Analysis Of Interference Tests Research Articles

Reducing uncertainty associated with CO2 injection and brine production in heterogeneous formations

Spatial heterogeneity and variability across many orders of magnitude are two properties of formation permeability that are challenging to effectively capture in subsurface flow models. With regard to geological CO2 storage, heterogeneity affects storage capacity, plume migration, pressure build-up around injection wells and, if utilized, the possibility of early breakthrough at brine extraction wells. Faced with under-characterized heterogeneity and an information-poor environment, the challenge is to make as much use as possible of the available data in reducing uncertainty associated with model prediction of a CO2 injection operation. The two types of data used here to inform models are point permeability measurements from each well and interference tests between wells; these are both obtained from a synthetic permeability distribution approximating a hypothetical CO2 storage formation. These data are used to reduce uncertainty in predictions of CO2 injection, brine and CO2 production rates, and CO2 breakthrough times obtained from simulations of five-spot CO2 injection/brine production performed on >600 conditional permeability realizations. First, assuming the underlying permeability field exhibits long-range correlation and a log-normal permeability distribution, a Bayesian analysis was undertaken using the point permeability measurements to reduce the likely magnitude of permeability heterogeneity. Comparison of realizations drawn from the prior and posterior indicate that the data were sufficient to exclude extreme scenarios with very rapid or very slow CO2 transport and breakthrough at brine production wells. Thirty-year prediction envelopes for net CO2 retention, brine and CO2 production were reduced by 40, 45 and 72%, respectively. In the second stage, simulated interference tests for each of the posterior realizations were compared against interference tests simulated for the synthetic “true” permeability field. Weighting functions derived from these comparisons are used to further refine predictions, providing additional reductions of uncertainty by 38 and 69% for brine and CO2 production rates, respectively. Predictions of CO2 breakthrough are especially sensitive to analysis of interference tests, with a good estimate of the correct time obtained in three out of four cases.

Analysis of Interference Tests With Horizontal Wells

Summary One of the common assumptions in horizontal-well interference-test analysis is to ignore fluid flow in and out of the horizontal observation well and represent it by a point. In some cases, the active well is also approximated by a vertical line source. Using a semianalytical model, this paper answers three fundamental questions: What is the critical distance between the wells to represent the horizontal observation well by an observation point? Where should the observation point be placed along the horizontal well? Under what conditions may the active well be approximated by a vertical line source and the exponential integral solution be used to analyze observation-well responses? Two correlations are presented to simplify the analysis of horizontal-well interference tests. Example applications are presented, and error bounds are documented.

The conceptualization of a channel network through macroscopic analysis of pumping and tracer tests in fractured chalk

A better conceptual understanding of flow and transport in fractured rocks can be gained through macroscopic interpretation of multi-borehole interference and tracer tests. A homogeneous dilution factor, expected in the pumping borehole in a forced-gradient tracer test, was developed based on flow-dimension analysis of an interference test. This expected dilution factor (HEDF) can be compared to the actual dilution factor (DF) inferred from an advection-based interpretation of the tracer test. These analyses were applied to tests performed in inclined boreholes intersecting fractured chalk in the Negev desert, Israel. The flow dimension observed in the interference test, the large differences between the HEDF and the DF calculated from the interference and tracer tests, respectively, combined with independent results of fracture surveys in nearby outcrops, imply that the dominant feature controlling flow at the site is a network of channels. This finding implies that parallel-plate-fracture transport models probably overestimate the role of matrix diffusion where channel flow predominates. A horizontal, homogeneous, isotropic channel dilution factor (HHICDF) was developed as a DF estimator, using interference-test analysis, and provided reasonable estimates of the dilution in the pumping borehole, for two independent tracer tests. This estimator can be used to predict the dilution of a solute injected near a pumping borehole. Finally, a simple method to estimate the contributions of fluxes from different injection boreholes to the pumping borehole in a multi-borehole tracer test is described. Such estimates can improve our understanding of aquifer anisotropy and heterogeneity at investigated sites.

Effect of Scaleup and Aggregation on the Analysis of Interference Tests

SummaryThe objective of this paper is to demonstrate the influence of detailed, small-scale heterogeneities on interference tests. Specific issues encountered when interference tests are analyzed in reservoirs with complex geological properties are discussed. These issues relate to questions concerning the use of low-resolution models, the degree of aggregation, the methodology of scaleup, and the reliability of conventional methods of analysis.This paper demonstrates the importance of capturing fine-scale heterogeneities to replicate the true transient behavior of interference tests at both active and observation wells. The paper shows the effects of aggregation and scaleup as used routinely in the industry on evaluating transient responses. The consequences of using low-resolution models in systems with complex geology is also demonstrated. If low-resolution models are used, reservoir properties may be adjusted unrealistically to match the transient behavior observed in high-resolution models. Though scaleup preserves pore volume, estimates of storativity predicted by low-resolution models will have a significant effect on reservoir behavior and resource management. If porosity values are not regressed, significant changes in vertical permeability values are observed. This is an important observation with potentially dramatic effects on reservoir performance, especially in processes involving mobility differences. Regression on a single-layer model (homogeneous, or based on aggregation) was also shown to yield totally different geological outcomes. This also shows the need to use geological constraints during inversion, aggregation, and scaleup.

Well Testing: Effect of Scaleup and Aggregation on the Analysis of Interference Tests

This article, written by Technology Editor Dennis Denney, contains highlights of paper SPE 84291, "Effect of Scaleup and Aggregation on the Analysis of Interference Tests," by Rajagopal Raghavan, SPE, and Ralph R. Roesler, SPE, ConocoPhillips, and O. Inanc Tureyen, SPE, Stanford U., prepared for the 2003 SPE Annual Technical Conference and Exhibition, Denver, 5-8 October.

New Methods For Analysis Of Constant Pressure Interference Testing

Abstract The existing body of theoretical studies on interference testing usually applies for constant-rate conditions at the active well. For constant-pressure situations, which are fairly commonly encountered during injection tests in low-permeability rocks (e.g., crystalline rocks, which are often tested for waste repository projects), alternative approaches must be sought for analysing interference tests. This paper presents a new method for analysis of interference tests with the active well at constant pressure. This new analytical technique makes use of both type curve matching and straight line fitting methods for analysis of such tests. We show in this paper that with a proper grouping of the relevant variables, a constant-pressure interference test can be analysed using constant-rate Cartesian (or semilog) derivative type curves for interference testing. Thus, this method utilizes existing constant-rate solutions for interpretation of constant pressure interference tests. The solution is exact and extends a previously presented approximate solution. Moreover, for rD > 20 and tDr2D > 0.5, we can also use a semilog plot to conduct a straight line analysis of the data from a constant pressure interference test for estimation of interwell transmissivity and storativity. Introduction In an interference test between two wells, the active well undergoes a variety of production or injection tests, with the observation well used only to monitor the pressure transients released into the formation by the active well. Analysis of interference tests are commonly performed using the assumption of a constant rate or of a series of constant rate steps. Such analyses of the observation well data can be performed using wellbore storage and skin at both active and observation wells(l). In the groundwater industry, constant pressure tests are fairly common in tight formations where a constant rate test is dominated by wellbore storage effects for a significantly long time. The constant pressure situation is also well-suited to injection testing, as constant rate methods need a prior knowledge of the formation permeability to select a suitable rate(2). Constant pressure situations are also a useful means of controlling off-site migration of contaminated groundwater(3). Uraiet and Raghavan(4,5), Ehlig-Economides and Ramey(6) and Ozkan et al.(7), among others, have presented a number of tools to aid in analysis of constant pressure tests in a variety of flow situations and reservoir conditions. Analytical methods to interpret constant pressure interference tests in a double porosity situation have been detailed by Grasman and Grader(8). In a very recent study, Hiller and Levy(3) demonstrated the use of an approximate method to analyse the late time data at an observation well, when the active well is being produced at a constant pressure. Their method yields the formation diffusivity directly from the analysis. Mishra and Guyonnet(9) presented a simple but elegant technique to compute formation transmissivity and storativity from analysis of observation well data during constant pressure tests. Their method involves a generalization of the Theis exponential integral solution for constant pressure situations.

Interference Testing In a Two-region Composite Reservoir With a Frontal Skin

Abstract A two-region composite reservoir model is used to analyze well-test data from a variety of enhanced oil recovery projects, geothermal reservoir, and acidization projects. Dynamic phenomena, such as phase changes and multi-phase flow effects in a region near the front, can cause a sharp pressure drop at the front. Such a sharp pressure drop can be modeled as a thin frontal skin. This study considers interference testing in a two-region composite reservoir with a thin frontal skin. Wellbore storage and skin at the active well are also included in the analytical solution to the problem. Correlating parameters are established in the presence of a frontal skin for type-curve marching analysis of interference data from such reservoirs. Our results indicate that for an observation well in the inner region surrounding the wellbore, the effects of storativity ratio (i.e. Φc, ratio) and frontal skin on interference tests are similar. Thus, frontal skin cannot be estimated independently of storativity ratio from an interference test on an observation well in the inner region. However, interference test data collected at an observation well located in the outer region beyond the front helps estimate storarivity ratio and frontal skin independently of each other. The information presented in this paper should be useful in obtaining a consistent analysis of well tests conducted in composite reservoir situations. Introduction This study considers interference pressure and pressure derivative responses in a two-region composite reservoir with an infinitesimally thin skin at the discontinuity. The observation well may be located in any region. Figure 1 shows a schematic diagram of a radial, two-region composite reservoir with an observation well located in the outer region (region 2) at a distance a from the active well. Region 1 (inner region) extends to a radius R, and a thin skin sr may occur at the discontinuity. Ambastha and Ramey(1) presented an analytical solution for transient pressure behavior at any point in a reservoir depicted by Figure 1. Their analytical solution as presented in the Appendix of this paper has been used to investigate interference test analysis in a radial, two-region composite reservoir with a frontal skin. All results presented in this study are for an infinite reservoir. FIGURE 1: Two-region composite reservoir. (Available in full paper) Correlating Parameters Satman(2) presented an study of interference responses in radial, two region infinite composite reservoir. He did not consider the effects of a thin skin at the discontinuity. He correlated transient interference pressure responses using CD/aD, CDe2s, a/R, M and F as correlating parameters. He defined dimensionless pressure and time using the properties in the outer region, and considered the interference pressure responses for the observation wells located in the outer region only. This study also considers the same correlating parameters as used by Satman(2). A thin skin at the discontinuity, Sr is an additional correlating parameter, Figure 2 through 7 verify the selected correlating parameters under different conditions. Figure 2 through 7 are for M = 10 and Fs = 100. TABLE 1: Parameters used to generate responses shown on Figures 3, 6 and 7. (Available in full paper)

Interference And Pulse Test Analysis By Nonlinear Regression

Abstract A nonlinear regression technique based on the method of least squares is developed for pulse lest analysis. The values of the transmissivity, kh// µ and storativity h Φc, that minimize the sum of squares of differences between observed and calculated pressures are determined. The equations that represent the conditions for minimum are solved by an iterative procedure based Oil a combination of the Newton-Raphson and the Regula-falsi methods. The pressure at any point is estimated using the line-source solution and the principle of superposition. The method can be used for the analysis of pulse testing of equal and unequal periods as well as cases that could not be analyzed by the tangent construction method of the conventional pulse testing methods. Such cases include situations of unequal pulse ratio and variable flow rate in the different cycles. The method is applicable for the general case of multiple-rate interference testing with pulse testing as a special case. The developed method was tested using simulated data. The method was found to converge rapidly. Excellent agreement was found between the assumed and estimated parameters for the different cases tested. Introduction Pulse testing is being widely considered as a method for obtaining interwell reservoir properties such as porosity and permeability(1–3). In pulse testing, the rate at an active welt is periodically changed between flowing and shut-in conditions while the pressure response at an observation well is recorded. The data is then analyzed graphically by drawing tangents to the pressure-time curve and determining the time lag and the pressure response amplitude of the different odd and even cycles. A set of correlations published by Kamal and Brigham(3) is then used to estimate the transmissivity, kh/ µ and storativity h Φc. Recently, Ogbe and Brigham(4) presented a method to correct for the skin and wellbore storage effects. They also found it necessary to correct the previously published Kamal-Brigham correlation curves. Moreover, the use of these correlations is limited to cases of constant pulse ratio, constant flow rate and constant cycle length of the different cycles. Cases where the lengths of the pulse and/or shut-in periods or flow rates are different in the different cycles cannot be analyzed by the conventional tangent construction method. Furthermore, the conventional graphical method cannot be used in a computer-based systematic analysis which is most desirable. Some attempts were made to apply the methods of regression analysis for the determination of reservoir characteristics from well test data (5–7). These methods, however, are coupled with numerical reservoir simulators that solve the diffusivity equation. For a presumably homogeneous reservoir for which an analytical solution exists, such methods are unnecessarily complicated. In a previous work, the method of least squares was applied for interference test analysis in the cases of constant rate and two rate tests(8). In this work, the method of least squares is used to develop a procedure for the analysis of the general case of multiplerate interference testing which includes pulse testing as a special case.

Toward a Unified Theory of Well Testing for Nonlinear-Radial-Flow Problems With Application to Interference Tests

Summary This work presents an analytical solution for the pseudopressure function that represents the reservoir and wellbore responses resulting from production at a constant oil rate in a solution-gas-drive reservoir. The solution can also be reduced to obtain the analytical solution for the corresponding single-phase-flow problem. The general analytical solution suggests a new definition for the dimensionless flow rate. The analytical solution is used to construct new type curves for analysis of interference tests conducted under multiphase-flow conditions. It is shown that if we ignore multiphase-flow effects and analyze interference data with the line-source-solution type curve, then the estimates of the permeability and porosity-compressibility product obtained may be in error by 20 to 40%.

A Correlation for Interference Testing With Wellbore-Storage and Skin Effects

Summary A new correlation and set of pressure-response and pressure-derivative type curves are presented for interference test analysis. The influence of wellbore storage and skin effects at active and observation wells on interference pressure response is examined. In the case of wellbore storage and skin in one well, the correlating parameter [CDe2s]CD/rD2 is used to combine wellbore storage and skin variables in a way that makes it possible to display, on a single type curve, all interference test data that would ordinarily require a number of type curves for various combinations of CD/rD2 and CDe2s. The product of the correlating parameter is used when wellbore storage and skin effects are active at both wells. The difference in the shapes of the single-well storage type curves compared to the two-well storage case at early times can be used as a diagnostic feature in interference testing.

Effect of a Partially Communicating Fault on Transient Pressure Behavior

Effect of a Partially Communicating Fault on Transient Pressure Behavior

Effect of Wellbore Storage and Wellbore Damage at the Active Well on Interference Test Analysis

This paper shows that wellbore storage and wellbore damage reduce the pressure response at an observation well, especially at early times, and pressure response at an observation well, especially at early times, and can cause great error in estimating transmissivity and storativity if not account for properly. New type curves are presented that include the effects of wellbore storage and damage. Introduction Interference testing is used to estimate the mobilitythickness product and the reservoir thickness -porositytotal compressibility product. These two terms are referred respectively to as transmissivity and storativity. In the past, wellbore storage and wellbore damage at the active well have been assumed to cause no detrimental effect on interference test analysis. Only one type curve has been used to analyze interference tests, namely the exponential-integral-solution type curve. Interference testing has been used to estimate transmissivity and storativity in the petroleum and ground-water industries for many years. The mathematical basis for interference testing was first presented by Theis. The most practical and easiest way to analyze interference tests is by type-curve matching. The method of type-curve matching is adequately described by Ramey and Earlougher and Kersch. The type curve is a plot of log PD vs log tD/rD. Thus, for the classical exponential-integral solution, only one theoretical type curve is required to analyze all interference tests. A recent paper presented type curves for a vertically fractured presented type curves for a vertically fractured reservoir with drawdown measured at the observation well. In single-well pressure transient tests, wellbore storage and wellbore damage have been recognized as adversely affecting the tests, and errors can be made in analyzing these tests if the period dominated by wellbore storage is not properly identified. In multiwell tests, wellbore storage and wellbore damage at the active well have always been ignored and assumed to have essentially no effect on the observation-well pressure response. Recently, Prats and Scotts presented the pressure response. Recently, Prats and Scotts presented the effects of wellbore storage at the responding well on pulse-test pressure response. pulse-test pressure response.This paper shows that wellbore storage and wellbore damage at the active well can, in certain cases, cause large error in determining transmissivity and storativity from an interference test or pulse test. The Model The mathematical model used to generate the following results is presented in the Appendix. This model solves the diffusivity equation by finite-difference techniques. Reservoir properties, flow rates. wellbore storage, and wellbore damage are variable in this model. However, the results presented in this paper assume an isotropic. homogeneous reservoir containing a slightly compressible fluid, the reservoir is infinite-acting for the time period under consideration, the surface flow rate at the period under consideration, the surface flow rate at the active well is constant; and the wellbore storage coefficient and wellbore damage are constant during the testing period. The Need To Account for Wellbore Storage Fig. 1 shows the increase in flowing bottom-hole pressure above initial pressure vs time in an injection well pressure above initial pressure vs time in an injection well for cases with dimensionless wellbore storage coefficient, CD, equal to zero and 10', where (1) JPT P. 851