Pore Geometry Factor Research Articles

Intrapore Geometry and Flow Rate Controls on the Transition of Non‐Fickian to Fickian Dispersion

AbstractHydraulic heterogeneity leads to non‐Fickian transport characteristics, which cannot be entirely accounted for by the continuum‐scale advection‐dispersion equation. In this pore‐scale computational study, we investigate the combined effects of flow rate (i.e., Peclet number, Pe) and first‐order hydraulic heterogeneity, that is, resulting from intrapore geometry exclusively, on the transition from non‐Fickian to Fickian dispersion. A set of intrapore geometries is designed and quantified by a dimensionless pore geometry factor (β), which accounts for a broad range of pore shapes likely found in nature. Navier‐Stokes and Advection‐Diffusion equations are solved numerically to study the transport phenomenon using velocity variance, residence time distribution, and coefficients of hydrodynamic dispersion and dispersivity. We determine the length scale (i.e., the linear distance in flow direction) for each pore shape and Pe when non‐Fickian features transition to the Fickian transport regime by incrementally extending the length, that is, the linear array of pores. We show how velocity distribution and variance (σ2) depend on β, and directly control the transition to Fickian dispersion. Pores with a larger β, that is, complex pore shapes with constricted pore‐body or with “slit‐type” attributes, result in a substantial non‐Fickian characteristics. The magnitude of non‐Fickian characteristics gets amplified with an increase in Pe requiring a significantly longer length scale, that is, up to 1 m or a linear array of 500 pores to transition to the Fickian transport regime. We find the hydrodynamic dispersion coefficient (Dh) exponentially depends on the pore shape factor β, with its exponent dependent on flow rate or Pe. We determine constitutive relations to quantify how σ2, β, and Pe, contribute to the degree of non‐Fickian characteristics, the length scale needed for the transition to Fickian transport regime, asymptotic Dh, and the length‐scale dependence of longitudinal dispersivity.

An improved method in petrophysical rock typing based on mercury-injection capillary pressure data

ABSTRACT Petrophysical rock typing plays a major role in carbonate reservoir characterization and geological modeling for reservoir simulation. In this study, based on 1120 samples of mercury-injection capillary pressure data, we have analyzed the contributions to rock permeability for the thick Cretaceous carbonate reservoir of Mishrif Formation in H Oilfield in Iraq. The analyses have been carried out for three types of pore-throat frequency distribution, i.e., monomodal, bimodal, and trimodal. The results show that for the bimodal and trimodal samples, the pore-throat frequency distribution of the first pore system contributes more than 95% of rock permeability. Further, the Thomeer function has been used to fit the mercury-injection capillary pressure curve, in which the displacement pressure, pore geometry factor, and bulk volume have been extracted. These three parameters have been utilized to characterize the pore structure and to fit with the rock permeability so as to obtain the reservoir classification parameter Mode. Then, we have established the relationship between permeability and mode, permeability and R35, and the correlation coefficients are 0.81 and 0.75, respectively. And permeability derived from Mode is more accurate than R35. The Modes of 1120 samples have been arranged in ascending order and plotted on the semi-logarithmic scales. After interpolation, derivation, and filtering, five rock types have been divided at the change in slope. The combination of Mode and this slope method is considered an improved method. The classification results of Mode, Winland R35, and Flow Zone Indicator have been compared with those of pore-throat distribution, T2 distribution of nuclear magnetic resonance, and conventional logging responses. The results demonstrate that the classification results of Mode are significantly better than those of Winland R35 and Flow Zone Indicator.

Estimating the Permeability of Naturally Structured Soil From Percolation Theory and Pore Space Characteristics Imaged by X‐Ray

AbstractThe saturated hydraulic conductivity of soil, Ks, is a critical parameter in hydrological models that remains notoriously difficult to predict. In this study, we test the capability of a model based on percolation theory and critical path analysis to estimate Ks measured on 95 undisturbed soil cores collected from contrasting soil types. One parameter (the pore geometry factor) was derived by model fitting, while the remaining two parameters (the critical pore diameter, dc, and the effective porosity) were derived from X‐ray computed tomography measurements. The model gave a highly significant fit to the Ks measurements (p < 0.0001) although only ~47% of the variation was explained and the fitted pore geometry factor was approximately 1 to 2 orders of magnitude larger than various theoretical values obtained for idealized porous media and pore network models. Apart from assumptions in the model that might not hold in reality, this could also be attributed to experimental error induced by, for example, air entrapment and changes in the soil pore structure occurring during sample presaturation and the measurement of Ks. Variation in the critical pore diameter, dc, was the dominant source of variation in Ks, which suggests that dc is a suitable length scale for predicting soil permeability. Thus, from the point of view of pedotransfer functions, it could be worthwhile to direct future research toward exploring the correlations of dc with basic soil properties and site attributes.

Assessment of Textural Variational Pattern and Electrical Conduction of Economic and Accessible Quaternary Hydrolithofacies via Geoelectric and Laboratory Methods in SE Nigeria: A Case Study of Select Locations in Akwa Ibom State

Abstract: Textural variational pattern of economic and accessible Quaternary aquifer repositories and its conductivity in the south-eastern Nigeria have been assessed through the integration of vertical electrical sounding and laboratory measurements. The results have shown the lithological attributes, pore-water and amount of residual clay minerals in the assumed clean sand; mechanism of charge fixation at the fluid - surface interface; intricate geometry of pores and pore channels; formation’s ability to transmit pore-water and cation exchange capacity.The connections of electrical and hydraulic properties and their distributions have been established. The average interface conductivity contributed by residual clay minerals in assumed clean sands of the aquifer repositories in the study area have been estimated as 30μS/m. Intrinsic average porosity and formation factor have been respectively deduced as 12% and 14.75. Comparing the simulated aquifer formation factor obtained from the observed porosity data with the observed aquifer formation factor, indicates the that study area has 0.5 ≤ a ≤ 0.8 pore geometry factor and 1.5 ≤ m ≤ 2.0 cementation factor as the best fitting values. The interrelations between aquifer parameters have been established through different plots and the aquifer have been empirically proved to be associated with residual clay minerals as the interface conductivity Cq is not equal to zero. The wide ranges of parameters estimated are an indication of variations in grain size. The estimated intrinsic average porosity, formation factor and the average BQv are viable in characterizing the aquifer flow dynamics and contaminant modelling in the associated aquifer sands For low pore geometry factors a (0.2) and low cementation factor m (0.5) the formation factor remains fairly constant. However, marked variability is noticed at higher a (1.0) and m (2.5). Despite the observed variability in formation factors at the indicated porosities, the spatial or geometrical spread of the formation factor remains unchanged in the aquifer units. The Tables for geoelectric and petrophysical parameters and the associated mathematical models generated in this study can be used for groundwater contaminant modelling and simulation of pore space parameters with reasonable accuracy.

WITHDRAWN: Estimation of porosity, formation resistivity factor, Archie cementation factor, pore geometry factor and tortuosity for a coastal aquifer

WITHDRAWN: Estimation of porosity, formation resistivity factor, Archie cementation factor, pore geometry factor and tortuosity for a coastal aquifer

Evaluation of Two‐Phase Relative Permeability and Capillary Pressure Relations for Unstable Displacements in a Pore Network

At the pore scale, unstable displacement is often observed for two‐fluid systems, depending on the capillary number and fluid viscosity ratio. At the continuum scale, unstable displacement is usually not considered. In this work, relations between nonwetting fluid relative permeabilities (krn), fluid saturations (Sn), and capillary pressure heads (hc) are evaluated to predict average Sn values using a continuum‐based simulator for displacements in a micromodel. To this end, a series of displacement experiments was conducted using five wetting–nonwetting immiscible fluid pairs in a homogenous pore network. The micromodel was initially saturated with either polyethylene glycol 200 (PEG) or water as a wetting fluid, which was subsequently displaced by a nonwetting fluid (dodecane, hexadecane, or mineral oil) at different flow rates. Nonwetting fluid saturations increased with increasing flow rates for all five fluid pairs. Viscous fingering occurred when PEG was displaced by either dodecane or hexadecane. For the displacements of water, capillary fingers were observed at low capillary numbers. Fitting the experimental Sn and hc data with the BrooksCorey relationship indicated that the fitted and computed entry pressure heads, based on pore geometry and fluid properties, compare reasonably well. However, the fitted pore geometry factor values for these displacements are considerably lower than what is expected for displacements in homogeneous, highly uniform, porous systems, demonstrating the impact of unstable displacement. It was shown that a continuum‐based multiphase simulator could be used to reasonably estimate the average Sn behavior for unstable wetting fluid displacement in a pore network as long as independently fitted hc–Sn and krn–Sn relations were used.

Determination of Porosity, Formation Resistivity Factor, Archie Cementation Factor, and Pore Geometry Factor for a Glacial Aquifer

Click to increase image sizeClick to decrease image sizeKeywords: Porosity Bulk And Pore-WATER Resistivities Formation Resistivity Factor Archie Cementation Factor Pore Geometry Factor Surface Electric Measurements Grain-SIZE And Water Analyses

New geometry factors for hydraulic property-based soil solution electrical conductivity models

Improved methods are needed to intensively measure ionic solutes in soils. The concentration Ci of ionic solutes in soils is directly proportional to soil solution electrical conductivity σw. Time domain reflectometry (TDR) measures both soil water content θ and bulk soil electrical conductivity σa using the same probes. However, physical/conceptual models are required along with TDR measurements in order to use TDR for in situ estimates of Ci. We discuss a modeling approach [Mualem and Friedman, 1991] based on assumed analogy between tortuosity of electrical and hydraulic flow paths in variably saturated soils. We review the model approach, then derive a general expression for a pore geometry factor FG considering flow of electrical current through randomly distributed capillary soil pores. Two FG are derived based on two conceptual considerations of tortuous capillary length. Four water retention models (WRM) are used to describe soil hydraulic properties in the FG. When fitted to the same measured water retention data, the four WRMs provided substantially different magnitudes for FG. The model was then compared in terms of σw estimates using the two new FG in combination with field-measured θ and σa. One of the new FG produced smaller estimated σw than did that proposed in the original model. This is desirable based on our own and several other published comparisons that indicated the original model may overestimate σw in comparison with independent measurements.

Petrophysical Evaluation of a Slope Fan/Basin-Floor Fan Complex: Cherry Canyon Formation, Ward County, Texas (1)

The Cherry Canyon Formation consists of a 925-ft (280-m) thick section of up to 25 different sandstone and siltstone units that were deposited in deep water in the Delaware basin. Lowstand sedimentation by fluid density currents with periodic turbidity currents resulted in a broad migrating channelized slope fan/basin-floor fan complex exhibiting a complex depositional architecture of reservoir sandstones. Original depositional fabric modified by diagenetic cements and authigenic clays create a range of petrophysical rock types. Type I reservoirs are found in channel sandstones; beds of lesser reservoir quality (type II) are present in laminated overbank/interchannel sandstones. A practical pore geometry classification scheme based on pore/grain shapes and pore throat rad i is used to understand fluid saturations and predict well performance within the context of the depositional framework and structural relief. Pore geometry factors combine with insufficient structural closure to create high water saturations throughout the oil column. Type I (macroporous) reservoirs exhibit oil-water transition zones, and are interbedded with type II (mesoporous to microporous) reservoirs which contain all or mostly water due to high capillarity associated with small pore throat size. Accurate reservoir water saturations can be derived using Archie's equation; when combined with a movable oil analysis and drainage relative-permeability/fractional-flow curves, initial watercuts can be predicted to maximize deliverability from optimal rock types. High original water saturations in the transition zone decrease average water saturations behind the waterflood front, resulting in inefficient secondary recovery. A combined application of sedimentological, petrophysical, logging, and reservoir engineering technologies is necessary to properly evaluate the Cherry Canyon reservoirs.

CRITICAL ANALYSIS OF CONDUCTOMETRIC PHASE TRANSITION POROSIMETRY: II. PORE GEOMETRY FACTORS

ABSTRACT This is the second of two papers which discuss the strengths and weaknesses of conductometric phase transition porosimetry. Potential errors in the determination of pore size distributions associated with the assumption that pore geometry factors are independent of pore size are discussed. Further, a comparison of CPTP pore size distributions with mercury intrusion porosimetry pore size distributions obtained from the testing of replicate samples of hydrated portland cement mortars is used to illustrate the inherent advantages of CPTP for investigations of the pore structure of water sensitive heterogeneous materials.

A Study of Formation Plugging With Bacteria

Abstract This study investigated the nature of formation plugging with bacteria and attempted to relate its characteristics to physical rock properties. Fifteen core samples of four specific formation types were defined and plugged using a commonly occurring, uniform sized dead bacteria, Bacillus subtilis. Two of the formation types were fairly uniform-grained sandstones and two were heterogeneous carbonates. The injection rate and concentration of solids in the brine were held constant during the test runs. The pore geometry factor G was a significant petro-physical rock characteristic for correlation with depth of plugging, but lacked importance as a parameter for rate of plugging. Although the G factor may not completely describe porous rock geometry for plugging predictions, for reservoirs with multi-pore systems, there is evidence that the pore geometry factor might form a basis for establishing injection water specification in more homogeneous reservoirs with only primary porosity development. Introduction GENERAL PURPOSE Injecting water into oil-bearing formations to increase recovery is common practice in the petroleum industry. One of the most serious operational problems involved with water injection wells is the tendency of the porous rock immediately adjacent to the injection wellbore to plug partially. This results in increased injection pressures and/or a decrease in the rate of injection. This plugging in injection wells can result from a number of causes, including bacteria contained in the injected water. The purpose of this work was to investigate the nature of injection plugging with bacteria and to attempt to relate its characteristics to physical rock properties. Many variables exist in research of this type, so, to reduce them, injection rate and concentration of bacteria in brine were held constant. The bacteria used for plugging was a uniform-sized, dead bacteria, Bacillus subtilis, a micro-organism commonly found in water, air and soils. Four specific porous rock types were plugged-two consolidated sandstones and two heterogeneous carbonates. The experimental work involved two distinct phases. The first concerned determining the physical rock properties and the second was the experimental work of actually plugging the selected core samples. PORE GEOMETRY FACTOR Capillary pressure is necessary to displace a wetting fluid from a capillary opening with a nonwetting fluid. The factors which govern capillary pressure are the surface or interfacial tension of the fluids involved, the system wettability and the equivalent pore radius. Thus: (1) Thomeer used the idea that the location and shape of the capillary pressure curve reflect characteristics of the pore structure of any porous media sample. He presented the mathematical description of capillary pressure curves and of indicated differences in pore geometry of samples. (2) where G = pore geometry factorpc = capillary pressurepd = displacement pressure(Vb)pc = fractional bulk volume occupied by thedisplacing fluid at any capillary pressure(Vb)px = fractional bulk volume occupied by thedisplacing fluid at infinite pressure ortotal inter-connected pore volumes. The shape of the curve is defined by the pore geometry factor G. The curve shape is related directly to the sorting and interconnection of the pores of the sample. The location of an infinite number of curves can be defined by the same asymptotes. However, these curves differ in shape, each curve being described by a specific value of G. Thus, the description of a curve is unique when, in addition to the position of its asymptotes, its shape is defined. These curves can be used graphically to determine the characteristic parameters of any arbitrarily located curve. Those parameters that can be approximated from any capillary pressure curve are: total interconnected pore volume, represented by (Vb)px; extrapolated displacement pressure, the abscissa axis; and pore geometry factor, by the curve shape. PROPERTIES OF BRINE AND BACTERIA The fluid used throughout this study was an aqueous solution of sodium chloride, 25,000 ppm by weight. The addition of salt to fresh water was intended to eliminate clay swelling in the sandstone cores and to retard leaching in the limestone cores. JPT P. 201ˆ