Optimization of Drilling Cost Using Artificial Intelligence

Introduction

Since drilling costs represent a major fraction of total exploration and production costs. Reduction in operations cost will impact the total time spent will drilling a well. As a result the ability to optimize drilling costs would not only encourage exploration for more reserves but also increase profitability even with the present low oil price making Oil and gas more competitive as an energy source. Although there are many methods of optimizing drilling cost most if not all of which depend on the ability to accurately predict penetration rate. Thus it is very important to be able to accurately predict ROP especially for directional wells.

Penetration rate is difficult to predict accurately especially for directional wells. This in turn makes cost optimization difficult. A potential area for optimization of drilling cost is bit use. This is particularly difficult due to its significance in both drilling time and bit cost. In this sense, as a particular bit gets used, it gets dull as its footage increases. The dullness of the bits affects its penetration rate. The reduction in penetration rate increases total drill time. Hence early changing of bits reduces drill time at the expense of bit cost. While late bit changes increase drill time while minimizing bit use. In order to optimize bit cost, it is desirable to find a trade-off between the two by a bit change policy to reduce cost.

Cost Optimization is a procedure which involves finding the most cost effective alternatives under a given set of constraints by maximizing desired factors and minimizing undesired ones. By extension, drilling cost optimization involves finding the most cost effective combination of drilling parameters in other to minimize drilling time and consequently drilling cost. Most drilling cost optimization techniques rely on the ability the accurately predict Rate of penetration or penetration rate. Hence a lot of work has been done to develop accurate rate of penetration models. The cost per footage drilled is given by the general equation 1.

( ) 1 / d b C R t C F   = + +   (1)

Where C = Total cost per footage drilled($/ft), R = Rig Operating Cost($/hr), t = total trip time(hrs), td = total drilling time(hrs), Cb= Total bit cost (hrs), F = Footage drilled(ft) The Rig operating cost is known as well as the footage drilled, the total drill time depends on the Penetration rate. For a given footage drilled, the total time can be expressed as shown in the equation 2.

0 1/ f t ROP =∫ (2)

Where t is the total drill time (hrs), ROP = Penetration rate (ft/hr) and f= footage drilled.

In recent times, drilling rate optimization techniques have been used to reduce drilling time which invariably translate to reduced cost of drilling. However Rate or penetration (ROP) which is the rate at which the drill bit deepens the well beneath usually reported in units of feet/hour is a complex non-linear function of various drilling parameters such as: Weight on Bit(WOB), Rotational speed (Revolutions per minute or N) flowrate(Q), bit diameter, bit tooth wear, bit hydraulics, formation strength, and formation abrasiveness. Given this complex non-linear relationship between Rate of Penetration and these variables, it is extremely difficult to develop a complete mathematical model to accurately predict ROP from these parameters.

Several ROP models have been proposed. Among these models, the most well-known ones are Burgoyne and Young, and Warren’s models. However, they did not provide satisfactory accuracy. In each of these models different parameters have been used to estimate the ROP. With advances in computer technology, Artificial neural networks are capable of learning the relationship between these parameters and Rate of penetration given a large enough data set, trained network can hence be used to predict ROP from the above parameters. An ‘artificial’ neural network (ANN), is a processing devices (algorithms or actual hardware) that are loosely modeled after the neuronal structure of the mammalian cerebral cortex but on much smaller scales. Once a neural network is ‘trained’ to a satisfactory level it may be used as an analytical tool on other data. Reinforcement Learning is a type of Machine learning and consequently artificial intelligence that allows a computer agent without being explicitly programmed to learn in a specific context, the ideal behavior or strategy to maximize its performance by making use of a simple reward feedback thereby maximizing rewards.

Reinforcement learning has been used in recent times to achieve state of the art technological breakthroughs including computer programs learning how to play certain games at a superhuman levels and in self driving cars. The first step in reinforcement learning is to design/develop the decision making environment for the environment to learn. The environment is modelled as a Fully Observable Markov Decision Process (MDP).

Value of A Policy

The expected value of a policy  π  for the discounted reward, with discount  γ, is defined in terms of two interrelated functions, Vπ and Qπ. defined recursively in terms of each other.

Let  Qπ(s,a),  where  s  is a state and  a  is an action, be the expected value of doing a in state s and then following policy  π, and Vπ(s),  where  s  is a state, expected value of following policy π in states.

If the agent is in state s, performs action a, and arrives in state  s’, it gets the immediate reward of  R(s,a,s’)  plus the discounted future reward,  γVπ(s’). When the agent is planning it does not know the actual resulting state, so it uses the expected value, averaged over the possible shown in the equation 3 , Q (s,a)= P(s'|s,a) [R(s,a,s')+ V (s' )] s π π γ ∑ (3) Vπ(s) is obtained by doing the action specified by π and then acting following π:

V (s)= Q (s, (s)) π π π (4)

Materials and Methodology

The first step in optimizing rate of penetration is developing a reasonably accurate model relating drilling parameters to rate of penetration. This model can then be optimized by a number of numerical or computer algorithms. Being that rate of Penetration is a complex non-linear function of several variables, and also these independent variables are not particularly defined. Different variables have made use of slightly different independent variables. These make it difficult to build a particularly accurate mathematical model. Statistical methods have hence been looked into to build the best possible approximations of Rate of Penetration models. A deep regression neural network using JAVA’s open source machine learning program DL4J. was used to develop this model, drilling reports were obtained from a directionally drilled well in the Niger Delta. The drilling reports spanning a period of two months containing all activities performed by the drilling contractors was obtained and the necessary data for the development of the model was extracted The following independent parameters: Inclination angle (Directional well) Mud pump( gpm), Minimum Weight on bit(KIPS), Maximum weight on bit(KIPS), Drill string (rpm), Mud weight (ppg), % Sand in mud, Depth (in), Depth out (ft),Bit Diameter(in), Depth previously drilled by bit, Torque, Slack off weight and Rotating weight were chosen for the 58 case studies:

Pre-Processing of Data: The pre-processing was carried out with the normal MinMAx scaler in the dl4j library and all the input Data Were First Normalized to Values Between 0 And 1 With The Targets Also Scaled (Normalized). Model Architecture: Some of the important architectural decisions made include: Number of hidden layers, Number of units in each layer, learning rate, loss function for each layer, activation function for each layer, Weight initialization system, Weight updater, Number of epochs, The model was than trained several times with a lot of tweaks and the differences in results were observed using different hyper- parameters. The eventual choices of hyper parameters were: Number of input neurons-12; Number of hidden layers-3, Number of neurons per hidden layer -10; Learning rate -0.01, Updater – NESTEROVS, Momentum- 0.9, Layer 1,2,3 activation – RELU, Layer 4 activation – Identity, and Output layer loss function – Mean Square error The model was trained with 50 data points and tested with 8.

Reward Function

The reward was set to zero for all states apart from the final depth. At the final depth, The total cost to drilling depth ignoring trip time is computed using the equation 10.

( ) ( ) bit rig C n C Cost time = × + × (10)

From the equation 10, it is observed that optimizing C involves a tradeoff between time and number of bits, using more bits causes the well to be drilled faster at the expense of bit cost. The MDP was set up as shown in Figure 1 and then solved by policy iteration over 160000 iterations to determine the optimal bit number, bit change depths and cost.

Assumptions and Simplifications

• Trip time was modelled as a linear function of depth
• A bit cost of $50,000 and a rig cost of $7000/hour were used
• The trip depths were maintained as in the original drilling operation

Results and Discussion

It was observed from the results for the Penetration rate prediction using the neural network architectures that there were trained with a single layer, two hidden layers, and three hidden layers. All layers had 10 hidden units per layer with an Optimization Algorithm- Stochastic Gradient Descent. The single layers had 20,000 iterations and 50,000 iterations for both two and three hidden layers. Their learning rate was 0.01 for single layer and 0.0065 for both two and three hidden layers. The momentum was 0.9 for single layer and 0.8 for both two and three hidden layers. Both the two and three hidden layers had RELU Activation function except for output layer, with Identity Activation function.

The result for the single hidden layer network is shown in the Figure 2. That for two hidden layers network training and test are presented in the Figures 3 & 4, respectively, while the same result for the three hidden layers presented in the Figures 5 & 6 respectively.

Click to enlarge

Click to enlarge

Click to enlarge

Click to enlarge

Click to enlarge

The Table 2 presents the summary of the statistical result of the training network for all the hidden layers from the result it can be seen that the two hidden layered neural network produced the best results, thus it would be used for further optimization work.

Conclusions

As oil and gas companies continue to explore and drill deep and ultra-deep water zones for hydrocarbons, there is an increasing need to have reduce personnel on board by automating as much as possible. This approach of training an intelligent agent to make decisions regarding bit change can replace and has been shown to be slightly more cost effective. In this study, the agent was shown to get better and more efficient with increasing iterations. With improved hardware and a more robust model involving much more samples and better bit wear models, much better agents can be developed and deployed for different drilling implications. This study also shows how reinforcement learning can be used to replace human intuition in decision making and can be extended to other oil and gas applications.

Lastly, it was shown that with good architecture and feature engineering, neural networks can be used to predict with groundbreaking accuracies Penetration rates in deviated wells and this can be applied to subsequently most other functional relationships in oil and gas.