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1-3 INCREMENTAL OIL Defintion A universal technical measure of the success of an EOR project is the amount of incremental oil recovered. Figure 1-3 defines incremental oil. Imagine a field, reservoir, or well whose oil rate is declining as from A to B. At B, an EOR project is initiated and, if successful, the rate should show a deviation from the projected decline at some time after B. Incremental oil is the difference between what was actually recovered, B to D, and what would have been recovered had the process not been initiated, B to C. Since areas under rate-time curves are amounts, this is the shaded region in Fig. 1-3.
Figure 1-3. Incremental oil recovery from typical EOR response (from Prats, 1982)
As simple as the concept in Fig. 1-3 is, EOR is difficult to determine in practice. There are several reasons for this. 1. Combined (comingled) production from EOR and nonEOR wells. Such production makes it difficult to allocate the EOR-produced oil to the EOR project. Comingling occurs when, as is usually the case, the EOR project is phased into a field undergoing other types of recovery. 2. Oil from other sources. Usually the EOR project has experienced substantial well cleanup or other improvements before startup. The oil produced as a result of such treatment is not easily differentiated from the EOR oil. 3. Inaccurate estimate of hypothetical decline. The curve from B to C in Fig. 13 must be accurately estimated. But since it did not occur, there is no way of assessing this accuracy. Ways to infer incremental oil recovery from production data range from highly sophisticated numerical models to graphical procedures. One of the latter, based on decine curve analysis, is covered in the next section. Estimating Incremental Oil Recovery Through Decline Curves Decline curve analysis can be applied to virtually any hydrocarbon production operation. The following is an abstraction of the practice as it applies to EOR. See Walsh and Lake (2003) for more discussion. The objective is to derive relations between oil rate and time, and then between cumulative production and rate. The oil rate q changes with time t in a manner that defines a decline rate D according to
1 dq q dt
The rate has units of (or [=]) amount or volume per time and D [=]1/time. Time is in units of days, months, or even years consistent with the units of q. D itself can be a function of rate, but we take it to be constant. Integrating Eq. 1.3-1 gives
where qi is the initial rate or q evaluated at t = 0. Equation 1.3-2 suggests a semilogarithmic relationship between rate and time as illustrated in Fig. 1-3. Exponential decline is the most common type of analysis employed.
qi -D Slope = 2.303 Decline period begins qEL
0 Figure 1-3. Schematic of exponential decline on a rate-time plot.
Figure 1-3 schematically illustrates a set of data (points) which begin an exponential decline at the ninth point where, by definition t = 0. The solid line represents the fit of the decline curve model to the data points. qi is the rate given by the model at t=0, not necessarily the measured rate at this point. The slope of the model is the negative of the decline rate divided by 2.303, since standard semilog graphs are plots of base 10 rather than natural logarithms. Because the model is a straight line, it can be extrapolated to some future rate. If we let qEL designate the economically limiting rate (simply the economic limit) of the project under consideration, then where the model extrapolation attains qEL is an estimate of the project’s (of well’s, etc.) economic life. The economic limit is a nominal measure of the rate at which the revenues become equal to operating expenses plus overhead. qEL can vary from a fraction to a few hundred barrels per day depending on the operating conditions. It is also a function of the prevailing economics: as oil price increases, qEL decreases, an important factor in reserve considerations. The rate-time analysis is useful, but the rate-cumulative curve is more helpful. The cumulative oil produced is given by t
The definition in this equation is general and will be employed throughout the text, but especially in Chap. 2. To derive a rate -cumulative expression, insert Eq. 1.3-1, integrate, and identify the resulting terms with (again) Eq. 1.3-1. This gives
Equation 1.3-3 says that a plot of oil rate versus cumulative production should be a straight line on linear coordinates. Figure 1-4 illustrates.
qi Slope = -D
Recoverable oil Np
0 Figure 1-4. Schematic of exponential decline on a rate-cumulative plot.
You should note that the cumulative oil points being plotted on the horizontal axis of this figure are from the oil rate data, not the decline curve. It this were not so, there would be no additional information in the rate-cumulative plot. Calculating Np normally requires a numerical integration with something like the trapezoid rule. Using model Eqs 1.3-2 and 1.3-3 to interpret a set of data as illustrated in Figs. 1-3 and 1-4 is the essence of reservoir engineering practice, namely 1. Develop a model as we have done to arrive at Eqs. 1.3-2 and 1.3-3. Often the model equations are far more complicated than these, but the method is the same regardless of the model. 2. Fit the model to the data. Remember that the points in Figs. 1-3 and 1-4 are data. The lines are the model. 3. With the model fit to the data (the model is now calibrated), extrapolate the model to make predictions.
At the onset of the decline period, the data again start to follow a straight line through which can be fit a linear model. In effect, what has occurred with this plot is that we have replaced time on Fig. 1-3 with cumulative oil produced on Fig. 1-4, but there is one very important distinction: both axes in Fig. 1-4 are now linear. This has three important consequences. 1. 2. 3.
The slope of the model is now –D since no correction for log scales is required. The origin of the model can be shifted in either direction by simple additions. The rate can now be extrapolated to zero.
Point 2 simply means that we can plot the cumulative oil produced for all periods prior to the decline curve period (or for previous decline curve periods) on the same rate-cumulative plot. Point 3 means that we can extrapolate the model to find the total mobile oil (when the rate is zero) rather than just the recoverable oil (when the rate is at the economic limit). Rate-cumulative plots are simple yet informative tools for interpreting EOR processes because they allow estimates of incremental oil recovery (IOR) by distinguishing between recoverable and mobile oil. We illustrate how this comes about through some idealized cases. Figure 1-5 shows a rate-cumulative plot for a project having an exponential decline just prior to and immediately after the initiation of an EOR process.
IOR Incremental mobile oil
Figure 1-5. Schematic of exponential decline curve behavior on a rate-cumulative plot. The EOR project produces both incremental oil (IOR), and increases the mobile oil. The pre- and post-EOR decline rates are the same. We have replaced the data points with the models only for ease of presentation. Placing both periods on the same horizontal axis is permissible because of the scaling arguments mentioned above. In this case, the EOR process did not accelerate the production because the decline rates in both periods are the same; however, the process did increase the amount of mobile oil, which in turn caused some incremental oil production. In this case, the incremental recovery and mobile oil are the same. Such idealized behavior would be characteristic of thermal, micellar-polymer, and solvent processes.
IOR qEL Np
Figure 1-6. Schematic of exponential decline curve behavior on a rate-cumulative plot. The EOR project produces incremental oil at the indicated economic limit but does not increase the mobile oil. Figure 1-6 shows another extreme where production is only accelerated, the pre- and post-EOR decline rates being different. Now the curves extrapolate to a common mobile oil but with still a nonzero IOR. We expect correctly that processes that behave as this will produce less oil than ones that increase mobile oil, but they can still be profitable, particularly, if the agent used to bring about this result is inexpensive. Processes that ideally behave in this manner are polymer floods and polymer gel processes, which do not affect residual oil saturation. Acceleration processes are especially sensitive to the economic limit; large economic limits imply large IOR.
Example 1-1. Estimating incremental oil recovery. Sometimes estimating IOR can be fairly subtle as this example illustrates. Figure 1-7 shows a portion of rate-cumulative data from a field that started EOR about half-way through the total production shown. 0.20
Pre EOR 0.10
Post EOR 0.05
qEL 0.00 0.0
2.0 3.0 4.0 5.0 Cumulative Oil Produced, M std. m3 Figure 1-7. Rate (vertical axis) - cumulative (horizontal axis) plot for a field undergoing and EOR process. a. Identify the pre- and post-EOR decline periods. The pre-EOR decline ends at about 2.5 M std. m3 of oil produced, at which time the post-EOR period begins. This point does not necessarily coincide with the start of the EOR process. The start cannot be inferred from the rate-cumulative plot. b. Calculate the decline rates ([=] mo-1) for both periods. Both decline periods are fitted by the straight lines indicated. The fitting is done through standard means; the difficulty is always identifying when the periods start and end. For the pre-EOR decline,
M std.m3 0.11 0.18 month 2.55 0 M std.m3
and for the post-EOR decline,
M std.m month 4 2.55 M std.m3
0.09 0.11 D
The EOR project has about halved the decline rate even though there is no increase in rate. c. Estimate the IOR ([=] M std. m3) for this project at the indicated economic limit. The oil to be recovered by continued operations is 4.7 M std. m3. That from EOR is (by extrapolation) 7 M std. m3 for an incremental oil recovery of 2.3 M std. m3.
1-4 CATEGORY COMPARISONS Comparative Performances Most of this text covers the details of EOR processes. At this point, we compare performances of the three basic EOR processes and introduce some issues to be discussed later in the form of screening guides. The performance is represented as typical oil recoveries (incremental oil expressed as a percent of original oil in place) and by various utilization factors. Both are based on actual experience. Utilization factors express the amount of an EOR agent required to produce a barrel of incremental oil. They are a rough measure of process profitability. Table 1-1 shows sensitivity to high salinities is common to all chemical flooding EOR. Total dissolved solids should be less than 100,000 g/m3, and hardness should be less than 2,000 g/m3. Chemical agents are also susceptible to loss through rock–fluid interactions. Maintaining adequate injectivity is a persistent issue with chemical methods. Historical oil recoveries have ranged from small to moderately large. Chemical utilization factors have meaning only when compared to the costs of the individual agents; polymer, for example, is usually three to four times as expensive (per unit mass) as surfactants. TABLE 1-1 CHEMICAL EOR PROCESSES Process Polymer Micellar polymer
Improves volumetric sweep by mobility reduction Same as polymer plus reduces capillary forces
Injectivity Stability High salinity Same as polymer plus chemical availability, retention, and high salinity
Typical recovery (%)
Typical agent utilization*
0.3–0.5 lb polymer per bbl oil produced
15–25 lb surfactant per bbl oil produced