Model Diagnosis for Layered Reservoirs

Abstract

Summary Interpretation models for layered reservoirs cannot be used effectively until a model has been identified for each reservoir layer. This paper introduces a new deconvolution form for presentation of multilayer transient(MLT) test measurements that is analogous to the log-log diagnostic plot used for model diagnosis of conventional transient test data. Introduction The MLT test technique was introduced by Kuchuk et al. in 1986. Since then, more than 100 MLT tests have been conducted in water injection, oil, gas, and gas injection wells. Permeabilities ranging from a few millidarcies to several darcies have been determined layer by layer along with skin factor estimates and the average pressure in each layer. Several MLT case studies have been published. Kuchuk et al. 2 analyzed a two-layer water injector. published. Kuchuk et al. 2 analyzed a two-layer water injector. Morris interpreted a two-layer oil reservoir with one infinite-acting layer and one layer with pressure support from an aquifer. Ref. 4 described a four-layer oil well example and Joseph et al. 5 provided an interpretation for a four-layer oilwell with parallel fault boundaries. parallel fault boundaries. Figs. 1 through3 show test configurations for commingled layers. The conventional way to test each layer is with isolation packers (Fig. 1). The isolated zone test string is lowered with the packers (Fig. 1). The isolated zone test string is lowered with the drillstem or tubing and thus is costly to conduct. Data interpretation is straightforward. The MLT test (Fig. 2) is conducted with a production logging too] that continuously measures pressure and sandface flow rate. Ref. 6describes the procedure pressure and sandface flow rate. Ref. 6 describes the procedure for MLT tests, which are conducted in cased wells. MLT test data interpretation is complicated by the presence of near-wellbore features, heterogeneity, or outer boundaries that cannot be identified readily layer by layer with current interpretation techniques. Fig. 3 shows an alternative testing technique called the commingled single-layer transient (CSLT) test that uses a production logging tool with more than one flowmeter. In an example of a CSLT test in a gas well, the analysis suggested that one or more of the layers had been vertically fractured. The CSLT test is almost as straightforward to interpret as an isolated zone test, but logistical and calibration difficulties discourage widespread application of this technique. Clark et al. provided another extension of the MLT test technique for unstable flow in oil wells produced under gas lift. produced under gas lift. With recently published analytical models, each layer in a multilayer reservoir simulation can be described by any model previously developed for single-layer interpretation. Ehlig-Economides previously developed for single-layer interpretation. Ehlig-Economides and Joseph provided a comprehensive survey of layered reservoir models published before 1985 and introduced a general layered model for commingled zones with communicating (crossflowing) layers in each zone. Mavor and Walkup described the "parallel resistance" model forcommingled layers. This generalization provides a multilayer model comprising a collection of single-layer models that have been formulated as solutions in Laplace space, Kuchuk and Wilkinson offered an elegant mathematical formulation for the commingled multilayer model using Green's functions. This paper included additional model features, such as layers with different initial pressures or layers opened to flow at different times. Larsen produced solutions for zones at different initial pressures and for zones with different fault boundaries. Bennett pressures and for zones with different fault boundaries. Bennett et al. provided a solution for layers commingled in a single vertical fracture, which was extended by Camacho-V. et al. for unequal layer fracture half-lengths. Spath et al. implemented a layered model that included fractured layers commingled in a well- bore with elliptical swept regions (for water injection wells), homogeneous or heterogeneous layers, and layers completed with a horizontal borehole. A complete characterization of the layered reservoir includes an adequate model for each layer. For isolated zone tests, selection of the interpretation model is accomplished by use of a log-log plot of the pressure change and its derivative. For CSLT tests, a log-log plot of the convolution derivative is used to diagnose the model. MLT test interpretations includes selective inflow performance (SIP) analysis, sandface rate-convolved (SFRC) analysis above each zone, sequential analysis, and simultaneous analysis. The MLT test interpretation provided by these steps determines permeability, skin factor, and average pressure for each layer. Parameters for other features, such as partial penetration. heterogeneity, and fault boundaries, can be estimated with sequential and simultaneous analyses if layer models have been diagnosed. Diagnosing the response for a given layer is complicated because the convolution derivative for each MLT measurement represents the combined response of all layers below the flowmeter. The new presentation of MLT test data in this paper resembles the conventional single-layer response as closely as possible, thus revealing the individual layer behavior. This presentation can be used with artificial intelligence to automate model selection and with nonlinear parameter estimation for automated matching. MLT Test Deconvolution The MLT test involves acquisition of transient flow rates measured continuously with a stationary flowmeter sensor situated just above an interval to be tested. At this depth. the flow rate is measured at reservoir pressure and temperature in barrels per day. Hence, in this paper, q is used to denote flow rate at reservoir conditions with (q) referring to a measurement just above Laver J. q is used for flow rates measured at the surface in stock tank barrels per day. Appendices A through D describe detailed formulations that are used for single-layer reservoirs and that can be used for multilayer systems as described in this section. When pressure and sandface rate are measured simultaneously, the Gladfelter deconvolution, or rate-normalized pressure, resembles the pressure-transient response to a step change in the sandfacerate. For the CSLT test in Fig. 3, flowmeters are positioned above and below the test interval. A simple subtraction, positioned above and below the test interval. A simple subtraction, [q (t)] - [q (t)], provides a direct measure of the zone flow rate. Once the continuous zone rate is known, a log-log plot of the convolution derivative (Appendix C) or the deconvolution derivative(Appendix D) is used to diagnose a reservoir model for the single layer. For the MLT test, measurements are made above and below the same interval, but they are acquired at different times with only one flowmeter. The MLT measurements are taken under flowing conditions and may be subject to some fluctuations in the surface flow rate. Also, each MLT is initiated by a change in the surface flow rate of arbitrary magnitude. As a result, it is not possible to subtract the flow rates from transient measurements taken at different times. However, if the time-dependent flow rate change from each transient is normalized(divided) by the simultaneously measured pressure change, the resultant pressure-normalized rate has been corrected for flow rate fluctuations and for the magnitude of the surface flow rate change that initiated the transient. The pressure-normalized rates computed from data acquired below anpressure-normalized rates computed from data acquired below an interval are subtracted from those computed from data acquired above the same interval. The reciprocal pressure-normalized rate (RPNR) difference is a convenient extension of the Gladfelter deconvolution. The log-log plot of the RPNR and its derivative with respect to the logarithm of time provides response patterns like those of the pressure change and its derivative. SPEFE P. 215

Overbalanced Perforating Yields Negative Skins in Layered Reservoir

“…Multirate production logging and transient testing and analysis techniques [16][17][18][19][20][21][22][23][24] can be used to obtain individual layer permeabilities and skin factors of commingled zones. Wells 5 and 6 ( Table 4) were good candidates on which to perform multilayered reservoir testing 31 because both had low water cuts to enable the use of a single-phase flow model.…”

Advances in Multilayer Reservoir Testing and Analysis using Numerical Well Testing and Reservoir Simulation

“…A multilayer transient (MLT) test or layered reservoir test (LRT) involves the acquisition of both sandface flow and wellbore pressure versus time during successive drawdown tests with the sensors in a static position, combined with production log surveys across all layers to determine the stabilised flow profile at each rate [5][6][7][8][9][10][11][12] . This test technique combines stabilised and transient flowrate and pressure measurements, and extends the concept of flow-after-flow or isochronal tests to multiple layers.…”

“…[5] Sandface rate convolution (SFRC) analysis of the pressure and flowrate transients for initial parameter estimation. [6] Sequential and simultaneous analysis using a layered model, with analytic or numerical methods using a reservoir simulator or both methods in combination. [7] Simulation and automated history matching and sensitivity analysis of the MLT test.…”

“…Horner, MDH) should be performed. For analysis of multilayer tests, two methods have been generally applied [5][6][7][8][9][10][11] . The methods, which are known as the sequential method and the simultaneous method, are summarized in the sections that follow.…”

“…This approach has strong theoretical basis [5][6][7][8][9][10][11][12] . This testing technique, which has been applied in many locations around the world 10,[13][14][15][16] , involves…”