To calculate the lag the hole dimensions must be known as well as the drill string dimension. Most holes have at least two sections of different diameters and towards the end of the well may will have more (riser, casing liner, and open hole). Added to this is the fact that the drill string will usually have sections of different diameters (drill pipe, heavyweight drill pipe and drill collars, etc).
Two techniques may be applied to calculating the annular volume, which are:
In The first method, the lengths and the dimensions of each section of the annulus are determined; the volumes are calculated and totalized. Then the lag equations are applied to determine the equivalent times and strokes.
The second method involves calculating the volume of the hole and the volume of the drill string (metal and internal capacity) and then subtracting the values from each other to determine the lag time and strokes for the whole well. The first method is the one preferred because it informs the logger of the exact nature of the various annular sections and their individual volumes.
An alternate to the tracer method of calculating the lag is available. This is by calculating the annular volume by using either one of the two approaches:
1. Principles of volume
2. Capacity/displacement tables
Using similar data as for the previous example: Hole depth = 11,000 feet
Drill pipe = 5 inches OD by 4.276 inches ID Pump data = .0997 barrels per stroke
In addition, we must consider the following data: Hole size = 12.25 inches
Depth of last casing = 9,500 feet
Size of last casing = 13.375 inches OD by 12.347 inches ID (72 pounds per foot) Size of Drill collars = 8 inches OD by 3 inches ID (147.0 pounds per foot)
Length of Drill collars =500 feet
These specifications result in a pictorial representation of the well geometry as follows: As noted, there are three distinct annular sections.
• Annular section 1 is formed by the drill pipe and casing • Annular section 2 is formed by the drill pipe and open hole • Annular section 3 is formed by the drill collars and open hole
The simplest method of arriving at a total annular volume is to calculate each section independently and the add up the results.
Capacity of the annulus in barrels per foot = (hole size or casing ID)2 - (drill pipe outside diameter)2 × 0.00097 or (hole size or casing ID)2 - (drill pipe outside diameter)2 ÷ 1029.4
Annular section 1 = (casing ID2 - drill pipe OD2) × 0.00097 (12.3472 - 52) × 0.00097 =.1236 barrels per foot Next barrels per foot × section length = barrels
0.1236 × 9500 = 1174 barrels
Annular section 2 = (hole size2 - drill pipe OD2) × 0.00097 (12.252 - 52) × 0.00097 = .1213 barrels per foot Next barrels per foot × section length = barrels
0.1213 × 1000 = 121.3 barrels
Annular section 3 = (hole size2 - drill collar OD2) × 0.00097 (12.252 - 82) × 0.00097 = .0835 barrels per foot Next barrels per foot × section length = barrels
0.0835 × 500 = 41.7 barrels Adding up the sections, we have:
1174 + 121.3 + 41.7 = 1337 barrels total annular volume
To convert this volume into pump strokes, divide the total annular volume by the pump output:
1337 barrels ÷ 0.0997 barrels per stroke = 13410 strokes
Divide the total strokes by the pump rate per minutes to obtain the bottoms up time. 13410 strokes ÷ 150 strokes per minute = 89.4 minutes
The lag stroke is then (13410 strokes) and its equivalent lag time according to rig pump rate is (89.4 minutes).
Note:
When logging, it will be observed that the calculated lag will invariably be less than that obtained by using the tracer method. Reasons for this are:
• Lag tracer materials or cutting will tend to slip behind the velocity of the mud with respect to their relative densities and the particular mud's carrying capabilities.
• Enlargement of the hole, due to erosion by the mud, is not accounted for when making the lag calculation.
• Mud flows are sometimes turbulent which results in a tendency for the cuttings and tracer
materials to rotate up the annulus rather than rising uniformly.
Due to the characteristics of drilling mud in laminar flow, the center annulus flow rate tends to be faster than that near the walls; thus, cuttings in the center annulus region tend to be moved over into the slower flow areas and subsequently are again moved back into the faster region. This is a similar effect to the previous paragraph although the rotational effects are much less harsh.
Cumulatively, these effects tend to delay the arrival at the surface of cutting samples. Conversely, gas samples will tend to rise at the same or possibly at a slightly higher rate than the mud, particularly if the mud is relatively thin. As gas rises in the annulus, a reduction of hydrostatic pressure will be exerted on the samples resulting in an expansion of the gas in proportion to its volume and original pressure. Hole enlargement will, however, have a similar effect on gas samples as with heavier materials.
The net result is that gas samples will tend to arrive at the surface sooner than cuttings. In any event, a lag calculation is a good approximation but should be corrected or checked for accuracy and corrected as necessary by noting the arrival of cuttings from a drill break or connection gas.
As a well deepens, the pump liners are sometimes replaced by liners of a smaller diameter make a periodical check as to the liner size. This normally takes place when a new casing string is run.
Most drilling rigs are equipped with two mud pumps, whereas, most of the deep water semisubmersible rigs will have three mud pumps. One of these pumps is normally used to boost the riser during drilling operations. Ensure that the software is properly configured to pumps, which are on the hole.
When the rig pumps are stopped the mud column stops. Also, if drilling is suspended and the well circulated out, the flow of information that is collected at the shale shakers and new information is no longer being supplied at the bottom of the hole. After the expiration of the lag, the bottom of the mud column will have reached the surface. Without the lag as an indexing tool, all the mud and cuttings analysis would apply to formation only at unknown depths and, as common sense would indicate, this information is almost useless without knowing at what depth the analysis pertains to. Therefore, with the lag calculation it is known exactly to what depths these analysis apply.
In conclusion, the annulus represents a continuous column of surface data logging information moving up and out of the hole, which is transferred to the computer by the logging engineer as part of the daily routine.