SECTION III: Engineering Decisions through Economic Impact Analysis: Applications and Real World Examples
This section could be considered the backbone of our text. It represents the application of economic analysis to many engineering problems encountered in various sectors of petroleum operations. It illustrates how economic analysis is applied to solve engineering problems in different facets of the oil industry. Addressing relevant problems involving oil-engineering decisions is our main target in this section. Feasibility studies are presented for a number of cases. Three main operations that underlie the oil and gas industry, from prospects to finished products are as shown next:

Section ///./: Upstream Operations (Subsurface Operations)
Three main operations that underlie the oil and gas industry, from prospects to finished products are as shown in the text.
SECTION III.II: Upstream Operations (Subsurface Operations): Exploration and Production (E&P)
(E&P) Exploration, Drilling, and Oil Production—Part 1
13.1 INTRODUCTION
Exploration includes prospecting, seismic, and drilling activities that take place before the development of a field is finally decided. Symbolically the two operations of exploration plus drilling leading to oil production are drawn as shown Figure 13.1.
Exploration and production (E&P) is known as the upstream segment of the oil and gas industry. Exploration involves two distinctive stages: Exploration surveying and Exploration drilling. The contents of the chapter include both types of exploration. In practice, the process of oil and gas exploration and production typically involves four stages:
- • Exploration
- • Well Development
- • Production
- • Abandonment
Exploration and drilling is presented first as an integrated topic because of the relationship of the two processes. This is followed by presenting oil production in Chapter 15.
13.2 EXPLORATION AND DRILLING
Hydrocarbon exploration is a high-risk investment and risk assessment is paramount for successful exploration portfolio management. Virtually every oilfield decision is founded on profitability. With no control of oil and gas prices, and facing steadily rising costs and declining reserves, companies' basic decisions are based on constantly moving targets. Simply we can say that a producing oil and gas property is a series of cash payments projected in the future.
Technology aspects covered in this chapter deal with the very first activity in finding oil. It highlights, first, methods used for search of oil or oil exploration. Types of drilled wells, their numbers, and spacing are discussed next; and the use of economic balance and binomial expansion is proposed to solve relevant problems. The cost of finding oil and the size of capital expenditures in oil fields are considered in the chapter as well.

FIGURE 13.1 A schematic representation for the interaction between exploration, drilling, and production.
Applications and case studies include problems on optimization of the number of wells to drill, the cumulative binomial probability of success in drilling wells, and many other operations.
Knowledge of the basic principles as well as some of the common terms and concepts encountered in the oil fields is desirable for complete understanding of the subject. Geological formations, origin and accumulation of petroleum, oil reservoirs and their classification, petroleum prospecting practices, drilling and development operations, and many others are important in our engineering economics discussion.
Since our purpose here is not an explanation of the technical operations in petroleum production, we intend to highlight only the topics pertinent to the economic appraisal or valuation of “an oil property”. The “oil property” as defined is meant to include any property with underground accumulations of liquid and/or gaseous hydrocarbons that might be produced at a profit.
Additional background materials on oil production methods and the estimation of recoverable oil reserves are given in the next chapter.
13.3 THE SEARCH FOR OIL: EXPLORATION
The first prerequisite to satisfying man’s requirements for refined petroleum products is to find crude oil. Oil searchers, like farmers and fishermen, are actually in a contest with nature to provide the products to meet human needs. They are all trying to harvest a crop.
But the oil searcher has one problem that the farmer does not have. Before the oil man can harvest his crop, he has to find it. Even the fisherman's problem is not as difficult, since locating a school of fish is simple compared to finding an oil field. The oil searcher is really a kind of detective. His hunt for new fields is a search that never ends; the needle in the haystack could not be harder to find than oil in previously untested territories.
Today, petroleum prospecting and hence its discovery is credited to what is called “subsurface studies”. This includes:
- • The use of geophysical instruments
- • Cuttings made by the bit as the well is drilled
- • Core samples collected from the well
- • Special graphs called “logsgenerated by running some tools into the oil wells during the drilling operations
The net result of these studies is the preparation of different kinds of geological maps that show the changes in the shape of subsurface structures with depth.
The geophysical techniques encompass three methods:
- 1. Seismic method
- 2. Magnetic method
- 3. Gravitational method
Each of these techniques utilizes the principles of physical forces and the properties of the earth. For example, in the seismic method, creation of artificial earthquake waves is established by firing high explosives into holes. The rates of travel of these waves are analyzed by echo sounding techniques. The most recently invented instruments are: reflection seismographs, gravimeters, and airborne magnetrometers. Such devices enable geophysicists to explore not only the surface and the subsurface conditions of the earth searching for oil, but the lunar surface and depths as well. These sophisticated lunar experiments monitor the earth’s magnetic and gravitational properties from space.
Stratigraphy, on the other hand, involves drilling a well basically to obtain stratigraphic correlation and information. Complete sections of the well formations are exposed and rock samples are taken while drilling operation is in progress. The success in finding oil will depend to a large degree on the accuracy of well logging. Several kinds of well logs are known; the most commonly accepted ones are:
- 1. Drillers logs
- 2. Sample logs
- 3. Electric logs
- 4. Radioactivity logs
- 5. Acoustic logs
Once the data are collected using core samples and wire-line logs of various kinds, contour maps are prepared. Generally a contour map consists of a number of contours, or lines, on which every point is at the same elevation above or below sea level of a given area. These lines must be at regular depth intervals to enable geologists to depict three-dimensional shapes.
Other means of exploring for oil include detailed ground geological surveys aided by preliminary results of aerial photography and photo-geological work.
13.4 OIL RESERVOIRS AND CLASSIFICATION
The two most important prerequisites for an oil accumulation to occur are:
- 1. A trap that acts as a barrier to fluid flow
- 2. A porous and permeable bed or reservoir rock
Thus, each geological formation, irrespective of age or composition, must process these physical properties of porosity and permeability in order to be described as a “reservoir rock”.
Some of the reservoir-rock characteristics are as follows:
- 1. Although porosity and permeability are important as individual parameters, neither of them is of value in the absence of the other.
- 2. The reservoir is judged by its thickness and porosity, that is, by the abundance of interconnected voids, which provide passages for the fluids to flow.
Flow capacity or permeability depends on porosity to some extent, but porosity does not depend on permeability. In other words, reservoir rocks of high porosity are not necessarily of high permeability, and those of low porosity are not necessarily of low permeability. Generally speaking, sandstone reservoirs are more porous than limestone.
A reservoir may be defined as anybody of underground rocks with a continuously connected system of void spaces filled with hydrocarbon fluids, which can move toward wells—drilled into the rocks—under the influence of either natural or artificial driving forces. If the volume of the hydrocarbons produced by the wells is sufficient to permit an “economic recovery”, then the accumulation is known as a commercial reservoir and usually referred to as a proven reserve.
Reservoirs, on the other hand, could be described as a “resource base”, which is the sum total of crude oil, natural gas, and natural gas liquids in the ground within an identified geographic area. The reservoir thus includes all stocks, including some stocks which are unrecoverable and therefore not included in “proven reserves”.
Proven reserves refer to the reserve stocks of immediate or short-term economic feasibility of extraction; therefore, stocks which are known to exist but cannot profitably be extracted are excluded from reserves. The cost limits, or as far as one can go on profitably employing these reserves, are those costs consistent with the taking of “normal” risk and commercial production.
The void spaces of proven reservoirs normally contain some interstitial water (or connate water) along with the hydrocarbons. Since most of this water is held in space by some sort of capillary forces, reservoir rocks turn out to be saturated with the three reservoir fluids: oil (liquid), gas, and water.
An oil field consists of all “pools” or reservoirs underlying a continuous geographic area, with no large enclosed subareas being considered unproductive.
13.5 THE ROLE OF DRILLED WELLS IN DEVELOPMENT
All of the activities described earlier for oil exploration lead only to an evaluation of the probability that oil is in a particular location. Once it seems probable that there really is oil, wells must be drilled. Reservoir and oil fields are discovered only by drilling to sufficient depths to verify what was recommended by an exploration team. The following stages in well drilling are identified: [1]
- 3. A successful wildcat well is called a discovery well.
- 4. Subsequent wells drilled into proven reservoirs for production purposes are called development wells.
Such a stage-wise classification is illustrated in Figure 13.2
As far as the “test wells” are concerned, the following should be noted:
a. Drilling of test wells is the most costly single operation in oil exploration (this will be discussed further).
b. One exploratory well alone does not indicate extensive oil accumulation. Other wells, carefully located near the well where oil has been discovered, are drilled to discover if there is a reservoir in the area and approximately how much is available and can be recovered. Thus, it is desirable:

FIGURE 13.2 Different stages in well drilling.
- 1st to obtain reliable information as to the quantity of oil (and gas) which is recoverable, so an economic and proper size and type of surface crude oil production plant can be setup, and
- 2nd to determine from the samples of the reservoir the characteristics of the oil itself, the nature and amount of oil in the reservoir. The raising of oil to the ground surface and then the handling of the oil at ground surface will depend to a great extent on the nature of the oil itself and its associated gas. Crude oil can range from very heavy viscous oil, almost a tar, with little or no gas dissolved in it and under very low pressure, down to an extremely light, straw-colored oil with a considerable volume of gas, known as a condensate-type crude. The condensate-type crude is more likely to be found at great depths. Under conditions of high pressure and temperature which exist at deep levels, the crude is usually in the gaseous stage. Between the extremes of a heavy viscous oil and a very light oil, there is an infinite variety of crude oil. The manner of producing these crudes is decided only after examining samples, which show their characteristics and physical attributes.
“Intelligent wells” are increasing in popularity. These contain permanent monitoring sensors that measure pressure, temperature, and flow and telemeter these data to surface. More importantly, these wells contain surface-adjustable downhole flow-control devices, so, based on the dynamic production information from all the wells in the reservoir, flow rates can be optimized without having to perform a costly intervention.
13.6 NUMBER OF WELLS AND WELL SPACING
The location as well as the number of wells drilled into a proven reservoir raises many questions:
“How many wells should we drill in the reservoir?”
“How close should the wells be?”
“How many wells do we need before we can lay pipelines economically?” Usually, use of the “economic balance” will provide answers to this type of question.
13.7 DRILLING OPERATIONS
There are two methods of drilling a well, the cable tool and the rotary methods. No matter which method is used, a derrick is necessary to support the drilling equipment.
Cable tool drilling is the older method of drilling. In this method a hole is punched into the earth by repeatedly lifting and dropping a heavy cutting tool, a bit, hung from a cable. Today, however, practically all wells are drilled by the rotary method.
Rotary drilling bores a hole into the earth much as a carpenter bores a hole into a piece of wood with a brace and bit. In the middle of the derrick floor there is a horizontal steel turntable, which is rotated by machinery. This rotary table grips and turns a pipe extending through it downward into the earth. At the lower end of the pipe, a bit is fastened to it.
As the drill chews its way farther and farther down, more drill pipe is attached to it at the upper end. As section after section of drill is added, the drill pipe becomes almost as flexible as a thin steel rod. Controlling the drill pipe under such conditions, and keeping the hole straight as well, is very difficult and requires great skill in drilling.
During the drilling, a mixture of water, special clays, and chemicals, known as drilling mud, is pumped down through the hollow drill pipe and circulated back to the surface in the space between the outside of the pipe and the walls of the pipe. This drilling mud serves several purposes, including lubricating and cooling the bit and flushing rock cuttings to the surface.
As the drilling hole is deepened, it is lined with successive lengths of steel pipe, called casings. Each string of casing slides down inside the previous one and extends all the ways to the surface. Cement is pumped between these successive strings of casing, and seals against any leakage of oil, gas, or water.
To achieve large annual additions to reserves and to output, the rate of drilling must be stepped up sharply. Barrels added per foot drilled are one of the best indicators of the results of drilling effort. This measure should not show a decline. A projection of the trend of barrels added per foot of drilling should be established for oil companies engaged in production.
13.8 FACTORS AFFECTING PENETRATION IN DRILLING
Studies made by experts from drilling and equivalent companies indicate that there is a positive effect of weight and speed of rotation on penetration rate, or feet per hour of drilling. This is true whether toothed or carbide-studded bits are used.
Past experience has shown that proper penetration rate of weight on bit rotary speed and hydraulic horsepower can be plotted on a graph to determine optimum drilling at minimum drilling cost. Thus, the penetration rate of a bit varies with weight on bit, rate of rotation, and hydraulic horsepower.
13.9 COSTS OF DRILLING
An increase in depth increases drilling costs. Actually, costs increase exponentially with depth, even for a “normal” trouble-free well. Also, an increase in depth can increase the chances of mechanical problems. This adds to the cost of drilling.
Increased depth also reduces available information about potential reservoirs, as to quality of crude oil and quantity available (proven reserves). Risks increase with uncertainties as to reservoir quantity and quality available.
Costs of drilling depend on:
- • The kind of oil and what potential energy the oil possesses by virtue of its initial pressure in its reservoir.
- • By the amount of dissolved gas it may contain. In many cases the crude may have enough potential energy to permit a well to flow large quantities of oil to the surface without any artificial assistance, such as use of gas or water injection.
This is quite prevalent in oil wells in the Middle East. But when oil cannot flow unaided, or when the pressure in the reservoir has decreased to a pressure that is too

FIGURE 13.3 Drilling cost as a function of well depth (Hossain and Al-Majed, 2015).
low to be economical, costly mechanisms which lift oil to the ground surface must be employed. Furthermore, low pressure in the reservoir and low gas content generally go together. This kind of crude, therefore, must be handled in a different manner.
Land rig operating rates vary between $8k/day and $45k/day, largely depending on the region and rig type. The North American market is the most important indicator of land rig rates. US High Spec Land Rigs Average Day Rates. Data is based on multiple companies reports, averaged and rounded up.
The cost of drilling has plummeted from $4.5 million to $2.6 million. The average drill cost per foot was lowered from $245 to $143. That means drilling costs have been reduced for Chesapeake by about 42%, which offsets the drop in the commodity cost (for natural gas).
Drilling costs will depend on the depth of the well and the daily rig rate. The rig daily rate will vary according to the rig type, water depth, distance from shore and drilling depth. One development well will cost 55-88 MM$ plus completion costs (+80%) totaling 99-158.4 MM$. Drilling cost as a function of well depth is given in Figure 13.3, by Hossain and Al-Majed, 2015.
13.9.1 Statistical Solution for Cost Estimation in Oil Well Drilling
A group at Mexico proposed Bit Program for an onshore well in Mexico. Traditional ly, the poor bit performances are discharged, understood as being the result of bad practices that shall not be repeated. A handful of good runs are elected as results to be repeated or improved.
Some wells are drilled with the casing itself replacing the conventional drill string, disclosed as economic by saving time circulating, running casing, and reducing non-productive time (Patel. D. et al, 2018).
Intervals of the planned well are divided by the expected rate of penetration (ROP) by depth, generating the Drilling Hours seen in a Bit Program (Table 13.1).
TABLE 13.1
Statistical Program for Cost Estimation of Oil Drilling
Bit |
Section |
Bit |
Bit |
Depth |
Length |
Drilling |
ROP |
Acc. |
WOB |
RPM |
Mud |
Remarks |
n° |
n° |
size |
type |
Out |
Drilled |
Hours |
- |
Hours |
- |
- |
Weight |
- |
- |
- |
(in) |
- |
(m) |
(m) |
(h) |
(m/h) |
(h) |
(ton) |
- |
(sg) |
- |
1 |
1 |
26 |
115 |
1,000 |
950 |
60 |
15.8 |
60 |
6-15 |
80-140 |
1.2 |
IADC 115 |
1 |
2 |
1 73/2 |
115 |
2,100 |
1,100 |
110.0 |
10.0 |
110 |
10-18 |
120-160 |
1.4 |
IADC 115 |
2 |
2 |
1 73/2 |
115 |
3,300 |
1,200 |
120.0 |
10.0 |
230 |
10-15 |
80-160 |
1.5 |
IADC 115 |
3 |
3 |
14.% |
PDC |
4,150 |
850 |
100.0 |
8.5 |
330 |
2-3 |
120-130 |
2.0 |
Bicenter Bit |
4 |
3 |
14.% |
PDC |
4,500 |
350 |
33.0 |
10.6 |
363 |
2-3 |
120-130 |
2.0 |
Pilot bit 8.5 |
5 |
4 |
12.'A |
PDC |
5,260 |
760 |
95.0 |
8.0 |
458 |
2-4 |
80-120 |
1.9 |
Pilot bit 8.5 |
6 |
4 |
12.'A |
PDC |
5,370 |
110 |
30.0 |
3.7 |
488 |
3-5 |
70-100 |
1.9 |
Pilot bit 8.5 |
7 |
4 |
12.'A |
PDC |
5,500 |
130 |
35.1 |
3.7 |
523 |
3-5 |
70-100 |
1.9 |
Pilot bit 8.5 |
8 |
5 |
8.V2 |
537 |
5,610 |
110 |
70.0 |
1.6 |
593 |
8-10 |
80-100 |
1.0 |
Metal seals |
9 |
5 |
8.V2 |
537 |
5,720 |
110 |
70.0 |
1.6 |
663 |
8-10 |
80-100 |
1.0 |
Metal seals |
10 |
5 |
8З/2 |
517 |
5,830 |
110 |
70.0 |
1.6 |
733 |
6-8 |
80-100 |
1.0 |
Metal seals |
11 |
5 |
8З/2 |
517 |
5,940 |
110 |
70.0 |
1.6 |
803 |
6-8 |
80-100 |
1.02 |
Metal seals |
12 |
6 |
6 |
517 |
6,090 |
150 |
90.0 |
1.7 |
893 |
4-6 |
80-100 |
0.67 |
Metal seals |
13 |
6 |
6 |
517 |
6,237 |
147 |
90.0 |
1.6 |
983 |
4-6 |
80-100 |
0.67 |
Metal seals |
14 |
6 |
6 |
517 |
6,384 |
147 |
90.0 |
1.6 |
1,073 |
2-5 |
80-100 |
0.67 |
Metal seals |
15 |
6 |
6 |
517 |
6,531 |
147 |
90.0 |
1.6 |
1,163 |
2-5 |
80-100 |
0.67 |
Metal seals |
(Source: R EM, Int. Eng. J. vol.72 no.4 Ouro Preto Oct./Dec. 2019 Epub Sep 16, 2019)
An example of actual day rate. Transocean signed a contract in December 2018 with Chevron to provide drilling services. The contract is for one rig, will span 5 years and is worth $830 million. The effective day rate for the rig is $455,000.
13.9.2 Economic Evaluation and Applications
The recovery of oil from underground, or offshore, reservoirs is a good application of the “principle of economic balance”. The problem is one of determining the optimum number of wells to drill, and the accurate spacing of these wells, to get maximum profit.
The following considerations highlight the subject:
- 1. Actually, the greater the number of wells, the larger will be the ultimate recovery, provided that the recovery rate does not exceed the “most efficient engineering rate”. But the most efficient engineering rate (economic balance) does not necessarily mean the optimum rate for maximum profits.
- 2. Economic balance, therefore, consists of a balance of:
a. greater fixed costs for a larger number of wells drilled plus usually higher operating costs for higher production rates against
b. greater ultimate recovery from the larger number of wells.
Thus, the principle of economic balance in the oil fields is:
To drill as many wells as possible and needed within fixed costs and operating cost limits relative to the greatest ultimate recovery in terms of the realizable value (sales value) for the recovery. There is an upper limit to the number of wells that can be drilled, however, because of technical considerations.
In other words, greater fixed costs plus higher operating costs must be considered when increasing the number of wells to be drilled in an attempt to obtain a greater ultimate recovery of oil. [2] [3]
single reservoir, the greater will be the ultimate recovery per surface area of oil and/or gas.
- 5. There is a practical limit to the number of wells, and hence the spacing of wells, that can be drilled, however, which is controlled by the cost of drilling and operation. This limit to the number of wells to be drilled is based on estimated ultimate recovery, in barrels of oil, from each well. Since depth is the principal factor governing drilling costs, depth has a bearing on the problem of well spacing.
- 6. There is no hard and fast rule on spacing of wells; the technical and nontechnical factors relative to the oil reservoir must be considered separately.
- 7. Oil wells drilled in the United States are widely spaced and located at the centers of 40-acre tracts or at like ends of 80-acre tracts. For gas wells, on the other hand, spacing ranges between 160 and 640 acres per well.
- 8. The acreage assigned to each development well is known as a drilling unit prior to completion of the well and as a production unit upon successful completion.
- 9. Usually, the greater the depth to reach productive zones of oil, the wider the spacing of wells. Furthermore, since viscous oils do not possess the mobility of ready passage through reservoirs, as lighter, less viscous oils do, a closer spacing of wells is usually needed with oils of heavy viscosity properties in order to effect maximum efficient drainage. In the case of gravity, the lighter-gravity oils (with the higher API) contain more dissolved gases, have more mobility, and are less viscous than the lower-gravity oils, and so will require fewer wells and wider spacing to effect maximum efficient drainage. On reservoir pressures, reservoirs with high pressures, particularly if pressures are maintained by some recycling operations such as use of water, gas, or air, offer higher recovery per well. Thus, a wider spacing can be employed in reservoirs with high pressures.
- 10. Such reservoir properties as porosity, the ability to contain fluids and permeability have an influence on well spacing. Porous and permeable reservoirs, which allow fluids such as oil to flow through the reservoir to the well bore, means that reservoirs can be effectively drained, so fewer wells with wide spacing is suitable under such conditions. Closer spacing of wells is necessary when “tight” reservoirs, with low porosity and permeability, are involved.
- 11. Some nontechnical factors also affect well spacing. These include, for instance, the rate of production desired because of terms of the oil lease, market price of crude, market demand, etc. Also, proration laws of a government can dictate the amount of oil or gas an oil company can produce. When this is the case, the number of wells drilled, and the spacing, may be affected. Where the rate of payout desired is lengthened, and deferment of income over a wide period because of income tax problems is the objective, the number of wells drilled may be cut back. Thus, spacing will tend to be wider under such conditions. The opposite of this, where the rate of payout desired is for a short period dictates more wells drilled with closer spacing.
CASE STUDY -13.1
The following simple example offers two alternatives relative to the number of wells to be drilled and spaced in a reservoir involving the following information:
Alternative 1: Drill 2 Wells |
Alternative 2: Drill 6 Wells |
|
Total capital investment ($) |
3,800,000 |
8,400,000 |
Annual operating costs |
560,000 |
1,800,000 |
Total production (bbl/day) |
20,000 |
100,000 |
REQUIRED
(a) Determine the spacing between wells, (b) Which alternative do you recommend: the wider spacing between two wells or the closer spacing between six wells?
SOLUTION
(a) Let us establish the following table using some common basis:
Alternative 1 |
Alternative 2 |
|
1. Capital investment/well ($) |
1,900,000 |
1,400,000 |
2. Annual operating cost/well ($) |
280,000 |
300,000 |
3. Capitalized cost of item (2) using interest rate of 10% |
2,800,000 |
3,000,000 |
4. Sum of items (1) + (3) |
4,700,000 |
4,400,000 |
5. Production bbl/(day)(well) |
10,000 |
16,667 |
Spacing is calculated on the assumption that a producing well is located on an area of one acre. Hence, daily oil production is reported on the basis of bbl/ (well)(acre).
In addition, income is reported by assigning an arbitrary value for the drilled oil equal to 33% of the well-head value of produced oil.
Now, for one day of production, and taking one well as a basis for our calculation, we obtain:

For alternative 1, spacing = 17 acres For alternative 2, spacing = 10 acres
Thus, a spacing of 17 acres between two wells is recommended for alternative 1, while 10 acres is to be used as a spacing for the six-well alternative.
(b) Although operating costs are greater in total and on a per-well basis with six wells, total production is greater, and hence total revenues earned, including profits, will be greater. Furthermore, the payout period favors the six-well alternative over the payout period of the alternative on two wells, since more overall production of six wells will increase total revenues received, sufficient to return investment more quickly.
Finally, capital investment per barrel produced per day favors alternative 2. Capital investment per barrel per day with six wells drilled is $84, whereas capital investment per barrel per day with two wells drilled is $190.
Obviously, Alternative 2, or six wells, is the selection, assuming everything else favors this alternative, including reservoir pressures, no limit on production, favorable permeability and porosity features, etc.
CASE STUDY -13.2
Explorers for crude oil try to determine how often success will be gained from a given program of N well (wells drilled). “What are the odds of success?” a company might ask. A company drilling, say, 20 or 30 wells per year might want to know the odds of making one, two, three, or five discoveries, with discovery meaning simply a producing well and not profitability of the well. How much oil there is, is not part of discovery, but comes under field size distribution. To find these odds of success to total wells drilled, a mathematical technique called binomial (two numbers) expansion is used.
For simplicity, assume that each well in the program has the same chance of success with an assumed 10% success rate. Oil explorers know that some prospects have better “odds” or chances of success than others. For most exploration programs, we can assume an “average success” rate with reasonable safety.
F indicates probability of failure (a dry hole), and S indicates probability
of success.
For one well (one outcome) F + S = 1.00, or we can write F + S (F + S)1. For two wells, there are four possible outcomes, FF + FS + SF + SS = 1.00; and, of course, FS + SF can be written 2FS. Then F2 + 2FS + S2 = 1.00.
Now, if you remember your algebra, F2 + 2FS + S2 is the product of (F + S) (F + S) and can be written as (F + S)2. So F2 + 2FS + S2 = (F + S)2. The left half of this equation is the expansion of the binomial (F + S) to (F + S)2.
Now, we can setup a cumulative binomial probability table as shown in Table 13.2, with an assumed 10% success rate, for any larger number of wells to be drilled and we will get some probabilities of success in number of discoveries to total number of wells drilled.
TABLE 13.2
Cumulative Binomial Probability (Using a 10% Success Rate)
No. of Wells Drilled |
No. of Discoveries |
Probability Success in No. of Discoveries (%) |
Odds of Success |
10 |
1 |
60 |
1 in 10 |
10 |
2 |
26 |
1 in 5 |
10 |
3 |
IS |
3 in 10 |
20 |
1 |
80 |
1 in 20 |
20 |
2 |
61 |
1 in 10 |
20 |
3 |
50 |
3 in 20 |
20 |
4 |
25 |
1 in 5 |
20 |
5 |
10 |
1 in 4 |
30 |
1 |
90 |
1 in 30 |
30 |
2 |
73 |
1 in 15 |
30 |
3 |
70 |
1 in 10 |
From Table 13.2, a graph can be drawn as shown in Figure 13.4, to illustrate tables of cumulative binomial probabilities. This graph provided the following information:
- 1. At least one discovery or more is 88% (or 88 chances of success in a total of 100 chances), or with 4.4 chances of S in five chances.
- 2. At least two discoveries is 60% (or 60 chances of success in 100 total chances), or 3 in 5 chances.

FIGURE 13.4 Commulative bionomial probablity, assuming 10% success.
- 3. At least three discoveries is 30% (30 chances of success in 100 chances), or about 1.5 in 5 chances.
- 4. At least four discoveries is 13% (13 chances of success in 100 chances), or about 1 in 8 chances.
The chance of drilling any number of dry holes in succession, like the chance of one dry hole “in succession”, is 1.00 - 0.10, or 0.90 (90%). For additional wells, they are as follows:
- 2 dry holes in succession = 81%, or 4 in 5 chances
- 5 dry holes in succession = 69%, or 3 in 5 chances
- 10 dry holes in succession = 35%, or 1 in 3 chances
- 20 dry holes in succession = 12%, or 1 in 8 chances
Thus, even with a 10% success rate, even in drilling 20 holes, we still face a 12% chance that all holes will be dry.
The employment of such a table and graph is a possibility for explorers for crude oil in their efforts to predict success and failure, or discoveries to dry holes. It can also be useful to oil engineers in estimating probabilities, or odds of success.
2nd: Using the binomial distribution to find the probability of an exact number of successes (discovery wells) in several trials (number of wells to be drilled), the following relation could be applied:
where:
p(x) = probability of obtaining exactly x successes in N trials N = size of the sample, or number of trials of an event x = number of successes, or favorable outcomes within the N trials p = probability of success q = 1 - p = probability of failure
(*) = C” = number of combination in which N objects can be displayed as groups of size x, where the order within the individual groups is unimportant
The mean, variance, and standard deviation of the binomial are given by:
Example 13.3
As an example, the probability of obtaining zero heads when a coin is tossed five times is calculated as follows; using Equations (12.2) and (12.3):
Roughly, the probability is 3 of 100 times. That is, where successive tosses were gathered into groups of five tosses in each group, out of 100 such groups, about three would contain no heads.
Example 13.4
Ten wells are to be drilled. The probability of success is taken to be 0.15. What is the probability of there being more than two successful wells?
SOLUTION
The answer to this can be found in one of two ways: (1) the individual probabilities of 3, 4, 5, 6, 7, 8, 9, and 10 successes can be calculated and added together, or (2) the individual probabilities of 0, 1, and 2 successes can be added together and then subtracted from 1 to obtain the same answer. The second method is shorter, and is given as follows:

Hence, probability is approximately 18%.
Most oil companies are not concerned with how far down drilling proceeds, but with how high the cost will be to get that deep and what the cost will be to go, say, another 100 ft or more. Marginal costs are some direct function of depth. If, then, we let Y be those costs which vary with depth, but no overhead costs, and let X be depth itself, a formula can then be written as:

Thus, depth affects marginal costs. For example, the rise of temperature with depth, among other things, increases the probability that a drilling bit will have to be replaced an additional time in a well drilled an additional 100 ft, because mechanical energy is lost as the drilling process continues. But also, some costs, such as the costs of additional “mud materials”, needed to drill a deeper well may actually increase rather slowly in relation to increase in depth, thus giving a decreasing marginal cost in relation to depth.
Possibly the one factor that most affects the costs of drilling is the average footage drilled per hookup. As more information on drilling tendencies in any one oil field become available, the number of changes in drilling hookup is reduced and the speed of the drilling operation is increased. Also, feet per hour at the bottom of the well, combined with the amount of time spent at the bottom, is perhaps the best measure of the relative efficiency and speed of a drilling operation in a particular oil well and for a given amount of controlled footage.
In sum, costs of drilling increase because of the following, usually in some combination:
- 1. A poorly designed casing program
- 2. An inadequate rig or incompetent personnel on the test drill
- 3. Poor selection of proper drilling bits for the formations to be penetrated
- 4. Insufficient drilling bit weight for maximum penetration (economic balance here relative)
The following are some of the expressions and definitions used in “cost terminology” and reserves reporting; which are used in this chapter as well as in the following chapters.
13.10 SOME BASIC DEFINITIONS
Development costs: expense and capital costs incurred to bring on-stream a producing property (includes development well drilling and equipment, enhanced recovery, and extraction and treatment facilities).
Discoveries: newly found proven reserves, including production sharing type reserves, which may or may not be included (booked) in annual reserve estimates.
Exploration costs: expense and capital costs to identify areas that may warrant examination (includes geophysical, geological, property retention costs, dry hole expenses, exploration drilling).
Extensions: additions to existing fields, normally booked in the same year.
Finding oil: includes exploration (search) for oil, development of successful exploration discoveries, including the drilling of wells, and, finally, the drilling and preparing of oil for commercial production, including the laying of gathering pipelines and pump installation for the movement of oil to central points for gas separation.
Finding and development costs: used by securities analysts to measure and compare petroleum company performances in acquiring reserves.
Improved recovery: additions to reserves due to secondary and tertiary recovery, booked when production commences.
Property acquisition costs: those costs incurred to purchase or lease proven or unproven reserve properties, capitalized when incurred.
Punchback: deepening to new' horizons or completing back to shallower horizons, the reserves of w'hich may or may not be booked.
Purchase of reserves in place: proven reserves purchased from outside companies.
Revisions: additions or deletions to previous reserve estimates based on updated information on production and ultimate recovery.
Once the oil has been explored, developed, and produced, all costs involved in getting the oil to the surface, where it becomes a commodity as it is piped in gathering lines to central points for gas separation, are called the cost of oil field operation. The basic question “What does oil cost to find, to develop, and to ready for commercial production?” would be comparably simple to answer if, during a short period of time—say l-3 years—an oil company could start in the oil-producing business, discover say 10 million bbl of oil. develop that 10 million bbl. and finally produce the 10 million bbl of crude. The cost of dinning, developing, and producing could then simply be found by dividing the total amount spent for exploratory, developing, and producing effort by 10 million bbl, w'hich would give a cost per barrel of crude.
But this is just “grocery store accounting”. Actual accounting for costs in the oil-producing industry is not that simple. When a company searches for oil, it may spend several years and millions of dollars on exploration and development before any substantial, and commercially feasible, amount of oil is located. In development alone, a company may work for several years and spend many dollars developing the oil reservoir which it is to produce over an even greater number of years; and also, all this time, the process is constantly repeating itself as more oil is being discovered, more oil is being developed, and more oil is being produced.
Finally, an oil company’s success is measured by its ability to discover reserves. In its search for oil. it spends substantial amounts of money in many different ventures in w'idely scattered areas. The oil company does this knowing that many of these ventures will be nonproductive and will eventually be abandoned.
On the other hand, the oil company recognizes that successes in other areas must be large enough to recoup all money spent in order to break even or to provide a profit. Thus, the true assets are the oil reserves, and these costs are capitalized. But the costs of nonproductive exploration activities and of dry holes are also a necessary part of the full cost of finding and developing these oil reserves.
CASE STUDY: TO CHOOSE BETWEEN TWO ALTERNATIVES FOR DRILLING WELL IN A RESERVOIR
GIVEN
The following is a case for an offer for two alternatives relative to the number of wells to be drilled and spaced in a reservoir involving the following information. The case was presented to P E students as ca sort of a senior project at KFUPM. Dhahran. Saudi Arabia.
Alternative 1: Drill 2 Wells |
Alternative 2: Drill 6 Wells |
|
Total capital investment ($) |
3,800,000 |
8,400,000 |
Annual operating costs |
560,000 |
1,800,000 |
Total production (bbl/day) |
20,000 |
100,000 |
GIVEN
Determine the spacing between wells, (b) Which alternative do you recommend: the w'ider spacing between two wells or the closer spacing between six wells?
SOLUTION
(a) Let us establish the following table using some common basis:
Alternative 1 |
Alternative 2 |
|
1. Capital investment/well ($) |
1,900,000 |
1,400,000 |
2. Annual operating cost/well ($) |
280,000 |
300,000 |
3. Capitalized cost of item (2) using interest rate of 10% |
2,800,000 |
3,000,000 |
4. Sum of items (1J + (3) |
4,700,000 |
4,400,000 |
5. Production bbl/(day)(well) |
10,000 |
16,667 |
Spacing is calculated on the assumption that a producing well is located on an area of one acre. Hence, daily oil production is reported on the basis of bbl/ (well)(acre).
In addition, income is reported by assigning an arbitrary value for the drilled oil equal to 33% of the well-head value of produced oil.
Now, for one day of production, and taking one well as a basis for our calculation, we obtain:

For alternative 1, spacing = 17 acres For alternative 2, spacing = 10 acres
Thus, a spacing of 17 acres between two wells is recommended for alternative 1, while 10 acres is to be used as a spacing for the six-well alternative.
(b) Although operating costs are greater in total and on a per-well basis with six wells, total production is greater, and hence total revenues earned, including profits, will be greater. Furthermore, the payout period favors the six-well alternative over the payout period of the alternative on two wells, since more overall production of six wells will increase total revenues received, sufficient to return investment more quickly.
Finally, capital investment per barrel produced per day favors alternative 2. Capital investment per barrel per day with six wells drilled is $84, whereas capital investment per barrel per day with two wells drilled is $190.
Obviously. Alternative 2, or six wells, is the selection, assuming everything else favors this alternative, including reservoir pressures, no limit on production, favorable permeability and porosity features, etc.
- [1] Wildcat wells, exploratory wells, or test wells are drilled first for such probing purposes. 2. An unsuccessful wildcat well is called a dry hole.
- [2] Upon discovery of large enough reserves for commercial drilling, the concept of well spacing becomes important to the oil engineer. The characteristics of reservoirs largely control the well-spacing pattern. For example,reservoirs with thick or multiple zones of oil will usually require morewells, and possibly closer spacing between wells, to take advantage of natural drainage (gravity flow) at its maximum than those reservoirs with thincrude oil composition located in single zones. Furthermore, porous reservoirs will produce more barrels of oil than “tight” reservoirs.
- [3] Other factors of a technical nature, which should be considered in thespacing of wells, besides thickness vs thinness of the crude itself andthe multiple zones vs single zones, include depth to the productive zonesof the oil, viscosity of the oil, gravity of the oil, reservoir pressures, andreservoir properties. Therefore, in well spacing, economics of anticipated recoveries based on thickness of oil and saturation of the pay zonebecome important. Obviously, the greater the number of wells drilled in a