Chen, Chaohui (Shell International Exploration and Production Company) | Gao, Guohua (Shell Global Solutions US Incorporated) | Li, Ruijian (Shell Exploration and Production Company) | Cao, Richard (Shell Exploration and Production Company) | Chen, Tianhong (Shell Exploration and Production Company) | Vink, Jeroen C. (Shell Global Solutions International) | Gelderblom, Paul (Shell Global Solutions International)
Although it is possible to apply traditional optimization algorithms together with the randomized-maximum-likelihood (RML) method to generate multiple conditional realizations, the computation cost is high. This paper presents a novel method to enhance the global-search capability of the distributed-Gauss-Newton (DGN) optimization method and integrates it with the RML method to generate multiple realizations conditioned to production data synchronously.
RML generates samples from an approximate posterior by minimizing a large ensemble of perturbed objective functions in which the observed data and prior mean values of uncertain model parameters have been perturbed with Gaussian noise. Rather than performing these minimizations in isolation using large sets of simulations to evaluate the finite-difference approximations of the gradients used to optimize each perturbed realization, we use a concurrent implementation in which simulation results are shared among different minimization tasks whenever these results are helping to converge to the global minimum of a specific minimization task. To improve sharing of results, we relax the accuracy of the finite-difference approximations for the gradients with more widely spaced simulation results. To avoid trapping in local optima, a novel method to enhance the global-search capability of the DGN algorithm is developed and integrated seamlessly with the RML formulation. In this way, we can improve the quality of RML conditional realizations that sample the approximate posterior.
The proposed work flow is first validated with a toy problem and then applied to a real-field unconventional asset. Numerical results indicate that the new method is very efficient compared with traditional methods. Hundreds of data-conditioned realizations can be generated in parallel within 20 to 40 iterations. The computational cost (central-processing-unit usage) is reduced significantly compared with the traditional RML approach.
The real-field case studies involve a history-matching study to generate history-matched realizations with the proposed method and an uncertainty quantification of production forecasting using those conditioned models. All conditioned models generate production forecasts that are consistent with real-production data in both the history-matching period and the blind-test period. Therefore, the new approach can enhance the confidence level of the estimated-ultimate-recovery (EUR) assessment using production-forecasting results generated from all conditional realizations, resulting in significant business impact.
Surfactant-mediated enhanced-oil-recovery (EOR) techniques, such as surfactant/polymer (SP) flooding, have received increased attention because of their ability to reduce capillary forces at the pore-scale to ultralow values and mobilize trapped oil. Recently, there have been increased efforts in microemulsion-phase-behavior modeling capabilities by relying on the hydrophilic/lipophilic-difference (HLD) measure for surfactant-affinity quantification. One common assumption of most microemulsion-phase-behavior models is the assumption of pure excess phases, which states that the surfactant component is only present in the microemulsion phase. This assumption can lead to significant errors for some surfactant systems, especially when applied to chemical simulations in which discontinuities may arise.
The main novelty of this paper is to allow for surfactant partitioning into both the water and oil excess phases by use of a simple approach, and then relate relevant surfactant-partitioning coefficients (i.e., K-values) to HLD. Surfactant screening that is based on surfactant-structure parameters is also considered based on estimated K-values. Key dimensionless groups are identified as a function of activity coefficients, which allow for a simplified description of the surfactant-partition coefficients. These surfactant-partition coefficients are combined with the chemical-potentials (CP) equation-of-state (EoS) model to describe and predict the phase behavior when the excess phases are not pure. Further, the developed surfactant-partitioning model can be used in other microemulsion-phase-behavior models to allow for impure excess phases.
Accumulation of oil and/or water at the bottom of an upward-inclined pipe is known to be the source of many industrial problems, such as corrosion and terrain slugging. Therefore, accurate prediction of the critical gas velocity that can avoid the liquid accumulation is of great importance.
An experimental study of onset of liquid-film reversal, which is believed to be the main cause of liquid accumulation, was conducted in a hilly-valley test section at low-liquid-loading condition. A new, easily implemented mechanistic model to predict critical gas velocity, which is specifically developed based on the liquid-film reversal in stratified flow, is proposed in this work. The new model was verified with the data acquired in the study and other studies from the open literature, showing a fair agreement. This work also reviewed and evaluated other critical-gas-velocity-prediction models. The new model performs best compared with other models, especially in terms of the inclination angle and liquid-flow-rate effect on critical gas velocity. The total average absolute error was reduced 6.0% compared with the current best-prediction model (Zhang et al. 2003), and 38.2% for the widely used Turner et al. (1969) droplet-removal model.
This paper presents results of an experimental study on how fluid viscoelastic properties would influence the particle removal from the sandbed deposited in horizontal annuli. Water and two different viscoelastic fluids were used for bed-erosion experiments. The particle-image-velocimetry (PIV) technique was used to measure the local fluid velocity at the fluid/sandbed interface, allowing for accurate estimation of the fluid-drag forces and the turbulence stresses.
It was found that polymer fluids needed to exert higher level drag forces (than those of water) on the sandbed to start movement of the particles. Results have also shown that, at the critical flow rate of bed erosion, the polymer fluids yielded higher local fluid velocities and turbulent stresses than those of water. Moreover, the local velocity measurements by means of the PIV technique and the resultant bed-shear-stress calculations indicated that enhancing polymer concentration under the constant flow rate should also enhance the drag forces acting on the sandbed. However, these improved fluid hydrodynamic forces did not result in any improvement in the bed erosion. Therefore, the mechanism causing the delay in the bed erosion by polymer additives could not be explained by any decrease in the local fluid velocity and the turbulence.
The primary reason for the delayed bed erosion by the polymer fluids was suggested to be linked to their viscoelastic properties. Two possible mechanisms arising from the elastic properties of the polymer fluids that hinder bed erosion were further discussed in the paper. The stress tensor of the viscoelastic-fluid flow was analyzed to determine the normal stress differences and the resultant normal fluid force acting on the particles at the fluid/sandbed interface. The normal force induced by the normal stress differences of the viscoelastic fluid was identified as one of the possible causes of the delayed bed erosion by these types of fluids.
An experimental study was conducted to investigate turbulent flow of water over a cuttings bed by use of a large-scale horizontal-flow loop. A nonintrusive laser-based-imaging technique was used to determine instantaneous local velocity near the stationary sandbed/fluid interface in the horizontal annulus. The velocity measured directly at the sandbed/fluid interface was then used for critical evaluation of the accuracy of the assumptions and correlations commonly used for development of mechanistic and semimechanistic sediment-transport models. In particular, effects of turbulent velocity fluctuations on the magnitude of the hydrodynamic drag and lift forces and the interfacial (bed) shear stress are investigated.
An expression is analytically presented for the shear dispersion, or Taylor (1953) and Aris (1956) dispersion, of a solute transporting in a coupled system, which consists of a matrix and a rough-walled fracture. To derive a shear-dispersion coefficient in a fracture with rough and porous walls, the continuities of solute concentrations and their fluxes are imposed at the fracture walls. The dispersion coefficient for the coupled system is obtained as a function of the Péclet number and relative roughness, where the latter parameter is defined as the ratio of the maximum height of the roughness to the minimum half-aperture of the fracture. Several models for fracture-roughness geometry, including periodically and randomly shaped roughness models, are applied to study the effect of fracture-aperture variation on dispersion. The dispersion coefficient for all rough-walled fractures identifies three different regions in terms of the degree of relative roughness. The results show that for small values of the relative roughness (0 < ε ≤ 0.1), the dispersion coefficient is at maximum for bell-shaped geometry and at minimum for triangular-shaped and randomly shaped geometries. When the relative roughness is within 0.1 < ε < 10, the dispersion is observed to be at maximum for rectangular-walled and at minimum for triangular-walled fractures. The results also reveal that for high values of the relative roughness (ε ≥ 10), the dispersion is higher for bell-shaped roughness, whereas the triangular-walled fracture results in the lowest dispersion. It is found that for all roughness geometries an increase in either the Péclet number or relative roughness leads to an increase in the dispersion.
A new concept is proposed in the local tubular mechanical model, which provides a more-sophisticated description of tubular mechanical behaviors from a local perspective. The principles and assumptions for the local mechanical model are presented. Under these assumptions, the mechanical behaviors of tubular strings with connectors under nonbuckling/lateral-buckling, interhelical-buckling, and intrahelical-buckling modes in vertical and inclined wellbores are studied. The critical interhelical-buckling and intrahelical-buckling loads are deduced with the assumed load-displacement curve and potential-energy factor. The contact states under every buckling mode are divided into no contact, point contact, and wrap contact, and the critical contact loads are deduced with critical contact conditions. The results of critical buckling loads, critical contact loads, contact forces, and maximum bending moments are compared, and these results are given in explicit forms for the convenience of application. The results show that buckling mode transforms from nonbuckling/lateral buckling to interhelical buckling to intrahelical buckling, and contact state transforms from no contact to point contact to wrap contact with the increase of axial force. The effects of connectors on buckling behaviors are determined by both the geometric and mechanical parameters of tubular strings with connectors. Connectors can inhibit the buckling problem and increase the axial force and torque transfer, but may increase the possibility of tubular failure. Therefore, these two effects of connectors should be considered comprehensively in the optimal design of connectors on tubular strings.
The study presented here uses order-of-one—or o(1)—scaling analysis to identify dimensionless groups specific to asphaltene deposition along production tubing. The precipitation and subsequent deposition of asphaltene can lead to significant complications related to oilfield production. Aside from the many complications within a reservoir as well as surface equipment, the reduction in cross-sectional area caused by its deposition leads to increased pressure losses, reductions in volumetric flow capacity, and possible flow perturbations within a wellbore. Attempts to mitigate these adverse effects have focused on both hindering the precipitation of asphaltene and preventing its deposition after precipitated. The study used here attempts to quantify various hydrodynamic controls specific to asphaltene deposition.
With o(1) scaling analysis, four independent dimensionless groups were generated from momentum and mass-balance equations relating hydrodynamic effects to the rate of asphaltene deposition. The dimensionless group π4 was of particular interest because of its inherent relationship to the rate of deposition. This group was compared with both data and existing correlations taken from literature, and noticeable trends in the deposition rate with respect to average stream velocity were observed. One of the most important trends discerned by these comparisons was a clear distinction whereby the rate of asphaltene deposition, related through π4, decreases with increasing Reynolds numbers (Re) in lower ranges, but actually increases in higher ranges. Although the data did not cover the specific region of transition, various correlations suggest a clear cutoff between what was deemed a favorable regime, or Regime I, and a nonfavorable regime, or Regime II.
Wang, Zhibin (Southwest Petroleum University and Xi'an Jiaotong University) | Guo, Liejin (Xi'an Jiaotong University) | Zhu, Suyang (Southwest Petroleum University) | Nydal, Ole Jørgen (Norwegian University of Science and Technology)
Analysis of the experimental data for liquid-entrainment rate, forces exerted on liquid droplet, and secondary flow occurring in the gas core show that the liquid is mainly carried in the form of film in the inclined annular flow. Therefore, it is more reasonable to establish a mathematical model from the bottom-film reversal than from the droplet reversal.
In this study, a new analytical model is developed from force balance of the bottom film of the inclined tubing after studying the bottom-film thickness and gas/liquid interfacial friction factor to reveal the liquid-loading mechanism. Furthermore, a new Belfroid-like empirical model is proposed that is based on the calculation results of a wide range of flowing parameters from the new analytical model to predict the liquid-loading status of gas wells. The new empirical model introduces a coefficient Cd,p,uSL,T to consider how the fluid properties under downhole flow condition affect the critical gas velocity. Cd,p,uSL,T in the new empirical model increases with the pipe diameter, liquid velocity, and flowing pressure, and decreases with the flowing temperature.
The new analytical model, having an average error of 8.45%, agrees well with the published experimental data, and it also performs well in predicting the pressure gradient at liquid unloading condition. The new empirical model could be applied for the prediction of real field operations and has been validated with an accuracy rate of 95% against data newly collected from 60 horizontal wells. The new work can accurately and easily judge the liquid-loading status, and it also reveals how the fluid properties under downhole flowing condition affect the liquid loading.
The conventional method for multiphase flash is the sequential usage of phase-stability and phase-split calculations. Multiphase flash requires the conventional method to obtain multiple false solutions in phase-split calculations and correct them in phase-stability analysis. Improvement of the robustness and efficiency of multiphase flash is important for compositional flow simulation with complex phase behavior.
This paper presents a new algorithm that solves for stationary points of the tangent-plane-distance (TPD) function defined at an equilibrium-phase composition for isobaric-isothermal (PT) flash. A solution from the new algorithm consists of two groups of stationary points: tangent and nontangent stationary points of the TPD function. Hence, equilibrium phases, at which the Gibbs free energy is tangent to the TPD function, are found as a subset of the solution.
Unlike the conventional method, the new algorithm does not require finding false solutions for robust multiphase flash. The advantage of the new algorithm in terms of robustness is more pronounced for more-complex phase behavior, for which multiple local minima of the Gibbs free energy are present. Case studies show that the new algorithm converges to a lower Gibbs free energy compared with the conventional method for the complex fluids tested. It is straightforward to implement the algorithm because of the simple formulation, which also allows for an arbitrary number of iterative compositions. It can be robustly initialized even when no K value correlation is available for the fluid of interest. Although the main focus of this paper is on robust solution of multiphase flash, the new algorithm can be used to initialize a second-order convergent method in the vicinity of a solution.