Hamidreza Hamdi

Layered fluvial reservoirs with internal fluid cross flow: a well-connected family of well test pressure transient responses

A new well testing response from lateral cross flow within layers is described. The response occurs when there is extremely low effective vertical permeability in the system at the larger scale. Low vertical permeability actually accentuates the layering and reduces vertical cross flow whilst enhancing lateral cross flow from within-layer heterogeneities. The response is investigated using numerical simulation of flow in end-member models of complex and geologically realistic architecture in high net-to-gross fluvial systems. This ‘ramp’ response is shown to form one member of a family of well test pressure transient responses. The other members of the family include previously-described negative geoskin and geochoke. The use of well test data to characterize these particular types of layered fluvial reservoirs is an important step in the static-dynamic integration of geological and reservoir engineering models.

Using geological well testing for improving the selection of appropriate reservoir models

Analytical well-test solutions are mainly derived for simplified and idealized reservoir models and therefore cannot always honour the true complexity of real reservoir heterogeneities. Pressure transients in the reservoir average out heterogeneities, and therefore some interpretations may not be relevant and could be misleading. Geological well testing refers to the numerical simulation of transient tests by setting up detailed geological models, within which different scales of heterogeneity are present. The concept of geological well testing described in this paper assists in selecting from multiple equi-probable static models. This approach is used to understand which heterogeneities can influence the pressure transients. In this paper, a low-energy multi-facies fluvial reservoir is studied, for which data from a well test of exceptionally long duration are available. The pervasive low reservoir quality facies and restricted macro cross-flow between the reservoir layers give rise to an effective commingled system of flow into the wellbore (i.e. zero or very low vertical cross-flow between the reservoir units). In our model, facies transitions produce lateral cross-flow transients that result in a ‘double-ramp-effect’ signature in the test response. A sophisticated multi-point statistical (MPS) facies modelling approach is utilized to simulate complex geological heterogeneities and to represent facies spatial connectivity within a set of generated static models. The geological well-test model responses to a real well-testing cycle are then evaluated using dynamic simulation. The pressure match between simulated and recorded data is improved by generating multiple facies and petrophysical realizations, and by applying an engineering-based hybridization algorithm to combine different models that match particular portions of the real well-test response. In this example, the reservoir dynamics are controlled by subtle interaction between high-permeability channels and low-permeability floodplain deposits. Effective integration of geology and dynamic data using modern methods can lead to better reservoir characterization and modelling of such complex reservoir systems.

Population-based sampling methods for geological well testing

In this paper, the application of a population-based sampling algorithm, i.e., differential evolution, in the geological well testing of a multi-layered faulted reservoir model is discussed. In this sense, the available multiple well test datasets are used to calibrate the geological model parameters rather than fitting simplified analytical models. In the exercise studied in this paper, the parameter space includes a range of geostatistical, petrophysical, and structural parameters. The differential evolution algorithm starts with an initial random population from the ranges of input variables and progresses with successive evaluation of the static models’ transient tests. The static models’ input parameters are perturbed to generate new populations, which can finally match the truth model well test derivative with lower misfits. The ensemble of population models (samples) along with the misfit values are used to highlight the value of well test data in reducing the uncertainty in the parameter space. A Bayesian framework is employed to implement the Markov chain Monte Carlo (McMC) methods to estimate the posterior distributions of the parameters. The results are confirmed by the sample-based Sobol sensitivity indices, which rank the influential parameters. To reduce the computational cost of the McMC and sensitivity indices, a cross-validated proxy model (i.e., Multivariate Adaptive Regression Spline) is constructed. The effect of different variants of differential evolution algorithm on the geological well test matching is also discussed. This paper provides a workflow for quantitative integration of well test data into the reservoir characterization workflow.

Sequential Bayesian Optimization Coupled with Differential Evolution for Geological Well Testing

This paper presents a novel approach for updating the reservoir model from well test data. A sequential Bayesian optimization technique, i.e. Gaussian Process, is coupled with the Differential Evolution (DE) algorithm, for guided sampling from the parameter space. The Gaussian process assumes the simulation outputs are normally distributed, and aims at modelling the current model and misfit data to predict the best next sampling locations. The next samples are chosen by maximizing the expected improvement gained by sampling from a new location. Differential evolution is used in the maximization process of the expected improvement. This procedure is successfully tested in matching a noisy well test data from a multi-layered faulted reservoir model. The samples from multiple well-test simulations are pooled together, and the Markov chain Monte Carlo (McMC) techniques are used to estimate the posterior distributions over the parameter space. The computational cost of McMC process is reduced by implementing a bootstrap Multivariate Adaptive Regression Spline.

ReservoirBench: An Interactive Educational Reservoir Engineering Workbench

ReservoirBench is an interactive workbench for educational geological science and engineering tasks. It is designed to facilitate education of novice audiences to teach them basic concepts of reservoir modeling and simulation workflow. Traditional training using lectures and software practice can lead to information overload, and retainability is questionable. As an alternative, we propose a physical workbench that is coupled with digital augmentation for the purpose of learning. We take advantage of the crucial role that spatiality and 3D representations play in petroleum reservoir modeling and allow basic domain concepts to be introduced and explored in a tangible and experiential manner. We describe the design of our prototype and reflect on the findings from our preliminary design critique.

Gaussian Processes for history-matching: application to an unconventional gas reservoir

The process of reservoir history-matching is a costly task. Many available history-matching algorithms either fail to perform such a task or they require a large number of simulation runs. To overcome such struggles, we apply the Gaussian Process (GP) modeling technique to approximate the costly objective functions and to expedite finding the global optima. A GP model is a proxy, which is employed to model the input-output relationships by assuming a multi-Gaussian distribution on the output values. An infill criterion is used in conjunction with a GP model to help sequentially add the samples with potentially lower outputs. The IC fault model is used to compare the efficiency of GP-based optimization method with other typical optimization methods for minimizing the objective function. In this paper, we present the applicability of using a GP modeling approach for reservoir history-matching problems, which is exemplified by numerical analysis of production data from a horizontal multi-stage fractured tight gas condensate well. The results for the case that is studied here show a quick convergence to the lowest objective values in less than 100 simulations for this 20-dimensional problem. This amounts to an almost 10 times faster performance compared to the Differential Evolution (DE) algorithm that is also known to be a powerful optimization technique. The sensitivities are conducted to explain the performance of the GP-based optimization technique with various correlation functions.

A Visual Analytics Framework for Exploring Uncertainties in Reservoir Models.

Geological uncertainty is an essential element that affects the prediction of hydrocarbon production. The standard approach to address the geological uncertainty is to generate a large number of random 3D geological models and then perform flow simulations for each of them. Such a brute-force approach is not efficient as the flow simulations are computationally costly and as a result, domain experts cannot afford running a large number of simulations. Therefore, it is critically important to be able to address the uncertainty using a few geological models, which can reasonably represent the overall uncertainty of the ensemble. Our goal is to design and develop a visual analytics framework to filter the geological models and to only select models that can potentially cover the uncertain space. This framework is based on the mutual information for the calculation of the distance between the models and clustering for the grouping of similar models. Interactive visualization tasks have also been designed to make the whole process more understandable. Finally, we evaluated our results by comparing with the existent brute force approach.

Geologically Consistent History Matching of SAGD Process Using Probability Perturbation Method

The overall objective of reservoir modeling is to reduce the uncertainty in the production forecasts by utilizing all available data to construct a calibrated reservoir model. Geological heterogeneities have a fundamental impact on the growth of the steam chamber and the performance of the SAGD. The objective of this work is to incorporate the geological heterogeneities into the history matching process using probability perturbation method (PPM) to preserve the geological consistency of the reservoir model.

Efficient Multi-Objective History-Matching Using Gaussian Processes

In a multiobjective optimization approach, a trade-off is sought to balance between the optimality of different objectives. In this paper, we introduce a new efficient multiobjective optimization approach using sequential Gaussian Process (GP) modeling that can quickly find the Pareto solutions in a minimal number of model evaluations. This is the first time that we present this approach for history-matching. The difference with other optimization algorithms is elucidated for the cases where we can only afford to run a limited number of simulations. Unlike other surrogate-based methods, we do not aim for a greedy approach by minimizing the surface itself as there can be a large uncertainty in the surrogate approximations. Instead, statistical criteria are introduced to account for both proxy model uncertainty as well as its extrema. This multiobjective optimization approach has been successfully applied for the first time to history match the production data (i.e. pressure, water and hydrocarbon rates) from a multi-fractured horizontal well in a tight formation. A GP surface is constructed for each misfit, to provide the predictions and the associated uncertainty for any unknown location. Multiobjective criteria, i.e., the hypervolume-based Probability of Improvement (PoI) and Expected Improvement (EI), are developed to account for the uncertainty of the misfit surfaces. The maximization of these statistical criteria ensures to balance between exploration and exploitation, even in higher dimensions. As such, a new point is selected whose values in different objectives are predicted to hopefully extend or dominate the solutions in the current Pareto set.

The Ability of Multiple-Point Geostatistics for Modelling Complex Fracture Networks in Tight and Shale Reservoirs

Fracturing horizontal wells is an important technology that can make production from tight and shale formations economical. The fractured tight and shale formations are recognized by complex fracture networks around the primary hydraulic fractures. Microseismic mapping is a technique which can shed light on the activities happen around the main fractures which can direct us towards the extent of the fracture half-length and the secondary fracture networks in the stimulated reservoir volume (SRV). However, microseismic mapping does not necessarily indicate if the observed events can be directly related to the increased conductivities around the wellbore. There is rather a large uncertainty about the interpretation of the extent of effective (reopened) fracture network which can have a large impact on the performance of the flow simulations. In this paper, a quantitative workflow is attempted to model the discrete fracture networks using multiple-point geostatistical algorithms to account for the uncertainty in the interpretation of the microseismic events. Uncertainty in microseismic data interpretation is also included in the algorithm (in terms of secondary probability maps) to account for the variability in the extent of the discrete fracture network within the stimulated reservoir volume (SRV). A sensitivity study is performed to understand the effect of different parameters on the well flow performance given different fracture network models. The results show that the connectivity of the fracture networks generated by the MPS method in this study is rather poor. Consequently, the permeability of the natural fractures has a dominant effect on the flow performance. In fact, the poor connectivity of fracture network does not allow to observe the effect of porosity of natural fracture and the permeability of hydraulic fracture on the flow performance. This research restresses that the MPS algorithm is not a push-a-button method to always generate reliable realizations. This work provides a guideline to better screen the generated geostatistical realization.