Saturation Height Modeling Research Articles

Implementing pore size distribution into saturation height function modelling of reservoir rock types: A case study on a carbonate gas reservoir

The accurate determination of saturation-height functions for modeling multiphase fluid flow in porous media is critical for applications, such as hydrocarbon recovery and subsurface CO2/H2 storage. The challenges associated with water saturation distribution in carbonate reservoirs arise from their inherent heterogeneity and complex pore systems. Addressing such challenges, this study aims to introduce a robust saturation-height function model that considers a non-linear relationship between capillary pressure and saturation, leading to more reliable estimates of fluid saturations. To achieve this, modifications were performed on a saturation height model based on the relationship between porosity, permeability, and pore size distribution (PSD). First of all, the capillary pressure model implemented in the previously introduced PSD-based approach was replaced by a model suitable for heterogeneous reservoirs, fitting the available mercury injection capillary pressure (MICP) data with higher accuracy. Additionally, the derivation of the relations between the optimum pore throat radius and matching parameters of the capillary pressure model was conducted by finding the best correlation among all the available data in the previous approach. For the first time in this study, considering the resemblance in rock properties like capillary pressure and PSD within each rock type, individual correlations among these parameters were established for each reservoir rock type. The predicted saturation height model was cross-checked against the log and core-derived saturation heights, demonstrating a high level of consistency, particularly along the gas-saturated regions. The obtained results were also compared with the conventional saturation height models, including the Leverett J-Function, Johnson's method, and Cuddy's approach. The significance of the modifications was underscored through a comparison of results with those achieved by the previous approach in which the rock typing was ignored. Although the PSD method, which ignored rock types, exhibited high consistency with log data, our modifications yielded far better predictions by improving the coefficient of determination from 0.68 to 0.84.

Petrophysical interpretation of logging-while-drilling borehole measurements in the presence of electrical anisotropy, mud-filtrate invasion, noise, and well deviation effects

Petrophysical interpretation of logging-while-drilling (LWD) borehole measurements in the presence of electrical anisotropy, mud-filtrate invasion, noise, and well deviation effects remains a challenge in formation evaluation. In high-angle and horizontal (HAHZ) wells penetrating electrically anisotropic sandstones, phase and attenuation apparent resistivity logs often exhibit values larger than resistivity parallel to bedding planes. Consequently, traditional interpretation methods often fail to accurately estimate hydrocarbon saturation when using only the long-spacing phase apparent resistivity log (P40H) in petrophysical calculations. We implement two approaches (analytical and Bayesian) to estimate horizontal and vertical resistivities from apparent resistivity measurements. The first analytical approach is based on the numerical simulation of LWD resistivity measurements using synthetic models under various conditions of electrical anisotropy and well inclination to derive analytical models. The relative error of analytical approximations is less than 6%. In the presence of measurement noise and shoulder-bed effects, we implement a Bayesian method for well-log inversion and uncertainty quantification. The relative error of Bayesian inversion is less than 2%. Estimates of horizontal and vertical resistivities then can be used for petrophysical analysis. A challenging set of synthetic and field examples of HAHZ wells penetrating electrically anisotropic formations is selected for examination and verification of the new methods. For radial lengths of invasion less than 20 cm (8 in), sensitivity analysis indicates that the effects of conductive mud-filtrate invasion on long-spacing resistivity logs are negligible. The long-spacing phase (P40H) and attenuation (A40H) apparent resistivities are used to estimate horizontal and vertical resistivities. In the field examples under study, electrical anisotropy is caused by intercalated laminations of coarse- and fine-grained sandstones; the volumetric concentration of shale is negligible. Considering that Archie’s parameters are direction dependent, sensitivity analysis indicates that the effective value of the saturation exponent parallel to bedding planes is less sensitive to the volumetric concentration of fine-grained sandstone layers compared with the saturation exponent perpendicular to bedding planes. Thus, water saturation of grain-laminated sandstones in HAHZ wells can be estimated using horizontal resistivity with Archie’s parameters that are consistent with petrophysical interpretations performed in vertical wells. Estimates of water saturation in the field examples using horizontal resistivity agree with saturation-height models. Compared with conventional interpretation methods that use P40H as the formation resistivity, the new approach improved the estimation of hydrocarbon saturation by 10%.

Saturation Height Modelling for Tight Sandstone Reservoirs with Gas Diffusion Dynamics Taken into Account

Interpreting and predicting the saturation of tight sandstone gas reservoirs are the key task to improve the reservoir development. The role of gas diffusion dynamics is stronger than that of buoyancy during the gas accumulation of tight sandstone reservoirs. In this study, a saturation height model that takes gas diffusion dynamics into account is proposed, which can complement logging saturation interpretation and provide a better practice in saturation prediction. Taking the study of the Sulige tight sandstone gas reservoir in China as an example, the saturation height model compares the controlling factors and uncertainties affecting the saturation distribution, characterizes the complex gas-water distribution, and determines the lower gas charging limits. This study concludes that the configuration between gas diffusion dynamics and reservoir capillary pressure controls the distribution of saturation. The buoyancy effect only serves to improve the saturation at regional uplifts with good petrophysical properties. The different saturation characteristics in the central, western, and eastern parts of the Sulige gas field are precisely caused by the different configurations of source rock quality and reservoir quality. This study provides a key reference for static model and development deployment.

New Iterative Resistivity Modeling Workflow Reduces Uncertainty in the Assessment of Water Saturation in Deeply Invaded Reservoirs

A new iterative modeling workflow has been designed to reduce the uncertainty of water saturation (Sw) calculations in the tight Barik sandstone in the Sultanate of Oman. Results from this case study indicate that Sw can be overestimated by up to 20 s.u. if the as-acquired deep resistivity is used in volumetric calculations. Overbalanced drilling causes deep invasion of water-based mud (WBM) filtrate into porous and permeable rocks, leading to the radial displacement of in-situ saturating fluids away from the wellbore. In low-porosity reservoirs drilled with WBM, the inability of the filtration process to quickly build impermeable mudcake translates into long radial transition zones. Under certain reservoir and drilling conditions, deep resistivity logs cannot reliably measure true formation resistivity and are, therefore, unable to provide an accurate assessment of hydrocarbon saturation. The effect of mud-filtrate invasion on resistivity logs has been extensively documented. Processing techniques use resistivity inversion and tool-specific forward modeling to provide uninvaded formation resistivity logs, which are much better suited for in-place resource volume assessment. However, sensitivity analysis shows that the accuracy of invasion-corrected logs dramatically decreases as the depth of invasion increases, whereby the inversion process needs to be further constrained. The new workflow is designed to reduce the non-uniqueness of true formation resistivity models so that they honor multiple and independent petrophysical data. The inversion routine utilizes a Bayesian algorithm coupled with Markov-Chain Monte Carlo (MCMC) sampling. Inversion results are iteratively modified based on two rock property models : one derived from rock-core data (helium expansion porosity and Dean-Stark saturations) and the other using an equivalent log interpretation of thick reservoir intervals from oil-based mud (OBM) wells. Simulated borehole resistivity is compared to field logs after each validation loop against rock property models. The new inversion-based workflow is extensively tested in the unconventional tight Barik Formation across water-free hydrocarbon and perched water intervals, and inversion-derived Sw models are independently validated by capillary-pressure-derived saturation-height models and fluid inflow rate from production logs.

Multivariate Characterization, Modeling of Paleo Zone Improves History Matching

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper IPTC 22034, “Rigorous Multivariate Characterization and Modeling of Paleo Zone for Simulation Model History Matching Under Reservoir Uncertainty,” by Nader Y. Bu-Khamseen, SPE, Marko Maucec, SPE, and Anwar R. Awan, SPE, Saudi Aramco, et al. The paper has not been peer reviewed. Copyright 2022 International Petroleum Technology Conference. Reproduced by permission. _ The presence of a paleo zone, which frequently exists below free-water-level (FWL) surfaces, can affect dynamic reconciliation of reservoir simulation models. In the complete paper, the authors present an approach that integrates characterization of paleo zones, parameterization of paleo-zone conductivity, and application of flow profiles as a guide in an accelerated history-matching study of a large-scale dual-porosity/dual-permeability model. The approach to probabilistic parameterization of paleo-zone conductivity has contributed to a model with high quality and rendered a reservoir simulation model with reliable predictive capability in accelerated time. Methods and Models Geological Modeling of Paleo Zone. Structural growth evidences the filling history and displacement occurred by regional tilting, stamping a record of relic (or paleo) oil in the pore system below the current FWL. Applicable saturation-height models are generated based on dedicated core petrophysical rock typing in conjunction with a robust FWL and paleo-oil FWL inversion, a process that allows reproduction of the saturation profile as seen from logs (original logs not affected by production) and the oil-saturation tail as seen below the FWL. The primary methodology behind the approach presented in the paper consists of determining the volume of paleo oil by modeling FWL and paleo-oil FWL surfaces, defining the corresponding paleo zone within the reservoir, and dynamic evaluation of communication between the aquifer, paleo oil, and oil zones; the two surfaces come from an inversion process of the saturation height function. Current developments for the incorporation of the most-important variables affecting dynamic conditions (assisted history matching, uncertainty quantification, multivariate parameterization, and static and dynamic calibration) in the reservoir have allowed incorporation of, and sensitivity studies of, some overlooked parameters, including paleo-oil characterization, modeling, and simulation. Adjusting Petrophysical Properties Inside the Paleo Regions. Petrophysical properties (porosity and permeability) inside the paleo-oil region are modeled based on the bulk volume of water (BVW) from log interpretation. The higher the BVW, the higher the chance of effective communication between the oil leg and the aquifer. These modeled multipliers represent the probability of the sealing character of the paleo-oil region because this accumulated hydrocarbon may not be entirely homogeneous nor uniformly distributed, as suggested by dynamic data and corroborated by core samples. The methodology implemented to represent the presence of the paleo zone in the interpreted and modeled region between the current FWL and the paleo-oil FWL incorporates the use of multipliers in porosity and permeability, allowing the reproduction of the blocking or baffling effect caused by the presence of residual-oil saturation.

Naturally Fractured Carbonate Reservoir Characterization: A Case Study of a Mature High-Pour Point Oil Field in Hungary

An integrated technical study was conducted for a field development project in west Hungary. This study offers a better solution for estimating petrophysical properties and fracture facies vertically along the well and laterally for 3D static and dynamic models of naturally fractured reservoirs in carbonate rocks. More than 30 wells with 40 years of production history were used in order to build reliable static and dynamic models. The fracture class/facies plays an essential role in the spatial distribution of petrophysical properties during 3D reservoir modeling. It was defined by integrating conventional logs, image logs, drilling parameters, and production or well test data. Three fracture facies are defined as macrofracture (including permeable subseismic fault), microfracture, and host rock. Subsequently, the fracture class’s spatial distribution is guided by seismic attributes of fault likelihood combined with the geological concept of the fault and damage zone. As a result, the established fracture classes along the wells are validated by static and dynamic subsurface data. A spherical self-organizing map (SOM) was also implemented for predicting the open-fracture location in wells having limited subsurface data. Moreover, fracture lateral distribution follows the distribution of the fault zone of the fault core, high damage zone, low damage zone, and host rock. The higher the fault displacement, the wider the damage zone and fault core formed. Macrofractures and microfractures frequently appear around the fault core and high damage zone. While only microfractures are dominantly present in the low damage zones, in contrast, the unfractured class is dominantly distributed in the host-rock area. Also, the lithologies are considered in distributing the fracture class because the rock mechanic properties and the number of fractures are strongly controlled by rock compositions. Once the fracture class is distributed, porosity, permeability, and water saturation are modeled in the three-dimensional (3D) geocellular model. Finally, this fracture class also plays a role as a rock typing for reservoir simulation. The saturation height model is built using the fracture class distribution resulting in the initialization, history-matching process, and production forecast from 20 wells showing excellent quality. As a novelty, this study offers a better understanding of fracture distribution and accelerates the history-matching process with a more confident result of the production forecast. In the absence of advanced technologies, like image logs and production logging (PLT) measurements, this study still effectively assists us in recognizing the fracture presence and its quality in both well-depth interval and 3D spatial space, and successfully guided us in proposing new infill drilling with strong confidence and delivering on the high end of expected results.

A new integrated approach to resolve the saturation profile using high-resolution facies in heterogenous reservoirs

The saturation calculation in complex reservoirs remains a major challenge to the oil and gas industry. In simple formations, a tendency towards simple saturation models such as Archie or Simandoux for clean and shaly reservoirs respectively is always preferable. These models were found to be working effectively in homogeneous formations within which the porosity and permeability are linked in the light of a simple facies scheme. Where the rocks show some degrees of heterogeneity, the well-logs are usually affected by different factors. This adversely results in a compromised or averaged log profiles that may affect the saturation calculations. Four wells drilled across a shaly sand of high heterogeneity have been studied in the Perth Basin, Western Australia. The aim is to resolve the hydrocarbon saturation and explain the high productivity results, despite the high water saturation, obtained through a conducted formation well test across the interested reservoir zones. A new integration technique between a suite of conventional and advanced logging tools together with the capillary pressure measurements has been carried out to generate a high-resolution reservoir saturation profile, that is lithofacies dependent. Three different independent methods were used in the studied wells to calculate the saturation and to reduce the uncertainty of the final estimated profiles. The methods are the resistivity-based saturation, the NMR-based irreducible saturation, and a new application through saturation height modeling. Furthermore, through the workflow, an effective calibration for the magnetic resonance T2 cutoff has been applied that is supported by the excellent reservoir production behavior from such complex reservoir. The methodology will help resolve the saturation calculation as one of the most challenging reservoir parameters, particularly where the resistivity logs are affected in complicated shaly sand environments. The effectiveness of the workflow shines the possibility to predict high resolution facies and saturation profiles in the lack of resistivity logs. A further possibility can complete the analysis on real time basis, which can certainly provide facies and saturation profiles extended to the uncored wells. Application of this methodology in the uncored wells has shown very encouraging results in various well trajectories, either vertical, deviated or horizontal long boreholes.

A New Approach to 3D Saturation Height Modeling by Coupling a Capillary Pressure Model with Pore Throat Size Distribution

A New Approach to 3D Saturation Height Modeling by Coupling a Capillary Pressure Model with Pore Throat Size Distribution

Water Saturation Modeling Challenges in Oil-Down-to Wells: An Example from a Multidarcy North Sea Reservoir

Summary The initial water saturation in a reservoir is important for both hydrocarbon volume estimation and distribution of multiphase flow properties such as relative permeability. Often, a practical reservoir engineering approach is to relate relative permeability to flow property regions by binning of the initial water saturation. The rationale behind this approach is that initial water saturation is related to both the pore-throat radius distribution and the wettability of the rock, both of which affect relative permeability. However, pore-throat radius and wettability are usually not explicitly included in geomodel property modeling. Therefore, the saturation height model should not only capture an average hydrocarbon pore volume but also reflect the underlying mechanisms from hydrocarbon migration history and its impact on initial water saturation distribution. This work introduces and describes a new term, excess water, for more precise classification of saturation height model scenarios in reservoirs in which multiple mechanisms have interacted and caused a complex water saturation distribution. An example of the presence of transition zones related to drained local perched aquifers (excess water) in oil-down-to (ODT) wells is shown using a limited data set from a North Sea reservoir. The physical basis for drainage and imbibition transition zones connected to both regional and perched aquifers is given. The distribution of initial water saturation in reservoirs containing excess water is demonstrated through numerical modeling of oil migration over millions of years. Highly permeable reservoirs are more likely to have locally trapped water because of lower capillary forces. A static situation occurs in areas where the capillary forces cannot maintain a high enough water saturation for further water drainage. On the other hand, both high- and low-permeability reservoirs may have significant excess water because of ongoing dynamic effects. In both cases, long distances for water to drain laterally to a regional aquifer enhance the possibility for a dynamic excess water situation.

Petrophysical modeling in the absence of core data in a small, marginal field in the Mumbai Offshore Basin, India

The best petrophysical models are based on direct measurements from the core. Unfortunately, core is not available in many cases, either for economic, logistical, or historical reasons. In this study, we needed to construct a detailed Field Development Plan (FDP) for the small, marginal B-9 field in the Western Offshore Basin, India, which did not merit core acquisition. The objective is to propose a workflow for building a petrophysical model with limited data sets instead of a typical FDP workflow. After analyzing the assumptions, limitations, and uncertainties involved in the petrophysical model, we used advanced petrophysical logs to reduce uncertainty and create a robust petrophysical model. We carried out a log-based petrophysical study to determine the volume of shale, porosity, saturation, and permeability. The advanced petrophysical logs including spectroscopy, nuclear magnetic resonance (NMR), formation pressures, and well testing data are used to calibrate the petrophysical model. Spectroscopy data are used to calibrate the mineralogical volumes and grain density, whereas the porosity is calibrated from NMR data. We calibrated log-derived permeability results with NMR permeability and mobility from well test data. We used heterogeneous rock analysis on petrophysical outputs to carry out petrophysical rock typing (PRT). This has helped in establishing the porosity-permeability relationship and saturation-height model for each PRT. In the absence of irreducible water saturation ([Formula: see text]) information from the core, NMR-derived [Formula: see text] is calculated and then used to calibrate the saturation model. Log-derived permeability and saturation are estimated, which agrees well with the available testing data. This provided a robust petrophysical model that served as a basis for geologic static and reservoir dynamic models. The gas-down-to and water-up-to methods are used to establish the contacts. The resulting saturation height model agreed well with the saturations derived from the log, which gave us confidence in our dynamic model.

A new method to improve the NMR log interpretation in drilling mud-invaded zones: A case study from the Brazilian Pre-salt

The Santos Basin hosts several giant carbonate oilfields in the Pre-salt province and is one of the most important hydrocarbon discoveries in the past years. These carbonate reservoirs present exceptional reservoir quality with a challenging depositional and diagenetic history that produced complex and heterogeneous pore systems. As one of the most effective tools for in-situ porosity and permeability evaluation, the nuclear magnetic resonance (NMR) well log plays an essential role in the Pre-salt petrophysical evaluation and its signal interpretation must be performed carefully. This work proposes a new approach to detect and improve the interpretation of zones with unreal NMR logging tool readings in areas heavily affected by drilling mud invasion in caverns/vugs, which causes a T2 distribution shift towards lower relaxation times. This work analyses well log data from 28 wells in the Sapinhoá Field, supported by special core analyses (SCAL) and routine core analyses (RCAL), as well as plugs, sidewall cores and thin sections data. The proposed approach generates synthetic NMR Free Fluid and T2 distributions with minimum error and replaces the faulty data, consisting in five main steps, (1) computing new curves to be used as inputs; (2) detecting the zones affected by the invasion; (3) water saturation calculation by the saturation height modeling method; (4) calculating a synthetic NMR free fluid curve based on a relationship between a NMR-derived water saturation and the saturation height model; and (5) using the Random Forests algorithm to estimate a synthetic T2 distribution. The proposed method has a minimized error and resulted an increase of up to 10% thickness in the pay zone and a reduction of up to 9% in water saturation average, which may represent enormous amounts of oil depending on the reservoir area. This study provides a new method, which can be used in the improvement of petrophysical interpretations in highly heterogeneous carbonate reservoirs and thus reducing the exploratory and development risks. • Drilling mud invades vug pores and results in misleading NMR readings; • A new methodology is proposed to create a synthetic NMR free fluid and T2 distribution with minimum error; • An increase of 10% in pay thickness and a reduction of 9% in average water saturation was achieved in the Pre-salt reservoirs; • The methodology is proper for the petrophysical evaluation of highly heterogeneous carbonate reservoirs

Estimation of Initial Hydrocarbon Saturation Applying Machine Learning Under Petrophysical Uncertainty

SummaryThe initial hydrocarbon saturation has a major effect on field-development planning and resource estimation. However, the bases of the initial hydrocarbon saturation are indirect measurements from spatially distributed wells applying saturation-height modeling using uncertain parameters. Because of the multitude of parameters, applying assisted-matching methods requires trade-offs regarding the quality of objective functions used for the various observed data. Applying machine learning (ML) in a Bayesian framework helps overcome these challenges. In the present study, the methodology is used to derive posterior parameter distributions for saturation-height modeling honoring the petrophysical uncertainty in a field. The results are used for dynamic model initialization and will be applied for forecasting under uncertainty. To determine the dynamic numerical model initial hydrocarbon saturation, the saturation-height model (SHM) needs to be conditioned to the petrophysically interpreted logs. There were 2,500 geological realizations generated to cover the interpreted ranges of porosity, permeability, and saturations for 15 wells. For the SHM, 12 parameters and their ranges were introduced. Latin hypercube sampling was used to generate a training set for ML models using the random forest algorithm. The trained ML models were conditioned to the petrophysical log-derived saturation data. To ensure a fieldwide consistency of the dynamic numerical models, only parameter combinations honoring the interpreted saturation range for all wells were selected. The presented method allows for consistent initialization and for rejection of parameters that do not fit the observed data. In our case study, the most-significant observation concerns the posterior parameter-distribution ranges, which are narrowed down dramatically, such as the free-water-level (FWL) range, which is reduced from 645–670 m subsea level (mSS) to 656–668 mSS. Furthermore, the SHM parameters are proved independent; thus, the resulting posterior parameter ranges for the SHM can be used for conditioning production data to models and subsequent hydrocarbon-production forecasting. Additional observations can be made from the ML results, such as the correlation between wells; this allows for interpreting groups of wells that have a similar behavior, favor the same combinations, and potentially belong to the same compartment.

Fluid distribution in a tight gas reservoir using the saturation-height model

The development of tight gas reservoirs requires detailed knowledge of gas volumes and their distribution in three-dimensional space. This information can be obtained using a Saturation Height Model (SHM) developed by combining mercury injection capillary pressure analysis and well logging data. The SHM is constructed using core data from two wells in the tight gas reservoir of Amin formation in Oman.The saturation-height model is represented by a tangent line function linked with porosity. The developed SHM accurately simulates water saturation from well logs in seven wells. The curve fitting procedure determines three baselines, designated as free water levels (FWL), increasing with depth in the order of FWL0, FWL1 and FWL2.In three wells, the best match for the water saturation curve is obtained using FWL1 for Upper Amin formations and FWL2 for Low and Middle Amin formations. Different FWLs in the wells indicate differences in well placement within blocks and depending on tectonic history.The described tight gas reservoir can rather be characterized as a composite type because gas accumulations are not only found in high positions, but they also exist deeper over a wide range of depths.The developed SHM and the determined FWLs can be used for 3D reservoir modeling, in situ gas volumetric analysis and Sw calculation in undrilled areas to formulate a field development plan and fracturing program. This information makes it possible to estimate the consumption of water and chemicals required for hydraulic fracturing operations, which, in turn, makes it possible to estimate the required capacities for treatment of produced water and gas and to identify the places of possible contamination and gas losses.

A new approach to reduce uncertainty in reservoir characterization using saturation height modeling, Mesaverde tight gas sandstones, western US basins

Tight gas sandstone (TGS) reservoirs are one of the most integral parts of the unconventional reservoirs pyramid. Uncertainty in petrophysical properties of a TGS reservoir will cause great challenges in reservoir characterization and also 3D properties modeling. The main goal of this study is to implement a new workflow based on saturation height modeling (SHM) to reduce this uncertainty in a TGS reservoir by acquiring a global in situ water saturation function and also calculating more accurate permeability values. Capillary pressure curves and well logs from ten different wells in four different giant basins of western US TGS reservoirs are the input data in this study. After grouping the capillary pressure curves based on the corresponding cores sorting, size, and texture, and also applying some initial corrections, five different SHM methods have been applied to each group. Using regression methods, the function of each model has been rewritten based on the cores’ petrophysical properties. By entering the porosity and permeability logs of each well in the rewritten functions and by implementing the height above free water level (HAFWL), a water saturation profile has been calculated for each well. Using standard error of estimate analysis between the calculated water saturation profile and the log-based water saturation profile as the base one, the most reliable SHM method has been recognized. Using water saturation and porosity logs and also HAFWL value in each well, accurate permeability values have been calculated based on the saturation height function of the best model. Finally, the regression method between the calculated permeability and the accurate cores permeability values approves the reliability of the results.

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.

Method Addresses Difficulty of Modeling Heterogeneous Carbonate Bimodal Rocks

This article, written by Special Publications Editor Adam Wilson, contains highlights of paper IPTC 18587, “Heterogeneous Carbonates: A Modeling Method Ensuring Consistency Between the Saturation-Height and Permeability Models for Bimodal Rocks,” by Iulian N. Hulea, Harm Dijk, SPE, Danila Karnaukh, and Mirano Spalburg, Shell, prepared for the 2016 International Petroleum Technology Conference, Bangkok, Thailand, 14–16 November. The paper has not been peer reviewed. Copyright 2016 International Petroleum Technology Conference. Reproduced by permission. Because of their heterogeneity, carbonate reservoirs are more difficult to model than clastic reservoirs. The main difficulty comes from the number of different pore types, compared with the typical interparticle pore type in clastics. By using saturation-height models (SHMs) in combination with conventional permeability measurements, a new approach attempts to extract the fundamental properties of individual pore systems. The key idea centers on identifying the governing pore systems from capillary pressure curves and permeability measurements. The approach results in the ability to predict permeability continuously as a function of pore-system mixing ratios. Introduction Because of the presence of multiple pore types, carbonate rocks are difficult to model. To account for their heterogeneity, carbonate rocks are often modeled using rock-typing schemes. Two particularly challenging properties are permeability and saturation. Although these properties have been recognized as being closely connected, little information is available on how to handle them consistently. Even when permeability and SHMs satisfactorily describe the core measurements, it is not trivial to ensure their consistency in 3D models. One possible situation is building SHMs that impose consistency through the governing parameters. Throughout this work, a Brooks-Corey function is used because it was found to describe unimodal mercury-injection capillary pressures (MICPs) satisfactorily. For the examples discussed in this contribution (Fig. 1), microporosity (corresponding to the pore system accessible beyond pore throats of 2 µm or less) forms between 40 and 70% of the pore volume and is mostly located within the micritic grains. A significant difference between the two examples shown in Figs. 1a and 1d is the relative contribution of microporosity on average equaling 0.53 for Rock Type 1 (RT1) and 0.75 for Rock Type 2 (RT2). For RT2, microporosity can be located in the mud between the grains. Capillary Pressure Curve Data Analysis and Modeling The MICP modeling strategy relies on treating the two pore systems as independent, fitting each one of the pore systems first then looking for the best correlation to predict the Brooks-Corey parameters. On the basis of the measured individual-core-plug properties, the standard deviation for both plug porosity and the relative ratio of microporosity to total porosity was derived. By making the plots with the same fundamental inputs (SHM, porosity, permeability transform), the properties predicted by the models can be highlighted and contrasted.

Saturation-Height Model of Omani deep tight gas reservoir

The focus of this study was on developing a Saturation-Height Model (SHM) based on mercury injection capillary pressure (MICP) analysis and core data of three wells drilled in a deep tight gas reservoir of the Amin formation, Oman, that can best fit to the water saturation calculated by logging data. The suggested SHM is a porosity dependent natural logarithmic function. The SHM indicated homogeneous transition zone with a deep fluid contact similar to all three wells.The calibration with logging data allowed for obtaining the GWC and more precise coefficients in the SHM equation for specific wells. The SHM closely simulated log-derived water saturation for entire Amin formation unaffected by rock type, which makes it useful for complex lithologies and un-cored intervals. The developed SHM can be used as a tool for water saturation evaluation independent from electrical rock properties obtained by logging.

Water saturation estimation in tight shaly gas sandstones by application of Progressive Quasi-Static (PQS) algorithm – A case study

Prediction of formation water saturation can be achieved through capillary pressure data in saturation-height modeling. The LSMPQS (Level Set Method Progressive Quasi Static) method is the newest numerical simulation which is basically utilized for determining critical curvatures for drainage and imbibitions curves; consequently it can be used for studies on saturation history. Thus, the amounts of water saturations were obtained by drainage simulation in saturation-height modeling.The saturation results from Indonesian model that is the best traditional log-derived saturation model in tight shaly sandstones were compared with this simulation results. It is concluded that there is a good match between log derived and simulation results. The simulation results show that it can be used as a tool for prediction of water saturation only with knowing the geometry of sedimentary environment in pore scale.

A novel integrated approach to estimating hydrocarbon saturation in the presence of pore-lining chlorites

Pore-lining chlorites are often associated with a low-resistivity contrast between corresponding reservoir units, making the identification and quantitation of hydrocarbon-bearing intervals difficult. In many low-resistivity situations, the traditional approach of using Archie’s equation to determine saturation from electrical resistivity fails, and modified Archie equations derived specifically for ‘shaly sands’ have been developed. In chlorite-bearing intervals, however, the effect of chlorite can be such that both Archie and the so-called shaly-sand models are inappropriate. Under these circumstances, calculating saturation from electrical resistivity can be circumvented by detailed analysis of the sedimentology and petrophysics, enabling the construction of a saturation height model based on core data. In this novel study we integrate a detailed core-based sedimentological facies scheme with wireline log data and petrophysical core data to demonstrate a clear link between chlorite occurrence, petrophysical characteristics and saturation height. Through this innovative approach, saturation is estimated without recourse to resistivity logs and improves hydrocarbon saturation estimates in chlorite-bearing reservoirs.

Relative Permeability Coupled Saturation-Height Models on the Basis of Hydraulic (Flow) Units in a Gas Field

Summary Saturation/height functions on the basis of unique flow units have been developed as part of an integrated petrophysical analysis of a gas field. Furthermore, coupling the saturation/height functions with appropriate relative permeability models has effectively quantified hydrocarbon saturation, classified producibility of intervals, and defined critical water saturation. The results show that linking depositional and diagenetic rock fabric with flow units and then linking the flow units with zones that have similar core capillary pressure and relative permeability relationships have enhanced the utility of the saturation models. The saturation/height functions provided more-accurate water saturation in the study field, and potentially they can overcome uncertainties associated with log interpretation by use of Archie or shaly-sand models. The saturation/height models were developed from core capillary pressure (Pc) data to calculate water saturation vs. depth, which is independent of logs. The relative permeability models were obtained from special-core analysis (SCA). Consequently, the core-based saturation/height functions can be useful in the calibration of log-based petrophysical models and with relative permeability can also be used to estimate water/gas ratios (WGRs) and critical water saturation. Capillary pressure and relative permeability curves from SCA studies were distributed into corresponding flow units, on the basis of the calculated flow-zone indicators(FZIs). Saturation/height functions were then developed for each unit and were used to calculate water saturation in the study field. The most accurate flow-unit-based saturation model that evolved is a function only of porosity and of height above the free-water level; it does not require permeability in its application; and it performed better than the Leverett J-function in this field. Coupled with hydraulic unit (HU)-based relative permeability curves, the saturation models may provide more comprehensive petrophysical interpretation in gas-bearing formations and may highlight potential differences in reservoir producibility.