Numerical Modeling of Permeability in Porous Media: Integrating Experimental and Computational Approaches for Enhanced Fluid Flow Prediction in Petroleum Reservoirs (original) (raw)
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Petroleum Science
Modeling reservoir permeability is one of the crucial tasks in reservoir simulation studies. Traditionally, it is done by kriging-based methods. More rigorous modeling of the permeability results in more reliable outputs of the reservoir models. Recently, a new category of geostatistical methods has been used for this purpose, namely multiple point statistics (MPS). By this new category of permeability modeling methods, one is able to predict the heterogeneity of the reservoir permeability as a continuous variable. These methods consider the direction of property variation in addition to the distances of known locations of the property. In this study, the reservoir performance of a modified version of the SPE 10 solution project as a pioneer case is used for investigating the efficiency of these methods and paralleling them with the kriging-based one. In this way, the permeability texture concept is introduced by applying some MPS methods. This study is accomplished in the condition...
Transport in Porous Media, 2012
We introduce a finite-difference method to simulate pore scale steady-state creeping fluid flow in porous media. First, a geometrical approximation is invoked to describe the interstitial space of grid-based images of porous media. Subsequently, a generalized Laplace equation is derived and solved to calculate fluid pressure and velocity distributions in the interstitial space domain. We use a previously validated lattice-Boltzmann method (LBM) as ground truth for modeling comparison purposes. Our method requires on average 17 % of the CPU time used by LBM to calculate permeability in the same pore-scale distributions. After grid refinement, calculations of permeability performed from velocity distributions converge with both methods, and our modeling results differ within 6 % from those yielded by LBM. However, without grid refinement, permeability calculations differ within 20 % from those yielded by LBM for the case of high-porosity rocks and by as much as 100 % in low-porosity and highly tortuous porous media. We confirm that grid refinement is essential to secure reliable results when modeling fluid flow in porous media. Without grid refinement, permeability results obtained with our modeling method are closer to converged results than those yielded by LBM in low-porosity and highly tortuous media. However, the accuracy of the presented model decreases in pores with elongated cross sections. A A septa-diagonal matrix, representing the relevant w for all grids, s B Boundary condition representing the inlet and outlet pressures, Pa s d Digital equivalent of r , dimensionless d max Digital equivalent of r max , dimensionless f c (d max ) Calibration function, dimensionless J, J z Mass flux, kg m −2 s −1 J tot Total mass flux, kg m −2 s −1 K Permeability, m 2 [1 D = 1 Darcy = 9.869 × 10 −13 m 2 ] L Porous media (tube) length, m P, P 1 , P 2 , P Pressure, Pa P avg Average pressure, Pa R Tube radius, m r Radial distance from the inner wall, m r max The largest inscribed radius, m S(d max ) Area of the smallest possible cross-section for a given d max , dimensionless V Volume flux, m s −1 w Weighting factor in the generalized Laplace equation, s Greek Symbols μ Viscosity, Pa s ν Local fluid velocity, m s −1 ρ
2022
Having understanding about equations of fluid flow and transport through porous media is very important for various applications such as in oil and gas production and petroleum reservoirs simulation. But modeling fluid flow and transport in porous media, on the other hand is still an enormous technical challenge. To capture the best model of fluid flow, true description of fluid interaction such as capillary pressure and relative permeability is inevitable. Considering these parameters, the complexity of numerical calculation will increase. The modeling of such physical flow process mainly requires solving the mass and momentum conservation equations associated with equations of capillary pressure, saturation and relative permeability. Due to that, solution of the governing equations for fluid flow and transport requires knowledge of functional relationships between fluid pressures, saturations, and permeabilities which has formulated on the basis of conceptual models of fluid-porous media interactions. Therefore, in this work, the basic fluid flow and transport equations have been developed for a hierarchy of models: single phase, two-phase, black oil, volatile oil, compositional, thermal, and chemical. This hierarchy of models correspond to different oil production stages. Their governing differential equations consist of the mass and energy conservation equations and Darcy's law. I have chosen to start with the simplest model for single phase flow and to end with the most complex model for chemical flooding. This approach can be reversed; that is, I can start with the chemical model, and in turn derive the thermal, compositional, volatile oil, black oil, two-phase, and single-phase models.
Coupling of Stress Dependent Relative Permeability and Reservoir Simulation
All Days, 2012
Geomechanics is increasingly being considered for inclusion in reservoir simulation, since conventional simulators do not honor deformation resulting from the interaction between stress and fluid flow response in a porous medium. When a reservoir responds to changes in effective stress, the bulk volume adjusts, changing the pore geometry and dependent parameters like porosity, absolute permeability and effective permeability, and phase saturations. Most of the recently developed sequentially coupled approaches for coupling flow and geomechanics have focused on updating porosity and absolute permeability while changes in relative permeability (due to geomechanics) is ignored. For multiphase flow systems, relative permeability functions are one of the most influential parameters controlling fluid movement and distribution. To examine how geomechanically-influenced relative permeability may impact flow, a sequentially coupled reservoir geomechanical simulation study was conducted. The ...
Permeability Modelling of a Sandstone Reservoir in Parts of the Niger Delta
Permeability Modelling of a Sandstone Reservoir in Parts of the Niger Delta , 2019
Aimed at determining a more reliable method of estimating permeability from well log data, in the absence of core data, 4 predictive empirical models for estimating permeabilities (RGPZ model, Van Baaren’s model, Timur’s model and Berg’s model) were applied to two dif ferent reservoirs in a single well from an oil field in the Niger Delta. With the models employed at different cementation factors (m=1.5, 1.65, 1.80, 1.95, 2.10, 2.25, 2.40, 2.55, 2.70, 2.85, 3.00), using well log data from the reservoirs of interest, as a function of depth, measures of normalized root mean square error (NRMSE), relative to permeabilities measured from core analysis at the same reservoir interval, were used to determine which predictive model was more reliable. Obtained results showed the most reliable predictive model at m=1.65. At this cementation factor, the NRMSE for RGPZ model, Van Baaren’s model, Timur’s model and Berg’s model were 4.95, 30.38, 1.85, and 1.20 respectively in the first reservoir and 4.28, 24.69, 1.56 and 1.09 respectively in the second reservoir. Hence, Van Baaren’s model provided a more reliable measure of in-situ permeabilities in the reservoirs of the Niger delta as it had a lower measure of NRMSE in the reservoirs of interest. Index Terms: Permeability, RGPZ Model, Van Baaren’s Model, Timur’s Model, Berg’s Model, Normalized root mean square error.
Numerical simulation without using experimental data of relative permeability
Journal of Petroleum Science and Engineering, 2008
This study proposes a numerical simulation approach without direct specification of relative permeability functions. Using this approach, it is not necessary to impose relative permeability functions as input to the simulator in order to conduct the numerical simulations of two-phase fluid flow. Instead only capillary pressure data need to be imposed and the relative permeabilities can be calculated consistently using specific models. Example numerical simulations at both core and reservoir scales were conducted to test the technique without the direct input of relative permeability functions from experimental data. The results showed that the production performance calculated from the numerical simulations without the input of relative permeability functions was almost the same as the experimental data. Using the method proposed in this study, the effects of pore size distribution index and entry capillary pressure on oil recovery by gravity drainage were investigated numerically at both core scale and reservoir scale. The technique may be especially suitable for reservoirs in which it is difficult to measure relative permeability curves. Such reservoirs include gas-condensate reservoirs, extremely low permeability reservoirs, and geothermal reservoirs. The proposed technique may also be useful to upscaling, numerical simulation while drilling, and other areas.
Permeability porosity relationships from numerical simulations of fluid flow
Geophysical Research Letters, 1998
Numerical calculations of permeability are obtained from a lattice Boltzmann simulation of flow in simplified 2D porous media over a range of solid fractions. The evolution equation governing the flow behaviour incorporates the effect of porous medium geometry through the definition of solid density ns, a real number, at each node of the simulation grid. The results obtained for homogeneous media are compared to commonly used theoretical and empirical relationships relating rock properties to permeability. Behaviour consistent with a Kozeny-Carman type relationship between porosity q) and permeability k is obtained for low to intermediate solid fractions. At high solid fractions the rapid decrease in k is consistent with a percolation process giving a powerlaw relationship for q) and k. Both the critical porosity and power-law exponent are in agreement with quoted values for the lattice geometry used. A comparison of the results for homogeneous media with k values, obtained by embedding a spanning planar fracture into the matrix, illustrates the importance of matrix-fracture flow interactions. The results for this case are consistent with experimental observations and illustrate the difficulties involved in using simplified assumptions to predict permeability from porosity in fractured porous rock.
Energies
Permeability prediction in hydrocarbon production is an important task. The decrease in permeability due to depletion leads to an increase in the time of oil or gas production. Permeability models usually are obtained by various methods, including coreflooding and the field testing of wells. The results of previous studies have shown that permeability has a power-law or exponential dependence on effective pressure; however, the difficulty in predicting permeability is associated with hysteresis, the causes of which remain not fully understood. To model permeability, as well as explain the causes of hysteresis, some authors have used mechanical reservoir models. Studies have shown that these models cannot be applied with small fluctuations in effective pressures in the initial period of hydrocarbon production. In this work, based on the analysis of well test data, we came to the conclusion that in the initial period of production under constant thermobaric conditions, the permeabilit...
Steady-state two-phase relative permeability functions of porous media: A revisit
Steady-state two-phase flow experiments are performed on a sand column equipped with two differential pressure transducers and six ring electrodes to measure the pressure drop across each phase, and electrical resistance across five successive column segments, respectively. The electrical resistivity index measured across various segments of the soil column is converted to water saturation by using the Archie equation. The results are analyzed by considering the water saturation and oil/water relative permeability as power functions of water and oil capillary numbers which are employed as independent variables. Results from earlier visualization studies on a glass-etched pore network are also analyzed by a similar manner to quantify the dependence of oil and water relative permeability on capillary numbers, and correlate the estimated parameters of power functions with the viscosity ratio. The new explicit relationships of relative permeabilities and water saturation with oil and water capillary numbers set the bases for a new conceptualization of the two-phase flow at reservoir-scale where the mobility of the fluids is decoupled from saturation and become non-linear functions of the local flow rates. The variation of the relative permeability exponents with the pore system dimensionality agrees qualitatively with the scaling behavior predicted by the gradient percolation approach.