Summary Allocation of gas to wells on continuous lift can affect profitability. Excessive gas input is costly because of high gas prices and compressing costs. Inefficient gas allocation in a field with limited gas availability also reduces profitability. To alleviate the problem of excessive gas usage, an economic slope that relates liquid production and gas injection to cost and profit has been developed. To resolve the problem of gas allocation in a field with limited gas, a method to allocate gas to wells efficiently under this situation is presented and a step by step procedure is given. An example problem consisting of a six-well field is solved to illustrate the procedures presented. Introduction The current energy situation and the increasing costs of gas lift are forcing oil operators to consider economic operations first rather than desired maximum production. As the market price of oil continues to increase, it is understandable that oil operators would prefer gas lift wells to produce at a maximum. In fact, optimization in continuous gas lift has come to mean the injection of gas until maximum production is achieved. On the other hand, gas prices and compression costs continue to increase, forcing the oil operator to approach maximum production cautiously. In view of this situation, the development of a procedure to determine the optimal economic point to produce a well or a group of wells was recognized as having a high potential for gas-lift design improvement. The economic slope concept offers a good approach to the problem. This slope relates the well and reservoir parameters to cost and profit. The performance of a well on continuous gas lift can be described by a typical gas requirement plot (liquid flow rate vs. gas injection) as shown in Fig. 1. Any point of tangency to the curve is unique and describes a certain situation. For instance, the point of tangency that occurs at 0 deg. slope indicates the gas injection that will yield maximum production. If this slope coincides with the economic slope, the determination of the economic optimum is clear-cut since only one maximum exist. However, the economic slope usually occurs at a slope greater than 0 deg., so obtaining the optimal economic point can become tedious. In fact, efforts made in the past yielded procedures that are very cumbersome. This paper, therefore, presents (1) the formulation of a simple slope, (2) the use of this economic slope in a simple procedure to allocate gas, at the optimal economic point, to a well or a group of wells(given an unlimited gas situation), and (3) the determination of total gas required for a field, thus simplifying compressor sizing. Another important aspect of gas allocation that deserves attention is the area of limited gas. A method is presented that uses a simple graphical procedure to allocate gas to wells efficiently in a field operating under such a condition. A six-well field is used to illustrate the procedures presented. Economic Formulation The gas requirement plot (Fig. 1) is indispensable in any useful analysis of gas allocation in continuous gas lift because it relates liquid production to gas injection. This liquid production/gas injection relationship is the cornerstone of any economic approach. To obtain an economic slope, it is necessary to formulate mathematically a function of gas injection and liquid production on one hand and cost and profit on the other. JPT P. 1887^

In a number of previous publications we have introduced the concept of Unified Fracture Design (UFD) with a central theme of maximizing the dimensionless productivity index (JD) following a hydraulic fracture treatment. We have shown that for a given mass of proppant to be injected in a well with an assigned drainage in a reservoir of a given permeability there exists a specific dimensionless fracture conductivity at which the JD becomes maximum. We called this the optimum conductivity. Smaller and larger values of this conductivity result in smaller JDs. All the important fracture and reservoir magnitudes of permeabilities and volumes are related through the Proppant Number. Once the optimum conductivity is determined (which for a large range of Proppant Numbers is equal to 1.6) then the ideal fracture dimensions (length and width) are de facto set and they should be considered as the desirable target. For each injected proppant mass there is a corresponding Proppant Number and at the optimum conductivity the dimensionless PI can be readily determined. Increasing the proppant mass or the proppant-pack permeability would result in an increase in the JD, which has a maximum limit of approximately 1.9. This value can never be accomplished in reality and there are three reasons preventing it, one economic and two physical. The economic reason is obvious. Increasing the job size would result in the flattening of benefits, not justifying the incremental costs. In the same vein, using a much better (and more expensive) proppant may not be justified by similarly flattening benefits. Of the physical problems, the first affects low-permeability reservoirs where the indicated fracture width may be too small; it cannot be less than three proppant diameters. For high-permeability reservoirs, indicated very large widths will certainly result in very large net pressures, exceeding operational limits. The latter may also lead to unacceptable fracture heights. We present here a series of parametric studies pushing the physical limits of fracturing in a wide range of reservoirs by injecting very large proppant volumes and experimenting with extraordinarily large proppant sizes (large proppant pack permeabilities) seeking the maximization of the JD within reasonable economic limits. This work appears to be particularly suited for high permeability formations and it shows that current industry practices are overly conservative and timid and a more bullish approach would lead to major production enhancement benefits. Introduction Valkó and Economides1,2 introduced a physical optimization technique to maximize the productivity index. The well performance depends on the x-direction penetration ratio, Ix:Equation 1 and the dimensionless fracture conductivity:Equation 2 Because the penetration and the dimensionless fracture conductivity, through width, compete for the same resource: the propped volume, the injected propped volume provides a constraint in the form:Equation 3 which, can be considered as the ratio of two cross-sectional areas: propped area to reservoir area - multiplied by the permeability ratio and by two. Multiplying both the numerator and denominator by the net pay thickness, hp leads to:Equation 4 where Nprop has been defined by Valkó and Economides as the dimensionless proppant number. Vp is the volume of the proppant in the pay. It is equal to the total volume times the ratio of the net height to the fracture height.

A systematic approach is presented for generating transient inflow performance relationship curves for finite conductivity vertically fractured wells. A semi-analytical model was developed to simulate dimensionless wellbore pressure drop and dimensionless pressure loss through the fracture vs. dimensionless time at constant-rate of production for wells intercepted by a finite-conductivity vertical fracture. Flowing bottom hole pressure can be predicted at any time period using these dimensionless variables. System average pressure at any stage of production can be obtained through material balance calculations. A straight line reference curve was observed at all times provided that the real gas pseudo-pressure function is used to plot m(pwf(t))/m(p¯R(t)) vs. qg(t)/qgmax (t). The advantage of normalizing the dimensionless variable in termas of pseudo-pressure function is that only one straight line relationship is obtained throughout the entire production life of the reservoir. This provides a more simple means for performance prediction purposes. The major contribution of this paper is the provision of a valuable tocl to study the sensitivity of fracture design parameters on ultimate well performance. The economic benefits of this approach can be substantial.

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractWe have established the concept of Unified Fracture Design (UFD) to maximize the dimensionless productivity index (J D ) following a hydraulic fracture treatment. For a given mass of proppant there is a specific dimensionless fracture conductivity, which we called the optimum, at which the J D becomes maximum. The Proppant Number is a seminal quantity unifying the propped fracture and the drainage volumes and the two permeabilities, those of the proppant pack and the reservoir.

A completely new approach is presented to show the effect of completion parameters on high volume gas wells typical of the Gulf Coast. The solution can be summarized in graphical form and it will consider the following sections of the total producing system: 1) flow in the porous media, 2) effect of completion, and 3) flow conduit performance. The result is that the controlling parameter in the total production system can be determined. Many wells are capable of producing very high rates but are restricted due to very restricted gravel pack parameters, while wells with very efficient gravel pack completions are tubing-dominated. The procedure presented approaches the completion sensitivity analysis from a complete production system concept.