Innovative Workflow for Grouping, Averaging, End-Point Scaling and Assessing Uncertainty of Water-Oil Relative-Permeability Curves, Considering Corresponding Normalized Water-Fractional-Flow Curves, Reservoir-Rock Types and Wettability Indexes

2017 ◽  
Author(s):  
F. C. Ferreira ◽  
F. Pairoys ◽  
D. V. Klemin ◽  
B. Baser-Langenau ◽  
S. Safonov ◽  
...  
Keyword(s):  
Relative Permeability ◽  
Reservoir Rock ◽  
Fractional Flow ◽  
Flow Curves ◽  
End Point ◽  
Rock Types ◽  
Relative Permeability Curves

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.

scholarly journals Variations in Permeability and Porosity of Synthetic Oil Reservoir Rock-Methods of Control

1965 ◽  
Vol 5 (04) ◽  
pp. 329-332 ◽  
Author(s):  
Larman J. Heath
Keyword(s):  
Porous Media ◽  
Relative Permeability ◽  
Reservoir Rock ◽  
Oil Reservoir ◽  
Natural Reservoir ◽  
Natural Rock ◽  
Unconsolidated Sand ◽  
Synthetic Rock ◽  
Porosity And Permeability ◽  
Relative Permeability Curves

Abstract Synthetic rock with predictable porosity and permeability bas been prepared from mixtures of sand, cement and water. Three series of mixes were investigated primarily for the relation between porosity and permeability for certain grain sizes and proportions. Synthetic rock prepared of 65 per cent large grains, 27 per cent small grains and 8 per cent Portland cement, gave measurable results ranging in porosity from 22.5 to 40 per cent and in permeability from 0.1 darcies to 6 darcies. This variation in porosity and permeability was caused by varying the amount of blending water. Drainage- cycle relative permeability characteristics of the synthetic rock were similar to those of natural reservoir rock. Introduction The fundamental behavior characteristics of fluids flowing through porous media have been described in the literature. Practical application of these flow characteristics to field conditions is too complicated except where assumptions are overly simplified. The use of dimensionally scaled models to simulate oil reservoirs has been described in the literature. These and other papers have presented the theoretical and experimental justification for model design. Others have presented elements of model construction and their operation. In most investigations the porous media have consisted of either unconsolidated sand, glass beads, broken glass or plastic-impregnated granular substances-materials in which the flow behavior is not identical to that in natural reservoir rock. The relative permeability curves for unconsolidated sands differ from those for consolidated sandstone. The effect of saturation history on relative permeability measurements A discussed by Geffen, et al. Wygal has shown quite conclusively that a process of artificial cementation can be used to render unconsolidated packs into synthetic sandstones having properties similar to those of natural rock. Many theoretical and experimental studies have been made in attempts to determine the structure and properties of unconsolidated sand, the most notable being by Naar and Wygal. Others have theorized and experimented with the fundamental characteristics of reservoir rocks. This study was conducted to determine if some general relationship could be established between the size of sand grains and the porosity and permeability in consolidated binary packs. This paper presents the results obtained by changing some of the factors which affect the porosity and permeability of synthetically prepared sandstone. In addition, drainage relative permeability curves are presented. EXPERIMENTAL PROCEDURE Mixtures of Portland cement with water and aggregate generally are designed to have certain characteristics, but essentially all are planned to be impervious to water or other liquids. Synthetic sandstone simulating oil reservoir rock, however, must be designed to have a given permeability (sometimes several darcies), a porosity which is primarily the effective porosity but quantitatively similar to natural rock, and other characteristics comparable to reservoir rock, such as wettability, pore geometry, tortuosity, etc. Unconsolidated ternary mixtures of spheres gave both a theoretically computed and an experimentally observed minimum porosity of about 25 per cent. By using a particle-distribution system, one-size particle packs had reproducible porosities in the reproducible range of 35 to 37 per cent. For model reservoir studies of the prototype system, a synthetic rock having a porosity of 25 per cent or less and a permeability of 2 darcies was required. The rock bad to be uniform and competent enough to handle. Synthetic sandstone cores mere prepared utilizing the technique developed by Wygal. Some tight variations in the procedure were incorporated. The sand was sieved through U.S. Standard sieves. SPEJ P. 329ˆ

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.

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]

Use of a Reservoir Simulator To Interpret Laboratory Waterflood Data

1973 ◽  
Vol 13 (06) ◽  
pp. 343-347 ◽  
Author(s):  
John S. Archer ◽  
S.W. Wong
Keyword(s):  
Relative Permeability ◽  
Core Sample ◽  
Reservoir Rock ◽  
Relative Permeabilities ◽  
Rock System ◽  
The Core ◽  
Water Breakthrough ◽  
Predicting Performance ◽  
Relative Permeability Curves ◽  
Reservoir Simulator

Abstract Relative permeability curves calculated from laboratory waterflood history by the method of Johnson, Bossler and Naumann (JBN) are often poorly defined or anomalous at low and intermediate poorly defined or anomalous at low and intermediate water saturations. Poor definition can be encountered with strongly water-wet homogeneous cores when the displacement is piston-like. Anomalous curve shapes are associated with laboratory-observed water breakthrough ahead of the main flood front and are common in cores that have contrasting permeability streaks. The JBN technique, although permeability streaks. The JBN technique, although valid for the conditions assumed in its development, is unsatisfactory for the conditions specified above. A reservoir simulator has been used to model laboratory tests and thereby provide an alternative interpretation procedure. The simulation uses core properties and trial-and-error relative permeabilities. properties and trial-and-error relative permeabilities. The shapes of the relative permeability curves are adjusted until calculated oil recovery and relative injectivity curves match those obtained from the laboratory displacement tests. The technique has been used successfully to obtain meaningful relative permeability curves for piston-like displacement, mixed wettability systems, piston-like displacement, mixed wettability systems, and heterogeneous carbonates. The technique has also been used in evaluating empirical equations for calculating relative permeability. Introduction Numerical reservoir simulators are finding increasing application in production history matching and performance predictions. Because of the degree of sophistication reached with these models, it is mandatory that the fluid flow properties be of the highest possible quality. Of all the rock and fluid properties required in predicting performance, it is properties required in predicting performance, it is often the relative permeability characteristics that are the most critically important. These data are usually obtained from laboratory waterflood tests using reservoir core samples. The laboratory waterflood test is an attempt to represent the linear displacement behavior of the oil/water/reservoir-rock system. The wettability properties of the rock system should be preserved properties of the rock system should be preserved in the laboratory core sample if reliable results are to be obtained. Furthermore, the viscosity ratio and surface tension of the oil/water system in the laboratory test should ideally be made the same as those in the reservoir. In interpreting laboratory waterflood tests the unsteady-state equations are usually solved by methods of Buckley-Leverett, Welge and Johnson, Bossler and Neumann (JBN). These interpretations are sometimes inadequate for defining relative permeability curves for heterogeneous reservoir permeability curves for heterogeneous reservoir rock systems or for water displacing a very light oil in a homogeneous sandstone. For example, a number of writers have observed anomalous changes in the relative permeability to water during the flooding of heterogeneous carbonate core samples. The relative permeability to water does not increase smoothly with increasing water saturation, but increases stepwise or even humps. Such behavior appears to reflect small-scale local heterogeneity in the core sample and is likely to be insignificant on a field scale. The heterogeneity is often indicated in the laboratory by an observed water breakthrough at the core-sample production face ahead of the main flood front. The time of water breakthrough is an important measurement used in the calculation of relative permeability by the JBN method. If the breakthrough permeability by the JBN method. If the breakthrough time observed is not that of the main flood front but is a little early, then the relative permeabilities calculated will not represent the properties of the bulk of the core sample. It is under these conditions that anomalous relative permeability curves usually occur. We suggest in this paper that, in many cases, the small changes in pressure and in oil and water production rate that accompany anomalous relative production rate that accompany anomalous relative permeability curves can be smoothed to reflect permeability curves can be smoothed to reflect properties more consistent with the bulk behavior properties more consistent with the bulk behavior of the core sample. In essence, we are saying that together the smoothed oil and water production history and the pressure history of the laboratory core sample represent a unique property of that sample. SPEJ P. 343

A Pore-Network-Modeling Approach To Predict Petrophysical Properties of Diatomaceous Reservoir Rock

2007 ◽  
Vol 10 (06) ◽  
pp. 597-608 ◽  
Author(s):  
Liping Jia ◽  
Cynthia Marie Ross ◽  
Anthony Robert Kovscek
Keyword(s):  
Multiphase Flow ◽  
Capillary Pressure ◽  
Network Model ◽  
Relative Permeability ◽  
Oil Recovery ◽  
Pore Network ◽  
Reservoir Rock ◽  
Pore Network Model ◽  
Rock Types ◽  
Capillary Pressure Curves

Summary A 3D pore-network model of two-phase flow was developed to compute permeability, relative permeability, and capillary pressure curves from pore-type, -size, and -shape information measured by means of high-resolution image analysis of diatomaceous-reservoir-rock samples. The diatomite model is constructed using pore-type proportions obtained from image analysis of epoxy-impregnated polished samples and mercury-injection capillary pressure curves for diatomite cores. Multiple pore types are measured, and each pore type has a unique pore-size and throat-size distribution that is incorporated in the model. Network results present acceptable agreement when compared to experimental measurements of relative permeability. The pore-network model is applicable to both drainage and imbibition within diatomaceous reservoir rock. Correlation of network-model results to well log data is discussed, thereby interpolating limited experimental results across the entire reservoir column. Importantly, our method has potential to predict the petrophysical properties for reservoir rocks with either limited core material or those for which conventional experimental measurements are difficult, unsuitable, or expensive. Introduction Model generation for reservoir simulation requires accurate entering of physical properties such as porosity, permeability, initial water saturation, residual-oil saturation, capillary pressure functions, and relative permeability curves. These functions and parameters are necessary to estimate production rate and ultimate oil recovery, and thereby optimize reservoir development. Accurate measurement and representation of such information is, therefore, essential for reservoir modeling. Relative permeability and capillary pressure curves are the most important constitutive relations to represent multiphase flow. Often, it is difficult to sample experimentally the range of relevant multiphase-flow behavior of a reservoir. In addition to the availability of rock samples, measurements are frequently time consuming to conduct, and conventional techniques are not suitable for all rock types (Schembre and Kovscek 2003). It is impossible, therefore, to measure all the unique relative permeability functions of different reservoir-rock types and variations within a rock type. This lack of constitutive information limits the accuracy of reservoir simulators to predict oil recovery. Simply put, other available data must be queried for their relevance to multiphase flow and must be used to interpret the available relative permeability and capillary pressure information.

Comparison of Calculated with Experimental Imbibition Relative Permeability

1971 ◽  
Vol 11 (04) ◽  
pp. 419-425 ◽  
Author(s):  
Carlon S. Land
Keyword(s):  
Relative Permeability ◽  
Reservoir Rock ◽  
Laboratory Measurements ◽  
Two Phase ◽  
Relative Permeability Curve ◽  
Gas Saturation ◽  
Phase Saturation ◽  
The Difference ◽  
Relative Permeability Curves ◽  
The Relationship

Abstract Two-phase imbibition relative permeability was measured in an attempt to validate a method of calculating imbibition relative permeability. The stationary-liquid-phase method was used to measure several hysteresis loops for alundum and Berea sandstone samples. The method of calculating imbibition relative permeability is described, and calculated relative permeability curves are compared with measured curves. The calculated relative Permeability is shown to be a reasonably good Permeability is shown to be a reasonably good approximation of measured values if an adjustment is made to some necessary data. Due to the compressibility of gas, which is used as the nonwetting phase, a correction to the measured trapped gas saturation is necessary to make it agree with the critical gas saturation of the imbibition relative permeability curve. Introduction The existence of hysteresis in the relationship of relative permeability to saturation has been recognized for many yews. Geden et al. and Osoba et al. called attention to the occurrence of hysteresis and the importance of the direction of saturation change on the relative permeability-saturation relations. It is generally believed that relative permeability is a function of saturation alone for a permeability is a function of saturation alone for a given direction of saturation change, but that there is a distinct difference in relative permeability curves for saturation changes in different directions. The reservoir engineer should be aware of this hysteresis, and he should select the relative permeability curve which is appropriate for the permeability curve which is appropriate for the recovery process of interest. The directions of saturation change have been designated "drainage" and "imbibition" in reference to changes in the wetting-phase saturation. In a two-phase system, an increase in the wetting-phase saturation is referred to as imbibition, while a decrease in wetting-phase saturation is called drainage. The solution-gas-drive recovery mechanism is controlled by relative permeability to oil and gas in which the saturation of oil, the wetting phase, is decreasing. In waterflooding a water-wet reservoir rock, the saturation of water, the wetting phase, is increasing. These two sets of relative permeability curves, gas-oil and oil-water, do not have the same relationship to the wetting-phase saturation. This difference is not due to the difference in fluid properties, but is a result of the difference in properties, but is a result of the difference in direction of saturation change. The flow properties of the drainage and imbibition systems differ because of the entrapment of the nonwetting phase during imbibition. As drainage occurs, the nonwetting phase occupies the most favorable flow channels. During imbibition, part of the nonwetting phase is bypassed by the increasing wetting phase, leaving a portion of the nonwetting phase in an immobile condition. This trapped part phase in an immobile condition. This trapped part of the nonwetting phase saturation does not contribute to the flow of that phase, and at a given saturation the relative permeability to the nonwetting phase is always less in the imbibition direction phase is always less in the imbibition direction than in the drainage direction. The concept that some of the nonwetting phase is mobile and some is immobile during a saturation change in the imbibition direction previously was used to develop equations for imbibition relative permeability. In this development, it was assumed permeability. In this development, it was assumed that the amount of entrapment at any saturation can be obtained from the relationship between initial nonwetting-phase saturations established in the drainage direction and residual saturations after complete imbibition. The equations for imbibition relative permeability were not verified by laboratory measurements. The purpose of this report is m give the results of a laboratory study of imbibition relative permeability and to present a comparison of calculated relative permeability with relative permeability from laboratory measurements. permeability from laboratory measurements. In two-phase systems, hysteresis is more prominent in the relative permeability to the nonwetting phase than in that to the wetting phase. The hysteresis in the wetting-phase relative permeability is believed to be very small, and thus difficult to distinguish tom normal experimental error. SPEJ P. 419

A Relative Permeability Rock-Typing Methodology With a Clustering Method Combined With a Heuristic Optimization Procedure

SPE Journal ◽  
2016 ◽  
Vol 21 (05) ◽  
pp. 1899-1915 ◽  
Author(s):  
A. L. Compan ◽  
G. C. Bodstein ◽  
P.. Couto
Keyword(s):  
Relative Permeability ◽  
Dimensional Space ◽  
Optimization Procedure ◽  
Clustering Methods ◽  
Clustering Method ◽  
Reservoir Model ◽  
Two Phase ◽  
Rock Types ◽  
Relative Permeability Curves ◽  
T Distribution

Summary Many methods are used to group and classify rocks, most of them designed to be applied to all petrophysical properties, in general. Some authors, however, point out that these generic classifications may not be able to capture the complexity of the relative permeability property, resulting in highly spread relative permeability groups. These authors use correlations between petrophysical data and relative permeability curves to obtain two-phase dynamic rock types through a manual process. The present work describes a general, systematic, and semiautomatic methodology to determine the relative permeability classes (rock types) from relative permeability experimental data, by use of a clustering method associated with an optimization procedure. Clustering methods are able to classify elements according to their similarities in an n-dimensional space of characteristics, but they may not be able to produce clusters with little data scattering of relative permeability, because these clusters must be related to the rock characteristics available in the reservoir model. The method proposed in this investigation uses a clustering method to obtain groups of reservoir-model rock characteristics associated with an optimization method to deform the space of characteristics (clustering space) such that the clusters become representative dynamic classes with minimum spread of relative permeability curves. The results show a significant decrease of the data scattering found among the relative permeability curves within the groups, therefore reducing the uncertainty of the relative permeability used in reservoir simulations. In our methodology, the relative permeability boundaries of each group are also defined, such that every group has its own set of relative permeability curves with some uncertainty for the curve that represents the group. The associated confidence interval of each curve is evaluated with the Student's-t distribution to determine the relative permeability optimistic and pessimistic curves for each group. These boundaries allow optimistic and pessimist scenarios to be drawn.

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