Commercial compositional simulators commonly apply correlations or empirical relations that are based on fitting experimental data to calculate phase relative permeabilities. These relations cannot adequately capture the effects of hysteresis, fluid compositional variations, and rock-wettability alteration. Furthermore, these relations require phases to be labeled, which is not accurate for complex miscible or near-miscible displacements with multiple hydrocarbon phases. Therefore, these relations can be discontinuous for compositional processes, causing inaccuracies and numerical problems in simulation.
This paper develops for the first time an equation-of-state (EOS) to model robustly and continuously the relative permeability as a function of phase saturations and distributions, fluid compositions, rock-surface properties, and rock structure. Phases are not labeled; instead, the phases in each gridblock are ordered on the basis of their compositional similarity. Phase compositions and rock-surface properties are used to calculate wettability and contact angles. The model is tuned to measured two-phase relative permeability curves with very few tuning parameters and then is used to predict relative permeability away from the measured experimental data. The model is applicable to all flow in porous-media processes, but is especially important for low-salinity polymer, surfactant, miscible gas, and water-alternating-gas (WAG) flooding. The results show excellent ability to match measured data, and to predict observed trends in hysteresis and oil-saturation trapping, including those from Land’s model and for a wide range in wettability. The results also show that relative permeabilities are continuous at critical points and yield a physically correct numerical solution when incorporated within a compositional simulator (PennSim 2013). The model has very few tuning parameters, and the parameters are directly related to physical properties of rock and fluid, which can be measured. The new model also offers the potential for incorporating results from computed-tomography (CT) scans and pore-network models to determine some input parameters for the new EOS.
Polymer flooding is a widely used commercial process with a low cost per barrel of produced oil, and hydrolyzed polyacrylamide (HPAM) polymers are the most widely used type of polymer. The objective of this research was to better understand and predict the behavior of HPAM polymers and their effect on residual oil saturation (ROS), to improve the capability of optimizing field design and performance. The corefloods were performed under typical field conditions of low pressure gradients and low capillary numbers. The polymer floods of the viscous oils recovered much more oil than the waterfloods, with up to 24% lower oil saturation after the polymer flood than after the waterflood. The experimental data are in good agreement with the fractional-flow analysis by use of the assumptions that the true ROSs and endpoint relative permeabilities are the same for both water and polymer. This suggests that, for more-viscous oils, the oil saturation at the end of a waterflood (i.e., at greater than 99% water cut) is better described as “remaining” oil saturation rather than the true “residual” oil saturation. This was true for all the corefloods, regardless of the core permeability and without the need for assuming a permeability-reduction factor in the fractional-flow analysis.
Matrix acidizing is a stimulation technique aiming at improving formation permeability or bypassing damaged zones. In this process, acid is injected through the well into the wellbore vicinity to dissolve the rock. For either production or injection wells, the formation may contain multiple phases (oil and water) near the wellbore region when acid treatment begins. In this paper, a two-phase two-scale continuum model is developed to simulate wormhole propagation under radial coordinates. The model describes the mechanisms of convection, dispersion, and reaction in two-phase flow during matrix acidizing. We have validated the simulation model with two methods: one is to compare with the previous simulation results; the other is to compare with the analytical solution. We have investigated conditions that will affect the wormhole-propagation process, including rock wettability, oil viscosity, and initial oil saturation. It is found that the water/oil mobility ratio is a key factor that affects acidizing efficiency. In addition, we have proposed a new criterion for acid breakthrough because the pressure response is affected not only by reaction, but also by overall mobility change in the formation. The traditional criterion for the single-phase model is no longer applicable to the current two-phase model. The results show that adverse water/oil mobility ratio leads to a higher efficiency for wormhole breakthrough. In carbonate reservoirs with heterogeneity, water/oil displacement and wormhole propagation contribute to narrower, less-branched channels. For the first time, it is possible to simulate formations with multiple phases during carbonate acidizing. The presented model improves our understanding in the optimization of carbonate acidizing.
Tagavifar, Mohsen (University of Texas at Austin) | Herath, Sumudu (University of Texas at Austin) | Weerasooriya, Upali P. (University of Texas at Austin) | Sepehrnoori, Kamy (University of Texas at Austin) | Pope, Gary (University of Texas at Austin)
The rheological behavior of microemulsion systems was systematically investigated with mixtures of oil, brine, surfactant, cosolvent, and in some cases polymer to determine their effects. A microemulsion-rheology model was developed and used to interpret the experimental results. The optimal microemulsion/oil-viscosity ratio without cosolvent was roughly 5:6, but it can be reduced to a more favorable ratio of approximately 2 by adding cosolvent. Even though the amount of cosolvent needed is case dependent, a clear trend of microemulsion-viscosity reduction with increasing cosolvent concentration was observed. Limited evidence suggests that large hydrolyzed polyacrylamide (HPAM) molecules with a narrow molecular-weight (MW) distribution have negligible partitioning to Type II and Type III microemulsions.
Gao, Guohua (Shell Global Solutions (US) Incorporated) | Jiang, Hao (Shell Global Solutions (US) Incorporated) | van Hagen, Paul (Shell Global Solutions International B.V.) | Vink, Jeroen C. (Shell Global Solutions International B.V.) | Wells, Terence (Shell Global Solutions International B.V.)
Solving the Gauss-Newton trust-region subproblem (TRS) with traditional solvers involves solving a symmetric linear system with dimensions the same as the number of uncertain parameters, and it is extremely computational expensive for history-matching problems with a large number of uncertain parameters. A new trust-region (TR) solver is developed to save both memory usage and computational cost, and its performance is compared with the well-known direct TR solver using factorization and iterative TR solver using the conjugate-gradient approach.
With application of the matrix inverse lemma, the original TRS is transformed to a new problem that involves solving a linear system with the number of observed data. For history-matching problems in which the number of uncertain parameters is much larger than the number of observed data, both memory usage and central-processing-unit (CPU) time can be significantly reduced compared with solving the original problem directly. An auto-adaptive power-law transformation technique is developed to transform the original strong nonlinear function to a new function that behaves more like a linear function. Finally, the Newton-Raphson method with some modifications is applied to solve the TRS.
The proposed approach is applied to find best-match solutions in Bayesian-style assisted-history-matching (AHM) problems. It is first validated on a set of synthetic test problems with different numbers of uncertain parameters and different numbers of observed data. In terms of efficiency, the new approach is shown to significantly reduce both the computational cost and memory usage compared with the direct TR solver of the GALAHAD optimization library (see http://www.galahad.rl.ac.uk/doc.html). In terms of robustness, the new approach is able to reduce the risk of failure to find the correct solution significantly, compared with the iterative TR solver of the GALAHAD optimization library. Our numerical results indicate that the new solver can solve large-scale TRSs with reasonably small amounts of CPU time (in seconds) and memory (in MB). Compared with the CPU time and memory used for completing one reservoir simulation run for the same problem (in hours and in GB), the cost for finding the best-match parameter values using our new TR solver is negligible. The proposed approach has been implemented in our in-house reservoir simulation and history-matching system, and has been validated on a real-reservoir-simulation model. This illustrates the main result of this paper: the development of a robust Gauss- Newton TR approach, which is applicable for large-scale history-matching problems with negligible extra cost in CPU and memory.
Microseismic mapping during the hydraulic-fracturing processes in the Vaca Muerta (VM) Shale in Argentina shows a group of microseismic events occurring at shallower depth and at later injection time, and they clearly deviate from the growing planar hydraulic fracture. This spatial and temporal behavior of these shallow microseismic events incurs some questions regarding the nature of these events and their connectivity to the hydraulic fracture. To answer these questions, in this article, we investigate these phenomena by use of a true 3D fracture-propagation-modeling tool along with statistical analysis on the properties of microseismic events.
First, we propose a novel technique in Abaqus incorporating fracture intersections in true 3D hydraulic-fracture-propagation simulations by use of a pore-pressure cohesive zone model (CZM), which is validated by comparing our numerical results with the Khristianovic-Geertsma-de Klerk (KGD) solution (Khristianovic and Zheltov 1955; Geertsma and de Klerk 1969). The simulations fully couple slot flow in the fracture with poroelasticity in the matrix and continuum-based leakoff on the fracture walls, and honor the fracture-tip effects in quasibrittle shales. By use of this model, we quantify vertical-natural-fracture activation and fluid infiltration depending on reservoir depth, fracturing-fluid viscosity, mechanical properties of the natural-fracture cohesive layer, natural-fracture conductivity, and horizontal stress contrast. The modeling results demonstrate this natural-fracture activation in coincidence with the hydraulic-fracture-growth complexities at the intersection, such as height throttling, sharp aperture reduction after the intersection, and multibranching at various heights and directions.
Finally, we investigate the hydraulic-fracture intersection with a natural fracture in the multilayer VM Shale. We infer the natural-fracture location and orientation from the microseismic-events map and formation microimager log in a nearby vertical well, respectively. We integrate the other field information such as mechanical, geological, and operational data to provide a realistic hydraulic-fracturing simulation in the presence of a natural fracture. Our 3D fracturing simulations equipped with the new fracture-intersection model rigorously simulate the growth of a realistic hydraulic-connection path toward the natural fracture at shallower depths, which was in agreement with our microseismic observations.
A novel method to map asymmetric hydraulic-fracture propagation using tiltmeter measurements is presented. Hydraulic fracturing is primarily used for oil-and-gas well stimulation, and is also applied to precondition rock before mining. The geometry of the developing fracture is often remotely monitored with tiltmeters—instruments that are able to remotely measure the fracture-induced deformations. However, conventional analysis of tiltmeter data is limited to determining the fracture orientation and volume. The objective of this work is to detect asymmetric fracture growth during a hydraulic-fracturing treatment, which will yield height-growth information for vertical fracture growth and horizontal asymmetry for lateral fracture growth or detect low preconditioning-treatment efficiency in mining. The technique proposed here uses the extended Kalman filter (EKF) to assimilate tilt data into a hydraulic-fracture model to track the geometry of the fracture front. The EKF uses the implicit level set algorithm (ILSA) as the dynamic model to locate the boundary of the fracture by solving the coupled fluid-flow/fracture-propagation equations, and uses the Okada half-space solution as the observation model (forward model) to relate the fracture geometry to the measured tilts. The 3D fracture model uses the Okada analytical expressions for the displacements and tilts caused by piecewise constant-displacement discontinuity elements to discretize the fracture area. The proposed technique is first validated by a numerical example in which synthetic tilt data are generated by assuming a confining-stress gradient to generate asymmetric fracture growth. The inversion is carried in a two-step process in which the fracture dip and dip direction are first obtained with an elliptical fracture-forward model, and then the ILSA-EKF model is used to obtain the fracture footprint by fixing the dip and dip direction to the values obtained in the first step. Finally, the ILSA-EKF scheme is used to predict the fracture width and geometry evolution from real field data, which are compared with intersection data obtained by temperature and pressure monitoring in offset boreholes. The results show that the procedure is able to satisfactorily capture fracture growth and asymmetry even though the field data contain significant noise, the tiltmeters are relatively far from the fracture, and the dynamic model contains significant “unmodeled dynamics” such as stress anisotropy, material heterogeneity, fluid leakoff into the formation, and other physical processes that have not been explicitly accounted for in the dynamic ILSA model. However, all the physical processes that affect the tilt signal are incorporated by the EKF when the tilt measurements are used to obtain the maximum likelihood estimates of the fracture widths and geometry.
Temperature traces from multiple rates are used to estimate the production-inflow profile and layer permeability and skin by use of a transient coupled reservoir/wellbore model. Production-logging-tool (PLT) temperature traces from two rates show heating of approximately 6–11°F above the geothermal because of the Joule-Thomson expansion of the reservoir oil. Production is single-phase oil from a high-pressure oil reservoir. Nonlinear regression was used to automatically adjust the layer permeability and skin values until the observation temperature traces from both rates were matched. History matching the temperature data provides a quantitative estimate of the skin and permeability within each contributing layer; this cannot be obtained from conventional pressure-transient analysis, which, unless for highly specialized cases, provides only a single value of permeability and skin. The production-inflow profile is then constructed by use of the history-matched layer permeability and skin values. In addition to the wellbore-temperature profiles, temperature and pressure profiles within the reservoir will be shown that illustrate the relative effect of the reservoir permeability and skin on the wellbore-temperature responses. The approach in this paper is different from many of the previous studies in the literature, in which only a single temperature trace is history matched and often under the assumption of steady-state conditions. Furthermore, no studies were found in which multiple temperature traces were matched by use of a transient model in which the temperature data were field data as opposed to synthetic data. Information on the coupled reservoir/wellbore model and the optimizer will be provided.
Annular casing pressure (ACP) is defined as the accumulated pressure on the casing head. If pressure returns after bleed-down, then the casing annulus is said to be showing sustained casing pressure (SCP). SCP is caused by late gas migration in the annular-fluid column above the top of leaking cement and may result in atmospheric emissions or underground blowouts. Removal of SCP is required in places where SCP is regulated, particularly before the well-plugging and abandonment operations. Annular-intervention methods for SCP removal, which are less expensive than the conventional downhole-intervention methods, typically involve injecting heavy fluid into the affected annulus that would displace the annular fluid (AF), balance the pressure at the top of cement, and stop the gas leakage. Previous studies stated that the use of immiscible combinations of two fluids is more effective for the purpose; however, inattentive applications may result in excessive use of heavy fluid. In this study, a 20-ft carbon-steel pilot-well annulus was manufactured and used for displacement experiments with various water-based drilling muds and heavy fluids with different properties. Pressure-change data were collected from four different levels of the annulus, and volumes of fluids going in and out of the annulus were measured. Experiments indicated the formation of a mixture zone that would build bottoms up and expand during ongoing displacement. The proposed pressure-buildup model suggests an exponential distribution of density of this zone, and shows its high dependency on fluids’ properties and injection rate. The mathematical models were also converted into dimensionless process measures and proposed for use in real-well applications. The study demonstrates the viability and recommends the correct application of the method.
Nanoscale porosity and permeability play important roles in the characterization of shale-gas reservoirs and predicting shale-gas-production behavior. The gas adsorption and stress effects are two crucial parameters that should be considered in shale rocks. Although stress-dependent porosity and permeability models have been introduced and applied to calculate effective porosity and permeability, the adsorption effect specified as pore volume (PV) occupied by adsorbate is not properly accounted. Generally, gas adsorption results in significant reduction of nanoscale porosity and permeability in shale-gas reservoirs because the PV is occupied by layers of adsorbed-gas molecules.
In this paper, correlations of effective porosity and permeability with the consideration of combining effects of gas adsorption and stress are developed for shale. For the adsorption effect, methane-adsorption capacity of shale rocks is measured on five shale-core samples in the laboratory by use of the gravimetric method. Methane-adsorption capacity is evaluated through performing regression analysis on Gibbs adsorption data from experimental measurements by use of the modified Dubinin-Astakhov (D-A) equation (Sakurovs et al. 2007) under the supercritical condition, from which the density of adsorbate is found. In addition, the Gibbs adsorption data are converted to absolute adsorption data to determine the volume of adsorbate. Furthermore, the stress-dependent porosity and permeability are calculated by use of McKee correlations (McKee et al. 1988) with the experimentally measured constant pore compressibility by use of the nonadsorptive-gas-expansion method.
The developed correlations illustrating the changes in porosity and permeability with pore pressure in shale are similar to those produced by the Shi and Durucan model (2005), which represents the decline of porosity and permeability with the increase of pore pressure in the coalbed. The tendency of porosity and permeability change is the inverse of the common stress-dependent regulation that porosity and permeability increase with the increase of pore pressure. Here, the gas-adsorption effect has a larger influence on PV than stress effect does, which is because more gas is attempting to adsorb on the surface of the matrix as pore pressure increases. Furthermore, the developed correlations are added into a numerical-simulation model at field scale, which successfully matches production data from a horizontal well with multistage hydraulic fractures in the Barnett Shale reservoir. The simulation results note that without considering the effect of PV occupied by adsorbed gas, characterization of reservoir properties and prediction of gas production by history matching cannot be performed reliably.
The purpose of this study is to introduce a model to calculate the volume of the adsorbed phase through the adsorption isotherm and propose correlations of effective porosity and permeability in shale rocks, including the consideration of the effects of both gas adsorption and stress. In addition, practical application of the developed correlations to reservoir-simulation work might achieve an appropriate evaluation of effective porosity and permeability and provide an accurate estimation of gas production in shale-gas reservoirs.