An improved understanding of how one fluid displaces another in a one-dimensional porous medium can be gained by measuring saturation as afunction of time and distance, a pro-cedure rarely undertaken. To this end, a series of immiscible displacements were conducted, at various viscosity ratios, in which in-situ saturations were measured using a relatively new R.G. Bentsen Ramon G. Bentsen graduated from the University of Oklahoma with a B.Sc. degree (petroleum engineering) in 1955. Subsequent to graduation, he worked f6r Schlumberger Sorenco in Venezuela and Colombia, and with McCullough Tool Company and Im-perial Oil Limited in Alberta. He then enrolled for advanced study at Pennsylvania State University, where he received M.Sc. (1964) and Ph.D. (1968) degrees in petroleum and natural gas engineering. After obtaining his Ph.D., he joined the Faculty of Engineering at the University of Alberta as a member of the Department of Chemical & Petroleum Engineering. Currently, Dr. Bentsen holds the position of Associate Professor of Petroleum Engineering in the Department of Mineral Engineering. He is a member of the CIM, the AIME and the Society of Sigma Xi. J. Saeedi Jawaid Saeedi holds two mechanical engineering degress, a B.Sc. degree (1970) from N.E.D. Government Engineering College, Univer-sity of Karachi and an M.Sc. degree (1973) from the Oklahoma State University. Subsequent to obtaining these degrees, he worked for three years with the Oil and Gas Development Corporation of Pakistan. He then attended the University of Alberta, where he ob-tained an M.Sc. degree (1979) in petroleum engineering. On gradua-tion from the University of Alberta, Mr. Saeedi worked for a year as a reservoir engineer with the Arabian Oil Company in Saudi Arabia. He is currently employed as a senior research assistant at the University of Petroleum and Minerals, Dhahran, Saudi Arabia. , Montreal technique based on microwave attenuation. The experimental saturation profiles obtained in this manner were compared with those obtained by solving numerically a recently derived Lagrangian formulation of the immiscible displacement equa-tion. Finally, the results obtained were analyzed in the light of published scaling groups and a recently proposed stability criterion. The results of this analysis suggest that one-dimensional, immiscible displacement theory reasonably represents displacements carried out at favourable mobility ratios. For adverse mobility ratio displacements, in horizontal systems, a stability criterion must be satisfied before the theory can be said to represent the displacement process. Introduction Steady-state methods for measuring relative permeability re-quire approximately one day to acquire a complete relative permeability curve. Extemal-drive methods, on the other hand, can acquire the same information in a few hours.However, it is well known that external-drive techniques have severe limitations for determining water-oil flow proper-tieS(1,2,3) These limitations may arise because of a violation of one or more of the...
Summary. An interwell pressure test, designed and implemented as a pulse test, was performed in the Arab zones of an offshore field in Abu Dhabi. The interpretation of three pulses yielded inconsistent results for transmissibility and storativity. The pressure response data were interpreted with a two-layer analytical model after a numerical simulator was used to modify the pressure response for the interference from a third well. The two-layer analytical model provided an excellent match of the modified pressure response. We conclude that conventional pulse-test interpretation methods cannot be satisfactorily applied to the pressure response in a two-layer system. Introduction An interwell pressure test results in transmissibility (kh/mu) and storativity (phi hct) estimates between the wells. Until recently, the analytical interpretation of a pulse or interference test was carried out with a single-layer reservoir model. It is very rare to have reservoirs that comprise only a single homogeneous layer. In a multilayer system, interpretation of an interwell pressure test requires a numerical simulator or analytical solutions (type curves) for a model formulated for more than one layer. An interwell test was designed, implemented, and interpreted for the Arab zones of an offshore Abu Dhabi oil field. Pulses of 18-hour duration were instigated in the active well. The first three pairs of time lags and pressure amplitudes were interpreted with conventional pulse-test analysis methods. All three pairs gave different answers for transmissibility and storativity, which should not be the case if the single-layer interpretation model is applicable. The reservoir connecting the two wells has two distinct permeable layers, so the pulse responses were interpreted with a two-layer analytical model. The two-layer analytical model generates a family of type curves for the pressure response in the observation well that depend on three main parameters: K, which quantifies the permeability contrast between the two layers; w, which depends on the layer permeability contrast between the two layers; w, which depends on the layer storativities; and lambda, which is an interlayer crossflow parameter. This paper demonstrates the successful use of a two-layer analytical model for the interpretation of an interwell test. It also shows how a numerical simulator was used to calculate the pressure response from a third producing well that was interfering with the pressure response in the observation well. The interpretation gives pressure response in the observation well. The interpretation gives the estimates of transmissibility and storativity for each layer. A sensitivity analysis for k, w, and lambda indicates that the pressure-pulse response is not sensitive to interlayer vertical pressure-pulse response is not sensitive to interlayer vertical permeability but is influenced by contrasts in layer permeability and permeability but is influenced by contrasts in layer permeability and porosity. porosity. Background The analytical principles of design and interpretation of interwell pressure tests (pulse or interference) are well known, and some of pressure tests (pulse or interference) are well known, and some of these techniques are given in Refs. 1 through 5. Most of the literature uses the line-source solution to the diffusivity equation as the building block for designing and interpreting interwell pulse and interference tests. The background pressure/time response need not be known to interpret the pulse test but is necessary to interpret the interference test. For heterogeneous reservoirs, the use of a numerical reservoir simulator has been recommended to interpret interwell pressure tests. Recently, analytical models have been made available to interpret such tests in layered reservoirs. We used Bourdet's model to interpret the interwell test presented in this paper. Although the principles of these tests are extensively published, few successful interpretations are documented. One documented case history is of interwell pressure tests done with conventional analytical interference- and pulse-test methods for China's Shengloil field. A successful application of interwell pressure tests was recently presented for a fractured reservoir. We used line- source-solution methods presented for a fractured reservoir. We used line- source-solution methods to design the interwell pressure test presented here as a pulse test. Our results, however, are interpreted as an interference test with a type curve based on a two-layer analytical model, after the interference from a third well was accounted for with a numerical reservoir simulator. Test Design Kamal and Brigham's charts-were used to perform the design and sensitivity analysis for various pulse-cycle lengths, delta tc, and pulse ratios, F'p=(delta tp/delta tc). The decision to use a specific pulse ratio and cycle length was based on the pulse-response amplitude, and dimensionless time lag, t L/delta tc. Design runs were made for pulse ratios of 0.3, 0.4, 0.5, and 0.6, while cycle lengths (producing pulse + shut-in pulse) of 24 and 36 hours were used. Table 1 shows the reservoir parameters used to design the test, and Table 2 gives the pulse-response amplitudes and the dimensionless time lags for odd and even pulses of the cycle lengths used. The total skin factor was taken as + 1 for both wells. The dimensionless wellbore storages, CD, for Wells 1 and 2 were estimated from a known wellbore volume of 660 bbl and an oil compressibility of 428 psi-1. The CD correction factors to the pressure amplitudes, taken from charts generated by Prats and Scott, were negligible for all pulses. From the pulse-test design results shown in Table 2, it is evident that a 36-hour cycle length and a 0.5 pulse ratio give the highest pressure amplitude in the observation well at reasonable lag times. pressure amplitude in the observation well at reasonable lag times. For shut-in and flowing pulses of 18 hours each, the amplitudes range from 3.1914 to 4.0632 psi. The design rate at the pulsing well was 1,000 STB/D. Fig. 1 shows the expected pulse response at Well 2 on the basis of the above design. Measurement This reservoir of Arab zones is offshore Abu Dhabi. At the time of the test, three wells were completed. Wells 1 and 3 had been producing for about 2 months, while Well 2, the observation well, producing for about 2 months, while Well 2, the observation well, was yet to be put on-stream. The rate pulses were instigated in Well 1, but the production rate at Well 3 was not disturbed during the test. The observation well was filled with diesel to minimize wellbore storage, and a downhole electronic gauge was used to monitor the pressure response. Pressure recording began at Well 2 about 2 hours pressure response. Pressure recording began at Well 2 about 2 hours before Well 1 was shut in. This period should have been much longer to reveal the background pressure trend in Well 2 caused by production from Wells 1 and 3. production from Wells 1 and 3. If Well 2 were in a single-layer reservoir, the data would have been analyzed with conventional pulse-test interpretation methods and the background pressure trend in the reservoir would not have been required for the analysis. Fig. 2 shows the pulse response in Well 2 with the rate pulses implemented in Well 1. Table 3 and Figs. 3 through 5 show the measured pressure amplitudes and time lags. Pulse Interpretation Pulse Interpretation The following interpretation procedure was used to obtain a satisfactory match to the pulses. SPEFE P. 453
A Layer Pulse Test was designed, implemented and analyzed in a pinnacle reef in Alberta. Two Repeat Formation Tester (RFT)* surveys were performed in the observation well at a pre-designed interval. The second RFT survey was performed after the pulsed well was put back on production. The design was based on an older, history-matched model of the reef. A geological and stratigraphic interpretation was performed to update the geological and the numerical model. Subsequently, a three-dimensional, three-phase, single equation numerical simulator was used to model the inter-well area and a history match was obtained to the pressure shift in the two RFT surveys. The vertical pressure profiles from the RFT surveys identified barriers to vertical flow while the geological interpretation and the history match to the pressure shift provided a quantitative distribution of horizontal and vertical permeabilities in the inter-well area. Introduction Pulse testing requires generating a series of pressure disturbances by intermittently shutting-in or running-on a producer or an injector. These pressure pulses are then recorded as superimposed pressure waves over the background pressure-time behavior, for that reservoir, at the observation well. For a single layer homogeneous reservoir the measured pressure pulse can be interpreted using analytical methods. This interpretation, among other parameters, should result in inter-well permeability. The pressure amplitude and time-lag of the pressure pulses are dependent on inter-well permeability, fluid viscosity, total compressibility and porosity. They are also dependent on the interwell distance and the injection/production rate of the pulsed well. For a multi-layer reservoir the analysis of pressure pulses is not that straight-forward. In such a situation the pressure amplitude and time-lag are also a function of the vertical permeability between the layers. Moreover to monitor a complete pressure wave for even a single pulse at every layer in the observation well is not operationally possible today. One way to overcome these hurdles is to catch two or more pressure points on every wave. The number of different waves will depend on the layering of that reservoir. A wireline formation tester (RFT) is an ideal tool to measure pressure points, layer by layer, at pre-designed time intervals. In a layered reservoir with interlayer communication and commingled flow in the pulsed well, the shift in the RFT measured pressure points is not interpretable using convenient analytical models. To interpret the pressure shifts in the RFT profiles an elegant, three-dimensional, three-phase, single equation numerical simulator has been formulated. The numerical simulator, RFTSIM, assumes that the saturation distribution during the course of the Layer Pulse Test remains constant. RFTSIM requires a history match to the shift in the RFT measured vertical pressure profiles. This history match quantifies the horizontal and vertical permeability distribution and ascertains barriers to flow. These barriers could be partial or sealing, they could be a result of a fault system or just a reservoir structural boundary. The Layer Pulse Test was first introduced by Dakel and since then several tests have been carried out, mostly in the North Sea. Two other North Sea tests reported were by Lasseter and Bunn. Lasseter used RFTSIM to interpret a two-layer pulse test, thereby obtaining the vertical and horizontal permeability in the inter-well area and the fault block geometry. Bunn designed, implemented and analyzed a Layer Pulse Test from the Cormorant Field in the North Sea and obtained the transmissibility of the partially sealing layer between two lithological layers. This paper will describe the design, measurement and the interpretation of a Layer Pulse Test conducted in a pinnacle reef in Alberta. (This Layer Pulse Test was the first one to be conducted in North America.) DESIGN OF THE LAYER PULSE TEST A history-matched, two-dimensional radial model of the reef was available. P. 543^
this article begins on the next page F F JCPT89-01-13 Am.lk AM Wr COMPLETIONS AND EVALUATIONS Layer pulse testing using the Repeat Formation Tester J. SAEEDI Schlumberger of Canada Calgary, Alberta ABSTRACT A conventional pulse test provides estimates of average transmissibility and storage capacity between the pulsed and the observation wells. In a layered reservoir the pressure waves, instigated by pulsating the active well, travel at dif-ferent velocities in individual layers. These velocities are func-tions of layer transmissibilities and storage capacities. The measurement and recording of these complete pressure waves at the observation well will require pressure sensors lodged, in individual layers, behind the casing. This is not practical with current technology. This measurement dilemma can be resolved if the observa-tion well is newly drilled and still uncased. Instead of measuring the complete pressure wave for every layer, a sequence of discrete pressure points can be recorded for these layers, at known times, using a Repeat Formation Tester. The Repeat Formation Tester (RFT) measures point pressures generally in an open-hole behind the mud-cake. A base RFT survey is done in the observation well prior to initiating a pressure wave in the pulsed (active) well. After this time a rate change is implemented at the active well. Subse-quently, at pre-designed time intervals one or more RFT surveys are done at the observation well. These discrete data from base and subsequent RFT surveys, together with the measured flow or injection profile in the pulsed well, are then amenable to conventional analytical interpretation for estimating layer permeabilities in non-communicating layers.If the layers are communicating, a numerical interpretation method is available based on vertical pressure profiles. The RFT data is plotted as vertical pressure profiles at different times. The differences between the base and subsequent RFT pressure profiles are history-matched using a three-dimen-sional numerical reservoir simulator. The history-match pro-vides an estimate of layer horizontal and vertical permeabilities between the pulsed and observation wells.This paper describes the measurement and the analysis methodology of a layer pulse test. The numerical simulator, necessary to analyze a layer pulse test in communicating layers, is validated using analytical methods. The description also includes the successful application of this technique in a pin-nacle reef having communicating layers. Now with Schlumberger Middle East S.A.Reservoir permeabilities over a scale which spans interwell distances, govern the performance of the reservoir in that interwell area. Single well pressure transient tests, if con-ducted long enough, help determine permeabilities over large scales, but the permeabilities are not directional in nature.Conventional pulse and interference tests do give directional permeabilities in the interwell area but are limited to a single permeability in any one direction. A layer pulse test which con-sists of su...
SPE Members Abstract The inflow performance formulas for horizontal wells presented in the literature are all for single-layer reservoirs. This paper presents formulas for evaluating the inflow performance of horizontal wells in vertically layered reservoirs with crossflow. The system has a rectangular drainage region in the x and y directions and is bounded at the top and the bottom by horizontal planes with no-flow and/or constant pressure boundary conditions. The well is located anywhere within the drainage volume and could be of any length. Analytical models for dynamic (transient), pseudosteady-state, and steady-state productivity indices for horizontal wells in layered and bounded reservoirs are developed. They may also be used for the analysis of transient pressure or flow rate data, and both from horizontal wells in bounded systems. We present a method for the selection of the well location in a layered system for maximizing the productivity index. We also show that in a layered system with variable vertical permeability distribution, the proper selection of the well location is important for maximizing the productivity. The layering effect for most systems may not be treated as a single layer with average properties. The vertical permeability of each layer is the controlling parameter for the productivity. The productivity model developed may be used as a screening tool before or during drilling to obtain the best well location for a horizontal well. It can also be used to fine-tune numerical simulators for horizontal wells in layered systems. Introduction Horizontal wells have recently become highly popular for producing oil and gas reservoirs and obtaining information about lateral variations of reservoir properties. The inflow performance formulas for horizontal wells presented in the literature are all for single-layer reservoirs. It is well-known that many oil-bearing formations, the world's most prolific reservoirs, consist of many different lithological units. In these reservoirs, rock properties vary considerably in the vertical direction. Depending on the depositional environment, formation properties vary gradually or rapidly. For example, layers consisting of siltstone or chert are usually low-permeability formations. Conglomerate formations are usually highly conductive. The objective of this paper is to examine the effect of layering on well productivity. In other words, in which layer and at what length should a horizontal well be drilled in order to have the maximum productivity if layer properties are known before the drilling (they can be obtained from nearby wells and/or the vertically drilled section)? In this paper, we present analytical solutions for obtaining a dynamic (time-dependent) and pseudosteady-state or steady-state productivity index for horizontal wells in layered systems. The model includes the no-flow or constant-pressure boundary effects in the x, y, and z directions. As shown in Fig. 1, the horizontal well may be placed anywhere within the drainage volume. P. 929^
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