We study sequential formulations for coupled multiphase flow and reservoir geomechanics. First, we identify the proper definition of effective stress in multiphase-fluid systems. Although the average pore-pressure p¯--defined as the sum of the product of saturation and pressure of all the fluid phases that occupy the pore space--is commonly used to describe multiphase-fluid flow in deformable porous media, it can be shown that the'equivalent' pore pressure pE --defined as p¯ minusthe interfacial energy--is the appropriate quantity (Coussy 2004). We show, bymeans of a fully implicit analysis of the system, that only the equivalent porepressure pE leads to a continuum problem that is thermodynamically stable (thus, numerical discretizations on the basis of the average pore pressure p¯ cannot render unconditionally stable and convergent schemes). We then study the convergence and stability properties of sequential-implicit coupling strategies. We show that the stability and convergence properties of sequential-implicit coupling strategies for single-phase flow carry over for multiphase systems if the equivalent pore pressure pE is used. Specifically, the undrained and fixed-stress schemes are unconditionally stable, and the fixed-stress split is superior to the undrained approach in terms of convergence rate. The findings from stability theory are verified by use of nonlinear simulations of two-phase flow in deformable reservoirs.
RANS computations of a ship with heave and pitch motions in head waves are presented. The added resistance, heave and pitch motions are investigated numerically. The computations are based on volume of fluid (VOF) and dynamic deformation mesh methods, discretized by finite volume method (FVM). A six-degree-of-freedom (6DoF) module is implemented to predict the ship motions. Four wave conditions with a wide range of wave steepness 400025 ≤ .ak ≥ 001005 are onsidered. The wave length for all conditions is one ship length, and the results show strong nonlinear features, especially for .ak D 00100, where the phenomenon of green water on deck is observed. The comparison of added resistance between the presented computational results and measurements shows good agreement. A grid convergence study with three different grids is performed at .ak D 00025 for validation. All computations are performed by our solver, naoe-Foam-SJTU, developed under the framework of the open source code, OpenFOAM.
Enhanced Oil Recovery (EOR) processes usually involve complex phase behavior between the injected fluid (e.g., steam, hydrocarbon, CO2, sour gas)and the in-situ rock-fluid system. Several fundamental questions remain regarding Equation-of-State (EOS) computations for mixtures that can form three, or more, phases at equilibrium. In addition, numerical and computational issues related to the proper coupling of the thermodynamic phase behavior with multi-component transport must be resolved to accurately and efficiently model the behavior of large-scale EOR processes.
Previous work has shown that the adaptive tabulation of tie-simplexes in the course of a compositional simulation is a reliable alternative to the conventional EOS-based compositional simulation. In this paper, we present the numerical results of reservoir flow simulation with adaptive tie-simplex parameterization of the compositional space. We study the behavior of thermal-compositional reservoir displacement processes across a wide range of fluid mixtures, pressures, and temperatures. We show that our approach rigorously accounts for tie-simplex degeneration across phase boundaries. We also focus on the complex behavior of the tie-triangles and tie-lines associated with three-phase, steam injection problems in heterogeneous formations. Our studies indicate that the tie-simplex-based simulation is a potential approach for fast EOS modeling of complex EOR processes.
Conditional beta distributions are proposed with examples to evaluate the probability of intercepting specific proportions of target rocks in well planning. Geological facies or rock-type proportions are random variables pk(x) at each location, x. This paper recalls and further demonstrates that facies proportions can be modeled by local beta distributions. However, the highly variable shapes of the conditional probability-density functions (PDFs) for the random variables in the field lead to complex nonstationarity and nonlinearity issues. A practical and robust approach is to transform the proportion random variables to Gaussian variables,thus enabling the use of classical geostatistics. Although a direct relationship between Gaussian and beta random variables appears intractable, a suitable transformation that involves second-order expectations of proportions is proposed. The conditional parameters of the beta variables are recovered from kriging estimates after back transformation to proportions through Riemann sums.
Salama, Amgad (King Abdullah University of Science and Technology) | Sun, Shuyu (King Abdullah University of Science and Technology) | El-Amin, Mohamed (King Abdullah University of Science and Technology)
The flow of two or more immiscible fluids in porous media is widespread, particularly in the oil industry. This includes secondary and tertiary oil recovery and carbon dioxide (CO2) sequestration. Accurate predictions of the development of these processes are important in estimating the benefits and consequences of the use of certain technologies. However, this accurate prediction depends--to a large extent--on two things. The first is related to our ability to correctly characterize the reservoir with all its complexities; the second depends on our ability to develop robust techniques that solve the governing equations efficiently and accurately. In this work, we introduce a new robust and efficient numerical technique for solving the conservation laws that govern the movement of two immiscible fluids in the subsurface. As an example, this work is applied to the problem of CO2 sequestration in deep saline aquifers; however, it can also be extended to incorporate more scenarios. The traditional solution algorithms to this problem are modeled after discretizing the governing laws on a generic cell and then proceed to the other cells within loops. Therefore, it is expected that calling and iterating these loops multiple times can take a significant amount of computer time. Furthermore, if this process is performed with programming languages that require repeated interpretation each time a loop is called, such as Matlab, Python, and others, much longer time is expected, particularly for larger systems. In this new algorithm, the solution is performed for all the nodes at once and not within loops. The solution methodology involves manipulating all the variables as column vectors. By use of shifting matrices, these vectors are shifted in such a way that subtracting relevant vectors produces the corresponding difference algorithm. It has been found that this technique significantly reduces the amount of central-processing-unit (CPU) time compared with a traditional technique implemented within the framework of Matlab.
This paper focuses on modeling nonisothermal multiphase outflow of high-temperature producer wells in Shell's in-situ-upgrading process (IUP).Subsurface heating and in-situ upgrading of bitumen involves installing heaters into the subsurface and raising reservoir temperatures to higher than 325°C. Consequently, flow conditions at the wellhead and along the tubing for atypical IUP producer well exceed pressure and temperature ratings of conventional equipment, particularly during peak production periods. Thus, the ability to reasonably predict pressure and temperature along the wellbore over the entire production cycle is important for designing IUP production wells and associated production facilities. A nonisothermal multiphase computational model has been developed for predicting the performance of IUP producer wells.
Complex multiphase transport phenomena occur inside an IUP producer wellduring the production of high-temperature, upgraded hydrocarbon products. These include gas/oil/water three-phase flow; turbulent convective heat transfer between the tubing wall and the surrounding formation; pressure drop along thewellbore caused by gravity, friction, and acceleration; and phase changes caused by condensation and evaporation caused by variations in pressure and temperature along the well. These processes are strongly coupled, and accurate analysis demands a coupled modeling approach. Pressure and temperature variations result in changes in mass density and velocity, which have a significant influence on convective-heat-transfer rates. Mass-flow rates in the wellbore vary significantly with time because of production requirements during the life of a producer well (5 to 8 years). Long durations of high production rates can raise the temperature of the wellbore in the overburden and lower overall heat-loss rates. Sustained periods of low or no flow can cause the wellbore to cool and result in different flow and heat-transfer characteristics upon reopening of the well. Therefore, conductive time scales in the near-well formation are important to accurately predict flow tubing temperatures and pressures.
An advanced wellbore model is developed for coupling the multiphase flow, heat transfer, and phase change phenomena in a high-temperature, unconventional oil producer well. Vapor/liquid/liquid (VLL) three-phase flash calculations are used to describe phase condensation and evaporation caused by changes in temperature and pressure along the wellbore. The model is formulated by use of k-values that are consistent with the CMG STARS reservoir model (STARS 2007) used for thermal simulation of Shell's IUP process. The drift-flux model is used to describe gas/liquid two-phase flow, and multiple transient energyequations are used for the wellbore, casing strings, and surrounding formation.The overall pressure gradient in the two-phase flow is formulated as the sum of gravitational, friction, and acceleration components. All transport equations are implicitly coupled for stable efficient transient calculations.
The model is validated with published data and simplified analytical solutions for limiting flow conditions. Computational results are compared with data from an IUP producer well in the oil sands of Alberta, Canada. Reasonable temperature and pressure matches were obtained, demonstrating that the model can predict transient and axial profiles of pressure, temperature, phase volume fraction, phase mass density, and component composition in a high-temperature flowing producer well during the entire production cycle.
Technology Focus - No abstract available.
Bailey, Jeffrey R (ExxonMobil Development Company) | Elsborg, Carsten C (ExxonMobil Exploration & Production Norway) | James, Richard W (ExxonMobil Development Company) | Pastusek, Paul (ExxonMobil Development) | Prim, Matthew T (ExxonMobil Development Company) | Watson, William W (ExxonMobil Development Company)
The development of modeling methods to characterize the relative vibration tendency of alternative bottomhole assemblies (BHAs) has enabled deliberate tool redesign to reduce vibrations. To achieve the greatest benefit, tool redesign is most effective if applied early in the tool-design cycle in which important configuration parameters are most easily adjusted. This paper outlines several design issues to resolve so that future generations of tools have inherently lower vibration levels. The use of multiple special-purpose tools [such as logging tools, rotary-steerable assemblies, and ream-while-drilling (RWD) tools] generates significant constraints onBHA-configuration options. A redesign methodology to achieve lower vibration indices can be used to investigate modified components, dimensions, and configurations to select the best BHA configuration for specific drilling-operating conditions. Case studies are used to investigate BHA designs with flex stabilizers above rotary-steerable tools. The flex stabilizer is composed of a stabilizer with a smaller-diameter connecting flex sub to facilitate rotary-steerable directional objectives. It is typically wired for tool signals and is frequently run by vendors. In one case study, the spacing below a reamer is evaluated, and drilling data are compared with other assemblies in the same formation. In this example, the spacer provides an increase in the distance between contact points, to allow both the stabilizer and the reamer to seek the centerline with less interference. Another case study evaluates changing contact locations in the BHA by swapping the order of logging tools, resulting in different borehole-contact positions. Finally, a theoretical modeling study illustrates how changing BHA components and dimensions affects the vibration indices. The operator has field experience with BHA redesign that has directly led to significant improvement in drilling performance. The benefits include a higher rate of penetration (ROP), a longer time on the bottom, less wear of drilling-tool components, and a reduced frequency of trips.
High-frequency responses extracted from measurements onboard a Panamax containership and a post-Panamax containership were assessed by calculating cumulative fatigue damage. Responses were superimposed on damage obtained from numerical rigid body sea keeping calculations. Numerical analyses accounted for duration of measured seaways, ship headings relative to prevailing directions of encountered seaways, and ship forward speeds. Only the post-Panamax containership on its Far East route encountered relatively mild seaways, resulting in relatively low damage ratios. To represent worldwide service routes, measured high-frequency contributions were extrapolated to obtain high-frequency response of both these ships operating in severe North Atlantic and North Pacific seaways.
This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 165138, "Produced-Water-Reinjection Design and Uncertainty Assessment," by Jalel Ochi, Dominique Dexheimer, and Vincent Corpel, Total EP France, prepared for the 2013 SPE European Formation Damage Conference and Exhibition, Noordwijk, the Netherlands, 5-7 June. The paper has not been peer reviewed.