Primary Drainage Capillary Pressure Research Articles

A new method in reservoir rock classification in carbonate and sandstone formations

Abstract This study aims to improve rock-type classification by analyzing core data based on the water–oil primary drainage capillary pressure method. A modified empirical equation is proposed using permeability, porosity, and irreducible water saturation to classify rock types based on water–oil primary drainage capillary pressure. We used primary drainage capillary pressure data measured in carbonate and sandstone samples in the Ahvaz Asmari and Mansouri oilfields to evaluate the characterization number (Cn) method. This study consists of two main parts. First, the Cn method is introduced to rock typing, and the permeability is calculated from well log data. In the second part, we present rock-type classification when the water saturation of the formation is more than the irreducible water saturation. The novelty of this work is a simple and efficient technique to rock-type classification using the Cn method. In addition, we present a procedure to assign rock types for the transition zone using the Cn method. Moreover, this study systematically investigates the role of irreducible water saturation in rock typing. The innovation of this work lies in its ability to classify rocks in heterogeneous reservoirs for carbonate and sandstone lithology and allow for the calculation of permeability more accurately from well log data. The comparison results between the Cn method and the flow zone indicator method show the robust clustering ability of the Cn method.

A novel equation to calculate primary drainage capillary pressure based on a porous plate model: Theory and application

This study aims to develop an equation for primary drainage capillary pressure as a function of water saturation based on the porous plate model. Several empirical and semiempirical equations are available to calculate Pc-Sw. The results of the previous equations are not ideal, so this is an attempt to present an accurate equation to calculate Pc-Sw based on governing theoretical physical analysis to describe two-phase immiscible displacement flow in porous media. Volumetric flow rates through the core plug and porous plate are applied to calculate the transport phenomena in porous media. The equation is derived from mass and momentum transfer through a core plug, and Darcy’s law is applied to water flow through a porous plate. Finally, the modified Bessel function is obtained to calculate Pc as a function of Sw. The findings of this study help provide a better understanding of two-phase immiscible displacement flow in porous media. The novelty of this work lies in the ability of the new Pc-Sw equation to accurately fit the primary drainage capillary pressure experimental data obtained from a porous plate, centrifugal, and mercury injection apparatus without restriction. The new equation can be used to calculate the relative permeability and initial fluid distribution in the reservoir. The accuracy of the new equation is a significant advantage compared to Brooks-Corey's Pc-Sw equation; therefore, the research results lead to an incremental advance in the field. This study fills the gap between analytical and empirical models to find the Pc-Sw equation.

A new approach to measure wettability by relative permeability measurements

Wettability is a key factor controlling the flow of fluids, solutes, heat and electrical current in porous media, and therefore it is important in studies of various processes including CO2 storage, secondary and tertiary oil recovery, as well as the displacement of water and nonaqueous phase liquid (NAPL). Although Amott-Harvey and USBM are conventional industry-standard techniques for measuring average wettability, they have some limitations. In this paper, we show that, in a plot of the relative permeability of a fluid, the area below the curve is closely related to the wettability. By using the areas below the water and oil relative permeability curves, we derive a new wettability index (called modified Lak). To demonstrate the applicability of this new index and testing other indices, we performed primary imbibition relative permeability, and primary imbibition and secondary drainage capillary pressure measurements on twenty carbonate reservoir samples. In general, all indices predicted oil-wet character of the tested rocks. USBM was associated with the broadest range of variation, whereas the new index corresponded to the smallest range of variation. Amott-Harvey and Lak, however, fell between USBM and the new index, with fairly similar ranges of variation. In addition, we report the correlations between different indices, and the change of wettability indices vs. reservoir depth. Advantages and limitations of different wettability indices are also discussed. Since each wettability index has some limitations in revealing the true state of wettability, none of these indices can be considered as an absolute measurement. Therefore, different indices should be regarded as complementary to each other, and determination of wettability should not be limited to only one method.

Analysis of the bounded and unbounded forms of USBM wettability index

Understanding wettability is important in many processes where porous media and fluids are in contact. The U.S. Bureau of Mines (USBM) is one of the industry standard techniques for measuring wettability. This index is calculated as USBM=lg(A1A2), where A1 and A2 are the areas under capillary pressure curves of oil-drive and water-drive processes, respectively. Usually, the USBM is mistakenly assumed to vary over the range of −1 to 1 and compared with other indices. In this study we indicate that the lower and upper bounds of this index are not fully known in practice. As a result, comparison between USBM and other indices may cause erroneous interpretations due to dissimilar ranges of variation. In addition, even during examining the USBM of a sample it may not be possible to accurately interpret its wettability. We highlight the bounded form of the USBM index (denoted as USBM∗=A1−A2A1+A2), which varies over the range of −1 to 1, and suggest that it should replace the traditional form of USBM index. Twenty limestone core-plugs were collected from Asmari and Fahlian formations in two Iranian fields. These samples were used for performing primary imbibition relative permeability measurements, as well as primary imbibition and secondary drainage capillary pressure tests. These experiments are used to show the differences between USBM and USBM∗ in comparative studies and compare them against other indices of Amott-Harvey, Lak and modified Lak.

A note on dynamic rock typing and TEM-function for grouping, averaging and assigning relative permeability data to reservoir simulation models

For years, rock typing based on two-phase flow characteristics was mainly founded on grouping primary drainage capillary pressure curves, while rock classification based on relative permeability measurements and its practical applications were overlooked. Recently, a dynamic rock typing approach was proposed by defining a True Effective Mobility tool (TEM-function) to convert relative permeability data to fluid flow indicators. This technical note sheds further light on the concept of dynamic rock typing and TEM-function. Moreover, in previous studies the fact that how identified petrophysical dynamic rock types (PDRTs) and their corresponding average relative permeability tables should be assigned to simulation grid cells was not addressed. We accordingly investigate whether a general property can be found to assign average relative permeability data to grid cells. For this purpose, we apply TEM-function to identify PDRTs and present average relative permeability tables using gas-oil relative permeability experiments on a subset of carbonate samples. We also analyze the PDRTs in a counter-part water-oil system and investigate their relationship with gas-oil PDRTs. Results show that the recent dynamic rock typing approach incorporates forward and inverse processes that are physically meaningful and consistent with laboratory analysis and reservoir simulation processes. The strong dependency of TEM-function on the ratio of permeability to porosity enables us to introduce a general property to assign average relative permeability data to grid cells. Furthermore, while PDRTs in the gas-oil systems were almost identical, PDRTs in the water-oil system were dissimilar and different from the gas-oil counterpart. This confirms that each saturation function needs its specific rock typing scheme.

New technique of True Effective Mobility (TEM-Function) in dynamic rock typing: Reduction of uncertainties in relative permeability data for reservoir simulation

Performance predictions made by reservoir simulators are highly dependent on experimentally-determined relative permeability data assigned to simulation grid cells. There is often no apparent relationship between this type of data and a quantifiable property of cells, meaning that samples within a group of neighboring relative permeability curves do not have similar values of a common characterization property. On the other hand, it is easier to correlate primary drainage capillary pressure data to cell properties and create a petrophysical static rock type (PSRT) from a group of similar capillary pressure data. The common approach is to average the relative permeability data corresponding to each PSRT and input that into a simulator. In practice, relative permeability curves corresponding to a given PSRT would exhibit a significant scatter, especially in carbonate formations. This will cause the resulting average relative permeability data to be highly uncertain and poorly representative of true dynamic behavior of the cells.In this study, a new technique is proposed to reduce uncertainties associated with classical methods of assigning relative permeability data to grid cells of a simulation model. The idea is based on a robust and universal criterion for characterization of dynamic characteristics of rocks from laboratory-derived flow data to define a petrophysical dynamic rock type (PDRT). A PDRT is defined as a collection of rocks with similar True Effective Mobility (TEM) behavior. A TEM-function for analysis of relative permeability is defined as a product of relative mobility by the square of a mean pore radius, and is analogous to the well-known J-function for scaling capillary pressure curves. For a given PDRT, a special weighted average of corresponding relative permeability data, or average TEM data should be used as input to a simulator. In the latter case, the simulator should have the capability to back-calculate cells’ quasi-relative permeabilities using the inputted average TEM data. Moreover, we show that factors such as wettability and pore-scale heterogeneity can cause phase-dependent dynamic characteristics (i.e., different dynamics with respect to each fluid phase). Hence, different dynamic rock typing schemes should be applied to the flow of each fluid in system. A structured methodology is presented to identify PDRTs using TEM-function and prepare input parameters to simulators by analyzing relative permeabilities using the universal criterion developed in this work. Ultimately, special core analysis data from the Asmari Formation, a carbonate reservoir from one of the Iranian Fields, is used to verify and demonstrate the applicability of the presented technique.

An Investigation into Different Correlation Methods between NMR T2 Distributions and Primary Drainage Capillary Pressure Curves Using an Extensive Sandstone Database

Many workers have recognised the link between Nuclear Magnetic Resonance (NMR) derived T2 distributions and pore size distributions in reservoir rocks. This property has been used to develop models to obtain primary drainage capillary pressure curves from T2 distributions. These models often assume that the rocks pore space resembles a simple bundle of capillary tubes. They do not consider the existence of multiple pore body connections and pore body restrictions/throats. The most successful models utilise variable scaling factors to convert T2 times to pore diameters and hence capillary pressure. The variable scaling factor approach recognises the existence of variable surface relaxivity throughout the pore space due to variations in mineralogy and pore topography. This investigation uses SCAL data from the ART NMR Sandstone Rock Catalogue to obtain core calibrated variable scaling factors for 174 reservoir sandstone samples. The depositional environments for these samples include; aeolian, fluvial, coastal and shallow and deep marine. The samples used have a wide variety of mineralogy, diagenetic overprints and cover six orders of magnitude in absolute permeability. Three different methods for obtaining the scaling factors are presented and the relative merits of each discussed. A global model to predict capillary pressure from NMR T2 distributions in reservoir sandstones has been developed using correlations between the variable scaling factors and permeability.

Saturation Modeling Under a Complex Fluid-Fill History: Drainage and Imbibition

This article, written by Special Publications Editor Adam Wilson, contains highlights of paper SPE 188594, “Saturation Modeling Under Complex Fluid-Fill History—Drainage and Imbibition,” by H. Xian, SPE, L. Beugelsdijk, SPE, and A. Kohli, SPE, Shell; E. Fokkema, SPE, Nederlandse Aardolie Maatschappij; and A. Cense, Shell, prepared for the 2017 Abu Dhabi International Petroleum Exhibition and Conference, Abu Dhabi, 13–16 November. The paper has not been peer reviewed. This paper presents a saturation-modeling approach for fields and reservoirs with complex hydrocarbon-charging histories. The model resolves saturation-height functions for the primary-drainage, imbibition, and secondary-drainage equilibriums. As part of the approach, a method of evaluating the residual-hydrocarbon saturation below the initial free-water level (FWL) is proposed. The developed theory is based on the principle of capillary-pressure/saturation hysteresis on the drainage/imbibition process in a water-wet system. Introduction Many discovered oil and gas fields are found to have gone through complex fluid-fill histories where residual hydrocarbons are observed below the FWL. To add to the complexity, some of these are giant fields and are divided into compartments with varying contacts and FWLs. To model saturation-height dependencies for reservoirs in fields under imbibition equilibrium, one of the adopted practices is to use a drainage model built from core data or log data to compute the saturation starting from the original FWL contact but only calculate the hydrocarbon-in-place volumes above the initial FWL. Another common practice is to build log-based drainage models using the current FWL while ignoring the uncertainties in the transition zone from the imbibition effect. These approaches typically lead to an inappropriate estimation of the hydrocarbon saturation in the transition zone and normally require separate models for different segments of the field. In this paper, an approach is presented for modeling the core capillary-pressure imbibition and secondary drainage cycles, integrating with log-based saturation-height models, and designing a work flow for upscaling and implementation in 3D reservoir models. Imbibition and Secondary-Drainage-Model Theory Hysteresis of Saturation/Capillary Pressure and Analytical Imbibition Model Method. Modeling of saturation/capillary pressure of primary-drainage-imbibition hysteresis is more complicated than other types of hysteresis effects because its cycle is not a closed loop; the imbibition route does not end at the starting point of the primary drainage route. Fig. 1 shows the multi cycle drainage/imbibition scanning curves in mixed-wet or strongly water-wet rock systems. Saturation changes caused by the imbibition-hysteresis effect are larger at lower capillary pressures in the transition zone but become insignificant over the higher capillary pressures across the main nonwetting-phase column. The primary-drainage capillary pressure can be measured by high-pressure mercury injection, porous plate, and centrifuge. Spontaneous imbibition can be measured only by use of the porous-plate technique or by use of an Amott cell. The forced imbibition part of the imbibition capillary pressure can be measured by porous plate and centrifuge.

A new approach in petrophysical rock typing

Petrophysical rock typing in reservoir characterization is an important input for successful drilling, production, injection, reservoir studies and simulation. In this study petrophysical rock typing is divided into two major categories: 1) a petrophysical static rock type (PSRT): a collection of rocks having the same primary drainage capillary pressure curves or unique water saturation for a given height above the free water level, 2) a petrophysical dynamic rock type (PDRT): a set of rocks with a similar fluid flow behavior. It was shown that static and dynamic rock types do not necessarily overlap or share petrophysical properties, regardless of wettability.In addition, a new index is developed to define PDRTs via the Kozeny-Carman equation and Darcy's law. We also proposed a different index for delineation of PSRTs by combining the Young–Laplace capillary pressure expression and the Kozeny-Carman equation. These new indices were compared with the existing theoretical and empirical indices. Results showed that our indices are representatives of previously developed models which were also tested with mercury injection capillary pressure, water-oil primary drainage capillary pressure, and water-oil relative permeability data on core plugs from a highly heterogeneous carbonate reservoir in an Iranian oil field. This study enabled us to modify the conventional J-function to enhance its capability of normalizing capillary pressure data universally.

A Blind Study of Four Digital Rock Physics Vendor Laboratories on Porosity, Absolute Permeability, and Primary Drainage Capillary Pressure Data on Tight Outcrops

A Blind Study of Four Digital Rock Physics Vendor Laboratories on Porosity, Absolute Permeability, and Primary Drainage Capillary Pressure Data on Tight Outcrops

A Blind Study of Four Digital Rock Physics Vendor Laboratories on Porosity, Absolute Permeability, and Primary Drainage Capillary Pressure Data on Tight Outcrops

A Blind Study of Four Digital Rock Physics Vendor Laboratories on Porosity, Absolute Permeability, and Primary Drainage Capillary Pressure Data on Tight Outcrops

Quantifying fluid distribution and phase connectivity with a simple 3D cubic pore network model constrained by NMR and MICP data

A computer algorithm is implemented to construct 3D cubic pore networks that simultaneously honor nuclear magnetic resonance (NMR) and mercury injection capillary pressure (MICP) measurements on core samples. The algorithm uses discretized pore-body size distributions from NMR and pore-throat size versus incremental pore-volume fraction information from MICP as initial inputs. Both pore-throat radius distribution and body–throat correlation are iteratively refined to match percolation-simulated primary drainage capillary pressure with MICP data. It outputs a pore-throat radius distribution which is not directly measurable with either NMR or MICP. In addition, quasi-static fluid distribution and single-phase connectivity are quantified at each capillary pressure stage. NMR measurements on desaturating core samples are simulated from the quantitative fluid distribution in a gas-displacing-water drainage process and are verified with laboratory measurements. We invoke effective medium theory to quantify the single-phase connectivity in two-phase flow by simulating percolation in equivalent sub-pore-networks that consider the remaining fluid phase as solid cementation. Primary drainage relative permeability curves quantified from fluid distribution and phase connectivity show petrophysical consistency after applying a hydrated-water saturation correction. Core measurements of tight-gas sandstone samples from the Cotton Valley formation, East Texas, are used to verify the new algorithm.

Measurements of the capillary trapping of super-critical carbon dioxide in Berea sandstone

[1] We measure primary drainage capillary pressure and the relationship between initial and residual non-wetting phase saturation for a supercritical carbon dioxide (CO2)-brine system in Berea sandstone. We use the semi-permeable disk (porous-plate) coreflood method. Brine and CO2 were equilibrated prior to injection to ensure immiscible displacement. A maximum CO2 saturation of 85% was measured for an applied capillary pressure of 296 kPa. After injection of brine the CO2 saturation dropped to 35%; this is less than the maximum trapped saturation of 48% measured in an equivalent n-decane (oil)-brine experiment. The dimensionless capillary pressure is the same to within experimental error for supercritical CO2-brine, n-decane-brine and a mercury-air system. CO2 is the non-wetting phase and significant quantities can be trapped by capillary forces. We discuss the implications for CO2 storage.

Impact of surfactant-induced wettability alterations on DNAPL invasion in quartz and iron oxide-coated sand systems

Dense non-aqueous phase liquids (DNAPLs) present in the subsurface may contain surface active compounds that impact DNAPL migration and distribution. While a number of studies have revealed the role surface active compounds play in altering the wettability of quartz sand, few have considered the implications for other minerals common to contaminated sites. This study extends understanding of DNAPL/surfactant wettability to iron oxide surfaces. Specifically, quartz and iron oxide-coated sands in a tetrachloroethene (PCE)/water system containing the organic base (an organic molecule that acts as a base) dodecylamine (DDA) were compared at a variety of scales. Wettability of the minerals' surfaces, and the impact of wettability on capillary resistance to DNAPL entry, were assessed as a function of pH through: (i) advancing and receding contact angles, (ii) primary drainage capillary pressure–saturation experiments, and (iii) small, two-dimensional, flow cell experiments. The work revealed that, at neutral pH and under identical boundary capillary pressures, DNAPL invaded quartz sand but not iron oxide-coated sand; however, at low pH, DNAPL invaded both sands equally. These differences were demonstrated to be due to wettability alterations associated with the strength of attractive forces between DDA and the mineral surface, dictated by the isolectric point of the minerals and system pH. Observed differences in DNAPL invasion behavior were consistent with measured intrinsic contact angles and P c–S relationships, the latter requiring scaling by the operative contact angle inside the porous medium for a meaningful comparison. This study suggests that the distribution of minerals (and, more specifically, their isoelectric points), as well as the aqueous phase pH at a given site, may have a significant impact on the DNAPL source zone architecture.

Capillary Pressure and Wettability Behavior of CO2 Sequestration in Coal at Elevated Pressures

SummaryEnhanced coalbed-methane (ECBM) recovery combines recovery of methane (CH4) from coal seams with storage of carbon dioxide (CO2). The efficiency of ECBM recovery depends on the CO2 transfer rate between the macrocleats, via the microcleats to the coal matrix. Diffusive transport of CO2 in the small cleats is enhanced when the coal is CO2-wet. Indeed, for water-wet conditions, the small fracture system is filled with water and the rate of CO2 sorption and CH4 desorption is affected by slow diffusion of CO2. This work investigates the wetting behavior of coal using capillary pressures between CO2 and water, measured continuously as a function of water saturation at in-situ conditions. To facilitate the interpretation of the coal measurements, we also obtain capillary pressure curves for unconsolidated-sand samples. For medium-and high-rank coal, the primary drainage capillary pressure curves show a water-wet behavior. Secondary forced-imbibition experiments show that the medium-rank coal becomes CO2-wet as the CO2 pressure increases. High-rank coal is CO2-wet during primary imbibition. The imbibition behavior is in agreement with contact-angle measurements. Hence, we conclude that imbibition tests provide the practically relevant data to evaluate the wetting properties of coal.

Intermediate wettability by chemical treatment

To study the effect of wettability on recovery, we used a chemical additive that changes the surface properties of natural rock samples while keeping interfacial tension and viscosity constant. The wettability change is weaker than for other chemical treatments (e.g., silane) and is therefore closer to reservoir cases. The chemical additive is a potassium methyl siliconate that is soluble in water. A polymerization of the adsorbed layer on the pore surface is obtained when the pH is lowered near neutral. Outcrop sandstone samples were treated either with or without the presence of oil (at Swirr) using carbon dioxide as a neutralizer. Efficiency of the treatment is determined mainly by comparing centrifuge (negative) imbibition capillary pressure curve on treated and untreated samples. Micropore membrane technique was also applied to measure the positive imbibition capillary pressure curve. The main results are (1) the final oil saturation (Sor) is reduced from 0.4 to 0.3 and 0.1 depending on how the treatment was performed; (2) there are only minor modifications on the primary drainage capillary pressure curve; and (3) water relative permeability at Sor measured after centrifuge forced imbibition is not modified by the treatment.

Statistical characterization and stochastic modeling of pore networks in relation to fluid flow

Flow properties of reservoir rocks can be computed from an accurate depiction of the porosity network in three dimensions available from synchrotron Xray microtomography. In order to relate computed transport properties to the input dataset, the complex pore networks must be described statistically. A porous media description was deemed adequate if a synthetic medium, possessing similar transport properties, could be generated from acquired statistical information. Synthetic media, based upon Berea sandstone extended variogram statistics, were generated with an actual slice from a 3-D microtomographic image as conditioning data. Control of local porosity variation was observed to be important in the stochastic simulation of porous media by the simulated annealing method, as inclusion of this higher order constraint data reproduced natural variations observed in pore-size distributions. Realizations with the traditional variogram as the only target in the objective function did not honor poresize distribution information. Permeability estimates by the lattice Boltzmann method indicated that the proper level of interConnectivity was not achieved during geostatistical modeling with only two point spatial statistics. Connectedness information, readily available from primary drainage capillary pressure data, forced permeability estimates of synthetic media in the direction of the permeability computed for the parent microtomographic image of Berea sandstone. As a result of this study, it was concluded that global spatial correlation statistics, for example, the traditional variogram, must be supplemented with local variability and connectivity information to adequately characterize a three-dimensional property distribution for fluid transport. Extended porosity spatial correlation structure, extracted from standard imaging techniques, and a capillary pressure drainage curve are perhaps sufficient to characterize a system in terms of pore size, connectedness, and permeability. However, more rapid algorithms are needed to introduce porosimetry information as standard practice in stochastic modeling by the simulated annealing method.

Influence of Organic Acid Solution Chemistry on Subsurface Transport Properties. 2. Capillary Pressure−Saturation

Two-phase flow models of subsurface transport often require the constitutive relationship of capillary pressure as a function of saturation as part of the data input. This part of the study correlates the solution chemistry findings from the previous paper with observed changes in the primary drainage capillary pressure−saturation relationship for a fine- to medium-grained quartz porous medium. The results showed that the solution chemistry was directly reflected in the capillary pressure−saturation relationship. The major factor determining the degree of reduction in capillary pressure was the concentration and speciation of octanoic acid dissolved in the aqueous phase, the same variables reported in part 1 as critical in determining the surface and interfacial tension. Because measurements of the contact angle showed that the system stayed strongly hydrophilic under all conditions, the capillary pressure relationships could be scaled adequately using the appropriate values of surface or interfacial tension only. Since organic acid speciation had opposite effects on capillary pressure in the air−water and o-xylene−water systems, the impact of pH on the movement of a contaminant front will depend on whether the contamination occurs in the vadose zone (air−aqueous phase system) or saturated zone (organic liquid−aqueous phase system).