Dependence Of Relative Permeability Research Articles

A proposed capillary number dependent model for prediction of relative permeability in gas condensate reservoirs: a robust non-linear regression analysis

Well deliverability reduction as a result of liquid (condensate) build up in near well regions is an important deal in the development of gas condensate reservoirs. The relative permeability is an imperative factor for characterization of the aforementioned problem. The dependence of relative permeability on the coupled effects of Interfacial Tension (IFT) and flow velocity (capillary number) together with phase saturation is well established in the literature. In gas condensate reservoirs, however, the influence of IFT and velocity on this parameter becomes more evident. The current paper aims to establish a new model for predicting the relative permeability of gas condensate reservoirs by employing the direct interpolation technique. To this end, the regression analysis was carried out using seven sets of literature published experimental data. The validity analysis was executed by utilizing statistical parameters integrated with graphical descriptions. Furthermore, a comparison was carried out between the proposed model and some literature published empirical models. The results of the examination demonstrated that the new model outperformed other correlations from the standpoints of accuracy and reliability.

Numerical modelling of cyclic CO2 injection in unconventional tight oil resources; trivial effects of heterogeneity and hysteresis in Bakken formation

The impact of rock heterogeneity on the performance of cyclic gas injection is a key element in tight oil reservoir modeling. Dependency of relative permeability on saturation history during cyclic CO2 injection (CCI) in various operational constraints affects the oil recovery in different ways. Numerous studies exist on the hydraulically fractured horizontal wells in unconventional resources, especially on cyclic gas injection performance. However, because of simplifications, the uncertainty due to permeability heterogeneity and dependency of reservoir gas extent on saturation history has not been considered in simulation models. A poor understanding of the variables affecting CO2 injection efficiency might result in unsuccessful treatments and project failures. The aim of the present work is to numerically model the physical properties of matrix heterogeneity and relative permeability hysteresis, which are influential in reservoir performance and should not be ignored during CCI. In this work, a compositional simulation model is built based on the Bakken formation geological settings, well production and crude oil PVT data. To embody heterogeneity, matrix and natural fracture effective permeability fields are log-normally populated. Four permeability maps based on Dykstra-Parsons (DP) coefficients are generated and applied in a sector model. A relative permeability hysteresis model is incorporated within the simulator using the Killough’s method. Hence, the effect of hysteresis-induced gas retardation on oil recovery and CO2 retention can be studied during CCI in which strong flow reversals happens. A compositional field-scale simulation of CCI is conducted and recovery performance is investigated as well as retained CO2 saturation. The simulation results revealed that production is greatly affected by heterogeneity at early stages of reservoir life. Uneven flow in the presence of heterogeneity leads to lower recovery during primary depletion. This effect is more highlighted after implementing CCI since injected gas is prevented from uniform distribution further and deep into the reservoir. Dissolution gas trapping is also modeled with inclusion of relative permeability hysteresis. Recovered oil from the hysteretic model illustrates a minor effect on CO2 trapping at near-miscible conditions. However, CO2 retention improves oil recovery at immiscible injection. In this model shortcomings of uncertainties associated with the simplified reservoir models in terms of uniformity in absolute permeability and relative permeability are reduced. Our results highlight the underlying mechanisms of lower recovery induced by heterogeneity and of improved efficiency due to hysteresis.

Relative Permeability of Near-Miscible Fluids in Compositional Simulators

Miscible gas injection is one of the most effective enhanced oil recovery techniques. There are several challenges in accurately modeling this process, which occurs in the near-miscible region. The adjustment of relative permeability for near-miscible processes is the main focus of this work. The dependence of relative permeability on phase identification can lead to significant complications while simulating near-miscible displacements. We present an analysis of how existing methods incorporate compositional dependence in relative permeability functions. The sensitivity of the different methods to the choice of reference points is presented with guidelines to limit the modification of the relative permeabilities to physically reasonable values. We distinguish between the two objectives of reflecting near-miscible behavior and ensuring smooth transitions across phase changes. We highlight an important link that combines the two objectives in a more general framework. We make use of Gibbs free energy as a compositional indicator in the generalized framework. The new approach was implemented in an automatic differentiation general purpose research simulator and tested on a set of near-miscible gas-injection problems. We show that including compositional dependencies in the relative permeability near the critical point impacts the simulation results with significant improvements in nonlinear convergence.

Solubility Of Methane, Nitrogen, and Carbon Dioxide in Bitumen and Water for SAGD Modelling

Summary Gases such as carbon dioxide, nitrogen, and methane that can be present in a steam-assisted gravity-drainage (SAGD) steam chamber (but do not condense into the liquid phase to any large degree at reservoir conditions) are referred to as noncondensable gases (NCGs). The coinjection of NCGs with steam during SAGD results in changes in production rate, total oil production, and the amount of steam required to mobilize the bitumen in place. To investigate the impact of NCGs on SAGD performance by means of numerical simulation, it is important to model gas solubility in both bitumen and water accurately. Also, the dependence of relative permeability on temperature needs to be accounted for to achieve reliable results. This study presents a systematic approach to predict the K-values for the gas/bitumen- and gas/water-phase equilibria over a wide range of pressures and temperatures.

A New Model for Modern Production-Decline Analysis of Gas/Condensate Reservoirs

Summary Modern production-decline analysis is a robust technique for analysis of production data from a well under variable operating conditions. It uses production rates and flowing pressures to provide reliable estimates of recoverable reserves and fluid in place. The mathematics behind this technique is similar to that of pressure-transient theory; however, the focus is different. It deals with long-term variable production data instead of short-term constant-rate transient data. Using modern decline analysis for two-phase-flow conditions (e.g., gas/condensate reservoirs) is under question because of the single-phase-flow assumption in the development of a "material-balance time" function. This is a time function that converts any decline (e.g., exponential decline) to harmonic decline to account for variable operating conditions. The purpose of this work is to develop a model to use the concepts of modern techniques for analyzing production data of single-porosity gas/condensate reservoirs. For this purpose, the governing flow equation is linearized, using appropriately defined pseudopressure and pseudotime functions. Then, the solution is obtained for constant-well-rate condition. This is followed by employing the superposition theorem to account for variable well pressure/rate conditions, resulting in definition of two-phase material-balance pseudotime. The solution developed here is coupled with an appropriate material-balance equation and used to estimate the average reservoir pressure and original gas in place from analyzing production data. The dependency of relative permeability on capillary number and non-Darcy flow is included in the formulation. Verification of the proposed method is obtained with the analysis of synthetic production data using a series of fine-grid compositional numerical simulations over a typical range of gas/condensate-reservoir parameters.

A new method for productivity calculation of perforated wells in Gas condensate reservoirs

Flow in perforated regions has been the subject of numerous investigations in the past 60 years. These studies have mainly concentrated on proposing practical tools for the productivity estimation of perforated wells. The skin factor proposed can be applied in an equivalent (one dimensional radial) open-hole system replicating the flow around the actual complex three dimensional flow geometry of the perforated region. However, the majority of these studies concentrate on single-phase flow conditions. In gas condensate systems at relatively low interfacial tension (IFT) values, phase change and dependency of relative permeability on velocity and interfacial tension add significant complexity to proposing such an efficient and much needed tool for practical applications. This work is aimed at the development of a practical and convenient method for defining an effective wellbore radius of an equivalent open-hole system, replicating flow around a perforated well in gas condensate reservoirs. The new method is based on the physics of the flow and applicable for both single-phase non-Darcy and two-phase gas condensate flow systems. Since the mechanical perforation skin formulations available in the literature are not accurate for highly anisotropic formations, a new more efficient skin formulation is introduced for such applications. In these exercises the finite-element based simulator developed by Jamiolahmady et al. (2007) was used to generate the large bank of data required to confirm the integrity of the proposed practical approach for productivity calculation of perforated wells in gas condensate reservoirs.

The Dependency of Relative Permeability on Dominated Flow Regimes Under Gas Gravity Assisted Flow

Gas-oil relative permeability is essential for performance predictions of reservoirs with solutions for gas drive, gas cap expansion, or gas injection. The nature of flow in reservoir is determined by the interplay of relative permeability and viscous, gravity, and capillary forces. Displacement experiments of the gas-oil system are performed on long core scale models by varying the petrophysical properties and flow conditions. Experiments are conducted in situations where capillary, gravity, and viscous forces are comparable. The effect of destabilized front velocity on relative permeability and residual saturation is investigated. The results indicate that the relative permeability varies with the balance between the gravity and viscous forces. The relative permeabilities determined by analytical and numerical approaches indicate that higher displacement velocity leads to a higher gas relative permeability and lower oil relative permeability. The residual oil saturation was increased by increasing the injection velocity and decreasing the permeability.

A Simulator for Solution-Gas Drive in Heavy Oils

Abstract Solution-gas drive in heavy oil reservoirs is a complex process, and the mechanisms involved are not fully understood. In the past, these reservoirs have been modelled by altering variables such as critical gas saturation, bubble point pressure, relative permeability curves, fluid properties, and rock properties during sand production. Numerous investigations have shown that gas mobility in heavy oil remains extremely low. Furthermore, experimental observations have suggested that gas mobility depends not only on gas saturation, but also on depletion rate and oil viscosity. It is therefore thought that the viscous forces at the microscopic level affect gas mobility. The dependence of relative permeability to gas on parameters other than gas saturation has been observed previously in processes such as foam flow through porous media, and displacement near miscible conditions, where the ratio of viscous forces to capillary forces is large. In this work, we have developed a numerical simulator where the "apparent" gas relative permeability is a function of rate and gas saturation. The developed model is used to simulate a previously reported set of experiments of solution-gas drive in heavy oils, where the dependence of gas mobility on depletion rate has been observed. It is shown that a model with rate-dependent relative permeability functions can explain many features of solution- gas drive in heavy oil, in particular, its rate-dependent recovery behaviour. Introduction Field experience in many heavy oil reservoirs in Canada and Venezuela have shown that recoveries in the order of 10 - 15% may be achieved under primary depletion(1, 2). Typical observations are high oil production rate, high primary oil recovery, and good pressure maintenance. This behaviour is in contrast with the traditional view of solution-gas drive, where gas flows much faster than oil, leading to high producing GOR, loss of reservoir energy, and low recovery. Many of these reservoirs are produced along with significant amounts of reservoir sand. In addition to the related geomechanical effects, a special fluid flow behaviour is necessary to explain some of the observations, including low producing GOR and high recoveries. There have been very different explanations for the abnormal characteristics observed during solution-gas drive in these heavy oil reservoirs. Smith(1) suggested a simultaneous oil and gas flow in porous media in which the gas is entrained in the oil as tiny bubbles. More recently, Kamp et al.(3) developed a model for the entrained flow of gas in oil, which incorporated a constitutive equation for the viscosity of the bubbly mixture. Maini et al.(4) conducted experiments using unconsolidated sand-packs with heavy oils, and observed high pressure gradients representative of very low gas mobilities. The authors attributed this behaviour to what they called "Foamy Oil Flow." Pooladi-Darvish and Firoozabadi(5) were the first to report quantitative estimates of the phase mobilities under solution-gas drive in heavy oil. They performed depletion experiments in a sand-pack saturated with live oil, and used both light and heavy oil for comparison. Analysis of the data suggested that gas relative permeabilities in heavy oil might be as low as 10−6 - 10−5.

Relative Permeability at Near-Critical Conditions

SummaryWe have measured a series of two-phase drainage relative permeability curves at near-critical conditions by means of the displacement method. As a fluid system we have used the model system methanol/n-hexane that exhibits a critical point at ambient conditions. In the measurements we have varied the interfacial tension and the flow rate.Our results show a clear trend from immiscible relative permeability functions to miscible relative permeability lines with decreasing interfacial tension and increasing superficial velocity. The relative permeability measurements show that the controlling parameter is the ratio of viscous to capillary forces on a pore scale, denoted by the capillary number Nc=k‖∇Φ‖/ϕσ.To demonstrate the significance of using the proper relative permeability functions, we have calculated the well impairment due to liquid drop-out in a model gas condensate reservoir, for four different rock types showing four different relations between relative permeability and the capillary number. The calculations show that near-miscible relative permeability functions come into play in the vicinity of the well bore. This is contrary to what happens if the relative permeability would be a function of interfacial tension alone. In addition, the results show that well impairment by condensate drop-out may be significantly overestimated if the dependence of relative permeability on the capillary number is ignored.

The Combined Effect of Near-Critical Relative Permeability and Non-Darcy Flow on Well Impairment by Condensate Drop Out

SummaryWe present a comprehensive numerical method to calculate well impairment based on steady-state radial flow. The method incorporates near-critical relative permeability and saturation-dependent inertial resistance.Example calculations show that near-critical relative permeability, which depends on the capillary number, and non-Darcy flow are strongly coupled. Inertial resistance gives rise to a higher capillary number. In its turn, the improved mobility of the gas phase caused by a higher capillary number enhances the importance of the inertial resistance.The effect of non-Darcy flow is much more pronounced in gas condensate reservoirs than in dry gas reservoirs. Well impairment may be grossly overestimated if the dependence of relative permeability on the capillary number is ignored.

General Three-Phase Relative Permeability Model for Prudhoe Bay

SummaryThis paper describes two- and three-phase relative permeability concepts important for Prudhoe Bay. It includes a three-phase relative permeability correlation that incorporates hysteresis in gas, oil, and water relative permeability as well as the dependence of relative permeability on composition and gas/oil interfacial tension (IFT). The functional forms chosen to correlate the relative permeability data were based on interpretation of the pore-level mechanisms that determine fluid flow. The three-phase correlation reduces to traditional models in various limits and is more consistent with available data and trends in the literature than previous correlations. Although this correlation was developed for Prudhoe Bay, it can be and has been applied to other mixed-wet reservoirs with changes in the input parameters. The correlation is particularly useful in situations where both compositional effects and hysteresis are important.

Modeling Gas-Condensate Well Deliverability

Summary This paper gives an accurate method for modeling the deliverability of gas-condensate wells. Well deliverability is calculated with a modified form of the Evinger-Muskat1 pseudopressure (originally proposed for solution-gas-drive oil wells). The producing gas/oil ratio (GOR) is needed to calculate pseudopressure, together with pressure/volume/temperature (PVT) properties (black-oil or compositional), and gas/oil relative permeabilities. The proposed method is successfully tested for radial, vertically fractured, and horizontal wells. Using the proposed deliverability model, we show that fine-grid single-well simulations can be reproduced almost exactly with a simple rate equation that uses pseudopressure. The key is knowing the producing GOR accurately. The effect of near-wellbore damage, vertical fracture, or flow improvement caused by horizontal well trajectory is readily incorporated into the rate equation as a constant skin term. The effect of gas/oil relative permeability is studied. We show that well deliverability impairment resulting from near-wellbore condensate "blockage" is dependent only on relative permeabilities within the range defined by 1 <krg/kro < 50. Usually this represents gas and oil relative permeabilities ranging from 0.05 to 0.3. Gas relative permeabilities at low oil saturations (krg > 0.3) affect deliverability only for richer gas condensates. A key observation and conclusion from this study is that critical oil saturation has no direct effect on well deliverability. We also show that interfacial tension (IFT) dependence of relative permeability has little or no effect on gas-condensate well performance (e.g., length of plateau production). The most important application of this study is to provide a simple method for calculating bottom-hole flowing pressure (BHFP) in coarse-grid models. We show that the proposed pseudopressure method is readily calculated for each well grid cell on the basis of only grid-cell pressure and saturation (i.e., producing GOR). Local grid refinement near wells is not necessary, and relatively large well grid cells can be used and still provide an accurate description of well deliverability.

Explicit relation between relative permeability and structural parameters in stochastic pore networks

It is shown, by suitable use of the effective medium approximation, that the relative permeability of a stochastic network consisting of idealised pores of randomly varying radius, which are progressively constrited and/or blocked, can be expressed analytically as an explicit function of suitable parameters characteristic of pore and network structure as well as the physics of flow. In this manner, it is possible to: (i) gain a much deeper insight into the dependence of relative permeability on the breadth and shape of the pore radius probability distribution as well as the network connectivity, and (ii) greatly simplify the approximate evaluation of the relative permeability of given stochastic networks under suitable conditions. These points are illustrated by a detailed study of the case of (Knudsen) gas relative permeability of cylindrical pore networks, in the presence of an adsorbed and condensed foreign vapour. Results of immediate importance for experimental pore structure analysis, which emerged from this study include the capability of: (i) estimating the network connetivity, and (ii) testing the self-consistency of pore size distributions determined experimentally by conventional vapour sorption isotherm analysis.