In this study for the first time we generalize streamline models to compressible flow using a rigorous formulation while retaining most of its computational advantages. Our new formulation is based on three major elements and requires only minor modifications to existing streamline models. First, we introduce a relative density for the total fluids along the streamlines. This density captures the changes in the fluid volume with pressure and can be conveniently and efficiently traced along streamlines. Thus, we simultaneously compute time of flight and volume changes along streamlines. Second, we incorporate a density-dependent source term in the streamline saturation/composition conservation equation to account for compressibility effects. Third, the relative density, fluid volumes and the time-of-flight information are used to incorporate cross-streamline effects via pressure updates and remapping of saturations. Our proposed approach preserves the 1-D nature of the conservation calculations and all the associated advantages of the streamline approach. The conservation calculations are fully decoupled from the underlying grid and can be carried out using large time steps without gridbased stability limits. We also extend the streamline simulation to compositional modeling including compressibility effects. Given the favorable computational scaling properties of streamline models, the potential advantage for compositional simulation can be even more compelling. Although several papers have discussed compositional simulation formulation, they all suffer from a major limitation, particularly for compressible flow. All of the previous works assume, either explicitly or implicitly, that the divergence of total flux along streamlines is negligible. This is not only incorrect for compressible flow but also introduces inconsistency between the pressure and conservation equations. We examine the implications of these assumptions on the accuracy of compositional streamline simulation using a novel and rigorous treatment of compressibility. We demonstrated the validity and practical utility of our approach using synthetic and field examples and comparison with a finite difference simulator. Throughout the validation for compositional model, we found out the importance of finer segments discretizations along streamlines. We introduce optimal coarsening of segments to minimize flash calculations on each segment while keeping the accuracy of finer segments.

Since oil and gas production from conventional fields is decreasing, the produc-tion of unconventional hydrocarbon reservoirs is becoming imperative, where geo-mechanical responses play an important role. This research presents a methodology that starts exploring the inclusion of geomechanics in streamline simulations using a two-way explicit coupling approach between a reservoir and geomechanical simulators. This was done in an effort of conducting field-scale simulations considering the impact of geomechanical parame-ters on reservoir static properties, which affect ultimate recovery. Porosity, permeability, and porosity and permeability were used as the coupling parameters; the influence that they have on the process is problem-dependant as well. The results obtained from the two study cases presented, reveal that the per-formance of the approach is problem-dependent; the more complex the models are, the larger the geomechanical response is. One of the main aspects of this study was the limitations of the simulators. When software and hardware capacities improve, so will the results of the coupling ap-proach. Until then, more complex models should be tested, as well as more rigorous techniques, to improve the results presented here. / Petroleum Engineering

Streamline simulators have received increased attention because of their ability to effectively handle multimillion cell detailed geologic models and large simulation models. The efficiency of streamline simulation has relied primarily on their ability to take large timesteps with fewer pressure solutions within an IMPES formulation. However, unlike conventional finite-difference simulators, no clear guidelines are currently available for the choice of timestep for pressure and velocity updates. That is why we need largely an uncontrolled approximation, either managed by engineering judgment or by potentially time-consuming timestep size sensitivity studies early in a project. This will clearly lead us to the lack of understanding of numerical stability and error estimates during the solution. This research presents a novel approach for timestep selection during streamline simulation that is based on three elements. First, we reformulate the equations to be solved by a streamline simulator to include all of the three-dimensional flux terms - both aligned with and transverse to the flow directions. These transverse flux terms are totally neglected within the existing streamline simulation formulations. Second, we propose a simple grid-based corrector algorithm to update the saturation to account for the transverse flux. Third, we provide a discrete CFL (Courant-Friedrich-Levy) formulation for the corrector step that leads to a mechanism to ensure numerical stability via the choice of a stable timestep for pressure updates. This discrete CFL formulation now provides us with the same tools for timestep control as are available within conventional reservoir simulators. We demonstrate the validity and utility of our approach using a series of numerical experiments in homogeneous and heterogeneous ¼ five-spot patterns at various mobility ratios. For these numerical experiments, we pay particular attention to favorable mobility ratio displacements, as they are known to be challenging to streamline simulation. Our results clearly demonstrate the impact of the transverse flux correction on the accuracy of the solution and on the appropriate choice of timestep, across a range of mobility ratios. The proposed approach eliminates much of the subjectivity associated with streamline simulation, and provides a basis for automatic control of pressure timestep within full field streamline applications.

Nowadays, field development strategy has become increasingly dependent on the results of reservoir simulation models. Reservoir studies demand fast and efficient results to make investment decisions that require a reasonable trade off between accuracy and simulation time. One of the suitable options to fulfill this requirement is streamline reservoir simulation technology, which has become very popular in the last few years. Streamline (SL) simulation provides an attractive alternative to conventional reservoir simulation because SL offers high computational efficiency and minimizes numerical diffusion and grid orientation effects. However, streamline methods have weaknesses incorporating complex physical processes and can also suffer numerical accuracy problems. The main objective of this research is to evaluate the numerical accuracy of the latest SL technology, and examine the influence of different factors that may impact the solution of SL simulation models. An extensive number of numerical experiments based on sensitivity analysis were performed to determine the effects of various influential elements on the stability and results of the solution. Those experiments were applied to various models to identify the impact of factors such as mobility ratios, mapping of saturation methods, number of streamlines, time step sizes, and gravity effects. This study provides a detailed investigation of some fundamental issues that are currently unresolved in streamline simulation.

Integrated reservoir modeling has become an important part of day-to-day decision analysis in oil and gas management practices. A very attractive and promising technology is the use of time-lapse or 4D seismic as an essential component in subsurface modeling. Today, 4D seismic is enabling oil companies to optimize production and increase recovery through monitoring fluid movements throughout the reservoir. 4D seismic advances are also being driven by an increased need by the petroleum engineering community to become more quantitative and accurate in our ability to monitor reservoir processes. Qualitative interpretations of time-lapse anomalies are being replaced by quantitative inversions of 4D seismic data to produce accurate maps of fluid saturations, pore pressure, temperature, among others. Within all steps involved in this subsurface modeling process, the most demanding one is integrating the geologic model with dynamic field data, including 4Dseismic when available. The validation of the geologic model with observed dynamic data is accomplished through a "history matching" (HM) process typically carried out with well-based measurements. Due to low resolution of production data, the validation process is severely limited in its reservoir areal coverage, compromising the quality of the model and any subsequent predictive exercise. This research will aim to provide a novel history matching approach that can use information from high-resolution seismic data to supplement the areally sparse production data. The proposed approach will utilize streamline-derived sensitivities as means of relating the forward model performance with the prior geologic model. The essential ideas underlying this approach are similar to those used for high-frequency approximations in seismic wave propagation. In both cases, this leads to solutions that are defined along "streamlines" (fluid flow), or "rays" (seismic wave propagation). Synthetic and field data examples will be used extensively to demonstrate the value and contribution of this work. Our results show that the problem of non-uniqueness in this complex history matching problem is greatly reduced when constraints in the form of saturation maps from spatially closely sampled seismic data are included. Further on, our methodology can be used to quickly identify discrepancies between static and dynamic modeling. Reducing this gap will ensure robust and reliable models leading to accurate predictions and ultimately an optimum hydrocarbon extraction.

Geologic models derived from static data alone typically fail to reproduce the production history of a reservoir, thus the importance of reconciling simulation models to the dynamic response of the reservoir. This necessity has been the motivation behind the active research work in history matching. Traditionally, history matching is performed manually by applying local and regional changes to reservoir properties. While this is still in general practice, the subjective overtone of this approach, the time and manpower requirements, and the potential loss of geologic consistency have led to the development of a variety of alternative workflows for assisted and automatic history matching. Automatic history matching requires the solution of an inverse problem by minimizing an appropriately defined misfit function. Recent advances in geostatistics have led to the building of high-resolution geologic models consisting of millions of cells. Most of these are scaled up to the submillion size for reservoir simulation purposes. History matching even the scaled up models is computationally prohibitive. The associated cost in terms of time and manpower has led to increased interest in efficient history matching techniques and in particular, to sensitivity-based algorithms because of their rapid convergence. Furthermore, of the sensitivity-based methods, streamline-based production data integration has proven to be extremely efficient computationally. In this work, we extend the history matching capability of the streamline-based technique to three-phase production while addressing in general, pertinent issues associated with history matching. We deviate from the typical approach of formulating the inverse problem in terms of derived quantities such as GOR and Watercut, or measured phase rates, but concentrate on the fundamental variables that characterize such quantities. The presented formulation is in terms of well node saturations and pressures. Production data is transformed to composite saturation quantities, the time variation of which is matched in the calibration exercise. The dependence of the transformation on pressure highlights its importance and thus a need for pressure match. To address this need, we follow a low frequency asymptotic formulation for the pressure equation. We propose a simultaneous inversion of the saturation and pressure components to account for the interdependence and thus, high non-linearity of three phase inversion. We also account for global parameters through experimental design methodology and response surface modeling. The validity of the proposed history matching technique is demonstrated through application to both synthetic and field cases.

Formation testing is a critical component of modern petrophysical analysis for determining pore pressure, pressure gradients, and reservoir connectivity, and for estimating static and dynamic formation properties. However, petrophysicists tend to avoid the analysis of transient formation-tester measurements because of the physical and mathematical complexities involved, including time-consuming numerical simulations, rock heterogeneity, anisotropy, presence of mud-filtrate invasion, and saturation-dependent properties. Additional technical challenges arise when modeling formation-tester measurements in heterogeneous reservoirs penetrated by high-angle wells. A new method is developed in this dissertation to efficiently simulate formation-tester measurements acquired in heterogeneous reservoirs penetrated by vertical and deviated wells. The method is based on tracing flow streamlines from the reservoir into the formation tester’s probe. Before tracing streamlines, an initial reservoir condition is imposed due to the pressure-saturation field resulting from mud-filtrate invasion. Subsequently, the spatial distribution of pressure is calculated via finite differences to account for the negative flow-rate source originating from the tester’s probe. Streamlines are retraced at various time intervals upon updating the pressure distribution resulting from dynamic fluid flow toward the source. The streamline-based simulation method is efficient and flexible in accounting for various probe configurations, including dual packers and point focused-sampling probes. Streamlines are also used to trace reservoir fluid and contamination into sample probes. In addition, graphical rendering of streamlines permits rapid assessment of flow regimes as a function of time. Simulation results obtained with finite-difference and streamline methods agree well, although the streamline-based method is computationally more efficient. However, the streamline method is not well suited for complicated fluid displacement, such as that arising in the presence of highly compressible flow, strong capillary-pressure effects, and variable phase behavior. Furthermore, criteria for enforcing pressure updates with finite differences raise additional difficulties in accurately modeling formation-tester measurements. Despite these limitations, forward simulation results indicate that both faster computation time and reduced computer-memory requirements resulting from use of the streamline-based method are ideal for inversion of formation-tester measurements used in estimating static and dynamic petrophysical properties. Synthetic and field examples of streamline-based inversion are considered to estimate petrophysical properties from transient data acquired with packer and probe-type formation testers. The method is applied to measurements acquired in two offshore field reservoirs penetrated by vertical and deviated wells to estimate permeability, anisotropy, and relative permeability. In the documented examples, each streamline-based simulation used to calculate the Jacobian matrix is up to 8.7 times faster than that obtained by using the finite-difference method. Inversion results also indicate that streamline trajectories are valuable in ascertaining the sensitivity of estimated formation properties in the presence of variable pressure/fluid sampling locations, variable wellbore orientations with respect to formation bedding, and reservoir heterogeneity in deviated and horizontal well models. / text

Streamline simulators have received increased attention because of their ability to effectively handle multimillion cell detailed geologic models and large simulation models. The efficiency of streamline simulation has relied primarily on their ability to take large timesteps with fewer pressure solutions within an IMPES formulation. However, unlike conventional finite-difference simulators, no clear guidelines are currently available for the choice of timestep for pressure and velocity updates. That is why we need largely an uncontrolled approximation, either managed by engineering judgment or by potentially time-consuming timestep size sensitivity studies early in a project. This will clearly lead us to the lack of understanding of numerical stability and error estimates during the solution. This research presents a novel approach for timestep selection during streamline simulation that is based on three elements. First, we reformulate the equations to be solved by a streamline simulator to include all of the three-dimensional flux terms - both aligned with and transverse to the flow directions. These transverse flux terms are totally neglected within the existing streamline simulation formulations. Second, we propose a simple grid-based corrector algorithm to update the saturation to account for the transverse flux. Third, we provide a discrete CFL (Courant-Friedrich-Levy) formulation for the corrector step that leads to a mechanism to ensure numerical stability via the choice of a stable timestep for pressure updates. This discrete CFL formulation now provides us with the same tools for timestep control as are available within conventional reservoir simulators. We demonstrate the validity and utility of our approach using a series of numerical experiments in homogeneous and heterogeneous ¼ five-spot patterns at various mobility ratios. For these numerical experiments, we pay particular attention to favorable mobility ratio displacements, as they are known to be challenging to streamline simulation. Our results clearly demonstrate the impact of the transverse flux correction on the accuracy of the solution and on the appropriate choice of timestep, across a range of mobility ratios. The proposed approach eliminates much of the subjectivity associated with streamline simulation, and provides a basis for automatic control of pressure timestep within full field streamline applications.

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