Estimation of Effective Permeabilities for Reservoirs Initially Above Bubblepoint Pressure

This study investigates the effects of heterogeneities on the estimates of effective or relative permeabilities from well-test pressure data obtained from a well producing a solution-gas-drive reservoir. The heterogeneous system considered in this work is that of a two-zone composite reservoir with different absolute permeability and/or relative permeability curves in the two regions. The estimation of effective (or relative) permeability values as a function of sandface oil saturation or wellbore pressure for both drawdown and buildup tests is presented. It is shown theoretically and computationally that for the two-zone problem of this work, one usually can obtain only one of the outer zone effective (or relative) permeabilities (either oil or gas) evaluated at the sandface value of oil saturation. It is also shown that the effective permeabilities estimated from pressure drawdown or buildup data reflect, at early times, the inner zone effective permeability data, and at later times reflect the outer zone effective permeability data for the oil phase. If the initial reservoir pressure is above the reservoir bubble-point pressure then the effective oil permeability of the inner or the outer zone might be obtained from the analysis of drawdown and/or buildup pressure data.

Interval pressure transient tests (IPTT) are commonly used in the industry to obtain permeability distribution along the wellbore. Despite the remarkable progress achieved in IPTT analysis in last two decades, interpretation of IPTT is still unclear if test interval consists of oil zone with vertically connected transition zone and water aquifer. One easy and common approach for interpreting such data is to assume that oil zone, transition zone, and water aquifer as a distinct zone and then perform non-linear regression to measured IPTT pressure data set using single phase layer cake model. In this approach, due to the single-phase nature of the model, capillary pressure and relative permeability effects are totally ignored, however, it is assumed that water saturation data is available from log analysis and saturation weighted viscosity value represents the transition zone. As expected, it is determined only effective horizontal and vertical permeability values from this analysis rather than absolute permeability. It is also important to highlight that reliable effective permeability data is estimated solely in the zone where a test is performed. In fact, accurate prediction well and reservoir performance require values of absolute permeability information. As a second approach to analyze IPTT data, it is assumed that water saturation, relative permeability, and capillary pressure data are known parameters and optimization technique is used based on numerical reservoir simulation to estimate absolute permeability values. Like the previous case, horizontal and vertical permeability values are reliably obtained only in the zone where a test is performed. The only difference with the previous approach is that estimated permeability values are absolute permeability values rather than effective permeability. In practice in IPTT jobs, water cut is generally measured with pressure data in various depths in the transition zone to fine tune free water level. It is also important to note that relative permeability and capillary pressure data are not always available before IPTT interpretation. As a last approach in this study, both pressure and water cut data are simultaneously used in the optimization to find each zone’s horizontal and vertical permeability values, relative permeability and capillary pressure curves. Fairly satisfactory estimations are obtained from simultaneous regression of water cut and pressure data obtained from IPTT.

Summary Methods for analyzing buildup data following a short flow period are presented, discussed, and illustrated. A new type curve for uniform-flux and infinite-conductivity vertically fractured wells is presented. By matching buildup data with this new type presented. By matching buildup data with this new type curve, we can determine the dimensionless flowing time before shut-in. A method for converting buildup data to equivalent drawdown data is discussed. This method can be used to combine buildup and drawdown data to obtain a longer band of data for type-curve matching. This method canbe used for constant-rate production, constant-pressure production, and for the case where both pressure and rate production, and for the case where both pressure and rate vary during production. Introduction Over the past decade, the use of type-curve matching toanalyze pressure data has gained increasing acceptance. The advantages and dis advantages of type-curve matchingare well recognized and the procedure has become astandard tool to analyze data qualitatively, to identify flow regimes, and, quantitatively, to determine iformation parameters. Virtually all type curves available in the literature examine the pressure response at a flowing well-i.e., only drawdown solutions have been examined. These type curves may be used to analyze shut-in pressure behavior provided that the flowing time before shut-in is provided that the flowing time before shut-in is significantly longer than the maximum shut-in time. This limitation has prevented type-curve analysis ofpressure buildup data following short flow periods. pressure buildup data following short flow periods. The effect of a short flow period on pressure buildup data influenced by either wellbore storage or vertical fractures was presented recently. It was shown that significant errors result if proper care is not taken in analyzing pressure buildup data when the producing timeis short. Procedures to account for the influence of producing time were outlined. producing time were outlined. The objectives of this paper areto present anew correlation that considerably simplifies the use of buildup type curves for vertically-fractured wells givenin Ref. 1, andto suggest a procedure to analyze pressure buildup data by means of drawdown type pressure buildup data by means of drawdown type curves. The procedures discussed here can be applied to single- or multiwell tests, to data obtained after shortor long flow periods, to constant or variable flow rates, and to virtually all wellbore conditions including data influenced by wellbore storage and skin and fracturesof finite or infinite conductivity. Theory The basic pressure buildup equation based on the principle of super position is given by principle of super position is given by (1) Here, t is flowing time and Delta t is shut-in time. Thesymbols p and t denote dimension less wellbore pressure drop and dimension less time, respectively, and are defined as follows. JPT P. 904

This work focuses on the analysis of pressure buildup data obtained at a well at the center of a cylindrical reservoir in which the absolute permeability is a function of distance from the well, i.e., is a function of the radial coordinate. It is shown that the permeability distribution can be estimated directly from pressure buildup data by application of an inverse solution algorithm. For cases where permeability is a function of both r and θ, it is shown that our inverse solution procedure yields an "equivalent" radial permeability distribution. It is also shown that the reservoir pressure profile at the instant of shut-in can be approximated from the buildup pressure data. Finally, we discuss briefly, the stabilized inflow performance relations for a well producing from the center of a cylindrical heterogeneous reservoir.

This paper describes a new method to estimate two- and three-phase relative permeabilities in-situ, using pressure transient analysis. The technique requires a short drawdown test, consisting of a number of steps of increasing flow rate. The resulting relative permeabilities reflect the properties of the whole drainage area, rather than those of a small laboratory core. The proposed technique is a major improvement over current historical performance methods. These existing methods need data over long periods, yet only cover a range of saturation up to present conditions – all future projections require extrapolation. By contrast, the new method estimates relative permeabilities at sandface saturations, which cover a range of future reservoir conditions. The well test can be repeated at a later stage of depletion to forecast still further into the future. The proposed technique applies the solutions of multiphase diffusivity equation in terms of the pseudopressure function, m(p). These solutions have already been reported for constant rate tests in solution gas-drive reservoirs. This paper extends the pseudopressure solutions to three-phase systems. Two- and three-phase solutions are then superposed to obtain multiple-rate solutions, the basis for two- and three-phase relative permeability equations. A saturation equation developed originally by Bϕe et al. for solution gas-drive reservoirs, is also extended here to three-phase reservoirs. These pressure-saturation equations can be used to estimate sandface saturations during the test. Using a commercial black-oil simulator, example well tests were simulated over a 40% range in gas saturation. Both two- and three-phase results show close agreement with input relative permeability curves. In cases where relative permeability is not homogeneous within the drainage area, the resulting estimates of relative permeability curves were very representative of in-situ heterogeneities. The proposed technique offers a means to estimate two- and three-phase relative permeabilities at in-situ reservoir conditions, accounting for heterogeneities, wettability and fluid composition. It also seems to be the most appropriate way to obtain estimates for subsequent reservoir engineering analysis.

Accurate relative permeability data are essential for predicting the performance of two-phase flow through porous media. Many factors, such as the rock and fluid properties, may affect the measurement of relative permeability. However, the saturation levels of the fluids flowing through a porous medium have the largest impact on the shape of the relative permeability curves. Because relative permeability is a strong function of saturation, an accurate measurement of saturation levels in various types of two-phase flow experiments is required. In addition to many non-invasive methods, weighing and volumetric methods are frequently used to estimate the average saturation during steady-state experiments. However, for unsteady-state flow experiments, material balance methods to determine the saturation levels are relatively difficult to use. This article presents a relatively new non-invasive saturation measurement method and the equipment used to obtain dynamic saturation profiles as a function of time and distance along the core-holder. The new saturation measurement system has been found to be equally good for steady-state and unsteady-state experiments. Typical dynamic saturation profiles, the equipment calibration method, and a set of typical relative permeability curves for a co-current flow experiment are presented. Based on the presented experimental results, it has been found that the new saturation measurement method and the equipment is reliable and can reproduce stable dynamic saturation profiles with a minimum level of uncertainty. Introduction Underlying the extension of single-phase flow theory for the simultaneous flow of two or more fluids are the concepts of effective and relative permeability. The effective permeability is a relative measure of the conductance of a porous medium for one fluid phase when the medium is saturated with more than one fluid(1). The relative permeability is defined as the ratio of the effective permeability of a phase to a base permeability [e.g., absolute permeability to air or water, Craig(2)]. Relative permeability data are essential for almost all two-phase flow studies related to reservoirs. The data are used in making estimations and predictions of the productivity, injectivity, and ultimate recovery from reservoirs for evaluation and future development plans. The relative permeability data can also be used to diagnose the formation damage expected under various operational conditions. Therefore, unquestionably, these data are one of the most important data sets required in reservoir engineering studies. Among several methods for obtaining relative permeability curves, laboratory techniques are considered to be the most reliable. These methods for relative permeability measurement are further classified into steady-state and unsteady-state methods. Aleman et al.(3) have concluded that the difference in the relative permeabilities obtained by the two approaches is negligible, provided that the magnitude of the local (not macroscopic) capillary number is larger than a limiting value. Numerous studies have been conducted to investigate the effect of important parameters during the measurement of relative permeability data. In addition to saturation, some of the other important parameters affecting relative permeability are wettability, IFT, flow regime, overburden pressure and temperature. Leverett and Lewis(4), Sarem(5), Saraf and Fatt(6), and Owens and Archer(7) have shown that for strongly water-wet unconsolidated sands the permeability to a wetting phase is dependent solely upon its own saturation.

Summary Improvements to more advanced tools, such as inflow control devices (ICDs), create a high drawdown regime close to wellbores. Gas liberation within the formation occurs when the drawdown pressure is reduced below the bubblepoint pressure, which in turn reduces oil mobility by reducing its relative permeability, and potentially reducing oil flow. The key input in any reservoir modeling to compare the competition between gas and liquid flow toward ICDs is the relative permeability of different phases. Pore-network modeling (PNM) has been used to compute the relative permeability curves of oil, gas, and water based on the pore structure of the formation. In this paper, we explain the variability of pore structure on its relative permeability, and for a similar formation and identical permeability, we explain how other factors, such as connectivity and throat radius distribution, can vary the characteristic curves. By using a boundary element method, we also incorporate the expected relative permeability and capillary pressure curves into the modeling. The results show that such variability in the pore network has a less than 10% impact on production gas rates, but its effect on oil production can be significant. Another important finding of such modeling is that providing the PNM-created relative permeabilities may provide totally different direction on setting the operational constraints. For example, in the case studied in this paper, PNM-created relative permeability curves suggest that a reduction of flowing bottomhole pressure (FBHP) increases the oil rate, but for the case modeled with a Corey correlation, changes in FBHP will not create any uplift. The results of such work show the importance of PNM in well completion design and probabilistic analysis of the performance, and can be extended based on different factors of the reservoir in future research. Although PNM has been widely used to study the multiphase flow in porous media in academia, the application of such modeling in reservoir and production engineering is quite narrow. In this study, we develop a framework that shows the general user the importance of PNM simulation and its implementation in day-to-day modeling. With this approach, the PNM can be used not just to provide relative permeability or capillary pressure curves on a core or pore- scale, but to preform simulations at the wellbore or reservoir scale as well to optimize the current completions.

Summary This work presents a procedure for estimating effective or relative permeability curves directly from well-test pressure data obtained from a well producing a solution-gas-drive reservoir. The method requires accurate drawdown data. The basic procedure developed and discussed in this study combines computed effective permeability versus pressure values with nonlinear regression analysis techniques to determine the parameters involved in Standing's and Corey's relative permeability correlations. Once these parameters are determined, effective or relative permeability curves as a function of saturation can be generated.

This paper focuses on the simultaneous estimation of the absolute permeability field and relative permeability curves from three-phase flow production data. Irreducible water saturation, critical gas saturation, and residual oil saturations are assumed to be known. The two-phase relative permeability curves for an oil-gas system and the two-phase relative permeability curves for an oil-water system are represented by power law models. The three-phase oil relative permeability curve is calculated from the two sets of two-phase curves using Stone's Model II. The adjoint method is applied to three-phase flow problems to calculate the sensitivity of production data to the absolute permeability field and the parameters defining the relative permeability functions. Using the calculated sensitivity coefficients, absolute permeability, and relative permeability fields are estimated by automatic history matching of production data. Introduction The main objective of this paper is to consider the feasibility of estimating absolute permeability fields and parameters that define relative permeability functions by automatic history matching of production data obtained under multiphase flow conditions. While the topic is not new, to the best of our knowledge, no paper in the petroleum engineering literature has considered this problemunder three-phase flow conditions. It appears that Archer and Wong(1) were the first authors to consider the estimation of relative permeability curves by applying a reservoir simulator to history match laboratory core flood data. They estimated only parameters that define the shape of relative permeability curves for simple empirical relative permeability models and adjusted relative permeabilities by a trial and error method during the history matching. Sigmund and McCaffery(2) were the first to apply nonlinear regression to the problem of history matching laboratory core flood data. They used power law expressions to model relative permeability curves and estimated only the two exponential parameters in these formulas. Kerig and Watson(3) considered a similar problem. They calculated predicted data from the Buckley- Leverett model, used cubic splines to parameterize relative permeability curves and compared relative permeability estimates obtained with such a representation to those obtained using a power law functional form. They showed that, in general, power law models do not contain enough degrees of freedom to represent the truth well, whereas cubic splines with a small number of knots appear to be sufficiently flexible to yield more accurate estimates of true relative permeability curves. In their results, they assume absolute permeability is known. Lee and Seinfeld(4) considered the simultaneous estimation of the absolute permeability field and relative permeabilities for a two-dimensional, two-phase flow oil-water system. They assumed power law relative permeability curves and assumed that the end point values of relative permeabilities were known. Thus, only the two exponents in the power law relative permeability functions were estimated. They modelled the two-dimensional isotropic heterogeneousermeability field using bi-cubic B-splines. In the specific xamples considered, they matched pressure and water cut data at wells producing from an oil reservoir under waterflood. Tikhonov(5) regularization was used to stabilize the nonlinear least squares problem.

The reservoir fluid flow is characterized by relative permeability data, whose measurements are conventionally made in the laboratory on the cores acquired downhole of different rock types. The major drawback of such conventional core (SCAL) studies is their inability to capture the native wettability and in-situ reservoir fluid flow characteristics. Moreover, this lab based relative permeability data is sometimes unavailable, which requires one to estimate the relative permeability curves based on understanding of the reservoir or public literature and further tune the curves to match the actual pressure and production history of the reservoir during dynamic modelling. This process also incurs additional cost and requires additional time and efforts. Hence, an attempt has been made in this study to develop a novel workflow to estimate the relative permeability curves downhole using formation testers. This new method for interpreting relative permeability curves will complement the already existing conventional methods like SCAL and can also be used directly in the absences of lab data. In this approach, the Single Probe (PS), Pump Out (PO), and Fluid Analyzer (FA) modules of the Modular Formation Dynamic Tester (MDT) tool were assembled and set at the desired depth. Subsequently, the PO module was used to draw out the fluids from the formation and aid in recording the production and pressure drawdown data. The relative permeability of both oil and water phases were estimated at endpoint saturation using steady state approach, and the JBN method was applied after breakthrough and during transition phase using the displacement data (production and pressure data). The advanced well logs were used to interpret the other reservoir properties like porosity, permeability, and etc.

Significant advances have been made in methods for accurate measurements of saturations and fluid distributions. Further research is needed to reduce (or properly account for) capillary end effects, to control hysteresis, and to minimize wettability changes involved in flow experiments. Studies are needed on modeling complex displacements in reservoirs with flow tests performed at idealized laboratory conditions. Similarly, improvements in interpretation of laboratory data and in scaling up for field use are still required. Until additional advances in technology are made, the best course of action is to generate both steady- and unsteady-state laboratory data, under simulated reservoir conditions, on carefully selected and preserved cores.

The effective and relative permeabilities of six coals, comprising thirty-five samples, to nitrogen and carbon dioxide were measured as functions of water saturation and overburden pressure. The coals consist of bituminous, sub-bituminous and lignite types. Simulated overburden pressures ranged from 200 psig to 550 psig. All tests were performed over a decreasing water saturation cycle. Values of porosity, absolute permeability, shrinkage and critical gas saturation were measured on numerous samples. Average values are correlated as to coal type and structural orientation whenever the latter was discernible. The results indicate that CO/sub 2/ reduces the effective permeabilities by a moderate amount vis-a-vis nitrogen. The effect of overburden pressure was to drastically reduce the effective permeabilities. The relative permeability curves were significantly distinct as regards coal type and generalized (averaged) results are presented for universal employment. The characteristic shape of the relative permeability curves remain approximately independent of the magnitude of the stress field. In all, sixty-seven cores were tested over the two year period of both contracts, yielding seventy-six effective permeability curves. Thirty-five samples were tested during the current contract period, yielding forty-four effective permeability curves. Numerous other samples were tested for various point values, such as porosity and absolute permeability.

Reservoir simulation requires a realistic spatial distribution of capillary pressure and relative permeability throughout the reservoir. This study aims at deriving relationships between capillary pressure and relative permeability on one hand and porosity, permeability, depositional environment and structural position on the other hand. This work is illustrated by two sandstone oil reservoirs. Sample permeability ranges from 10 mD to several Darcies. Available data include 1) More than one hundred drainage and imbibition capillary pressure curves. Both gas/water, mercury injection and water/oil data was analysed. 2) More than fifty water/oil relative permeability curves. Both fresh and restored- state, steady and unsteady-state corefloods were analysed. Main conclusions are:Drainage capillary pressure curves and irreducible water saturation are strongly correlated with permeability, whatever the experimental technique used.Irreducible wetting phase saturation is significantly larger for water/oil drainage than for gas/water or mercury injection tests.There is no clear trend between drainage capillary pressure curves and depositional environment.Correlation between water/oil imbibition capillary pressure curve and permeability is very weak, unlike drainage.A significant correlation exists between permeability and end-point water permeability or final recovery.Both end-point water permeability and final recovery are found strongly correlated with the height above the initial water/oil contact, whatever the experimental technique used. This reflects the combined influence of initial water saturation and wettability variations.Reservoir trends are often obscured by use of inappropriate laboratory techniques. Introduction There is an increasing agreement that a reservoir model should include a full range of heterogeneities from the lamina scale, to the bedform-scale and then the formation-scale. Fine-grid models are frequently built in order to capture the reservoir heterogeneity and to predict or mimic the field performance. The construction of these fine-grid models is a multi-step process. Over the past decade, several studies illustrated this process for porosity and permeability. Once the large scale reservoir architecture and the sandbody connectivity has been assessed using well and analog outcrop data, the corresponding facies must be populated with petrophysical values. Firstly, fine-scale, three-dimensional (3D), models of porosity and permeability are built for each facies using core and outcrop data. Secondly, suitable values for drainage and imbibition capillary pressure curves or relative permeability are assigned to fine gridblocks Finally, fine-scale models are upscaled and effective permeability values and pseudo relative permeabilities are input in coarse grid cells. Recently, the generation of petrophysical groups has been proposed to improve the mapping of porosity and permeability. A petrophysical group is a set of reservoir zones with similar porosity, permeability, and grain density. Petrophysical groups are built using clustering techniques and the large amount of routine poroperm data generally available from cored wells. On the other hand, populating fine-scale 3D models with capillary pressure and relative permeability data has received little attention. This process is largely controlled by the data availability and quality and it is sometimes assumed that a single coreflood test is representative of a whole reservoir unit, genetic facies or depositional environment. A few studies evidenced a significant scatter in two-phase properties but also some fair correlations with permeability, grainsize or structural position. P. 585^

Reservoir Permeability Upscaling Indicators From Welltest Analysis. Abstract A methodology has been developed, for a non-fractured reservoir, to:–Correlate effective permeability values from upscaled core data with those inferred from welltest analysis.–Estimate a potential well's initial productivity It could be applied to screen and rank potential development well locations, by relative initial productivity, based on appraisal well data. The observations are based on the analysis of core and welltest data from a Middle East carbonate reservoir which has been on production for over 30 years. Introduction Correlating effective permeability values from upscaled core data with those inferred from welltest analysis has traditionally been an issue of concern for reservoir engineers. The effective single-phase permeability of a region, characterized by a fine-scale permeability distribution, is defined to be the permeability of an equivalent spatially homogeneous permeability region which would produce the same flow rate for a given pressure drop applied across the region in any given direction. The effective permeability depends on both the frequency and the spatial distribution of the fine-scale permeability values. Higher fine-scale permeability values will result in a higher effective permeability and vice versa. To understand the influence of the second factor, please refer to Figure 1. It shows a typical plot of the effect of anisotropy on a region's effective permeability. Anisotropy characterizes the degree of layering in the system. For a spatially isotropic system, which is characterized by an anisotropy value of 1, the effective permeability Ke will be the same in all directions and can be approximated by the geometric average of the fine-scale permeability values. The fluid flow characteristics will be 100% random in nature. The effective horizontal permeability Keh will be the same as the effective vertical permeability Kev. As the anisotropy increases, Keh will increase while Kev will decrease. In the limit, for a perfectly layered system, Keh is given by the arithmetic average of the fine-scale horizontal permeability values and Kev is given by the harmonic average of the fine-scale vertical permeability values. The fluid flow will essentially be 100% parallel. Table 1 lists the three traditionally used permeability averaging equations. Please note that both the geometric and the harmonic averaging equations are "biased" by zero fine-scale permeability values. Cut-offs need to be used to screen the fine-scale permeability values being input into either equation. Noetinger and Jacquin developed a general and rigorous theoretical framework for upscaling single-phase fine-scale permeability values in a 3D control volume and proposed an equation for determining the effective permeability of a region. In this study, a method has been proposed to modify their equation and apply it to upscale fine-scale core-plug permeability data and correlate the core-based effective permeability with that inferred from welltest analysis in a non-fractured reservoir. As mentioned before, the analyses are based on data from a Middle East carbonate reservoir. Most of the core data, from 17 wells, was obtained on non-preserved rock under ambient conditions. Detailed description of core from 5 wells indicated that the reservoir is not fractured. Analysis of the 87Sr/86Sr isotope ratio in the residual salt present in core samples was coupled with log, core and pressure data to determine the presence of vertical flow barriers. This was used to better define the effective flow intervals for welltest analysis. Several pressure build-up tests were available for each well. However, most tests were plagued by missing early time data and poor data quality. Special steps had to be taken to account for the geology, address the uncertainty in the computed parameters and extract meaningful information from old welltest data. This paper discusses the steps taken to address the limitations and uncertainty associated with analyzing old core and welltest data, provides the details of the methodology for correlating core and welltest KH data in a non-fractured reservoir and highlights the procedure that could be used to estimate the relative initial productivity of potential well locations. P. 1

Summary This paper investigates the effect of wellbore storage on the analysis of pressure drawdown data obtained at a well producing a solution-gas-drive reservoir. Wellbore storage effects are incorporated by specifying a sandface oil flow rate that increases exponentially from zero to the specified constant value of the oil flow rate at the surface. Use of new computational equations derived here shows that effective oil permeability as a pointwise function of pressure can be computed directly from the measured values of the flowing wellbore pressure, provided the sandface oil flow rate is measured and incorporated into the analysis. If the sandface flow rate is unknown, effective permeability can be computed only after wellbore storage effects become negligible. In all cases, a semilog plot of wellbore pressure squared vs. time is shown to be a viable method for estimating effective oil permeability at initial conditions, effective oil permeability at the final flowing wellbore pressure value, and mechanical skin factor.