Multi-Scale Approach to Estimating Two-Phase Relative Permeability from Unstable Heavy Oil Displacement by History Matching

2018 ◽  
Author(s):  
Usman Taura ◽  
Pedram Mahzari ◽  
Mehran Sohrabi ◽  
Yahya Al-Wahaibi
Keyword(s):  
Relative Permeability ◽  
Heavy Oil ◽  
History Matching ◽  
Two Phase ◽  
Multi Scale ◽  
Oil Displacement

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.

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

Evaluation of Normalized Stone's Methods for Estimating Three-Phase Relative Permeabilities

1984 ◽  
Vol 24 (02) ◽  
pp. 224-232 ◽  
Author(s):  
F.J. Fayers ◽  
J.D. Matthews
Keyword(s):  
Relative Permeability ◽  
Gas Oil ◽  
Residual Oil ◽  
Relative Permeabilities ◽  
Two Phase ◽  
Mobile Water ◽  
Oil Displacement ◽  
Three Phase ◽  
Phase Data ◽  
Definition Of

Abstract This paper examines normalized forms of Stone's two methods for predicting three-phase relative permeabilities. Recommendations are made on selection of the residual oil parameter, S om, in Method I. The methods are tested against selected published three-phase experimental data, using the plotting program called CPS-1 to infer improved data fitting. It is concluded that the normalized Method I with the recommended form for S om, is superior to Method II. Introduction Stone has produced two methods for estimating three-phase relative permeability from two-phase data. Both models assume a dominant wetting phase (usually water), a dominant nonwetting phase (gas), and an intermediate wetting phase (usually oil). The relative permeabilities for the water and gas are assumed to permeabilities for the water and gas are assumed to depend entirely on their individual saturations because they occupy the smallest and largest pores, respectively. The oil occupies the intermediate-size pores so that the oil relative permeability is an unknown function of water and gas saturation. For his first method, Stone proposed a formula for oil relative, permeability that was a product of oil relative permeability in the absence of gas, oil relative permeability in the absence of gas, oil relative permeability in the absence of mobile water, and some permeability in the absence of mobile water, and some variable scaling factors. He compared this formula with the experimental results of Corey et al., Dalton et al., and Saraf and Fatt. The formula is likely to be most in error at low oil relative permeability where more data are needed that show the behavior of residual oil saturation as a function of mixed gas and water saturations. In particular, the best value for the parameter S om that occurs in the model is not well resolved. In his second method, Stone developed a new formula and compared it against the data of Corey et al., Dalton et al., Saraf And Fatt, and some residual oil data from Holmgren and Morse. Stone suggested that his second method gave reasonable agreement with experiments without the need to include the parameter S om. If in the absence of residual oil data, S om = 0 is used in the first method, the second method is then better than the first method, although it tends to under predict relative permeability. Dietrich and Bondor later showed that Stone's second method did not adequately approximate the two-phase data unless the oil relative permeability at connate water saturation, k rocw, was close to unity. Dietrich and Bondor suggested a normalization that achieved consistency with the two-phase data when k rocw, was not unity. This normalization can be unsatisfactory because k roc an exceed unity in some saturation ranges if k rocw is small. More recently this objection has been overcome by the normalization of Method II introduced by Aziz and Settari. Aziz and Settari also pointed out a similar normalization problem with Stone's first method and suggested an alternative to overcome the deficiency. However, no attempt was made to investigate the accuracy of these normalized formulas with respect to experimental data. In the next section of the paper we review the principal forms of Stone's formulas, and introduce some new ideas on the use and choice of the parameter S om. Later we examine the first of Stone's assumptions that water and gas relative permeabilities are functions only of their respective saturations for a water-wet system. This involves a critical review of all the published experimental measurements. Earlier reviews did not take into account some of the available data. Last, we examine the predictions of normalized Stone's methods for oil relative permeability against the more reliable experimental results. It is concluded that the normalized Stone's Method I with the improved definition of S om is more accurate than the normalized Method II. Mathematical Definition of Three-Phase Relative Permeabilities We briefly review the principal forms of the Stone's formulas that use the two-phase relative permeabilities defined by water/oil displacement in the absence of gas, k rw = k rw (S w) and k row = k row (S w) and gas/oil displacement in the presence of connate water, k rg = k rg (S g) and k rog = k rog (S g). SPEJ p. 224

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