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.

Measurement of Three-Phase Relative Permeability with IFT Variation

2005 ◽  
Vol 8 (01) ◽  
pp. 33-43 ◽  
Author(s):  
Yildiray Cinar ◽  
Franklin M. Orr
Keyword(s):  
Experimental Data ◽  
Relative Permeability ◽  
Oil And Gas ◽  
Gas Injection ◽  
Relative Permeabilities ◽  
Two Phase ◽  
Rich Phase ◽  
Injection Process ◽  
Three Phase ◽  
Relative Permeability Curves

Summary In this paper, we present results of an experimental investigation of the effects of variations in interfacial tension (IFT) on three-phase relative permeability. We report results that demonstrate the effect of low IFT between two of three phases on the three-phase relative permeabilities. To create three-phase systems in which IFT can be con-trolled systematically, we used a quaternary liquid system composed of hexadecane(C16), n-butanol (NBA), water (H2O), and isopropanol (IPA). Measured equilibrium phase compositions and IFTs are reported. The reported phase behavior of the quaternary system shows that the H2O-rich phase should represent the "gas" phase, the NBA-rich phase should represent the "oil" phase, and the C16-rich phase should represent the "aqueous" phase. Therefore, we used oil-wet Teflon (PTFE) bead packs to simulate the fluid flow in a water-wet oil reservoir. We determined phase saturations and three-phase relative permeabilities from recovery and pressure-drop data using an extension of the combined Welge/Johnson-Bossler-Naumann (JBN) method to three-phase flow. Measured three-phase relative permeabilities are reported. The experimental results indicate that the wetting-phase relative permeability was not affected by IFT variation, whereas the other two-phase relative permeabilities were clearly affected. As IFT decreases, the oil and gas phases become more mobile at the same phase saturations. For gas/oil IFTs in the range of 0.03 to 2.3 mN/m, we observed an approximately 10-fold increase in the oil and gas relative permeabilities against an approximately 100-fold decrease in the IFT. Introduction Variations in gas and oil relative permeabilities as a function of IFT are of particular importance in the area of compositional processes such as high-pressure gas injection, where oil and gas compositions can vary significantly both spatially and temporally. Because gas-injection processes routinely include three-phase flow (either because the reservoir has been water-flooded previously or because water is injected alternately with gas to improve overall reservoir sweep efficiency), the effect of IFT variations on three-phase relative permeabilities must be delineated if the performance of the gas-injection process is to be predicted accurately. The development of multicontact miscibility in a gas-injection process will create zones of low IFT between gas and oil phases in the presence of water. Although there have been studies of the effect of low IFT on two-phase relative permeability,1–14 there are limited experimental data published so far analyzing the effect of low IFT on three-phase relative permeabilities.15,16 Most authors have focused on the effect of IFT on oil and solvent relative permeabilities.17 Experimental results show that residual oil saturation and relative permeability are strongly affected by IFT, especially when the IFT is lower than approximately 0.1 mN/m (corresponding to a range of capillary number of 10–2 to 10–3). Bardon and Longeron3 observed that oil relative permeability increased linearly as IFT was reduced from approximately 12.5 mN/m to 0.04 mN/m and that for IFT below 0.04, the oil relative permeability curves shifted more rapidly with further reductions in IFT. Later, Asar and Handy6 showed that oil relative permeability curves began to shift as IFT was reduced below 0.18 mN/m for a gas/condensate system near the critical point. Delshad et al.15 presented experimental data for low-IFT three-phase relative permeabilities in Berea sandstone cores. They used a brine/oil/surfactant/alcohol mixture that included a microemulsion and excess oil and brine. The measurements were done at steady-state conditions with a constant capillary number of 10–2 between the microemulsion and other phases. The IFTs of microemulsion/oil and microemulsion/brine were low, whereas the IFT between oil and brine was high. They concluded that low-IFT three-phase relative permeabilities are functions of their own saturations only. Amin and Smith18 recently have published experimental data showing that the IFTs for each binary mixture of brine, oil, and gas phases vary as pressure increases(Fig. 1). Fig. 1 shows that the IFT of a gas/oil pair decreases as the pressure increases, whereas the IFTs of the gas/brine and oil/brine pairs approach each other.

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

A Case Study in Scaleup for Multicontact Miscible Hydrocarbon Gas Injection

1998 ◽  
Vol 1 (06) ◽  
pp. 575-582 ◽  
Author(s):  
G.R. Jerauld
Keyword(s):  
Relative Permeability ◽  
Oil Recovery ◽  
History Matching ◽  
Fine Grid ◽  
Full Field ◽  
Compositional Model ◽  
Three Phase ◽  
Solvent Retention ◽  
Hydrocarbon Gas ◽  
Relative Permeability Curves

Summary We describe the strategy and results of scaleup done to simulate a multicontact miscible hydrocarbon water alternating gas (WAG) injection process. To adequately model both oil recovery and solvent retention in WAG, one must model three-phase flow including gas trapping. Scaleup of the multicontact miscible gas process is particularly difficult because of the very fine-scale structure of the gas fingers and the miscible front. The case studied is a heterogeneous mixed wet reservoir with a transition zone down to an underlying aquifer. The objective was to develop pseudo relative permeability curves and other parameters that are suitable for running in a full-field limited compositional model with three hydrocarbon components. Both history-matching and systematic approaches were used to generate pseudo relative permeability curves that reproduced results of high-resolution, fully compositional (FC) reference simulations. Dynamic pseudoization techniques were used to derive first guesses at pseudos, but required further calibration to reproduce reference simulations successfully. In matching incremental miscible gas/oil recovery timing and solvent retention, varying three phase water relative permeability was much more effective than varying the mixing parameter. The predictive capability of pseudos was tested for changes with respect to slug size, WAG ratio, and solvent enrichment. Pseudos derived for one pattern or cross section were tested in other patterns or cross sections. Pseudos worked well with respect to changes in WAG ratio, fairly well with respect to changes in solvent enrichment, and moderately well for changes in slug size. They were less robust with respect to changes in description. Introduction Estimation of the incremental recovery and solvent utilization in a multicontact miscible hydrocarbon gas process is challenging. On one hand, important features of the process occur over small-length scales and cannot be estimated readily without very fine-grid, FC simulation. The condensing/vaporizing drive entails the concentration of enriching components into a narrow miscible front that is smeared by coarse areal gridding. High vertical grid refinement is needed to capture thin gas fingers that form within layers of high permeability. SPE 53006 was revised for publication from paper SPE 39626, first presented at the 1998 SPE/DOE Improved Oil Recovery Symposium, Tulsa, Oklahoma, 19-22 April.

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.

An Equation To Predict Two-Phase Relative Permeability Curves in Fractures

2010 ◽  
Author(s):  
Andres Chima ◽  
Efren Antonio Chavez Iriarte ◽  
Zuly Himelda Calderon Carrillo
Keyword(s):  
Relative Permeability ◽  
Two Phase ◽  
Relative Permeability Curves

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.

scholarly journals Insights, Trends and Challenges Associated with Measuring Coal Relative Permeability

2019 ◽  
Vol 89 ◽  
pp. 01004
Author(s):  
Dylan Shaw ◽  
Peyman Mostaghimi ◽  
Furqan Hussain ◽  
Ryan T. Armstrong
Keyword(s):  
Relative Permeability ◽  
Effective Stress ◽  
History Matching ◽  
Water Saturation ◽  
Laboratory Data ◽  
Stress Regime ◽  
Cross Point ◽  
Irreducible Water Saturation ◽  
Relative Permeability Curves ◽  
The Right

Due to the poroelasticity of coal, both porosity and permeability change over the life of the field as pore pressure decreases and effective stress increases. The relative permeability also changes as the effective stress regime shifts from one state to another. This paper examines coal relative permeability trends for changes in effective stress. The unsteady-state technique was used to determine experimental relativepermeability curves, which were then corrected for capillary-end effect through history matching. A modified Brooks-Corey correlation was sufficient for generating relative permeability curves and was successfully used to history match the laboratory data. Analysis of the corrected curves indicate that as effective stress increases, gas relative permeability increases, irreducible water saturation increases and the relative permeability cross-point shifts to the right.

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