Alaskar, Mohammed N. (Stanford University) | Ames, Morgan F. (Stanford University) | Connor, Steve T. (Stanford University) | Liu, Chong (Stanford University) | Cui, Yi (Stanford University) | Li, Kewen (Stanford University) | Horne, Roland N. (Stanford University)
Existing reservoir-characterization tools allow pressure and temperature to be measured only at the wellbore. The development of temperature-and pressuresensitive nanosensors will enable in-situ measurements within the reservoir. This paper provides the details of the experimental work performed in the process of developing temperature nanosensors. The study investigated the parameters involved in the mobility of nanoparticles through porous and fractured media. These parameters include particle size or size distribution, shape, and surface charge or affinity to rock materials. The principal findings of this study were that spherically shaped nanoparticles of a certain size and surface charge compatible with that expected in formation rock are most likely to be transported successfully, without being trapped because of physical straining, chemical, or electrostatic effects. We found that tinbismuth (Sn-Bi) nanoparticles of 200 nm and smaller were transported through Berea sandstone. Larger particles were trapped at the inlet of the core, indicating that there was an optimum particle size range. We also found that the entrapment of silver (Ag) nanowires was primarily because of their shape. This conclusion was supported by the recovery of the spherical Ag nanoparticles with the same surface characteristics through the same porous media used during the Ag nanowires injection. The entrapment of hematite nanorice was attributed to its affinity to the porous matrix caused by surface charge. The hematite coated with surfactant (which modified its surface charge to one compatible with flow media) flowed through the glass beads, emphasizing the importance of particle surface charge. Preliminary investigation of the flow mechanism of nanoparticles through a naturally fractured greywacke core was conducted by injecting fluorescent silica microspheres. We found that silica microspheres of different sizes (smaller than the fracture opening) could be transported through the fracture. We demonstrated the possibility of using microspheres to estimate fracture aperture by injecting a polydisperse microsphere sample. It was observed that only spheres of 20 lm and smaller were transported. This result agreed reasonably well with the measurement of hydraulic fracture aperture (27 lm), as determined by the cubic law. Original manuscript received for review 8 July 2011. Revised manuscript received for review 11 June 2012. Paper peer approved 17 June 2012.
M. Karimi-Fard and L.J. Durlofsky, SPE, Stanford University Summary We present a new approach for representing wells in coarse-scale reservoir simulation models. The technique is based on an expanded well model concept which provides a systematic procedure for the construction of the near-well grid. The method proceeds by first defining an underlying fine-scale model, in which the well and any key near-well features such as hydraulic fractures are fully resolved using an unstructured grid. In the (coarse) simulation model, the geometry of the grid in the expanded well region, and the associated "radial" transmissibilities, are determined from the solution of a fine-scale, single-phase, well-driven flow problem. The coarse-scale transmissibilities outside of the well region are computed using existing local upscaling techniques or by applying a new global upscaling procedure. Thus, through use of near-well flow-based gridding and generalized local grid refinement, this methodology efficiently incorporates the advantages of highly-resolved unstructured grid representations of wells into coarse models. The overall model provided by this technique is compatible with any reservoir simulator that allows general unstructured cell-to-cell connections (model capabilities, in terms of flow physics, are defined by the simulator). The expanded well modeling approach is applied to challenging 3D problems involving injection and production in a low-permeability heterogeneous reservoir, tight-gas production by a hydraulically-fractured well, and production in a gas-condensate reservoir. In the first two cases, where it is possible to simulate the fine-grid unstructured model, results using the expanded well model closely match the reference solutions, while standard approaches lead to significant error. In the gas-condensate example, which involves a nine-component compositional model, the reference solution is not computed, but the solution using the expanded well model is shown to be physically reasonable while standard coarse-grid solutions show large variation under grid refinement. Introduction The accurate computation of well performance is very important for reservoir management and optimization. Standard large-scale reservoir simulators, however, typically do not resolve important near-well physics such as the detailed interaction between the local pressure gradient, reservoir heterogeneity, and well completion components. This is because these effects occur on scales that are very small compared to typical simulation gridblocks. Our goal in this work is to introduce a general procedure that enables coarse models to capture these important near-well effects.
Immiscible displacement of one fluid by another in porous media has practical applications when viscous oil is produced by water injection. A greater understanding of the flow patterns that evolve during such unstable displacements yields insights into improving predictive capability and increasing oil recovery. Immiscible multiphase displacement exhibits a wide range of behaviors depending on the relative magnitude of viscous, capillary, and gravity forces. Using flow-visualization images from forced-imbibition experiments carried out in etched-silicon micromodels, we show that the conventional Darcy-type modeling of fluid flux is not predictive under unstable, immiscible, forced-imbibition conditions at the scale of interest. When a less viscous fluid displaces a more viscous fluid at low capillary numbers, the displacement patterns show viscous instabilities in the form of fingers and local capillary control of interface movement. We show that such complex displacement patterns are well modeled using statistical theories. We derive a scaling model to describe quantitatively the functional forms for saturation, fractional flow, and capillary dispersion profiles using the self-similar characteristics inherent in the displacement patterns. For the specific range of flow rates (Nc ~ 10-7) and oil/water viscosity ratios (M ~ 8-400) considered in our experiments, both capillary and viscous forces are important, and the displacement pattern indicates fractal features. Results show that functional relations of the scaling model are in considerable agreement with our experimental data.
Most of the "easy?? oil in high permeability reservoirs has been explored and developed to a great extent. More and more "difficult?? oil has been discovered. There are many problems in developing the "difficult?? oil in low or extremely low permeability reservoirs. One of the problems is the pressure sensitivity of permeability which declines significantly as pore pressure decreases or net overburden pressure increases. There have been a few mathematical models to calculate oil or gas production by considering the pressure sensitivity of permeability. However most of the models have not been verified using field production data. In this study, a new production model has been derived theoretically with the pressure sensitivity of permeability considered. Using the production data from a low permeability (less than 1.0×10-3µm2) oil field (Yushulin, Daqing), the model has been tested and verified. The pressure sensitivity coefficient of permeability has been calculated by using the new model with the field data. The results calculated using the new model also showed that the permeability near the well bottom decreased significantly because of the drop in pressure in low permeability reservoirs. An obvious permeability decline funnel could be formed even the formation was homogeneous before development. It was found that the productivity index is no longer a constant in low permeability reservoirs with serious pressure sensitivity of permeability. According to this study, it is necessary to consider the pressure sensitivity of permeability when low permeability reservoirs are being developed. Otherwise, the production will be greatly overestimated.
Halpert, Adam D. (Stanford University)
Image Segmentations Finally, we should examine the effect of MH filtering on automatic segmentation results. Figure 8(a) is the result of segmenting the original, unfiltered image in Figure 6. Segments belonging inside the salt body have been assigned the same color to facilitate evaluation of the results. "Leakages" from the salt body into the surrounding sediments are apparent, especially at the locations indicated by the intersecting lines. When the MH-filtered image is segmented, however, the leakage problem is greatly ameliorated (Figure 8(b)). In this example, hybrid-MH filtering has allowed for more accurate segmentation results; furthermore, the computational efficiency (and simple parallelization) of the algorithm make it especially attractive since, in this example, smoothing the image required only a fraction of the time needed for the already-efficient PRC segmentation algorithm.
The slowness sensitivity kernel is calculated by back-projecting a perturbation of ρ that has one single spike at x 0. The sensitivity kernels of operator ρ/ s are shown in figure 1. As it is shown by the Toldi operator (Toldi, 1985), the characteristic shape of such a sensitivity kernel is a center lobe, with two side lobes with opposite polarity, which reaffirms the well-known fact that velocity perturbations at near angles and far angles will change the curvature of ADCIGs toward opposite directions. Yet the overall average is positive, which would give the correct update in case of a constant slowness error. Finally, as we can compute the gradient in eq.(9), any gradientbased optimization method can be used to maximize the objective function defined in eq.(3). Nonetheless, as we notice that in terms of finding the step size, evaluating eq.(3) (which is an approximation of eq.(1) purely based on kinematics) is more expensive than evaluating the original objective function (1). In our implementation we choose (1) as the maximization goal while using the search direction computed from eq.(3).
The coupled effect of adsorption and Knudsen diffusion is modeled for a wide range of pore pressures on a digital kerogen body that is rendered in three dimensions from a 2D scanning electron microscope (SEM) image by thresholding and sequential indicator simulation (SISIM). Introduction Declining production from national conventional natural gas resources over the past 15 years has created a significant increase in the demand for unconventional resources. In this vein, it is projected (EIA, 2010a) that gas shale reservoirs will supply 6.0 TCF of natural gas in 2035 as compared to 2.4 TCF produced in 2009, potentially accounting for 6% of all energy consumed in the US. As of 2009, 60.6 TCF of total gas shale resources in the US are believed to be proven reserves - 21.3% of all economically recoverable natural gas reserves in the US (EIA, 2010b). Subsequently, it is important that we develop a fundamental understanding of the transport properties of gas shale resources.