History Matching in Two-Phase Petroleum Reservoirs: Incompressible Flow

1977 ◽  
Vol 17 (06) ◽  
pp. 398-406 ◽  
Author(s):  
Bruno van den Bosch ◽  
John H. Seinfeld
Keyword(s):  
Relative Permeability ◽  
Incompressible Flow ◽  
History Matching ◽  
Single Phase ◽  
Absolute Permeability ◽  
Petroleum Reservoir ◽  
Reservoir Properties ◽  
Two Phase ◽  
Pressure Behavior ◽  
Three Phase

Abstract The estimation of porosity, absolute permeability, and relative permeability-saturation relations in a two-phase petroleum reservoir is considered The data available for estimation are assumed to be the oil flow rates and the pressures at the wells. A situation in which the reservoir may be represented by incompressible flow of oil and water also is considered. A hypothetical, circular reservoir with a centrally located producing well is studied in detail. In principle, the porosity can be estimated on the basis of saturation behavior, absolute permeability on The basis of pressure behavior, and permeability on The basis of pressure behavior, and coefficients in the relative permeability-saturation relations on the basis of both saturation and pressure behavior. The ability to achieve good pressure behavior. The ability to achieve good estimates was found to depend on the nature of the flow in a given situation. Introduction The estimation of petroleum reservoir properties on the basis of data obtained during production, so-called history matching, has received considerable attention. By and large, the development of theories for history matching and their application have been confined to reservoirs that can be modeled as containing a single phase. (Wasserman et al. considered the estimation of absolute permeability and porosity in a three-phase reservoir permeability and porosity in a three-phase reservoir by the use of pseudo single-phase model.) Since in the single-phase case only a single partial-differential equation is needed to describe partial-differential equation is needed to describe the reservoir, identification techniques can be tested most conveniently on such a system. The customary parameters to be estimated are the rock porosity (or the storage coefficient) and the porosity (or the storage coefficient) and the directional permeabilities (or the transmissibilities), which are not uniform throughout the reservoir but a function of location. The history matching of single-phase reservoirs through the estimation of these functional properties now appears to be understood quite well. Numerical algorithms have been thoroughly studied and tested. The most difficult aspect is the ill-conditioned nature of the problem arising from the large number of unknowns problem arising from the large number of unknowns relative to the available data. A recent study has elucidated the basic structure of single-phase history-matching problems and has shown how the degree of ill-conditioning may be assessed quantitatively. Reservoirs generally contain more than one fluid phase, however, and consequently are described by phase, however, and consequently are described by mathematical models accounting for the multiphase nature of the system. The porosity and absolute permeabilities still must be estimated as in the permeabilities still must be estimated as in the single-phase case. In addition, it may be necessary to estimate the relative permeability-saturation relationships. Ordinarily, relative permeability vs saturation curves are determined through experiments on core samples. Because it may be difficult to reproduce actual reservoir flow conditions in a laboratory core sample, it is desirable to consider the direct estimation of relative permeability-saturation relationships on the basis of permeability-saturation relationships on the basis of reservoir data that ordinarily would be available during the course of production. This paper represents an initial investigation of the complex identification problem in two-phase reservoirs. The major objective problem in two-phase reservoirs. The major objective of this study is to investigate the feasibility of parameter estimation in two-phase reservoirs in parameter estimation in two-phase reservoirs in which the reservoir is described by a two-phase incompressible flow model. In the next section we present basic equations governing two-phase (oil-water) reservoirs. We first define the general history-matching problem for these reservoirs and then consider a hypothetical reservoir, circularly symmetric with a central producing well in which the flow may be taken as producing well in which the flow may be taken as incompressible. The radial flow reservoir represents a situation in which oil is produced from a water drive. We wanted to estimate reservoir properties based on data obtained at the well. Considering the flow as incompressible enables us to draw a direct comparison to the classic incompressible linear-flow case for which the problem of estimating relative permeabilities is well established. Thus, we permeabilities is well established. Thus, we seek to understand fully the incompressible flow case as a prelude to the general problem of history matching in two-phase compressible flow reservoirs. SPEJ P. 398

Estimation of the Location of the Boundary of a Petroleum Reservoir

1975 ◽  
Vol 15 (01) ◽  
pp. 19-38 ◽  
Author(s):  
Wen H. Chen ◽  
John H. Seinfeld
Keyword(s):  
History Matching ◽  
Single Phase ◽  
Steepest Descent ◽  
Petroleum Reservoir ◽  
Pressure Data ◽  
Reservoir Properties ◽  
Matching Problems ◽  
Reservoir Property ◽  
Boundary Location

Abstract This paper considers the problem of estimating the shape of a petroleum reservoir on the basis of pressure data from wells within the boundaries of pressure data from wells within the boundaries of the reservoir. It is assumed that the reservoir properties, such as permeability and porosity, are properties, such as permeability and porosity, are known but that the location of the boundary is unknown. Thus, this paper addresses a new class of history-matching problems in which the boundary position is the reservoir property to be estimated. position is the reservoir property to be estimated. The problem is formulated as an optimal-control problem (the location of the boundary being the problem (the location of the boundary being the control variable). Two iterative methods are derived for the determination of the boundary location that minimizes a functional, depending on the deviation between observed and predicted pressures at the wells. The steepest-descent pressures at the wells. The steepest-descent algorithm is illustrated in two sample problems:the estimation of the radius of a bounded circular reservoir with a centrally located well, andthe estimation of the shape of a two-dimensional, single-phase reservoir with a constant-pressure outer boundary. Introduction A problem of substantial economic importance is the determination of the size and shape of a reservoir. Seismic data serve to define early the probable area occupied by the reservoir; however, probable area occupied by the reservoir; however, a means of using initial well-pressure data to determine further the volume and shape of the reservoir would be valuable. On the basis of representing the pressure behavior in a single-phase bounded reservoir in terms of an eigenfunction expansion, Gavalas and Seinfeld have shown how the total pore volume of an arbitrarily shaped reservoir can be estimated from late transient pressure data at the completed wells. We consider pressure data at the completed wells. We consider here the related problem of the estimation of the shape (or the location of the boundary) of a reservoir from pressure data at an arbitrary number of wells. For reasons of economy, the time allowable for closing wells is limited. It is important, therefore, that any method developed for estimating the shape of a reservoir be applicable, in principle, from the time at which the wells are completed until the current time. Thus, the problem we consider here may be viewed as one in the general realm of history matching, but also one in which the boundary location is the property to be estimated rather than the reserved physical properties. The formulation in the present study assumes that everything is known about the reservoir except its boundary. In actual practice, the reverse is generally true. (By the time sufficient information is available regarding the spatial distribution of permeability and porosity, the boundaries may be fairly well known.) Nevertheless, relatively early in the life of a reservoir, when initial drillstem tests have served to identify an approximate distribution of properties, it may be of some importance to attempt to estimate the reservoir shape. Since knowledge of reservoir properties such as permeability and porosity is at properties such as permeability and porosity is at best a result of initial estimates from well testing, core data, etc., the assumption that these properties are known will, of course, lead only to an approximate reservoir boundary. As the physical properties are identified more accurately, the reservoir boundary can be more accurately estimated. It is the object of this paper to formulate in a general manner and develop and initially test computational algorithms for the class of history-matching problems in which the boundary is the unknown property.There are virtually no prior available results on the estimation of the location of the boundary of a region over which the dependent variable(s) is governed by partial differential equations. The method developed here, based on the variation of a functional on a variable region, is applicable to a system governed by a set of nonlinear partial differential equations with general boundary conditions. The derivation of necessary conditions for optimality and the development of two computational gradient algorithms for determination of the optimal boundary are presented in the Appendix. To illustrate the steepest-descent algorithm we present two computational examples using simulated reservoir data. SPEJ P. 19

Identifiability of Estimates of Two-Phase Reservoir Properties in History Matching

1984 ◽  
Vol 24 (06) ◽  
pp. 697-706 ◽  
Author(s):  
A.T. Watson ◽  
G.R. Gavalas ◽  
J.H. Seinfeld
Keyword(s):  
Pressure Drop ◽  
History Matching ◽  
Single Phase ◽  
Pressure Data ◽  
Relative Permeabilities ◽  
Unknown Parameters ◽  
Reservoir Properties ◽  
Matching Problem ◽  
Two Phase ◽  
Reservoir History Matching

Abstract Since the number of parameters to be estimated in a reservoir history match is potentially quite large, it is important to determine which parameters can be estimated with reasonable accuracy from the available data. This aspect can be called determining the identifiability of the parameters. The identifiability of porosity and absolute parameters. The identifiability of porosity and absolute and relative permeabilities on the basis of flow and pressure data in a two-phase (oil/water) reservoir is pressure data in a two-phase (oil/water) reservoir is considered. The question posed is: How accurately can one expect to estimate spatially variable porosity and absolute permeability and relative permeabilities given typical permeability and relative permeabilities given typical production and pressure data" To gain insight into this production and pressure data" To gain insight into this question, analytical solutions for pressure and saturation in a one-dimensional (1D) waterflood are used. The following, conclusions are obtained.Only the average value of the porosity can be determined on the basis of water/oil flow measurements.The permeability distribution can be determined from pressure drop data with an accuracy depending on the pressure drop data with an accuracy depending on the mobility ratio.Exponents in a power function representation of the relative permeabilities can he determined from WOR data alone but not nearly so accurately as when pressure drop and flow data are used simultaneously. Introduction The utility of reservoir simulation in predicting reservoir behavior is limited by the accuracy with which reservoir properties can be estimated. Because of the high costs properties can be estimated. Because of the high costs associated with coring analysis, reservoir engineers must rely, on history matching as a means of estimating reservoir properties. In this process a history match is carried out by choosing the reservoir properties as those that result in simulated well pressure and flow data that match as closely as possible those measured during production. In general, reservoir properties at each gridblock in the simulator represent the unknown values to be determined. Although there are efficient methods for estimating such a large number of unknowns, it has long been recognized from the results of single phase history matching exercises that many different sets of parameter values may yield a nearly identical match of observed and predicted pressures. The conventional single phase predicted pressures. The conventional single phase history matching problem is in fact a mathematically illposed problem, which explains its nonunique behavior. Such a situation is, in short, the result of the large number of unknowns to be estimated on the basis of the available data and the lack of sensitivity of the simulator solutions to the parameters. Because of this lack of sensitivity, the need to reduce the number of unknown Parameters or to introduce some additional constraints, such as "smoothness" of the estimated parameters, has been recognized. A problem as important as that of choosing which minimization method to employ in history matching is that of choosing, on the basis of the available well data. which properties actually should be estimated. This selection properties actually should be estimated. This selection depends on the relationship of the unknown parameters to the simulated well data. Ideally one would want to knowwhich parameters can be determined uniquely if the measurements were exact, andgiven the expected level of error in the measurements, how accurately we can expect to be able to estimate the parameters. The first question, that of establishing uniqueness of the estimated parameters, is notoriously difficult to answer, and for a parameters, is notoriously difficult to answer, and for a problem as complicated as reservoir history matching, problem as complicated as reservoir history matching, there are virtually no general results available that allow one to establish uniqueness for permeability or porosity. Thus, it is not possible in general to base our choice of which parameters to estimate on rigorous mathematical uniqueness results. In lieu of an answer to Question 1, the selection of parameters to be estimated can be based on Question 2, parameters to be estimated can be based on Question 2, which is amenable to theoretical analysis. If the expected errors in estimation of any of the parameters, or any linear combination of the parameters, are extremely large, then that parameter or set of parameters can be judged as not identifiable. In such a case, steps may be taken to reduce the number of unknown parameters. In summary, the reservoir history matching problem is a difficult parameter estimation problem, and understanding the relationship between the unknown parameters and the measured data is essential to obtaining meaningful estimates of the reservoir properties. Quantitative studies regarding the accuracy of estimates for single-phase history matching problems have been reported by Shah et al. and Dogru et al. Shah et al,. investigated the optimal level of zonation for use with 1D single-phase (oil) situations. SPEJ P. 697

A Semianalytical Approach for Analysis of Wells Exhibiting Multiphase Transient Linear Flow: Application to Field Data

SPE Journal ◽  
2020 ◽  
Vol 25 (06) ◽  
pp. 3265-3279
Author(s):  
Hamidreza Hamdi ◽  
Hamid Behmanesh ◽  
Christopher R. Clarkson
Keyword(s):  
Numerical Model ◽  
Relative Permeability ◽  
History Matching ◽  
Volatile Oil ◽  
Low Permeability ◽  
Two Phase ◽  
Linear Flow ◽  
Field Case ◽  
Three Phase ◽  
Relative Permeability Curves

Summary Rate-transient analysis (RTA) is a useful reservoir/hydraulic fracture characterization method that can be applied to multifractured horizontal wells (MFHWs) producing from low-permeability (tight) and shale reservoirs. In this paper, we applied a recently developed three-phase RTA technique to the analysis of production data from an MFHW completed in a low-permeability volatile oil reservoir in the Western Canadian Sedimentary Basin. This RTA technique is used to analyze the transient linear flow regime for wells operated under constant flowing bottomhole pressure (BHP) conditions. With this method, the slope of the square-root-of-time plot applied to any of the producing phases can be used to directly calculate the linear flow parameter xfk without defining pseudovariables. The method requires a set of input pressure/volume/temperature (PVT) data and an estimate of two-phase relative permeability curves. For the field case studied herein, the PVT model is constructed by tuning an equation of state (EOS) from a set of PVT experiments, while the relative permeability curves are estimated from numerical model history-matchingresults. The subject well, an MFHW completed in 15 stages, produces oil, water, and gas at a nearly constant (measured downhole) flowing BHP. This well is completed in a low-permeability,near-critical volatile oil system. For this field case, application of the recently proposed RTA method leads to an estimate of xfk that is in close agreement (within 7%) with the results of a numerical model history match performed in parallel. The RTA method also provides pressure–saturation (P–S) relationships for all three phases that are within 2% of those derived from the numerical model. The derived P–S relationships are central to the use of other RTA methods that require calculation of multiphase pseudovariables. The three-phase RTA technique developed herein is a simple-yet-rigorous and accurate alternative to numerical model history matching for estimating xfk when fluid properties and relative permeability data are available.

Novel Method for Characterizing Single-Phase Polymer Flooding

SPE Journal ◽  
2013 ◽  
Vol 19 (04) ◽  
pp. 695-702 ◽  
Author(s):  
Kewen Li ◽  
Wenjie Sun ◽  
Fen Li ◽  
Yantao Qu ◽  
Yaozhong Yang
Keyword(s):  
Fluid Flow ◽  
Shear Rate ◽  
Polymer Solution ◽  
Relative Permeability ◽  
Single Phase ◽  
Polymer Solutions ◽  
Polymer Flooding ◽  
New Method ◽  
Absolute Permeability ◽  
Two Phase

Summary Polymer flooding has been used to enhance oil production and reduce water cut for a long time. However, there are still many fundamental challenges in characterizing the multiphase-fluid flow, even the single-phase-fluid flow, associated with polymer flooding. For example, it is difficult to measure and calculate two-phase polymer solution/oil relative permeability. One of the difficulties comes from the non-Newtonian and time-dependent properties of polymer solutions; another comes from the change in absolute permeability caused by the adsorption of polymer on rock surfaces. Almost all the methods for computing relative permeability are based on the assumption that the absolute permeability is constant. It may be helpful to further understand the mechanisms and develop more-reliable methods for calculating two-phase polymer solution/oil relative permeability by investigating single-phase polymer flooding more profoundly. In this study, a new method has been developed to calculate the pseudopermeability during single-phase polymer flooding. The non-Newtonian property of the polymer solutions was considered in the new method. Polymer-flooding experiments with different concentrations of polymers were designed and conducted to study the single-phase flow of polymer solution in rocks with different permeabilities. The values of the pseudopermeability of single-phase polymer flooding were then calculated with the method. It has been found that the relationships between the pseudopermeability and the reciprocal of shear rate were linear. The polymer-flooding pseudopermeability extrapolated at the infinite shear rate was close to the brine-flooding permeability after polymer injections in many cases.

A Robust Methodology To Simulate Water-Alternating-Gas Experiments at Different Scenarios Under Near-Miscible Conditions

SPE Journal ◽  
2017 ◽  
Vol 22 (05) ◽  
pp. 1506-1518 ◽  
Author(s):  
Pedram Mahzari ◽  
Mehran Sohrabi
Keyword(s):  
Porous Media ◽  
History Matching ◽  
Flow In Porous Media ◽  
Phase Flow ◽  
Two Phase ◽  
Matching Process ◽  
Water Alternating Gas ◽  
Three Phase ◽  
Three Phase Flow ◽  
Cycle Dependent

Summary Three-phase flow in porous media during water-alternating-gas (WAG) injections and the associated cycle-dependent hysteresis have been subject of studies experimentally and theoretically. In spite of attempts to develop models and simulation methods for WAG injections and three-phase flow, current lack of a solid approach to handle hysteresis effects in simulating WAG-injection scenarios has resulted in misinterpretations of simulation outcomes in laboratory and field scales. In this work, by use of our improved methodology, the first cycle of the WAG experiments (first waterflood and the subsequent gasflood) was history matched to estimate the two-phase krs (oil/water and gas/oil). For subsequent cycles, pertinent parameters of the WAG hysteresis model are included in the automatic-history-matching process to reproduce all WAG cycles together. The results indicate that history matching the whole WAG experiment would lead to a significantly improved simulation outcome, which highlights the importance of two elements in evaluating WAG experiments: inclusion of the full WAG experiments in history matching and use of a more-representative set of two-phase krs, which was originated from our new methodology to estimate two-phase krs from the first cycle of a WAG experiment. Because WAG-related parameters should be able to model any three-phase flow irrespective of WAG scenarios, in another exercise, the tuned parameters obtained from a WAG experiment (starting with water) were used in a similar coreflood test (WAG starting with gas) to assess predictive capability for simulating three-phase flow in porous media. After identifying shortcomings of existing models, an improved methodology was used to history match multiple coreflood experiments simultaneously to estimate parameters that can reasonably capture processes taking place in WAG at different scenarios—that is, starting with water or gas. The comprehensive simulation study performed here would shed some light on a consolidated methodology to estimate saturation functions that can simulate WAG injections at different scenarios.

History Matching in Two-Phase Petroleum Reservoirs

1980 ◽  
Vol 20 (06) ◽  
pp. 521-532 ◽  
Author(s):  
A.T. Watson ◽  
J.H. Seinfeld ◽  
G.R. Gavalas ◽  
P.T. Woo
Keyword(s):  
Optimal Control ◽  
Parameter Estimation ◽  
Objective Function ◽  
History Matching ◽  
Computing Time ◽  
Absolute Permeability ◽  
Two Phase ◽  
Automatic History Matching ◽  
Control Approach ◽  
First Order

Abstract An automatic history-matching algorithm based onan optimal control approach has been formulated forjoint estimation of spatially varying permeability andporosity and coefficients of relative permeabilityfunctions in two-phase reservoirs. The algorithm usespressure and production rate data simultaneously. The performance of the algorithm for thewaterflooding of one- and two-dimensional hypotheticalreservoirs is examined, and properties associatedwith the parameter estimation problem are discussed. Introduction There has been considerable interest in thedevelopment of automatic history-matchingalgorithms. Most of the published work to date onautomatic history matching has been devoted tosingle-phase reservoirs in which the unknownparameters to be estimated are often the reservoirporosity (or storage) and absolute permeability (ortransmissibility). In the single-phase problem, theobjective function usually consists of the deviationsbetween the predicted and measured reservoirpressures at the wells. Parameter estimation, orhistory matching, in multiphase reservoirs isfundamentally more difficult than in single-phasereservoirs. The multiphase equations are nonlinear, and in addition to the porosity and absolutepermeability, the relative permeabilities of each phasemay be unknown and subject to estimation. Measurements of the relative rates of flow of oil, water, and gas at the wells also may be available forthe objective function. The aspect of the reservoir history-matchingproblem that distinguishes it from other parameterestimation problems in science and engineering is thelarge dimensionality of both the system state and theunknown parameters. As a result of this largedimensionality, computational efficiency becomes aprime consideration in the implementation of anautomatic history-matching method. In all parameterestimation methods, a trade-off exists between theamount of computation performed per iteration andthe speed of convergence of the method. Animportant saving in computing time was realized insingle-phase automatic history matching through theintroduction of optimal control theory as a methodfor calculating the gradient of the objective functionwith respect to the unknown parameters. Thistechnique currently is limited to first-order gradientmethods. First-order gradient methods generallyconverge more slowly than those of higher order.Nevertheless, the amount of computation requiredper iteration is significantly less than that requiredfor higher-order optimization methods; thus, first-order methods are attractive for automatic historymatching. The optimal control algorithm forautomatic history matching has been shown toproduce excellent results when applied to field problems. Therefore, the first approach to thedevelopment of a general automatic history-matchingalgorithm for multiphase reservoirs wouldseem to proceed through the development of anoptimal control approach for calculating the gradientof the objective function with respect to theparameters for use in a first-order method. SPEJ P. 521＾

Simultaneous Interpretation of Three-Phase Relative Permeability and Capillary Pressure for a Tight Carbonate Reservoir From Wireline Formation Testing

2019 ◽  
Vol 142 (6) ◽  
Author(s):  
Xiangnan Liu ◽  
Daoyong Yang
Keyword(s):  
Capillary Pressure ◽  
Relative Permeability ◽  
History Matching ◽  
Carbonate Reservoir ◽  
Reservoir Rock ◽  
Fluid Saturation ◽  
Three Phase ◽  
Tight Carbonate ◽  
Wet Condition ◽  
Oil Gas

Abstract In this paper, techniques have been developed to interpret three-phase relative permeability and water–oil capillary pressure simultaneously in a tight carbonate reservoir from numerically simulating wireline formation tester (WFT) measurements. A high-resolution cylindrical near-wellbore model is built based on a set of pressures and flow rates collected by dual packer WFT in a tight carbonate reservoir. The grid quality is validated, the effective thickness of the WFT measurements is examined, and the effectiveness of the techniques is confirmed prior to performing history matching for both the measured pressure drawdown and buildup profiles. Water–oil relative permeability, oil–gas relative permeability, and water–oil capillary pressure are interpreted based on power-law functions and under the assumption of a water-wet reservoir and an oil-wet reservoir, respectively. Subsequently, three-phase relative permeability for the oil phase is determined using the modified Stone II model. Both the relative permeability and the capillary pressure of a water–oil system interpreted under an oil-wet condition match well with the measured relative permeability and capillary pressure of a similar reservoir rock type collected from the literature, while the relative permeability of an oil–gas system and the three-phase relative permeability bear a relatively high uncertainty. Not only is the reservoir determined as oil-wet but also the initial oil saturation is found to impose an impact on the interpreted water relative permeability under an oil-wet condition. Changes in water and oil viscosities and mud filtrate invasion depth affect the range of the movable fluid saturation of the interpreted water–oil relative permeabilities.

Relative Permeability Characterization for Water-Alternating-Gas Injection in Oil Reservoirs

SPE Journal ◽  
2016 ◽  
Vol 21 (03) ◽  
pp. 0799-0808 ◽  
Author(s):  
H.. Shahverdi ◽  
M.. Sohrabi
Keyword(s):  
Relative Permeability ◽  
Gas Injection ◽  
Hysteresis Effect ◽  
Oil Reservoirs ◽  
Unsteady State ◽  
Two Phase ◽  
Water Alternating Gas ◽  
Three Phase ◽  
Phase Water ◽  
Wag Injection

Summary Large quantities of oil usually remain in oil reservoirs after conventional waterfloods. A significant part of this remaining oil can still be economically recovered by water-alternating-gas (WAG) injection. WAG injection involves drainage and imbibition processes taking place sequentially; therefore, the numerical simulation of the WAG process requires reliable knowledge of three-phase relative permeability (kr) accounting for cyclic-hysteresis effects. In this study, the results of a series of unsteady-state two-phase displacements and WAG coreflood experiments were used to investigate the behavior of three-phase kr and hysteresis effects in the WAG process. The experiments were performed on two different cores with different characteristics and wettability conditions. An in-house coreflood simulator was developed to obtain three-phase relative permeability values directly from unsteady-state WAG experiments by history matching the measured recovery and differential-pressure profiles. The results show that three-phase gas relative permeability is reduced in consecutive gas-injection cycles and consequently the gas mobility and injectivity drop significantly with successive gas injections during the WAG process, under different rock conditions. The trend of hysteresis in the relative permeabilty of gas (krg) partly contradicts the existing hysteresis models available in the literature. The three-phase water relative permeability (krw) of the water-wet (WW) core does not exhibit considerable hysteresis effect during different water injections, whereas the mixed-wet (MW) core shows slight cyclic hysteresis. This may indicate a slight increase of the water injectivity in the subsequent water injections in the WAG process under MW conditions. Insignificant hysteresis is observed in the oil relative permeability (kro) during different gas-injection cycles for both WW and MW rocks. However, a considerable cyclic-hysteresis effect in kro is observed during water-injection cycles of WAG, which is attributed to the reduction of the residual oil saturation (ROS) during successive water injections. The kro of the WW core exhibits much-more cyclic-hysteresis effect than that of the MW core. No models currently exist in reservoir simulators that can capture the observed cyclic-hysteresis effect in oil relative permeability for the WAG process. Investigation of relative permeability data obtained from these displacement tests at different rock conditions revealed that there is a significant discrepancy between two-phase and three-phase relative permeability of all fluids. This highlights that not only the three-phase relative permeability of the intermediate phase (oil), but also the three-phase kr of the wetting phase (water) and nonwetting phase (gas) are functions of two independent saturations.

An Experimental Investigation of Viscous-Oil Recovery Efficiency as a Function of Voidage-Replacement Ratio

SPE Journal ◽  
2016 ◽  
Vol 21 (04) ◽  
pp. 1236-1253 ◽  
Author(s):  
Tae Wook Kim ◽  
E.. Vittoratos ◽  
A. R. Kovscek
Keyword(s):  
Relative Permeability ◽  
Oil Recovery ◽  
Crude Oils ◽  
Replacement Ratio ◽  
Two Phase ◽  
Foamy Oil ◽  
Three Phase ◽  
Solution Gas Drive ◽  
Gas Drive ◽  
Solution Gas

Summary Recovery processes with a voidage-replacement ratio (VRR) (VRR = injected volume/produced volume) of unity rely solely on viscous forces to displace oil, whereas a VRR of zero relies on solution-gas drive. Activating a solution-gas-drive mechanism in combination with waterflooding with periods of VRR less than unity (VRR < 1) may be optimal for recovery. Laboratory evidence suggests that recovery for VRR < 1 is enhanced by emulsion flow and foamy (i.e., bubbly) crude oil at pressures under bubblepoint for some crude oils. This paper investigates the effect of VRR for two crude oils referred to as A1 (88 cp and 6.2 wt% asphaltene) and A2 (600 cp and 2.5 wt% asphaltene) in a sandpack system (18-in. length and 2-in. diameter). The crude oils are characterized with viscosity, asphaltene fraction, and acid/base numbers. A high-pressure experimental sandpack system (1 darcy and Swi = 0) was used to conduct experiments with VRRs of 1.0, 0.7, and 0 for both oils. During waterflood experiments, we controlled and monitored the rate of fluid injection and production to obtain well-characterized VRR. On the basis of the production ratio of fluids, the gas/oil and /water relative permeabilities were estimated under two-phase-flow conditions. For a VRR of zero, the gas relative permeability of both oils exhibited extremely low values (10−6−10−4) caused by internal gas drive. Waterfloods with VRR < 1 displayed encouraging recovery results. In particular, the final oil recovery with VRR = 0.7 [66.2% original oil in place (OOIP)] is more than 15% greater than that with VRR = 1 (55.6% OOIP) with A1 crude oil. Recovery for A2 with VRR = 0.7 (60.5% OOIP) was identical to the sum of oil recovery for solution-gas drive (19.1% OOIP) plus waterflooding (40.1% OOIP). An in-line viewing cell permitted inspection of produced fluid morphology. For A1 and VRR = 0.7, produced oil was emulsified, and gas was dispersed as bubbles, as expected for a foamy oil. For A2 and VRR < 1, foamy oil was not clearly observed in the viewing cell. In all cases, the water cut of VRR = 1 is clearly greater than that of VRR = 0.7. Finally, three-phase relative permeability was explored on the basis of the experimentally determined two-phase oil/water and liquid/gas relative permeability curves. Well-known algorithms for three-phase relative permeability, however, did not result in good history matches to the experimental data. Numerical simulations matched the experimental recovery vs. production time acceptably after modification of the measured krg and krow relationships. A concave shape for oil relative permeability that is suggestive of emulsified oil in situ was noted for both systems. The degree of agreement with experimental data is sensitive to the details of gas (gas/oil system) and oil (oil/water system) mobility.

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