weights. An adaptive evolutionary optimisation algorithm has been used for the history matching loop. Local and global reservoir parameters are perturbed in this process, which include porosity, permeability, net-to-gross, and fault transmissibility.
This production and seismic history matching has been applied on a UKCS field, it shows that a acceptalbe production data matching is achieved while honouring saturation information obtained from 4D seismic surveys.
Time-lapse seismic monitoring is a powerful technique for reservoir management and the optimization of hydrocarbon recovery. In time-lapse seismic datasets, the difference in seismic properties across different vintages enables the detection of spatio-temporal changes in saturated properties and structure induced by production. The main objectives are (1) to identify bypass pay zones in time-lapse seismic data for the deepwater Amberjack field, located in the Gulf of Mexico, (2) confirm the identified bypass pay zones in the results of reservoir simulation, and (3) recommend well planning strategies to exploit these bypassed resources.
A high-fidelity seismic-to-simulation 4D workflow that incorporates seismic, petrophysics, petrophysical property modeling, and reservoir simulation was employed, which leveraged cross-discipline interaction, interpretation, and integration to extend asset management capabilities. The workflow addresses geology (well log interpretation and framework development), geophysics (seismic interpretation, velocity modeling, and seismic inversion), and petrophysical property modeling (earth models and co-located co-simulation of petrophysical properties with P-impedance from seismic inversion). An embedded petro-elastic model (PEM) in the reservoir simulator is then used to affiliate spatial dry rock properties with saturation properties to compute dynamic elastic properties, which can be related to multi-vintage P-impedance from time-lapse seismic inversion. In the absence of the requisite dry rock properties for the PEM, a small data engine is used to determine these absent properties using metaheuristic optimization techniques. Specifically, two particle swarm optimization (PSO) applications, including an exterior penalty function (EPF), are modified resulting in the development of nested and average methods, respectively. These methods simultaneously calculate the missing rock parameters (dry rock bulk modulus, shear modulus, and density) necessary for dynamic, embedded P-impedance calculation in the history-constrained reservoir simulation results. Afterward, a graphic-enabled method was devised to appropriately classify the threshold to discriminate non-reservoir (including bypassed pay) and reservoir from the P-impedance difference. Its results are compared to unsupervised learning (k-means clustering and hierarchical clustering). From seismic data, one can identify bypassed pay locations, which are confirmed from reservoir simulation after conducting a seismic-driven history match. Finally, infill wells are planned, and then modeled in the reservoir simulator.