Absolute Permeability

2013 ◽  
pp. 63-94
Keyword(s):  
Absolute Permeability

Permeability-porosity transforms from small sandstone fragments

Geophysics ◽  
2006 ◽  
Vol 71 (1) ◽  
pp. N11-N19 ◽  
Author(s):  
Ayako Kameda ◽  
Jack Dvorkin ◽  
Youngseuk Keehm ◽  
Amos Nur ◽  
William Bosl
Keyword(s):  
Pore Space ◽  
Petroleum Industry ◽  
Rock Physics ◽  
Three Dimensions ◽  
Absolute Permeability ◽  
High Porosity ◽  
Drill Cuttings ◽  
Thin Sections ◽  
Numerical Experimentation ◽  
The Absolute

Numerical simulation of laboratory experiments on rocks, or digital rock physics, is an emerging field that may eventually benefit the petroleum industry. For numerical experimentation to find its way into the mainstream, it must be practical and easily repeatable — i.e., implemented on standard hardware and in real time. This condition reduces the size of a digital sample to just a few grains across. Also, small physical fragments of rock, such as cuttings, may be the only material available to produce digital images. Will the results be meaningful for a larger rock volume? To address this question, we use a number of natural and artificial medium- to high-porosity, well-sorted sandstones. The 3D microtomography volumes are obtained from each physical sample. Then, analogous to making thin sections of drill cuttings, we select a large number of small 2D slices from a 3D scan. As a result, a single physical sample produces hundreds of 2D virtual-drill-cuttings images. Corresponding 3D pore-space realizations are generated statistically from these 2D images; fluid flow is simulated in three dimensions, and the absolute permeability is computed. The results show that small fragments of medium– to high-porosity sandstones that are statistically subrepresentative of a larger sample will not yield the exact porosity and permeability of the sample. However, a significant number of small fragments will yield a site-specific permeability-porosity trend that can then be used to estimate the absolute permeability from independent porosity data obtained in the well or inferred from seismic techniques.

History Matching in Two-Phase Petroleum Reservoirs

1980 ◽  
Vol 20 (06) ◽  
pp. 521-532 ◽  
Author(s):  
A.T. Watson ◽  
J.H. Seinfeld ◽  
G.R. Gavalas ◽  
P.T. Woo
Keyword(s):  
Optimal Control ◽  
Parameter Estimation ◽  
Objective Function ◽  
History Matching ◽  
Computing Time ◽  
Absolute Permeability ◽  
Two Phase ◽  
Automatic History Matching ◽  
Control Approach ◽  
First Order

Abstract An automatic history-matching algorithm based onan optimal control approach has been formulated forjoint estimation of spatially varying permeability andporosity and coefficients of relative permeabilityfunctions in two-phase reservoirs. The algorithm usespressure and production rate data simultaneously. The performance of the algorithm for thewaterflooding of one- and two-dimensional hypotheticalreservoirs is examined, and properties associatedwith the parameter estimation problem are discussed. Introduction There has been considerable interest in thedevelopment of automatic history-matchingalgorithms. Most of the published work to date onautomatic history matching has been devoted tosingle-phase reservoirs in which the unknownparameters to be estimated are often the reservoirporosity (or storage) and absolute permeability (ortransmissibility). In the single-phase problem, theobjective function usually consists of the deviationsbetween the predicted and measured reservoirpressures at the wells. Parameter estimation, orhistory matching, in multiphase reservoirs isfundamentally more difficult than in single-phasereservoirs. The multiphase equations are nonlinear, and in addition to the porosity and absolutepermeability, the relative permeabilities of each phasemay be unknown and subject to estimation. Measurements of the relative rates of flow of oil, water, and gas at the wells also may be available forthe objective function. The aspect of the reservoir history-matchingproblem that distinguishes it from other parameterestimation problems in science and engineering is thelarge dimensionality of both the system state and theunknown parameters. As a result of this largedimensionality, computational efficiency becomes aprime consideration in the implementation of anautomatic history-matching method. In all parameterestimation methods, a trade-off exists between theamount of computation performed per iteration andthe speed of convergence of the method. Animportant saving in computing time was realized insingle-phase automatic history matching through theintroduction of optimal control theory as a methodfor calculating the gradient of the objective functionwith respect to the unknown parameters. Thistechnique currently is limited to first-order gradientmethods. First-order gradient methods generallyconverge more slowly than those of higher order.Nevertheless, the amount of computation requiredper iteration is significantly less than that requiredfor higher-order optimization methods; thus, first-order methods are attractive for automatic historymatching. The optimal control algorithm forautomatic history matching has been shown toproduce excellent results when applied to field problems. Therefore, the first approach to thedevelopment of a general automatic history-matchingalgorithm for multiphase reservoirs wouldseem to proceed through the development of anoptimal control approach for calculating the gradientof the objective function with respect to theparameters for use in a first-order method. SPEJ P. 521＾

scholarly journals Statistical Inversion of Absolute Permeability in Single-phase Darcy Flow

2015 ◽  
Vol 51 ◽  
pp. 1188-1197 ◽  
Author(s):  
Thilo Strauss ◽  
Xiaolin Fan ◽  
Shuyu Sun ◽  
Taufiquar Khan
Keyword(s):  
Single Phase ◽  
Darcy Flow ◽  
Absolute Permeability

Wettability Alteration to Intermediate Gas-Wetting in Gas-Condensate Reservoirs at High Temperatures

SPE Journal ◽  
2007 ◽  
Vol 12 (04) ◽  
pp. 397-407 ◽  
Author(s):  
Mashhad Mousa Fahes ◽  
Abbas Firoozabadi
Keyword(s):  
Hydraulic Fracturing ◽  
Production Rate ◽  
High Temperatures ◽  
Gas Production ◽  
Reservoir Rock ◽  
Wettability Alteration ◽  
Absolute Permeability ◽  
Low Permeability ◽  
Gas Well ◽  
Water Blocking

Summary Wettability of two types of sandstone cores, Berea (permeability on the order of 600 md), and a reservoir rock (permeability on the order of 10 md), is altered from liquid-wetting to intermediate gas-wetting at a high temperature of 140C. Previous work on wettability alteration to intermediate gas-wetting has been limited to 90C. In this work, chemicals previously used at 90C for wettability alteration are found to be ineffective at 140C. New chemicals are used which alter wettability at high temperatures. The results show that:wettability could be permanently altered from liquid-wetting to intermediate gas-wetting at high reservoir temperatures,wettability alteration has a substantial effect on increasing liquid mobility at reservoir conditions,wettability alteration results in improved gas productivity, andwettability alteration does not have a measurable effect on the absolute permeability of the rock for some chemicals. We also find the reservoir rock, unlike Berea, is not strongly water-wet in the gas/water/rock system. Introduction A sharp reduction in gas well deliverability is often observed in many low-permeability gas-condensate reservoirs even at very high reservoir pressure. The decrease in well deliverability is attributed to condensate accumulation (Hinchman and Barree 1985; Afidick et al. 1994) and water blocking (Engineer 1985; Cimolai et al. 1983). As the pressure drops below the dewpoint, liquid accumulates around the wellbore in high saturations, reducing gas relative permeability (Barnum et al. 1995; El-Banbi et al. 2000); the result is a decrease in the gas production rate. Several techniques have been used to increase gas well deliverability after the initial decline. Hydraulic fracturing is used to increase absolute permeability (Haimson and Fairhurst 1969). Solvent injection is implemented in order to remove the accumulated liquid (Al-Anazi et al. 2005). Gas deliverability often increases after the reduction of the condensate saturation around the wellbore. In a successful methanol treatment in Hatter's Pond field in Alabama (Al-Anazi et al. 2005), after the initial decline in well deliverability by a factor of three to five owing to condensate blocking, gas deliverability increased by a factor of two after the removal of water and condensate liquids from the near-wellbore region. The increased rates were, however, sustained for a period of 4 months only. The approach is not a permanent solution to the problem, because the condensate bank will form again. On the other hand, when hydraulic fracturing is used by injecting aqueous fluids, the cleanup of water accumulation from the formation after fracturing is essential to obtain an increased productivity. Water is removed in two phases: immiscible displacement by gas, followed by vaporization by the expanding gas flow (Mahadevan and Sharma 2003). Because of the low permeability and the wettability characteristics, it may take a long time to perform the cleanup; in some cases, as little as 10 to 15% of the water load could be recovered (Mahadevan and Sharma 2003; Penny et al. 1983). Even when the problem of water blocking is not significant, the accumulation of condensate around the fracture face when the pressure falls below dewpoint pressure could result in a reduction in the gas production rate (Economides et al. 1989; Sognesand 1991; Baig et al. 2005).

Integration of Partial Differential Equation for Transient Linear Flow of Gas-Condensate Fluids in Porous Structures

1964 ◽  
Vol 4 (04) ◽  
pp. 291-306 ◽  
Author(s):  
C. Kenneth Eilerts
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Effective Permeability ◽  
Flow Characteristics ◽  
Compressibility Factor ◽  
Variable Coefficients ◽  
Back Pressure ◽  
Absolute Permeability ◽  
Partial Differential ◽  
Linear Flow

Abstract Finite difference equations were programmed and used to integrate the second-order, second-degree, partial differential equation with variable coefficients that represents the transient linear flow of gas-condensate fluids. Effect was given to the change with pressure of the compressibility factor, the viscosity, and the effective permeability and to change of the absolute permeability with distance. Integrations used as illustrations include recovery of fluid from a reservoir at a constant production rate followed by recovery at a declining rate calculated to maintain a constant pressure at the producing boundary. The time required to attain such a limiting pressure and the fraction of the reserve recovered in that time vary markedly with properties of the fluid represented by the coefficients. Fluid also is returned to the reservoir at a constant rate, until initial formation pressure is attained at the input boundary, and then at a calculated rate that will maintain but not exceed the limiting pressure. The computing programs were used to calculate the results that would be obtained in a series of back-pressure tests made at selected intervals of reservoir depletion. If effect is given to the variations in properties of the fluid that actually occur, then a series of back-pressure curves one for each stage of reserve depletion -- is required to indicate open-flow capacity and related flow characteristics dependably. The isochronal performance method for determining flow characteristics of a well was simulated by computation. Introduction The back-pressure test procedure is based on a derivation of the equation for steady-state radial flow of a gas, the properties of which are of necessity assumed to remain unchanged in applying the test results. The properties of most natural gases being recovered from reservoirs change as the reserve is depleted and pressures decline, and the results of an early back-pressure test may not be dependable for estimating the future delivery capacity of a well. The compressibility factor of a fluid under an initial pressure of 10,000 psia can change 45 per cent and the viscosity can change 70 per cent during the productive life of the reservoir. There are indications that the effective permeability to the flowing fluid can become 50 per cent of the original absolute permeability before enough liquid collects in the structure about a well as pressure declines to permit flow of liquid into the well. The advent of programmed electronic computing made practicable the integration of nonlinear, second-order, partial differential equations pertaining to flow in reservoirs. Aronofsky and Porter represented the compressibility factor and the viscosity by a linear relationship, and integrated the equation for radial flow of gas for pressures up to 1,200 psi. Bruce, Peaceman, Rachford and Rice integrated the partial differential equations for both linear and radial unsteady-state flow of ideal gas in porous media. Their published results were a substantial guide in this study of integration of the partial differential equation of linear flow with coefficients of the equation variable. The computing program was developed to treat effective permeability as being both distance-dependent and pressure-dependent. In this study all examples of effective permeability are assumptions designed primarily to aid in developing programs for giving effect to this and other variable coefficients. The accumulation of data for expressing the pressure dependency of the effective permeability is the objective of a concurrent investigation. SPEJ P. 291^

Foam Flow in Different Pore Systems—Part 1: The Roles of Pore Attributes and Their Variation on Trapping and Apparent Viscosity of Foam

SPE Journal ◽  
2021 ◽  
pp. 1-18 ◽  
Author(s):  
Abdulrauf Rasheed Adebayo
Keyword(s):  
Porous Medium ◽  
Aspect Ratio ◽  
Pore Size ◽  
Coordination Number ◽  
Apparent Viscosity ◽  
Absolute Permeability ◽  
Surface Relaxation ◽  
Foam Flow ◽  
Rock Samples ◽  
Lower Permeability

Summary Lateral propagation of foam in heterogeneous reservoirs, where pore geometries vary laterally, depends on the roles of pore geometries on the foam properties. In this paper, the pore attributes of 12 different rock samples were characterized in terms of porosity, permeability, pore shape, pore size, throat size, aspect ratio, coordination number, and log mean of surface relaxation times (T2LM). These were measured from gas porosimeter and permeameter, X-ray microcomputed tomography (CT)-basedpore-network models, thin-section photomicrographs, and nuclear magnetic resonance (NMR) surface relaxometry. The samples have a wide range of porosity: 12 to 29%; permeability: 1 to 5,000 md; average pore size: 3.7 to 9 µm; average throat size: 2.4 to 8 µm; average aspect ratio: 1 to 1.7; average coordination number: 2.6 to 5.2; and T2LM: 9.4 to 740 ms. Nitrogen foam flow experiments (without oil) were then conducted on each rock sample using a specialized coreflood apparatus. A graphical analysis of the coreflood data was used to estimate the total saturation of trapped foam (10 to 66%), flowing foam (3 to 14%), and apparent viscosity of foam (3.2 to 73 cp). Trapped foam saturation and apparent viscosity values were then correlated with each of the measured pore attributes. The results revealed that all pore attributes, except aspect ratio, have positive correlations with foam trapping and apparent viscosity. The best correlation with trapped foam saturation was obtained when the most influential pore attributes (pore size, throat size, aspect ratio, and coordination number) were combined into a single mathematical function. Foam apparent viscosity also appears to be mostly influenced by trapped foam saturation, permeability, and coordination number of pore systems. Trapping is also likely enhanced by the presence of fenestral or channel pores. Furthermore, the shape and angularity of pores seem to facilitate snap-off and trapping of foam, because rock samples with angular pores trapped the highest foam saturation compared with other samples with rounded and subrounded pores. It was also shown that the correlation between trapped foam saturation (and foam apparent viscosity) and the absolute permeability of porous media may reverse at some high-permeability values (greater than several darcies), when one or both of the following conditions exist: (1) The aspect ratio of a lower-permeability porous medium is lower than that of a higher-permeability porous medium, and (2) the coordination number of a lower-permeability porous medium is higher than that of a higher-permeability porous medium. Finally, T2LM showed a good correlation with foam trapping, making NMR logging a prospective tool for pre-evaluating foam performance in targeted reservoir sections.

scholarly journals Analysis of filtration and electrical properties anisotropy of terrigenous reservoir rocks (for DDB axial zone reservoirs)

2019 ◽  
Keyword(s):  
Electrical Resistivity ◽  
Gas Permeability ◽  
Vertical Direction ◽  
Absolute Permeability ◽  
Electrical Anisotropy ◽  
Reservoir Rocks ◽  
Vertical Permeability ◽  
Irreducible Water Saturation ◽  
Horizontal Permeability ◽  
Filtration Properties

The paper focuses on the filtration and electrical anisotropy coefficients and relationship between vertical and horizontal permeability in sandstone reservoir rocks. Field case study of DDB reservoir rocks. Petrophysical properties and parameters are estimated from core and log data from a Moscovian and Serpukhovian stages of Dnipro-Donetsk Basin (West-Shebelynka area well 701-Bis and South-Kolomak area well 31). Routine core analysis included estimation of absolute permeability, open porosity, irreducible water saturation and electrical resistivity (on dry and saturated by mineralized solution) of 40 core samples along two orthogonal directions. Shale fraction is estimated using well logging data in wells which are analyzed. The authors report that reservoir rocks are represented by compacted poor-porous (φ <10 %), low permeable (k<1mD) laminated sandstone with different ratios of clay minerals (Vsh from 0,03 to 0,7) and high volume of micaceous minerals (in some cases 20-30 %). Research theory. One of the main objectives of the work is to develop empirical correlation between vertical permeability and other capacitive and filtration properties for compacted sandstone reservoirs. A modified Kozeny-Carman equation and the concept of hydraulic average radius form the basis for the technique. Results. Coefficients of the anisotropy of gas permeability (IA) and electrical resistivity (λ) are defined based on the results of petrophysical studies. The experiments proved that IA lies in a range from 0,49 to 5 and λ from 0,77 to 1,06. Permeability and electrical resistivity anisotropy in most cases have horizontal distribution. It has been shown that in West-Shebelynka area sample №1 (depth 4933 m) there is probably no fluids flow in vertical direction and in samples №№3 and 15 fractures have the vertical orientation. We have also found that the values of electrical and filtration anisotropy for all samples of South-Kolomak area are similar, this characterized the unidirectionality in their filtration properties, as well as the fact that the motion of the fluid flow mainly in the horizontal direction. In the studied rocks the degree of anisotropy has been concluded to depend on the volume of clay and micaceous minerals, their stratification, fractures, density, and their orientation. New correlation between vertical permeability, horizontal permeability and effective porosity are developed for Late Carboniferous DDB intervals that are analyzed.

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