A Machine Learning Methodology for Rock-Typing Using Relative Permeability Curves

2021 ◽  
Author(s):  
Carlos Esteban Alfonso ◽  
Frédérique Fournier ◽  
Victor Alcobia
Keyword(s):  
Machine Learning ◽  
Capillary Pressure ◽  
Relative Permeability ◽  
Fractional Flow ◽  
Flow Curves ◽  
Rock Types ◽  
Rock Typing ◽  
Relative Permeability Curves ◽  
Permeability Data

Abstract The determination of the petrophysical rock-types often lacks the inclusion of measured multiphase flow properties as the relative permeability curves. This is either the consequence of a limited number of SCAL relative permeability experiments, or due to the difficulty of linking the relative permeability characteristics to standard rock-types stemming from porosity, permeability and capillary pressure. However, as soon as the number of relative permeability curves is significant, they can be processed under the machine learning methodology stated by this paper. The process leads to an automatic definition of relative permeability based rock-types, from a precise and objective characterization of the curve shapes, which would not be achieved with a manual process. It improves the characterization of petrophysical rock-types, prior to their use in static and dynamic modeling. The machine learning approach analyzes the shapes of curves for their automatic classification. It develops a pattern recognition process combining the use of principal component analysis with a non-supervised clustering scheme. Before this, the set of relative permeability curves are pre-processed (normalization with the integration of irreducible water and residual oil saturations for the SCAL relative permeability samples from an imbibition experiment) and integrated under fractional flow curves. Fractional flow curves proved to be an effective way to unify the relative permeability of the two fluid phases, in a unique curve that characterizes the specific poral efficiency displacement of this rock sample. The methodology has been tested in a real data set from a carbonate reservoir having a significant number of relative permeability curves available for the study, in addition to capillary pressure, porosity and permeability data. The results evidenced the successful grouping of the relative permeability samples, according to their fractional flow curves, which allowed the classification of the rocks from poor to best displacement efficiency. This demonstrates the feasibility of the machine learning process for defining automatically rock-types from relative permeability data. The fractional flow rock-types were compared to rock-types obtained from capillary pressure analysis. The results indicated a lack of correspondence between the two series of rock-types, which testifies the additional information brought by the relative permeability data in a rock-typing study. Our results also expose the importance of having good quality SCAL experiments, with an accurate characterization of the saturation end-points, which are used for the normalization of the curves, and a consistent sampling for both capillary pressure and relative permeability measurements.

Rock Typing as an Effective Tool for Permeability and Water-Saturation Modeling: A Case Study in a Clastic Reservoir in the Oriente Basin

2007 ◽  
Vol 10 (06) ◽  
pp. 730-739 ◽  
Author(s):  
Genliang Guo ◽  
Marlon A. Diaz ◽  
Francisco Jose Paz ◽  
Joe Smalley ◽  
Eric A. Waninger
Keyword(s):  
Relative Permeability ◽  
Reservoir Simulation ◽  
Water Saturation ◽  
Rock Type ◽  
Permeability Model ◽  
Initial Water ◽  
Rock Types ◽  
Rock Typing ◽  
Relative Permeability Curves ◽  
Clastic Reservoirs

Summary In clastic reservoirs in the Oriente basin, South America, the rock-quality index (RQI) and flow-zone indicator (FZI) have proved to be effective techniques for rock-type classifications. It has long been recognized that excellent permeability/porosity relationships can be obtained once the conventional core data are grouped according to their rock types. Furthermore, it was also observed from this study that the capillary pressure curves, as well as the relative permeability curves, show close relationships with the defined rock types in the basin. These results lead us to believe that if the rock type is defined properly, then a realistic permeability model, a unique set of relative permeability curves, and a consistent J function can be developed for a given rock type. The primary purpose of this paper is to demonstrate the procedure for implementing this technique in our reservoir modeling. First, conventional core data were used to define the rock types for the cored intervals. The wireline log measurements at the cored depths were extracted, normalized, and subsequently analyzed together with the calculated rock types. A mathematical model was then built to predict the rock type in uncored intervals and in uncored wells. This allows the generation of a synthetic rock-type log for all wells with modern log suites. Geostatistical techniques can then be used to populate the rock type throughout a reservoir. After rock type and porosity are populated properly, the permeability can be estimated by use of the unique permeability/porosity relationship for a given rock type. The initial water saturation for a reservoir can be estimated subsequently by use of the corresponding rock-type, porosity, and permeability models as well as the rock-type-based J functions. We observed that a global permeability multiplier became unnecessary in our reservoir-simulation models when the permeability model is constructed with this technique. Consistent initial-water-saturation models (i.e., calculated and log-measured water saturations are in excellent agreement) can be obtained when the proper J function is used for a given rock type. As a result, the uncertainty associated with volumetric calculations is greatly reduced as a more accurate initial-water-saturation model is used. The true dynamic characteristics (i.e., the flow capacity) of the reservoir are captured in the reservoir-simulation model when a more reliable permeability model is used. Introduction Rock typing is a process of classifying reservoir rocks into distinct units, each of which was deposited under similar geological conditions and has undergone similar diagenetic alterations (Gunter et al. 1997). When properly classified, a given rock type is imprinted by a unique permeability/porosity relationship, capillary pressure profile (or J function), and set of relative permeability curves (Gunter et al. 1997; Hartmann and Farina 2004; Amaefule et al. 1993). As a result, when properly applied, rock typing can lead to the accurate estimation of formation permeability in uncored intervals and in uncored wells; reliable generation of initial-water-saturation profile; and subsequently, the consistent and realistic simulation of reservoir dynamic behavior and production performance. Of the various quantitative rock-typing techniques (Gunter et al. 1997; Hartmann and Farina 2004; Amaefule et al. 1993; Porras and Campos 2001; Jennings and Lucia 2001; Rincones et al. 2000; Soto et al. 2001) presented in the literature, two techniques (RQI/FZI and Winland's R35) appear to be used more widely than the others for clastic reservoirs (Gunter et al. 1997, Amaefule et al. 1993). In the RQI/FZI approach (Amaefule et al. 1993), rock types are classified with the following three equations: [equations]

Unleashing the Potential of Relative Permeability Using Artificial Intelligence

2021 ◽  
Author(s):  
Abdur Rahman Shah ◽  
Kassem Ghorayeb ◽  
Hussein Mustapha ◽  
Samat Ramatullayev ◽  
Nour El Droubi ◽  
...  
Keyword(s):  
Artificial Intelligence ◽  
Dynamic Model ◽  
Relative Permeability ◽  
Full Potential ◽  
Fully Integrated ◽  
Digital Twin ◽  
Rock Types ◽  
Rock Typing ◽  
Artificial Intelligence Models ◽  
Permeability Data

Abstract One of the most important aspects of any dynamic model is relative permeability. To unlock the potential of large relative permeability data bases, the proposed workflow integrates data analysis, machine learning, and artificial intelligence (AI). The workflow allows for the automated generation of a clean database and a digital twin of relative permeability data. The workflow employs artificial intelligence to identify analogue data from nearby fields by extending the rock typing scheme across multiple fields for the same formation. We created a fully integrated and intelligent tool for extracting SCAL data from laboratory reports, then processing and modeling the data using AI and automation. After the endpoints and Corey coefficients have been extracted, the quality of the relative permeability samples is checked using an automated history match and simulation of core flood experiments. An AI model that has been trained is used to identify analogues for various rock types from other fields that produce from the same formations. Finally, based on the output of the AI model, the relative permeabilities are calculated using data from the same and analog fields. The workflow solution offers a solid and well-integrated methodology for creating a clean database for relative permeability. The workflow made it possible to create a digital twin of the relative permeability data using the Corey and LET methods in a systematic manner. The simulation runs were designed so that the pressure measurements are history matched with the adjustment and refinement of the relative permeability curve. The AI workflow enabled us to realize the full potential of the massive database of relative permeability samples from various fields. To ensure utilization in the dynamic model, high, mid, and low cases were created in a robust manner. The workflow solution employs artificial intelligence models to identify rock typing analogues from the same formation across multiple fields. The AI-generated analogues, combined with a robust workflow for quickly QC’ing the relative permeability data, allow for the creation of a fully integrated relative permeability database. The proposed solution is agile and scalable, and it can adapt to any data and be applied to any field.

Analytical Solutions for Spontaneous Imbibition: Fractional-Flow Theory and Experimental Analysis

SPE Journal ◽  
2016 ◽  
Vol 21 (06) ◽  
pp. 2308-2316 ◽  
Author(s):  
K. S. Schmid ◽  
N.. Alyafei ◽  
S.. Geiger ◽  
M. J. Blunt
Keyword(s):  
Capillary Pressure ◽  
Relative Permeability ◽  
Analytical Solutions ◽  
Flow Theory ◽  
Spontaneous Imbibition ◽  
Fractional Flow ◽  
Matrix Block ◽  
Relative Permeability Curves ◽  
Fractional Flow Theory ◽  
Saturation Profiles

Summary We present analytical solutions for capillary-controlled displacement in one dimension by use of fractional-flow theory. We show how to construct solutions with a spreadsheet that can be used for the analysis of experiments as well as matrix-block-scale recovery in field settings. The solutions can be understood as the capillary analog to the classical Buckley-Leverett solution (Buckley and Leverett 1942) for viscous-dominated flow, and are valid for cocurrent and countercurrent spontaneous imbibition (SI), as well as for arbitrary capillary pressure and relative permeability curves. They can be used to study the influence of wettability, predicting saturation profiles and production rates characteristic for water-wet and mixed-wet conditions. We compare our results with in-situ measurements of saturation profiles for SI in a water-wet medium. We show that the characteristic shape of the saturation profile is consistent with the expected form of the relative permeabilities. We discuss how measurements of imbibition profiles, in combination with other measurements, could be used to determine relative permeability and capillary pressure.

scholarly journals Reliability of Relative Permeability Measurements for Heterogeneous Rocks Using Horizontal Core Flood Experiments

2021 ◽  
Vol 13 (5) ◽  
pp. 2744
Author(s):  
Chia-Wei Kuo ◽  
Sally M. Benson
Keyword(s):  
Capillary Pressure ◽  
Relative Permeability ◽  
Synthetic Data ◽  
Critical Value ◽  
Core Flooding ◽  
Fractional Flow ◽  
The Core ◽  
Heterogeneous Rocks ◽  
Core Flood ◽  
Relative Permeability Curves

New guidelines and suggestions for taking reliable effective relative permeability measurements in heterogeneous rocks are presented. The results are based on a combination of high resolution of 3D core-flooding simulations and semi-analytical solutions for the heterogeneous cores. Synthetic “data sets” are generated using TOUGH2 and are subsequently used to calculate effective relative permeability curves. A comparison between the input relative permeability curves and “calculated” relative permeability is used to assess the accuracy of the “measured” values. The results show that, for a capillary number (Ncv = kLpc × A/H2μCO2qt) smaller than a critical value, flows are viscous dominated. Under these conditions, saturation depends only on the fractional flow as well as capillary heterogeneity, and is independent of flow rate, gravity, permeability, core length, and interfacial tension. Accurate whole-core effective relative permeability measurements can be obtained regardless of the orientation of the core and for a high degree of heterogeneity under a range of relevant and practical conditions. Importantly, the transition from the viscous to gravity/capillary dominated flow regimes occurs at much higher flow rates for heterogeneous rocks. For the capillary numbers larger than the critical value, saturation gradients develop along the length of the core and accurate relative permeability measurements are not obtained using traditional steady-state methods. However, if capillary pressure measurements at the end of the core are available or can be estimated from independently measured capillary pressure curves and the measured saturation at the inlet and outlet of the core, accurate effective relative permeability measurements can be obtained even when there is a small saturation gradient across the core.

scholarly journals Improved method for complete gas-brine imbibition relative permeability curves

2020 ◽  
Vol 146 ◽  
pp. 03003
Author(s):  
M. Ben Clennell ◽  
Cameron White ◽  
Ausama Giwelli ◽  
Matt Myers ◽  
Lionel Esteban ◽  
...  
Keyword(s):  
Relative Permeability ◽  
Gas Permeability ◽  
Test Methods ◽  
Standard Test ◽  
High Rate ◽  
Fractional Flow ◽  
Gas Reservoirs ◽  
Data Gap ◽  
Small Increments ◽  
Relative Permeability Curves

Standard test methods for measuring imbibition gas-brine relative permeability on reservoir core samples often lead to non-uniform brine saturation. During co-current flow, the brine tends to bank up at the sample inlet and redistributes slowly, even with fractional flow of gas to brine of 400:1 or more. The first reliable Rel Perm point is often only attained after a brine saturation of around Sw=40% is achieved, leaving a data gap between Swirr and this point. The consequent poor definition of the shape of the Rel Perm function can lead to uncertainty in the performance of gas reservoirs undergoing depletion drive with an encroaching aquifer or subjected to a water flood. We have developed new procedures to pre-condition brine saturation outside of the test rig and progress it in small increments to fill in the data gap at low Sw, before continuing with a co-current flood to the gas permeability end-point. The method was applied to series of sandstone samples from gas reservoirs from the NW Shelf of Australia, and a Berea standard. We found that the complete imbibition relative permeability curve is typically ‘S’ shaped or has a rolling over, convex-up shape that is markedly different from the concave-up, Corey Rel Perm curve usually fitted to SCAL test data. This finding may have an economic upside if the reservoir produces gas at a high rate for longer than was originally predicted based on the old Rel Perm curves.

scholarly journals Uncertainty span for relative permeability and capillary pressure by varying wettability and spatial flow directions utilizing pore scale modelling

2020 ◽  
Vol 146 ◽  
pp. 01002
Author(s):  
Thomas Ramstad ◽  
Anders Kristoffersen ◽  
Einar Ebeltoft
Keyword(s):  
Continental Shelf ◽  
Pore Structure ◽  
Capillary Pressure ◽  
Relative Permeability ◽  
Phase Flow ◽  
Pore Scale ◽  
Full Field ◽  
Scale Modelling ◽  
Relative Permeability Curves ◽  
Norwegian Continental Shelf

Relative permeability and capillary pressure are key properties within special core analysis and provide crucial information for full field simulation models. These properties are traditionally obtained by multi-phase flow experiments, however pore scale modelling has during the last decade shown to add significant information as well as being less time-consuming to obtain. Pore scale modelling has been performed by using the lattice-Boltzmann method directly on the digital rock models obtained by high resolution micro-CT images on end-trims available when plugs are prepared for traditional SCAL-experiments. These digital rock models map the pore-structure and are used for direct simulations of two-phase flow to relative permeability curves. Various types of wettability conditions are introduced by a wettability map that opens for local variations of wettability on the pore space at the pore level. Focus have been to distribute realistic wettabilities representative for the Norwegian Continental Shelf which is experiencing weakly-wetting conditions and no strong preference neither to water nor oil. Spanning a realistic wettability-map and enabling flow in three directions, a large amount of relative permeability curves is obtained. The resulting relative permeabilities hence estimate the uncertainty of the obtained flow properties on a spatial but specific pore structure with varying, but realistic wettabilities. The obtained relative permeability curves are compared with results obtained by traditional SCAL-analysis on similar core material from the Norwegian Continental Shelf. The results are also compared with the SCAL-model provided for full field simulations for the same field. The results from the pore scale simulations are within the uncertainty span of the SCAL models, mimic the traditional SCAL-experiments and shows that pore scale modelling can provide a time- and cost-effective tool to provide SCAL-models with uncertainties.

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