We suggest alternative objective functions based on the concept of thermoeconomics (or exergoeconomics) that could be used for simultaneous maximization of economics and energy efficiency of oil-production systems. The suggested functions are evaluated for an oil reservoir, where water is injected to improve its recovery factor. We find that life-cycle optimization of water-injection projects in terms of net present value (NPV) and net cumulative exergy (NCE) leads to consistent results. We show that managing reservoirs based on a long-term objective leads to significant reduction in their CO₂ footprint. For oil production by water injection, commitment to reduce CO₂ emission provides an opportunity to maximize the NPV of these projects. The sustainability of water injection into hydrocarbon reservoirs is highly dependent on the volumes of the injected and produced liquids. Above a critical water cut (80% in this study), the energy efficiency of the project decreases dramatically, and its CO₂ footprint increases exponentially.

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A potential solution to mitigate the adverse effects of viscous fingering, gravity override, and reservoir heterogeneity on the efficiency of gas injection in porous media is to inject the gas with a solution containing surface-active agents such as surfactants or nanoparticles. The efficiency of these processes largely depends on the generation and stability of the lamellae residing in the pores, both of which are influenced by the physicochemical properties of the rock and the surfactant solution. This study investigates the effect of surfactant concentration on the transient and steady-state behaviors of foam in porous media. It is found that the rate of foam generation is affected by the surfactant concentration, i.e., the transition from coarse-textured to fine-textured (strong) foam occurs earlier with the increasing surfactant concentration. However, when a sufficient amount of the surfactant is injected, strong foam is generated even with a very low surfactant concentration in the low-quality regime. Furthermore, because foam stability is governed by the limiting capillary pressure in the high-quality regime, the steady-state pressure behavior of foam (or foam strength) in this regime is significantly impacted by the surfactant concentration. We find that the current (equilibrium or steady-state) foam models cannot mimic the observed behavior in our experiments because it scales both high-and low-quality regimes with the surfactant concentration. Consequently, modifications are suggested to overcome the shortcomings of the model.@en

A potential solution to mitigate the adverse effects of viscous fingering, gravity override, and reservoir heterogeneity on the efficiency of gas injection in porous media is to inject the gas with a solution containing surface-active agents such as surfactants or nanoparticles. The efficiency of these processes largely depends on the generation and stability of the lamellae residing in the pores, both of which are influenced by the physicochemical properties of the rock and surfactant solution. In this study, the effect of surfactant concentration on the transient and steady-state foam behavior in porous media was investigated. Several core flood experiments were conducted, in which the nitrogen gas and surfactant solutions with different concentrations were simultaneously injected into a Bentheimer sandstone core. Moreover, the ability of the current foam models in simulating the effect of surfactant concentration was examined and modifications were suggested accordingly. @en

Foam can be used for gas mobility control in different subsurface applications. The success of foam-injection process depends on foam-generation and propagation rate inside the porous medium. In some cases, foam properties depend on the history of the flow or concentration of the surfactant, i.e., the hysteresis effect. Foam may show hysteresis behavior by exhibiting multiple states at the same injection conditions, where coarse-textured foam is converted into strong foam with fine texture at a critical injection velocity or pressure gradient. This study aims to investigate the effects of injection velocity and surfactant concentration on foam generation and hysteresis behavior as a function of foam quality. We find that the transition from coarse-foam to strong-foam (i.e., the minimum pressure gradient for foam generation) is almost independent of flowrate, surfactant concentration, and foam quality. Moreover, the hysteresis behavior in foam generation occurs only at high-quality regimes and when the pressure gradient is below a certain value regardless of the total flow rate and surfactant concentration. We also observe that the rheological behavior of foam is strongly dependent on liquid velocity.

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Foam can potentially solve the associated problems with gas injection by reducing the mobility of the injected gas leading to a more stable displacement front. It is known that under immiscible conditions, the presence of oil can be detrimental for foam stability through several mechanisms. Under miscible conditions, there is no separate oil or gas phase; instead, CO2 and oil mix in different proportions forming a phase with varying composition at the proximity of the displacement front. There are then two fundamental questions, which arise from addition of surfactant to the system: (1) what is the nature of the “mixed phase” in the presence of the surfactant, and (2) how do the properties of this mixture change with compositional variations? This study reports the results of core-flood experiments conducted using CO2 and decane (nC10) as the model oil under miscible conditions. Surfactant and a mixture of CO2-decane were co-injected with variations of CO2 molar fractions, mixture volume fractions and total flow rates. We found that separate injection of CO2 or oil with the surfactant solution into the cores creates in-situ fluids that exhibit both low-quality (increasing viscosity with decreasing fraction of surfactant) and high-quality (decreasing viscosity with decreasing fraction of surfactant) regimes. However, upon simultaneous injection of CO2 and oil with the surfactant solution and depending on the molar fraction of CO2 in CO2- decane mixture (xCO2), three distinct regimes were observed. In Regime 1 (xCO2>0.8) the apparent viscosity of the in-situ fluid was the highest and increased with increasing xCO2. In Regime 2 (xCO2<2) the apparent viscosity increased with decreasing xCO2. In Regime 3 (0.2< xCO2<0.8) the apparent viscosity of the fluid remained relatively low and insensitive to the value of xCO2. Shear-thinning rheology was observed in all three regimes: supercritical CO2 foam (xCO2 =1), decane emulsion (xCO2 = 0), as well as CO2-decane-surfactant floods. Moreover, in Regime 1 and Regime 2, there is a transition at shear rates from 10 s-1 to 100 s-1, where the apparent viscosity increases by one order of magnitude. In Regime 3, however, this transition is not observed. Finally, we found that the current implicit-texture foam model cannot simulate our experimental data. @en

Gas injection was introduced to the petroleum industry in the early 1950s. Nevertheless, the process efficiency is impacted by the low density and viscosity of the gas, which decrease sweep efficiency. Foam for Enhanced Oil Recovery (EOR) can overcome the downside of the viscous fingering by increasing the apparent viscosity of the Foam EOR improves the sweep efficiency by reducing gas mobility and creating a stable displacement front. In the field application, the surfactant concentration and flow rate vary in the reservoir, influencing dramatically the foam mobility. However, the variations of surfactant concentration and flow rate do not relate monotonously to the foam properties. In some cases, the foam properties depends on the history of the flow, i.e., a hysteresis effect. But hysteresis in foam flood has not been well characterized and understood. This study aims to understand hysteresis behavior of foam in porous media. To this end two series of experiments have been conducted: 1) Hysteresis behavior due to flow rate variations and 2) Hysteresis behavior due to surfactant concentration variations. In the flow rate experiments, several shear-thinning experiments at different volume fractions of gas (foam quality) are conducted in order to understand the effect of gas fraction and total velocity on foam generation mechanisms. In the surfactant concentration experiment, experiments have been performed at different surfactant concentrations and at different volume fractions of gas (foam quality). Results showed that a transition from weak to strong foam is more pronounced in high-quality regimes (gas fractional flow above 90%) than low-quality regimes (gas fractional flow below 80%). Remarkably, no hysteresis behavior has been observed in low-quality regimes, while hysteresis behavior occurred in high quality regimes. Furthermore, the effect of surfactant concentration on hysteresis behavior has been also investigated at high- and low-quality regimes. Contrary to some previous works, hysteresis behavior does not occur for surfactant variation. Remarkably, the apparent viscosity remains almost constant in lowquality regime for different surfactant concentrations. These results have important implications of the injection strategy and the economics of foam EOR. The surfactant concentration could be decreased and less gas could be injected, and in the same time, the foam performance could be maintained. gas. Importantly, the structure of the foam evolves with time due to gas diffusion between bubbles (coarsening). In a bulk foam, the coarsening behaviour is well defined, but there is a lack of understanding of coarsening behaviour in confined geometries, especially in porous media. Nonnekes et al [2014] predicted numerically and analytically that coarsening will cause the foam lamellae to move to low energy configurations in the pore throats, resulting in greater capillary resistance when trying to restart flow. This study describes foam coarsening in a porous medium and the implications for foam propagation. Foam coarsening experiments have been conducted in both a micromodel and in a rock core. The micromodel is etched with an irregular hexagonal pattern, with a Gaussian distribution of pore diameters. Foam was generated by coinjecting surfactant solution and nitrogen gas into the micromodel. Once steady state flow had been achieved, the flow was stopped. The coarsening behaviour of the foam was recorded using time-lapse photography. The core flood coarsening experiments were carried out using a Bentheimer Sandstone core. Foam was produced by coinjecting surfactant solution and nitrogen at the base of the core. Once a steady state flow was achieved, the flow was stopped and the core sealed off. When flow restarted, the additional driving pressure required to reinitiate flow was measured, and this could be attributed to the stable configuration of the coarsened foam. The microfluidic results found that the bubbles coarsened rapidly (t < 10 minutes) to the size of the pores. At the completion of coarsening the majority of the lamellae were located in the pore throats with minimum length. Because of the effect of the walls, the behaviour did not conform to the unconstricted coarsening growth laws. Furthermore, results on coreflood showed that coarsening is a rapid process, in agreement with microfluidic results. An increase in the additional pressure required to re-initiate flow was observed for the first 1 – 5 minutes of flow stoppages, while the pressure peaks did not increase for durations above 5 min. The implications of this behaviour for the field scale are also discussed. @en

Classic identifiability analysis of flow barriers in incompressible single-phase flow reveals that it is not possible to identify the location and permeability of low-permeability barriers from production data (wellbore pressures and rates), and that only averaged reservoir properties in between wells can be identified. We extend the classic analysis by including compressibility effects. We use two approaches: a twin experiment with synthetic production data for use with a time-domain parameter-estimation technique, and a transfer-function formalism in the form of bilaterally coupled four-ports allowing for an analysis in the frequency domain. We investigate the identifiability, from noisy production data, of the location and the magnitude of a low-permeability barrier to slightly compressible flow in a 1D configuration. We use an unregularized adjoint-based optimization scheme for the numerical time-domain estimation, by use of various levels of sensor noise, and confirm the results by use of the semianalytical transfer-function approach. Both the numerical and semianalytical results show that it is possible to identify the location and the magnitude of the permeability in the barrier from noise-free data. By introducing increasingly higher noise levels, the identifiability gradually deteriorates, but the location of the barrier remains identifiable for much-higher noise levels than the permeability. The shape of the objective-function surface, in normalized variables, indeed indicates a much-higher sensitivity of the well data to the location of the barrier than to its magnitude. These theoretical results appear to support the empirical finding that unregularized gradient-based history matching in large reservoir models, which is well-known to be a severely ill-posed problem, occasionally leads to useful results in the form of model-parameter updates with unrealistic magnitudes but indicating the correct location of model deficiencies.@en

We present a method to determine lower and upper bounds to the predicted production or any other economic objective from history-matched reservoir models. The method consists of two steps: 1) performing a traditional computer-assisted history match of a reservoir model with the objective to minimize the mismatch between predicted and observed production data through adjusting the grid block permeability values of the model. 2) performing two optimization exercises to minimize and maximize an economic objective over the remaining field life, for a fixed production strategy, by manipulating the same grid block permeabilities, however without significantly changing the mismatch obtained under step 1. This is accomplished through a hierarchical optimization procedure that limits the solution space of a secondary optimization problem to the (approximate) null space of the primary optimization problem. We applied this procedure to two different reservoir models. We performed a history match based on synthetic data, starting from a uniform prior and using a gradient-based minimization procedure. After history matching, minimization and maximization of the net present value (NPV), using a fixed control strategy, were executed as secondary optimization problems by changing the model parameters while staying close to the null space of the primary optimization problem. In other words, we optimized the secondary objective functions, while requiring that optimality of the primary objective (a good history match) was preserved. This method therefore provides a way to quantify the economic consequences of the well-known problem that history matching is a strongly ill-posed problem. We also investigated how this method can be used as a means to assess the cost-effectiveness of acquiring different data types to reduce the uncertainty in the expected NPV.@en

With an increase in the number of applications of ensemble optimization (EnOpt) for production optimization, the theoretical understanding of the gradient quality has received little attention. An important factor that influences the quality of the gradient estimate is the number of samples. In this study we use principles from statistical hypothesis testing to quantify the number of samples needed to estimate an ensemble gradient that is comparable in quality to an accurate adjoint gradient. We develop a methodology to estimate the necessary ensemble size to obtain an approximate gradient that is within a predefined angle compared to the adjoint gradient, with a predefined statistical confidence. The method is first applied to the Rosenbrock function (a standard optimization test problem), for a single realization, and subsequently for a case with uncertainty, represented by multiple realizations (robust optimization). The maximum allowed error applied in both experiments is a 10° angle between the directions of the EnOpt gradient and the exact gradient. For the single-realization case we need, depending on the perturbation size, 900, 5 and 3 samples to estimate a "good" gradient with 95% confidence at 50 points in the optimization space for 50 different random sequences. For the robust case, the conventional EnOpt approach is to couple one model realization with one control sample, which leads to a computationally efficient technique to estimate a mean gradient. However, our results show that in order to be 95% confident the original one-to-one model realization to control sample ratio formulation is not sufficient. To achieve the required confidence requires a ratio of 1:1100, i.e. each model realization is paired with 1100 control samples using the original formulation. However, using a modified formulation we need a ratio of 1:10 to stay within the maximum allowed error for 95% of the points in space, though a 1:1 ratio is sufficient for 85% of the points. We also tested our methodology on a reservoir case for deterministic and robust cases, where we observe similar trends in the results. Our results provide insight into the necessary number of samples required for EnOpt, in particular for robust optimization, to achieve a gradient comparable to an adjoint gradient.@en