Now to continue my Saturday posts reflecting on Wayne Grudem's Systematic Theology from the standpoint of Wesleyan-Arminian thought. My last post was some time ago on his chapter on Miracles (chap. 17).
Chapter 18: Prayer
There is little in this chapter to which a Wesleyan-Arminian would object. A WA would object to how Grudem thinks prayer works, but Grudem does not explicitly get into that here. He writes the chapter in a way that a WA could agree with. His two-dimensional use of Scripture will continue to annoy anyone with a historical consciousness, but that is a critique we have already noted repeatedly.
A. Why pray?
Grudem gives three reasons. First, it is an expression of trust and faith, which is a good thing. Second, it brings us into deeper fellowship with God. Third, it involves us in things that are eternally important. Fair enough.
B. Effective prayer
1. First, Grudem notes that prayer changes the way God acts. "When we ask, God responds" (377).
The way that Grudem words this section is completely in sync with WA thought. Where WAs would disagree with him is in the underlying mechanism. For a WA, God knows whether we are going to pray or not and also knows how he will respond accordingly. But God empowers us to decide freely whether to pray.
For Grudem, God not only knows but he decides whether to make us pray or not. So while Grudem says "prayer changes the way God acts," the assumption is that God is determining whether we pray and thus how he will respond. There is no free act of prayer in Grudem's theology.
Grudem is a soft determinist, which means that we experience our actions as free even though they are ultimately determined by God.
However, because Grudem does not make these assumptions of the chapter explicit, there is nothing in this section that a WA could not also say. Indeed, this section really would be more natural for a WA to say than for Grudem. God chooses to act differently depending on whether we pray. The stakes of prayer are thus even more crucial for a WA than for Grudem.
2. Second, prayer is made possible by Christ. Grudem rightly notes that God knows everything, so God "hears" every prayer in the sense that he is aware of all prayers. It is common in some circles to act as if God isn't even aware of the prayer of someone who does not trust in Christ. Grudem rightly points out that God knows everything.
However, God has not promised to answer the prayers of the unbeliever. For Grudem, however, it is ultimately God's choice, which again is sound. Through Christ, however, the believer has confidence to approach God in prayer. 
3. Grudem's third, fourth, and fifth points in this section have to do with praying in Jesus' name, whether we should pray to Jesus and the Holy Spirit, and the role of the Holy Spirit in prayer.
Grudem notes that praying in Jesus' name is not merely saying those words at the end of a prayer, "in Jesus' name." It means that we are praying with his authorization to pray (379). This urges us to pray in a way that is consistent with his character. Grudem actually discourages a ritualistic or formulaic use of the phrase, where it becomes empty. "Genuine prayer is conversation" (380).
Grudem notes that most of the prayers in the New Testament are to God the Father, but that some are to Jesus (e.g., 1 Cor. 16:22).  He suggests that prayer to Jesus and the Holy Spirit is not inappropriate, for they are God, but he suggests it should not be our dominant form of prayer, since it is not the New Testament pattern.
This is a very interesting section, for it reflects Grudem filling in gaps in the Bible by way of reasoning. This is completely appropriate, even necessary. Grudem is normally hesitant to do it and is cautious even here. Nevertheless, reason is a necessary element in all theologizing.
Finally, Grudem rightly points to Romans 8:26-27 for the key function of the Holy Spirit in helping us in prayer.
C. Important considerations
Most of the rest of the chapter covers miscellaneous issues in the Bible relating to prayer. For example, he addresses praying according to God's will. If we pray something that is in Scripture, we know we are praying according to his will and all is good. If we do not know God's will, we should pray with a spirit of "If it is your will." (383).
We should pray with faith. A person can have a sort of "settled assurance" that God is going to answer (384). Our disobedience hinders our prayers. We can pray in confession of our sins. We need to forgive others before we expect God to forgive us. Humility is the right attitude to have in prayer.
We need to pray regularly and with a significant time investment, not using empty phrases but being earnest in any repetition of prayer. Jesus did. "Intensity and depth of emotional involvement in prayer should never be faked" (387). We may have to wait on the Lord to respond. We should pray in private and with others.
Fasting appropriately accompanies prayer for many reasons, most of which sharpens us in self-discipline and humility, but also expresses our earnestness and urgency. God does not grant every prayer but there will be some unanswered prayers in God's sovereignty and also because of our failings.
D. Finally, praise and thanksgiving are essential elements in prayer.
Again, there is little if anything in this chapter that a Wesleyan-Arminian will find objectionable, especially since Grudem does not get into the mechanisms he would say are behind the scenes. He presents us as individuals who make choices, which is the key difference between the WA and Calvinist traditions.
A WA would thus only accentuate the claim that prayer changes things. God, in his sovereignty, has given us this great privilege and responsibility to pray. He actually factors our prayers into his decisions on whether to intervene in the natural flow of events. What a fearsome honor!
 I personally believe that passages in Romans 8 and Hebrews that have to do with the intercession of Christ are specifically about intercession relating to atonement.
 Prayer to Jesus is one of the key arguments of Larry Hurtado that earliest Christianity was "binitarian," worshiping Jesus alongside God the Father. See One God One Lord (Minneapolis: Fortress, 1988).