Depletion Performance of Layered Reservoirs Without Crossflow

Abstract

Summary. This paper presents a study of the rate/time and pressure/cumulative-production depletion performance of a two-layered gas reservoir producing without crossflow. The gas reservoir has produced for more than 20 years at an effectively constant wellbore pressure, thus giving continuously declining rate/time and pressure/cumulative-production data for analysis. The field data demonstrate that Arps depletion-decline exponents between 0.5 and 1 can be obtained with a no-crossflow, layered reservoir description. Rate-vs.-time and pressure-vs. cumulative-production predictions were developed from both 2D numerical and simplified tank models of a two layered, no-crossflow system. These results demonstrate the effects of changes in reservoir layer volumes, permeability, and skin on the depletion performance. Introduction Of all the papers about noncommunicating layered reservoirs, only a few have attempted to deal with the subject of depletion and long-term production forecasting. Tempelaar-Lietz originally discussed the effect of the oil production rate from a volumetric reservoir with more than one layer. Lefkovits et al. modified the Tempelaar-Lietz constant-rate, two-layer, single-phase-liquid depletion equations to account for two layers of unequal thickness. Fetkovich applied the constant-wellbore-pressure, single-phase-liquid solution to rate/time production data from a layered reservoir to demonstrate that when two noncommunicating layers, each characterized by a single-phase-liquid exponential decline, b=0, were produced commingled, the result was that b increased to 0.2. Hypothetical solution-gas-drive reservoir studies for noncommunicating layers were conducted by Keller et al to investigate the effects of recovery efficiency and GOR behavior and by Gentry and McCray to study the effects of producing noncommunicating layers on the decline-curve exponent, b. Both studies used singlecell models that did not include transient effects. In addition, both used a conventional PI relationship, g = J(delta p), to define a rate equation, instead of an inflow-performance-rate relationship that is a function of the difference in pressure squared--i.e., q = J(delta p2). By their nature, more sophisticated multiphase-flow studies would still have difficulty in assigning realistic kro and krg relationships for each layer. Further, the difficulty in obtaining the necessary field data, such as individual well measured oil and gas rates, frequent bottomhole shut-in pressures, and a nonlinear p-vs. Np relationship presents a serious verification problem. A similar problem exists for a single-phase-liquid situation because few oil reservoirs are totally, or even highly, undersaturated and produced to abandonment by simple liquid expansion. Those that are highly undersaturated often develop strong waterdrives because of the large reservoir-pressure decline with small production volumes. Such fields often are placed immediately under waterflood. The single-phase-liquid solutions of Tempelaar-Lietz, however, could find application in very-high-pressured gas reservoirs. To date, we know of no published field-case history that illustrates depletion-performance characteristics [other than repeat-formation-tester (RFT) layer pressures] to identify no-crossflow layered-reservoir behavior. Single-phase volumetric gas fields and wells offer the best opportunity for detection of layered-reservoir responses because only single-phase flow exists. Furthermore, production data are measured separately for each well, and annual shutin pressures are normally taken, sometimes with 48- or 72-hour deliverability tests. For the gas reservoir described in this paper, the simplified rate/time and cumulative-production/time equations of Ref. 3 and the p/z-vs.-Gp equation provided support that we were dealing with a noncommunicating layered reservoir. The field has produced for more than 20 years at effectively a low constant wellbore pressure, thus giving continuous, declining rate/time data for analysis. The total field and individual wells examined in our study exhibited a rate/time depletion-decline exponent approaching 1.0 with very little early-time transient data evident. A gas well producing from a single homogeneous layer at a flowing wellbore pressure near zero has a maximum depletion-decline exponent of 0.5. Further confirmation and greater flexibility were then obtained with a conventional single-cell, pseudosteady-state, gas-forecasting program that combines gas material balance and a stabilized back-pressure curve for each layer. In addition, a fully implicit radial numerical model consisting of two fifty-cell layers was used to simulate annual 72-hour shut-ins and 48-hour deliverability tests and to verify the results obtained from simplified approaches. Throughout this paper, these approaches will be referred to as the backpressure-curve/material-balance and the radial-model methods, respectively. All basic results and conclusions drawn in this paper, however, can be made with any of the approaches described above. In all figures, the simulated 72-hour shut-in points are strictly the product of the radial model; all other results were consistently obtained by both the backpressure-curve/material-balance and the radial-model approaches. Both constant-wellbore-pressure and constant-rate depletion were investigated. Graphical presentations of rate vs. time and pressure vs. cumulative production clearly demonstrate the effects of changes in the reservoir layer volumes, per-meability, k, and skin, s, on the depletion performance of two-layered system without crossflow. Field Description Development drilling began in our field of study in 1961; 212 gas wells had been drilled by early 1966. The reservoir consists of about 350 ft of gross sandstone thickness at 1,800 ft. Initial reservoir pressure was about 428 psia. Other parameters include a reservoir temperature of 80 degrees, an average porosity of 15%, a water saturation of 51 %, and a gas gravity of 0.7. A shale barrier averaging 50 ft thick was clearly identified and correlated across the entire field. Core data indicate a bimodal distribution with a permeability ratio between 10:1 and 20:1. Wells were generally stimulated upon completion with 500 to 1,000 gal of 15% HCl, followed by a sand fracture, which included 20,000 gal of gel and 40,000 lbm of 20/40 sand. Table 1 shows stimulation results in terms of skin effect along with other results obtained from initial isochronal tests. In most cases, the exponent of the backpressure curve, n, was 1.0. Of the four tests that did not yield a backpressure exponent of 1.0, one is actually a flowafterflow test, and the others had not adequately cleaned up after stimulation. All our studies are based on the assumption that nonDarcy flow is not present in the reservoir--i.e., n=1.0 for each layer. The field came on production virtually wide open against an essentially constant wellbore pressure. A type-curve analysis and regression fit of the total field rate/time production data yielded b=0.89, practically identical to what we later found from individual well analysis. P. 310⁁